texts:
This might seem like an odd question but seeing as I haven't had any formal education in solving ratex models yet, it is something I have been thinking about a lot recently. Consider the following state space representation of an arbitrary model:

$\Gamma_{0}y_{t} = \Gamma_{1}y_{t-1}$

Where the gamma's are coefficient vectors. To solve this system we can simply pre-multiply by $\Gamma_{0}^{-1}$, define $A =\Gamma_{0}^{-1} \Gamma_{1}$ and then decompose $A$ in to its Jordan canonical form $A = P \Lambda P^{-1}$. $\Lambda$ being a vector with eigenvalues on the diagonal and the P's being right and left eigenvectors.

I am fine with applying this method to different models but I feel like I don't have the intuition pinned down. I don't quite understand why I do this decomposition. If I have understood correctly, eigenvalues originate from differential equations where you assume the solution to be on the form $e^{\Lambda t}$ and I suppose that is fine. But then we have to ensure that the eigenvalues are less than one in absolute terms or in some cases that one is inside the unit circle while the other is outside. When solving linear difference equations I can appreciate why we need coefficients to be inside the unit circle (to prevent explosive behavior) but I don't understand how this links to eigenvalues.

So I suppose my question is: what do eigenvector and eigenvalues tell us about the system? Why do we even have to decompose $A$? Is there a visual representation? I am sure in physics eigenvectors have a 'visual' meaning. Is there a similar way to look at eigenvectors in economics? A while back I recall reading a paper that showed the relationship between eigenvectors and the number of initial conditions needed to solve a model. If anyone has references similar to this I would very much like to read them.

I understand that this question is quite vague but I am just trying to understand why I am doing what I am doing.


texts: How does the Contract Law definition of 'consumer surplus' relate to the Microeconomics definition?

texts:
O'Sullivan & Hilliard's The Law of Contract (2018 8 ed). 16.23 starts on p. 387, 16.35 on p. 391.

Right: Pindyck, Rubinfeld. Microeconomics, Global Edition (2017 9 ed). p. 152.

Richard and Damian Taylor. Contract Law Directions (2019 7 ed).

  Difference in value or cost of cure? (Section 11.3.1)
  The £2,500 award made in Ruxley for Mr Forsyth’s ‘loss of amenity’ can be interpreted as
  damages for non-pecuniary loss, based on the fact that the contract was a consumer
  contract for enjoyment (see the opinions of Lords Clyde and Hutton in Farley v Skinner
  (2001)). However, the award may also be interpreted as a response to the need for a
  wider principle of recovery based on the loss of ‘consumer surplus’. Consumer surplus is
  the difference in value between what a thing is worth commercially and the higher value
  at which a consumer subjectively values it. So, whilst an extra few inches on the swimming pool added no financial value, the £2,500 represented Mr Forsyth’s consumer surplus:
  to him, and him alone, the pool was a more valuable asset if it was deeper (i.e. if his
  contract was fully performed). He had contracted for this extra depth and it had not been
  provided, so you could argue that the award of £2,500 was compensation for loss of this
  consumer surplus.

I'm not a microeconomist, but these terms appear to be defined wholly differently? Or am I overlooking something similar that underlies  them?


texts:
In Section 10.2, Monopoly Power, in Pindyck's text on Microeconomics, an example says that suppose $N$ firms produce a particular product and the market demand curve is $P = -aQ + b$. An individual firm is likely to face a demand curve which is more elastic than the market demand curve.

Problem here is, while finding the individual demand curve, we first find $Q = (b-P)/a$, which is the market demand. We divide this by $N$ to get the individual firm's demand curve, given by $Q = (b-P)/Na$

If I compute the elasticity of demand in both cases, which is just equal to $(dQ/dP)(P/Q)$, I get the same value, which is not expected. Is there some mistake in my calculation, for finding the elasticity? Could someone please explain what's going on, and possibly show the exact calculation.

A good check would be that as $N \to \infty$, there is perfect competition and hence perfectly elastic demand (right?)

Thank you!


texts: What are some of the barriers to trading services?

texts:
As I understand it countries negotiate free trade agreements in services using the WTO GATS.

But what are some of the barriers to the transnational exchange of services that an FTA would seek to address?

Surely something as ephemeral as a service can be sold across national borders easily because there are few or no physical components?


texts: Utility function that generates a demand curve which will have an U shaped MR curve

texts:
This is based off an answer given by @Ubiquitous in here: Can marginal revenue be increasing?

The solution he proposed involved a MR curve that sloped down, then up and then down. His equation for the demand curve (for example) to generate such a MR is $P(q)=1−q+3q^2−3q^3$ (see comments below his answer).

My question is:

Is there an Utility function that can generate a demand curve which gives, say an U-shape looking MR?

Note: I am not looking for an utility function that replicates Ubiquitous's MR.


texts: Pure and Mixed Nash Equilibrium algorithm gives different results

texts:
I have a game represented by following table:

It is clear that there is a pure Nash equilibrium at 4,2 (both players do not cooperate, player 1 awarded 4 points and player 2 awarded 2 points).

Now if I used mixed strategy Nash equlibrium algorithm I get a = 1 and b = -1 as the probability of player 1 plays Cooperate and player 2 plays Cooperate respectively. To my understanding, a and b should be equal to 0 so that both players should play the above pure equilibrium strategy.

Why is there such a difference in pure and mixed strategy?

Edit 1: mixed strategy Nash equlibrium algorithm:

The expected ultility for player 2 playing cooperate is: a*2 + (1-a)*1 (This means that some of the time player 1 plays Cooperate, so the probability is a).
The expected ultility for player 2 playing non-cooperate is: a*2 + (1-a)*2.
By equating the two formuala I have (1-a) = 2*(1-a) so a = 1.
Simmilarly, the expected ultility for player 1 playing cooperate is: 6*b + 3*(1 - b).
The expected ultility for player 1 playing non-cooperate is: 8*b + 4*(1 - b).
By equating the two formuala I have 0 = 2*b + (1-b) so b = -1.


texts: Price difference of substitute goods when the supply increases?

texts:
In a competitive market, there are 3 types of goods: X, Y and money (m). X and Y are substitute goods, and the utility functions are quasi-linear with respect to money, i.e:

$$U(x,y,m) = u(x,y) + m$$

The supply of X and Y is  determined exogeneously, and the prices $p_x$ and $p_y$ are then determined such that the system is in equilibrium (i.e. demands for X and Y equal their supply).

Now the supply of X is increased, and a new equilibrium is achieved with new prices $p_x'$ and $p_y'$. What can we say about the new prices?

Certainly $p_x'<p_x$, since we must have new consumers buying the newly available units of X.
Certainly $p_y'\leq p_y$, since X and Y are substitutes (when the price of X decreases, the demand for Y weakly decreases so the price of Y also weakly decreases).
My main question is: what happens to the price difference $p_x-p_y$? I did some anecdotal simulations, and it seems that $p_x'-p_y'\leq p_x-p_y$. I.e, even if there is a decrease in the price of Y, the decrease in the price of X is weakly larger.

Is this observation correct?

What really happens to the price difference when the supply increases?


texts: What is the difference between budget constraint and budget line?

texts: Are those things mean the same thing or they are actually different?


texts: Inflation, cause or result of monetary emission?

texts:
The argentine economist Fernanda Vallejos, while trying to protect the government because of the inflation, the following:

  Inflation is not the result but the cause of monetary emission. As
  there's inflation (because of other reasons not important here),
  people need more money and the central bank needs to print more money.

How can you argue against that?  As it seems to be the opposite of modern theory on inflation.

Context: This is in Argentina, where it has an important deficit, monetary emission and inflation are around 40%.


texts: Insect farming as future of protein nutrition: reality check

texts:
Currently, about 2bn people consume insects, so there must be a scaled industry already as well.

Then, you can buy cricket powder at roughly $100/kg.

Now my concern is:

if this is already a common nutrition source, why the price? (could not imagine, those 2bn people pay that)
nevertheless insect farming wherever it takes involves lot of manual labour

In my understanding, a future source of food should match the following criteria:

sustainable (OK)
cheap (not clear)
scalable through automation (I think this is currently very limited)

Compared to a meat brewery, if they will mature, seems easier to scale, even if entrypoint is harder.

So why is the price currently so high and how exactly are these insects will become the future of food (media excitement put aside) - is a realistic criteria market turnover?


texts: Uncovered interest parity and asymmetric capital controls

texts:
To derive the uncovered interest parity (UIP) condition we assume, among other things, that there is free movement of capital across countries.

But this cannot be directly applied to India because of capital controls. While foreigners are relatively free to hold Indian assets, Indians are in general forbidden to hold foreign assets.

Is there a variant of the UIP that we can expect to hold (given the other assumptions) under such asymmetric restrictions on asset holding?


texts: Is over-valuation of a start up genuinely detrimental to the start up's future?

texts:
I recently watched S02E01 of Silicon Valley.

In it, having demonstrated a breakthrough algorithm, the guys are pursued by investors with increasing funding offers.

However, the founder is warned with a higher valuation, there are higher expectations of performance, and that this may make it harder for to get funding in the future when the company is more mature.

See this Mashable article for a summary of the episode.

  Her offer? \$20 million at a \$100 million valuation.

  Naturally, Richard jumps at the opportunity, but Monica warns him
  against taking it to avoid a runaway valuation and potential for a
  future down round. After some initial resistance, Richard comes
  around, and decides to make Laurie a counteroffer she can't refuse:
  \$10 million at a \$50 million valuation.

The question is, is this a genuine dilemma for start ups, or is the rational decision always to 'take as much money as you can'?


texts: Why do stocks that don’t pay any dividends change price when the company does better?

texts: I don’t understand why (non-dividend paying) stocks increase in price when a company is successful; is it just because everyone expects that everyone else will find it more valuable because the company is doing better? Is the link between this type of stock and the company really just psychological? If investors are getting something other than dividends or just “ownership,” from buying this type of stock, what is it?


texts: World Bank and OECD statistics unmatch tax revenue as % of GDP

texts:
I have been looking for statistics on tax revenue to GDP ratio of different countries. I've found it on World Bank website.
https://data.worldbank.org/indicator/GC.TAX.TOTL.GD.ZS?view=chart
which claims that it is 11.5% for Germany (2018) for example.
Then I have seen this page from OECD website
https://www.oecd.org/tax/revenue-statistics-germany.pdf
which claims that it is 38.5% for Germany (2018).
How come there's such a huge difference between these two sources? Is there something I'm getting wrong here? How can there be 27% difference, OECD number is more than 3 times world bank number! Can anyone enlighten me please?


texts: Question about gordon growth and expected stock prices

texts:
I have problems understanding the solution to the following question and would like to ask if you could help me with the interpretation?

  A house is an asset which generates a benefit to its owners: a stream
  of housing services in the future. Similarly a stock generates a
  stream of dividends in the future. One measure of the value of this
  housing service is the rent one would have to pay on an equivalent
  house. For the purposes of this assignment, assume $D_{t+1}$ is the rent
  you have to pay over the next year (we know this number at time $t$),
  and $P_t$ is the price of the house today. The return on housing is
  $r_{t+1} =  (P_{t+1}+D_{t+1}-P_t)/Pt$. If the discount rate and growth rate of rent were constant, this setup satisfies the Gordon equation, $P_t = D_{t+1}
/ (r – g)$, where $r$ is the expected return on housing and $g$ is the growth
  rate of rent. You can ignore issues about taxes and transaction costs
  on houses.

  Suppose the Gordon equation were correct. In this world, looking at a
  specific city over time, suppose we start out at $D_{t+1} = \$10,000$ a
  year, $P_t =\$200,000$, $r$ is $10$% and $g$ is $5$%. Over time, would the
  price be constant, rising, or falling?

If I plug in the numbers into the Gordon formula I get $P=10.000/(10\text{%}-5\text{%})=200.000$.
Thus the price stays constant.

However the answer is:

  Since the expected return is $10$% but the “divided yield” is only $5$%,
  the price has to rise $5$% a year.

Could someone explain me if there is a way to understand the solution using the Gordon growth formula or some other intuitive approach?

Thank you very much in advance!


texts: What would the price of carbon emissions need to be for the EU to achieve its objective to be carbon neutral by 2050?

texts:
The EU committed to net zero green house emissions by 2050. (Source)

It is regularly said that the a carbon tax of USD 40-80 / t CO2e (USD 50-100 by 2030) would be sufficient to reach the Paris commitment for 2030, a 40% reduction vs 1990. (Source)

Presumably the price of carbon emissions would need to increase exponentially after 2030 since the low hanging fruits will have been picked by then. Some demand could be discouraged through direct regulation but there may be a residual carbon intensity in the economy that would need fairly high emissions prices before considering substitutes.


texts: What value do virtual traders of commodity add to the market?

texts:
Many if not most companies trading in commodities are only trading them on paper. They will not use the commodity they are buying and can not take deliver of the physically commodity.

What value do these investment brokers/banks bring to the market? Specifically since they are not able to take delivery, even for storage. What is the economic rational that would have governments allow and promote this type of business activity?


texts: Fractional reserve banking and the value of someone else's currency

texts:
Suppose there are two countries: $A$ and $B$. $A$ is a large, stable, democratic country with its own currency, the dollar. $B$ does not have its own currency. All prices and financial transactions in $B$ use the dollar and $B$'s citizens have a positive quantity of dollars that they hold domestically.

Country $B$ has a monopoly retail bank that is required to hold 5% of the value of its deposits as reserves in the safe keeping of an independent central bank, also located and controlled within $B$.

My question is: does this suffice for the bank in country $B$ to practice fractional reserve banking? If so, am I correct in thinking that the bank in country $B$ is exerting an externality on the people of country $A$ by devaluing their currency every time it creates a new loan? Is there anything that $A$ can do to prevent this?


texts: What limits central banks from setting highly negative interest rates?

texts:
What limits central banks from setting highly negative interest rates if needed? Is it only that people can take out a lot of cash and put it in a vault, or are there other reasons?

If we had removed cash and only had electronic money, could central banks set interest rates highly negative, for instance, -10%? Could they set it to -20%? Or would people just have started to use other means of value, like foreign currencies, crypto currencies or gold?


texts: Cournot oligopoly - first-order condition

texts:
I am reading an article that has this description of the first-order condition for a Cournot n-firm game:
Take $P(Q) = Q^{-1}$, $\pi_i(q_i, Q) = (Q^{-1} - c_i)q_i$.
Then the first-order condition for an interior profit-maximizing choice of $q_i$ requires that
$$ \frac{\partial \pi_i}{\partial q_i} + \frac{\partial \pi_i}{\partial Q} = Q^{-1} - c_i - q_iQ^{-2} = 0.$$
I am trying to understand why it is OK to simply take $\frac{\partial \pi_i}{\partial Q}$ ignoring the fact that $Q$ is actually a function of $q_i$. If I expand the term so that $Q = q_i + q_{-i}$ and take the partial derivatives $\frac{\partial \pi_i}{\partial q_i} + \frac{\partial \pi_i}{\partial q_{-i}}$, the solution is not the same as the one that is written in the article. Would appreciate any explanation.


texts:
The source below says
"According to this document from the US Treasury, SWIFT handles about \$5 trillion per day, or given about 250 business days per year, about \$1.25 quadrillion dollars a year.".
How much money is wire transferred every year worldwide?

However this source below says
"Worldwide, 230 million people send \$500 billion in remittances each year".
https://qz.com/775159/theres-a-500-billion-remittance-market-and-bitcoin-startups-want-in-on-it/

Why is the annual transferred money worldwide quite different?
Could you tell me the correct figure?


texts: Equities-dollar correlation was mostly positive in the 2000s and switched to negative since the GFC. Are there any structural drivers explaining this change in correlation?


texts:
I know that the GDP (the value of all final goods and services produced within a country during a given period of time) is useful for determining the productivity of a nation, the size of the nation's economy, and the standard of living.  The GNP (the value of all final goods and services produced by individuals belonging to a particular nation, both domestic and abroad, during a given period of time), I believe, is used in very similar ways.
Overall, however, it seems that the GDP gives similar information and is easier to calculate  than the GNP.  That being said, what is the point of calculating the GNP?


texts: Original formulation of the axioms of rationality

texts:
Completeness and transitivity are considered to be the two axioms of rationality in case of decisions under certainty. I wanted to know when were these axioms first proposed, by whom and the first paper where they were proposed.
I know Allen and Hicks broke away from the paradigm of Cardinal Utility and that Pareto and Fisher had also noted the possible efficacy of an ordinal view of utility. Samuelson developed the Revealed Preference Approach around the same time.
Did Allen and Hicks first propose the axioms mathematically? What was the paper? How was it received initially?


texts: Search and Matching model with 2 agents?

texts: I would like to know if you know any model with Search and matching framework (Mortenses-Pisarides style) with 2 types of workers (like Ricardian and rule of thumb consumers for exemple) ? I would like to see such a model featuring different wages, hours worked and unemployment rates between the 2 consumers. In the end I would like to implement such a framework to a DSGE model with Ricardian and rule of thumb consumers. Thank you.


texts: Multidimensional product differentiation and density functions

texts:
I’m having trouble with a model (link) I’m working on for a review.
The author uses a two firms hotelling model with a multidimensional product space (x,y)with orthogonal characteristics, which are uniformly distributed over the unit square. Preferences are standard:
$$ U_i = V - p_i -t |x-x_i| - t |y-y_i| $$
I understand the mechanics of the model (find indifferent consumer, derive demand, find profits, best response, and eq.), but I have a problem with the math behind some profit functions and consumer surplus functions. In particular, the integrals over the densities and cdf really bug me.
In the proof (eq. 31) the author finds the  demand in the case when $p_1 > p_2$ through an integral like the following:
$$ D_1 = \int_0^\hat{x} F(y \leq \tilde y(x)) f(x) dx$$
$\hat{x}$ is the intercept of the locus of indifferent consumers. $\tilde{y}$ is firm 1’s marginal consumer. F() should be the CDF and f(x) the marginal density. My understanding is that $$F(y \leq \tilde y(x)) = \int_0^{\tilde{y}} f(y) dy = y ]_0^\tilde{y} $$
Is this correct?
Then, I don’t understand what $f(x)$ is... given that x is the standard uniform, shouldn’t this be just 1 that after integration would become $x]_0^\hat{x}$?
Sorry, it’s very late and my brain is out of energy. I have to ask since I am very far from my comfort zone... hoping that you could help a bit.


texts: Income Inequality as an indicator of wealth

texts:
My employer has assigned me the project of trying to understand where our current and potential International Private Banking clients are, and where they are moving to.

To understand this, we are buying compiled data (Income as an indicator of wealth [no wealth tax in these  countries, so no wealth data] combined with the destination countries of the emigrants) from statistical bureaus of certain countries but have run into a privacy issue. Any identified "class" with fewer than five members is excluded. Say there are 500 people moving to Japan, but only 3 of those earn enough to be considered potential clients, then that data would be withheld. This is very likely to be a problem for a number of our important markets, enough so that it is not worth our buying this data in its current format.

We have considered a number of alternatives: average incomes, combining years of data, a lower income threshold, etc... but have concluded that combining enough years of data/lowering the threshold enough for data not to be suppressed would render our data not useful, and that comparing average incomes doesn't give a fair representation of the distribution of income.

Additionally, we have identified that classes with such small numbers of people can vary wildly (percentage-wise) from year to year along a normal distribution, meaning that trends will be difficult to assess.

So finally, we are considering using an index for income inequality to measure how big the spread of income is. Given the definition that someone earning more than 150k p.a.is considered to be a potential client and a very small percentage of people earn that (for one of our countries it's 0.7% including capital income), and that data that is excluded is impossible to establish any trends from  -  how do we do this?

Which measure of income inequality is best for this use case, and why, how should the data be handled? Should anyone earning below say 80k be discounted, and then an income inequality measure be used there? How do the different measures handle small datasets? Does a bias appear when there are fewer than say 100 people in a class?

So... is there a best answer? Were we unfair in dismissing any of the alternatives as a good measure? Is there an alternative I haven't considered?

Thanks for all the help it's really appreciated!


texts: Can there be too little unemployment for the health of the economy?

texts: The cyclical rate of unemployment can be negative, which implies that the business cycle sometimes produces too little unemployment. How can there be “too little” unemployment for the health of the economy?


texts: If Bitcoin becomes a globally accepted store of value, would it be liable to the same problems that mired the gold standard?

texts:
I am reading this article here that explains why bitcoin is a better store of value than gold.
In sum, here are some of the reasons proposed:

If someday a "bitcoin standard" does come to fruition, would it still be susceptible to the problems that plagued the gold standard?


texts: Alternative normalisation to triangular restriction on cointegrating vectors

texts:
Johansen recommends that cointegrating vectors must be normalised for inference making purposes. All software packages use triangular normalisation of the cointegrating vectors i.e. the top $r$ by $r$ block of the estimated $\beta$ matrix is an identity matrix. Usually, this is achieved by deriving the row echelon form of the estimated long-run equations (cointegrating equations matrix).

Does any one know of any other normalisation forms? or methods to formulate different normalisation?
Thanks


texts: Adverse selection in competitive markets- labor market

texts:
I'm referring to the Figure 13.B.1 titled 'A competitive equilibrium with adverse selection' from 'Microeconomics Theory' by Mas Colel et al. It basically graphs the expected value of the workers' productivity ($E[\theta|r(\theta)\leq w])$ against the wage offered $w$ in an attempt to explain the wage equilibrium when the opportunity cost $r(\theta)$ is lower than $\theta$ for all $\theta$.. For the life of it, I cannot understand why this function is a curve (as opposed to straight line) in the graph. What is the distributional assumption for worker's type $\theta$ that is made in order to obtain the curve?

Thanks.


texts:
I'm still kind of new to these things and some countries seem to be forbiding sharing more about hedge funds to casual people (at least what I understood from it), but anyway:

What is/was the largest hedge fund in the world and how big influence it had on economy (of any country):

during its existence
at its highest peaks
when it started to fall down?

Asking just of pure curiosity as a person needs quite large amount of money to at least enter such fund, which I guess will cause some change in the economy, right?


texts: Limit of random walk auto correlation function

texts: Given the random walk process $y_{t}=y_{t-1}+e_{t}$, the auto correlation function is given by $corr(y_{t}, y_{t-h})=(\frac{t-h}{t})^{1/2}=(1-\frac{h}{t})^{1/2}$, which tends to 0 as t tends to infinity. What is the intuition behind this result?


texts: Good economic indicators for presidential performance

texts:
I'm trying to put together a good list of economic indicators that press and economists look to when evaluating a president's "performance". These indicators should be ones that are updated at the least monthly.

What I have so far (with notes where necessary):

Unemployment rate
Debt
Deficit
GDP growth rate
Median household income (is this updated monthly?)
Median home value (is this updated monthly?)
Gallon of gasoline
DJIA
S&P 500
NASDAQ

Am I missing any and are the ones I flagged updated enough to be relevant?

Thanks


texts: Why is it the case that contractual liability is usually defined by basis of foreseeability rather than negligence (like in tort law)? I am looking a good explanation for this from economics. I understand that contract breach can be seen itself as negligent act. I also understand the economic reasoning behind foreseeability doctrine (or Hadley-Baxendale).


texts: Infinitely repeated game with stationary and symmetric equilibrium

texts:
We have two players playing a repeated game. At every period, each player decides to stay or to quit. If both decide to stay, then they both receive 1. If either decides to quit, then the quitter receives 10 for the period while the other player receives 0. The game terminates once someone decides to quit.
Utilities are discounted with the factor $d$. We want to solve for the equilibrium in which both players choose to stay with probability $p$ at every period.
I hope someone could help me check my approach or offer any different approaches.
Since the game could terminate at any period, we first need to find the expected payoff for either player. Suppose the value of the game is $v$. For either player at any period, the game has a probability $p^2$ to continue on, and a probability $1-p$ that the player quits and receives the payment.
So $v=p^2(1+dv)+(1-p)10 \implies v=\frac{p^2+(1-p)10}{1-p^2d}$.
Now, at every period, each player must be indifferent between staying and quitting.
For that the be the case, the payoff between quitting and staying muse be equal $10=p(1+dv)$.
Plugging in $v$, we have $10=p(1+d\frac{p^2+(1-p)10}{1-p^2d})$.
Solve. $p=\frac{10}{1+10d}$.
If $d\leq 0.9$, both players would always play stay. Otherwise, they would mix according to $p$.


texts: What's the relation between deadweight-loss and alpha in Cobb-Douglas?

texts:
I'm studying for an exam and facing a question about the relationship between the $\alpha$ of the Cobb-Douglas function and the loss of utility of imposing taxes.

If I have understood correctly, given a function ${X}^{\alpha}Y^{1-\alpha}$, the DWL because of a tax on good X is defined as the lump-sum tax the agent would pay to avoid the tax minus the income from the tax.

The lump-sum tax is $m(1-\frac{p}{p+t}^\alpha)$ where $m$ is the income and $p$ the before-tax price and the income from the tax is $\alpha \frac{m}{p+t} t$ where $\alpha \frac{m}{m+t}$ is the quantity of good X consumed and $t$ is the tax income by unit of x.

Deriving the DWL in Wolfram Alpha I get $\frac{d}{da}=-m\frac{p}{p+t}^\alpha log\frac{p}{p+t} - \frac{mt}{p+t}$, where the first term is always positive for a tax since $\frac{p}{p+t} < 1$.

I don't know how to go from here. Would the answer be that there is no clear effect for a change in $\alpha$ in the DWL? My intuition is that a high value of $\alpha$ means a higher lose of utility for the individual but also a higher income from the tax because MRS is higher and therefore good X can't be easily substituted by good Y. Is that correct?


texts: Is the dictator game studied by game theory or by decision theory?

texts: Is the dictator game/dilemma studied by game theory or by decision theory? I'm not sure because of the lack of other interactive agents.


texts: Why was 'structural' chosen to mean 'structural unemployment'?

texts:
Source: Economics (3 ed, 2014) by N Gregory Mankiw, Mark P. Taylor

  structural unemployment [=] unemployment that results because the number of jobs available in some labour markets is
  insufficient to provide a job for everyone who wants one

Please help me dig deeper than the definition above, the meaning of which I already understand and so ask not about. Instead, I don't understand why structural was selected for the above.  Why not adjectivize this type of unemployment with another word?

This definition (below) doesn't answer my question; all unemployment is caused by structure of the economy. So what's so structural about structural unemployment?

  c. :  involved in or caused by structure[,] especially of the economy


texts: Do local taxes help in paying back foreign debts?

texts:
I always wonder if increasing local taxes could help countries in paying off the foreign debts?

I think taxes generate income in local currency. While foreign debts (from IMF, World Bank etc.) are to be paid in USD. How could this help out?


texts: What did Karl Marx mean by "the movement of this antithesis"?

texts:
In a lecture about ancient and modern cities, a quote came up on the slides from Karl Marx's Capital where he writes

  "The foundation of every division of labor that is well developed, and brought about by the exchange of commodities, is the separation between town and country. It may be said that the whole economic history of society is summed up in the movement of this antithesis."

What does a movement of an antithesis mean ? And I don't understand what antithesis he is referring to in this excerpt; what is being contrasted; the well-established separation of divisions of labour and the exchange of their resulting specialised products ? Or the well-established foundations of divided labour and how that was brought about by exchanging commodities (or that commodities could be exchanged at all) ? Or am I missing something else completely ? Is this a translation thing, an English thing or an economics thing ?


texts: Simulating a simple economy with ... price-makers? arriving at competitive equilibrium

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I'm new to economics and thinking about graduate study. My background is mathematics.

I started reading a book on microeconomics by Mas-Colell, Whinston and Green. My goal is to understand how groups of buyers and sellers arrive at a equilibrium.

I understand the three criteria satisfying the definition of a competitive equilibrium with the assumption of price-taking firms: clearing markets, maximized profits for the firms, and and maximized utility for the consumers subject to some wealth constraints.

What I would like to do is make a simple python program which has firms, and consumers that (perhaps according to some distribution) decide their own ask and bid prices respectively (that would self adjust after some trial and error to transact) which tend to the situation of having an equilibrium (I'm not sure if a competitive equilibrium applies here since the firms are no longer price-takers).

For the consumers, I was going to use the Cobb-Doulglas utitlity funtion for all consumers for an easy first simulation.

What I would like to know is: Is there some sub-area that deals with consumers and firms battling it out which arrives at equilibrium? Are there any resources that axiomatically treat this scenario?

I tried looking at bayesian games, but it seemed that it was geared toward something a little different.

My inspiration for this project was this video: https://www.youtube.com/watch?v=PNtKXWNKGN8


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The next recession is coming up soon and I've been wondering how effective our expansionary monetary policy will be. The interest rate doesn't have a ton of room to be lowered and bond yields are half of what they were before the great recession, which leads me to my question.

Since QE suppresses bond yields, if bond yields start out low already and can't be lowered much more, does that mean QE would fail to stimulate investment? And if so, might the government start purchasing other assets like corporate bonds or stocks?

Or am i wrong and bond yields do not effect QE? Maybe QE does not seek to lower bond yields but to only increase market liquidity? (though low-yield treasuries are pretty liquid already)


texts: Derive the cost function and supply function from production function

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I didn't study economics, but am quite interested in the topic. I came to the question whether I could derive the supply curve / marginal cost function from the production function and I actually found a quite straight forward method, that I couldn't find online, so I would really appreciate if you could confirm (or correct) the result.

We are given the production function (we assume Cobb-Douglas), where capital is fixed and the only input is labor: $$Y(L)=L^a, t 1>0$$ The cost function is just wage times labor input: $$K=wL$$ We can manipulate our Production function, so that The labor supply is isolated and can then be substituted in the cost function: $$Y^{(1/a)}=L$$ Substitution gives: $$K=wY^{(1/a)}$$ where
$$w=\frac{dY}{dL}=aA^{(a-1)}=a(Y^{(1/a)})^{(1/a)}=aY^{(1/(a^2))}$$ Plugged in into the cost function: $$K=aY^{(1/(a^2))}Y^{(1/a)}=aY^{(1/(a^2)+1/a)}$$ The supply function is equal to the marginal costs, so: $$t S=\frac{dK}{dY}$$ which is, dependent on a) a function of high degree. Eg. at $a=0.3$, $S=0.3Y^{14,4}$.

Is this result correct? I mean it is just easy manipulation so there should be nothing wrong about it. And we made no usage of any more “complicate” optimization as I found online.

And now that I've already registered here and took the time to pose a question: is there any “proof” (theoretically) or evidence that the compensation is always the marginal rate. I mean, as a manager I would always charge the average costs or pay my employees their average contribution, also in the “not equilibrium” state.

Please excuse if I made any language mistakes. I'm not a native speaker.


texts: Does an instant settlement system (such as blockchains) eliminate the possibility for short selling?

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My understanding is that a short sell is possible because you can sell positions you don't have and then buy at a later point to cover your position (with the price hopefully being more favorable) to settle the trade.

In an instant settlement system (blockchains are the obvious examples, such as Bitcoin or Ethereum) would it be possible to have perform a short sell? Is there some other means of achieving the same thing?


texts: Estimating multi-output production technologies

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For a given firm, is it ever appropriate to estimate an independent production function for each output? For example, a university produces journal articles $A$ and services a number of students $S$ each semester:
$A_t = f(K_t,L_t,M_t)$
$S_t = f(K_t,L_t,M_t)$
If $A$ and $S$ had differing inputs, I would use SUR. Is there a standard approach to estimating multi-output production technologies $-$ maybe SEM? Thanks for any insight.


texts: Uncovered Interest Parity (UIP) condition approximation

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Until otherwise $e=\frac{\text{Domestic currency}}{\text{Foreign currency}}$.

The UIP condition can be written in the following form: Investing now in a domestic bond, must give the same return as investing in a foreign bond, which means, $1+i_t=e^{-1}_t\left(1+i^*_t\right)e^E_{t+1}$, implying

$$\frac{1+i_t}{1+i^*_t}=\frac{e^E_{t+1}}{e_{t}}=\frac{1}{1+\frac{e_{t}-e^E_{t+1}}{e^E_{t+1}}}$$ where $i_t$ is the domestic nominal interest rate at time t, $i^*_t$ is the foreign nominal interest rate at time t, $e^E_{t+1}$ is the expected exchange rate at time $t+1$.

Using the derivations presented here I get:
$$i_t-i^*_t=-\frac{e_{t}-e^E_{t+1}}{e^E_{t+1}}$$

However, if we define the $e=\frac{\text{Foreign currency}}{\text{Domestic currency}}$, we get $1+i_t=e_t\left(1+i^*_t\right)\left(e^E_{t+1}\right)^{-1}$, and using an analogous reasoning to the above:
$$i_t-i^*_t=-\frac{e^E_{t+1}-e_{t}}{e_{t}}$$

However, this wiki link gives(notice the missing minus sign):

$$i_t-i^*_t=\frac{e^E_{t+1}-e_{t}}{e_{t}}$$

It's not the first time I see this last(wiki) approximation being used.

What's the reasoning for this last approximation? are my approximations wrong? I would really like to know the reason for the minus signs to be missing.

Any help would be appreciated.


texts: What does it mean if the controls in my IV model are correlated with my instrument?

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I am seeking to understand what it means for my 2SLS IV model if my controls are correlated with my instrument (such that when I add additional controls to my model that are positively correlated with Y, the coefficient on my instrument declines).

Is it correct to conclude that my instrument is "invalid"?
Or is my instrument still valid, and this is normal?

I am having difficulty locating an answer. Thank you!


texts: What's the econ word for "Savings and efficiencies gained via consolidation"?

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For example, say you had 5 kitchens making cookies in 5 parts of the city.
But, then you bought 1 big kitchen, and moved all of your 5 kitchens to this 1 big location.

Due to mass production, we would expect the 1 big kitchen to operate more efficiently, and use fewer employees.

Is there a name for this in econ?

consolidation efficiencies?
mass production?


texts: Lump sum taxation in the overlapping generations model

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I am working through my textbook's problems, using the overlapping generation's model. In this economy, people are endowed with $y$ goods when young, and nothing when old. They will choose to exchange some of their endowment for money, and hence real money demand is given by
$$N(y-c_{1, t})$$
for the population $N$ of young people, and the value $v^t$ of money.

In this question, the money supply is shrinking such that $M_{t+1} = zM_{t}$ with $0<z<1$. The old are taxed $\tau$ goods by the government, payable in terms of fiat money. It then destroys this revenue.

I have already found that the rate of return of money is given by
$$\frac{v_{t+1}}{v_t} = \frac{1}{z} > 1$$

The question asks for proof that this situation will not maximise individuals' welfare. I first find the lifetime budget constraint:

$$c_{1, t} + zc_{2, t+1} \leq y - z\tau$$

and then find the feasible set for consumption for each individual:

$$c_1 + c_2 + \tau \leq y$$

When I now compare the first and second period consumption intersections, I appear to find that consumption for both periods will be more than is feasible. For instance my feasible set intersections are

$$c_1 = y - \tau, c_2 = y - \tau$$

whereas for the equilibrium, I get

$$c_1 = y - z\tau, c_2 = \frac{y}{z} - \tau$$

both of which are more than their feasible equivalents, since $z < 1$. What have I done wrong here?


texts: Dynamic Bertrand competition when players take turns

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Consider the following game:

There are two players, $i\in\{1,2\}$
Time is discrete and runs to infinity during periods $t=\{1,2,\ldots\}$
At eat point in time, players have a price $p_i(t)\in\mathbb{R}_+$
Initialise the game with $p_1=p_2=p(0)$.
In odd-numbered periods, player 1 can change his price to any $p_1\in\mathbb{R}_+$. Player 2 cannot change his price.
In even-numbered periods, player 2 can change his price to any $p_2\in\mathbb{R}_+$. Player 1 cannot change his price.
For each price, there is a demand $D(p)$, which is a decreasing function. The firm with the lowest price at the end of each period captures the whole demand, receiving payoff $D(p_i)p_i$ for that period. The firm with the highest price receives a payoff of zero for the period. If prices are equal then each firm gets a payoff of $pD(p)/2$.
Players discount the future at common rate $0\leq\delta\leq1$ so a payoff of $\pi$ that occurs $t$ periods in the future has present value $\pi\delta^t$.
Write $p^*$ for the monopoly price that maximises $D(p)p$.

The question is: can we identify a complete characterization of the set of Nash equilibria of this game?

Note that a valid strategy is a complete contingent plan, which specifies the choice of action for any history of the game.

This question follows the discussion here: What determines the outcome of a price war, and why isn't that outcome reached instantaneously?


texts: Does a stock market crash "undo” the multiplier effect's money creation?

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The economy grows for multiple reasons, but one is the multiplier effect due to fractional reserve banking.

When there is a crash, is that artificially created money essentially destroyed, resetting the economy to how much money is "really" in the system?

Sorry, I know this may be phrased informally but my knowledge of economics is limited. I just know that a crash is regarded as an economic "reset", while "multiplying" money is artificial and depends on the market's confidence.

(originally posted here, I hope at least one of these forums is the correct place: https://money.stackexchange.com/questions/77099/is-a-market-crash-the-undoing-of-the-multiplier-effect)


texts: What is the use of knowing elasticity of average product?

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Firstly they have given output elasticity of a factor, use of which is clear to me. It says to what degree my total output will vary due to a change in the quantity of a factor.
But what else do we get to know from elasticity of Average product?


texts: Can anyone explain the connection between complete market and perfect risk sharing?

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I understand that in complete market, ex post consumption growth is equal for all investors. Why is that perfect risk sharing? The book also states that

  only aggregate shocks should matter for risk prices. Any idiosyncratic risk will be equally shared.

Why is this case in complete market?
What does it have to do with financial innovation?


texts: If I make an international purchase with a card which contains domestic currency, is this currency converted to the currency of the seller?

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Let's say that I buy an app from the Play store. The seller quotes in Dollars, and I pay in Rupees (INR) --how does this transaction happen?

Is my ₹ converted into $? Does this transaction also influence the forex markets (of course, negligibly --I'm only asking for understanding's sake).

If I have to purchase a physical good while in the US, I'd have to convert my domestic currency into dollars and that'd push the dollar prices up since there is demand for more dollars.

Does the same happen when I'm at a different country and purchase a good in dollars?


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Currency is represented as an exchange for something valuable, whether it be an object or work.

Prices for objects can change over time, depending on demand and supply, making objects unreliable to measure inflation. Most countries use precious metals to measure or establish currencies, but the prices for metals can also change over time. The amount of work it takes someone to complete a task depends on their physical and mental abilities, in which no two humans are the same.

Is there something that does not change its value that can be used to measure currency inflation?


texts: Monetary Policy and international reserves-- interpretation of the estimated coefficient

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I have a problem in interpreting a coefficient in my regression below:

I am estimating the following regression in the spirit of an event study analysis with daily data:

$\Delta ER_t = \beta_1 MPS_t +\beta_2 MPS_t \Delta Res_{t'} +\epsilon_t$

in which $\Delta ER_t$ is the exchange rate between day $t$ and day $t-1$, $MPS_t$ is a monetary policy shock at time $t$ and $\Delta Res_{t'}$ is the change in foreign exchange reserve between the $\textbf{month}$ following the monetary policy shock and the $\textbf{month}$ previous to the monetary policy shock (I do not have daily data on international reserves but only monthly data).

How should I interpret $\beta_2$, the interaction term between the monetary policy shock and the change in international reserves? It is clearly not uncovering causation since $\Delta Res_{t'}$ includes a lead variable (the level of reserves one month after the shock), but then can I still argue for an inverse causation effect? For example if I find that the $\beta_2$ is positive and significant, can I claim that larger future international reserves (which increase $\Delta Res$) arise as a consequence of monetary policy shocks that have a larger impact on the exchange rate today?


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Can someone provide a formula (or set of formulas) for growth models for subscription based businesses?  I've looked, but could only find general references about this business model -- no formulas.

I could probably re-purpose a growth formula and model churn (and other parameters) by adjusting the growth rate, but I was hoping for something tailored to a subscription based business.


texts: Potential solutions of the $n$-player Prisoner's Dilemma

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Suppose we want to model a real-world phenomenon as an $n$-player Prisoner's Dilemma.

To be more specific, suppose we use RM Dawes' paper "The commons dilemma game: An n-person mixed-motive game with a dominating strategy for defection, 1973" which generally formalize the Prisoner's Dilemma for $n$ players along with a tragedy of the commons (Hardin's tragedy 1968).

Although modelling might seem "easy," how one can properly analyze in Game theory? How can we justify the validity of the game with the real world?

Also, even if we model the real-world phenomenon as a Prisoner's Dilemma, what would be some of the potential solutions to prevent the tragedy?

To be more exact, what are some of the standard methodologies to prevent universal defection?

I'd appreciate any help.


texts: Best resources to self-educate myself in economics

texts: I want to learn Economics by myself and I'm looking to build a path with people who're in this field to how and in what order should I learn Economics, I did some research and I've found many resources to learn from and I'm sure all of the information could be helpful to me in the future but I'm quite sure that not all of the material is practical. I'm ready to invest as many hours and buy all of the books required in-order to learn the material but there's just one thing to keep in mind in this path that I'm asking you to help me build which is: Practicality of the material and how fast I could start to use this knowledge to do trial and error to maximize my learning with the available resources of money I currently have.


texts: Central Bank Balance Sheets and foreign bonds

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I have a question relating to central bank's balance sheets, taken from Krugman and Obstfelds' "International Macroeconomics" textbook.

They mention that when the central bank purchases foreign bonds, the domestic money supply increases. This is paid for with domestic currency.

My question is: how does this look like in practice? So say the Fed buys the government of England's bonds. Will they convert it first to pounds? Or would Bank of England sell the bond for dollars? I am struggling to understand how the increase in purchase of foreign bonds increases domestic money supply.

Any help is much appreciated.


texts: Definition: What Is The "Trend Growth Rate"?

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I am a bit unsure about how the "trend growth rate" is defined in macroeconomics. Is it to correct to say that if a time series $\{y_t\}$ may be decomposed as $$y_t=d_t+c_t,$$ where $d_t$ is a deterministic trend and $c_t$ a cyclical component, then $$(d_{t+1}-d_t)/d_t$$ is the "trend growth rate", i.e. the growth rate in $y_t$ assuming $c_t=0$? And if it can be decomposed as $$\log(y_t)=d'_t+c'_t,$$ with another trend and cyclical component, then $$[\exp(d'_{t+1})-\exp(d'_t)]/\exp(d'_t)$$ is the "trend growth rate", i.e. the growth rate in $y_t$ assuming $c'_t=0$?

Sometimes I feel that the definition is $(d_{t+1}-d_t)/d_t$ and $(d'_{t+1}-d'_t)/d'_t$ in the two cases, referring to the growth rate in the trend component and not to the growth rate in the dependent variable $y_t$ ignoring the cyclical component (i.e., setting $c_t=0$ for all $t$).

That is, I interpret "trend growth rate" as the growth rate in $y_t$ ignoring the cyclical component. Is that a correct interpretation?


texts: Why in the quantitative equation: $MV=PY$, $V$ and $Y$ can be taken as fixed?

texts:
To  equation is
\begin{align}
MV=PY
\end{align}
where $V=\frac{1}{k}$.
Why $V$ and $Y$ can be taken as fixed or constant?
Why can $V=\frac{1}{k}$ too?
Thanks in advance


texts: How to estimate Italian parking data starting from German parking data?

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I am currently investigating the economic impact of the parking pain in Italy. I have just found out this INRIX Research which is absolutely stunning, but it only focuses on US, UK and Germany market.
I was wondering if there is any indicator/KPI to derive the Italian Parking Pain Cost starting from Germany's data.
You can find below a summary snapshot from the report:

Here you can find a direct link to the public report.
Do you know any indexes or KPIs to take in consideration? How would you solve this problem?


texts: In which market structure does the consumer has almost zero knowledge about the good?

texts: Consider goods that are almost identical (e.g. cement) and require technical knowledge to understand their merit, which an ordinary consumer might not possess. What then is the feature characteristic of its market structure?


texts: If prices stay the same, how's lending money the same as lending real goods?

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I was watching American TV. They interviewed an economist from Ivy League university. He said

It's called a real interest rate because if prices stay the same, lending money is the same as lending real goods.

Please see the title of this post. That's my question 1.

How does "if prices stay the same, lending money is the same as lending real goods" explain why the real interest rate is called the real interest rate?


texts: how to find Cournot equilibrium for 2 firms having different MC?

texts: When MC function is different for both the firms, how will MR = MC work ?


texts: Why does allocative efficiency occur when P=MC rather than MB=MC

texts: I understand that allocative efficiency is where the demand curve and supply curve intersect, i.e. where MB=MC as demand and supply can be interpreted as marginal benefit and cost respectively; however, where do we get P=MC from?


texts: Whats the math behind calculating the price of cryptocurrency through supply and demand?

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"The value of currencies (including most popular cryptocurrencies) is set by a market. Price rises or falls until the supply and demand of the currency are equalized"

Why exchange rates of national currency are usually stable, where as cryptocurrency like bitcoin and ethereum is highly volatile?

But how does the market calculate the price based on supply and demand that is visible in the cryptocurrency exchange? Can someone give some kind of simple math to understand? For example, I mint some utility coins or cryptocurrency on ethereum from thin air, decide an incentive system. How will the cryptocurrency gain value through trading?


texts:
Studying the model of Krugman, 1991: the one in which good varieties are country-specific so that there is trade because in presence of increasing returns, each good is produced in only one country, I find its conclusions a bit counter-intuitive.

The model states that a country will specialize in the production of the good for which it has the larger home market, the so-called home market effect. Thus, a country will the larger home market for a given good will be a net exporter of that good.

Now, here is my question: let's analyze two European countries, i.e. Germany and Spain. For a given level of transportation costs, Germany will produce more varieties than Spain because it is larger (larger home market). If the EU Commission would propose the creation of a Single Market, i.e. a reduction of trade barriers, that we can interpret as transportation costs going down, will Spain accept?


texts: How much inflation will changes to official wage benchmarks cause?

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For example, right now Livable Wage hovers around \$20 an hour. That's around \$40,000 a year.

Let's say the US somehow will give \$50,000 a year as a "Guaranteed basic income".

How high will the "Livable Wage" go?


texts: What are the assumptions of real business cycle theory and Keynesian theory?

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What are the differences between the approaches of Keynes and Real Business Cycle theorists? What are the assumptions made by both the theories?
How do they differ in their methodology?
Do they contradict each other??

I wish to get a basic idea of the theories with a  slight bit ofrigour.


texts: GDP Calculation and treatment of Personal Savings

texts: While calculating GDP of nation, how personal savings which is not invested in economy or has become part mandatory reserve ratio of government is treated? Similarly do we include import and export of financial asset in Net Exchange(Export - Import)


texts: What is the point of monetary policy if most monetary variables are determined by non-monetary factors?

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Monetary policy today is largely focused on setting interest rates in order to reach an inflation target / value of the currency. Interest rates are used to affect inflation by changing the demand and supply for saving and borrowing, i.e. demand. It is entirely monetary. However, I get the impression that inflation rates respond primarily to non-monetary factors, such as technological innovation, business growth, and the expansion of international trade. I also feel that this is true of the long-run interest rate, which has apparently fallen due to demographic changes (ageing populations causing a savings glut) and international trade imbalances (funds from trade surpluses in exporting nations being invested in importing nations' financial markets). None of these factors are the responsibility of a central bank to manage yet they seem to be the ultimate determinants of monetary conditions, at least in the long-run. Friedman's quote 'Inflation is always and everywhere a monetary phenomenon' springs to mind as a argument against what I am saying. Is my chain of thought a fair criticism of monetary policy?
These are simply thoughts I have been having so I apologise for the vagueness of the question. I'm looking for someone else's thoughts on the matter and possible ideas to develop the argument further.


texts: Papers on time it takes to reach market equilibrium?

texts: Are there any models which calculate the time (i.e. minutes, hours, days ect.) it takes for equilibrium to occur? I.e how long it takes for market forces to settle.


texts: How do I calculate the services sector as a percentage of GDP?

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Could anyone explain how I should calculate the share of services sector as a percentage of GDP?

I get the numbers for US GDP from Table 3: https://www.bea.gov/system/files/2019-10/gdp3q19_adv_0.pdf

The GDP in 2018 (numbers in billions of $) was 20,580.2 and services accounted for 9,633.9, which gives us 46.8% of total GDP. However, there are many resources that say services make up about 80% of the US economy, including Statista  or Wikipedia (under the 4.1 Nominal GDP sector composition section).
Note that I use the numbers for 2018, Statista only up to 2016, and Wikipedia  for 2015-16, but that shouldn't make so much of a difference.

What am I missing in my calculations?


texts: Doubt about Mixed Strategy Nash Equilibrium

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Here's the video I will be referring too.
Now I am a complete beginner in game theory, so sorry if this sounds like a stupid question, but why would a player want to balance out the payoffs of another player through his strategy.
Like it doesn't make much intuitive sense to me as to why he would want to do that. How exactly is this the best response to the situation?
Edit:
Sorry for not making the question self contained. So the game concerned is the Battle of the Sexes game, and this is the payoff matrix.


texts: Application of Intermediate Value Theorem for General Equilibrium

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Here's a problem restated from Ross Starr's General Equilibrium Theory.

  Consider a two-commodity economy with an excess demand function $Z(p)=(Z_1(p),Z_2(p))$. The price space is $p \in P = \left \{ p | p \in \mathbb{R}^{2}, p \geq 0, p_1 + p_2 =1 \right \}$. Let $Z(p)$ be continuous, bounded and fulfill Walras' Law as an equality, that is $p_1Z_1(p)+p_2Z_2(p)=0$. Assume $Z_1(0,1)>0$, $Z_1(1,0)<0$, $Z_2(0,1)<0$, $Z_2(1,0)>0$.
  Use the intermediate value theorem and Walras' Law to show that the economy has a competive equilibrium. That is, demonstrate that there is a price vector $p* \in P$ so that $Z(p*)=(0,0)$.

And I have a hint: Characterize $Z(p)$ as $Z(\alpha , 1- \alpha)$ for $0 \leq \alpha \leq 1$. Use the intermediate value theorem to find $0 \leq \alpha \leq 1$ so that $Z_1(\alpha , 1- \alpha)=0$. Then apply Walras' Law.

I'm having problem finding $\alpha$, how could I find it?


texts: I am trying to run a time series analysis on some variables - GDP being my dependent variable, and my independent variables are oil revenues, government expenditure, exports and FDI inflows. My data contains missing values for some years for at least 3 variables. I have been able to ascertain that they are non-stationary. However, I am unable to perform the Johansen test of cointegration due to the missing variables in between the data set. How do I resolve this?


texts:
According to this TTIP paper, a European family of four will see their annual disposable income increase by €545 on average:

  These gains can also be translated into household
  disposable income. One of the most widely quoted
  figures from the CEPR study is its estimation that
  a European family of four would see their annual
  disposable income increase by an average of €545
  per year as a result of the agreement. This figure
  takes account not only of increases in wages and
  other household income but also price reductions.

If on average all European households gain €545, does my purchasing power actually increase? If not (what I presume), why is this seen as an advantage?


texts:
I’m reading through a textbook in auction design when it describes a term, virtual valuation

$$\phi_i(v_i) = v_i - \frac{1 - F(v_i)}{f(v_i)}$$

where $f$ is the pdf of a bidders valuation and $F$ is the corresponding cdf.

It is described as the price you want to charge minus the cost of not knowing $v_i$. Can someone explain how the cost was derived from the probability distributions? Note I’m not an economics student by training.


texts: Something Terrible is Happening - But When Is it Likely to have Happened?

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We live in continuous time $t$ and something terrible is happening at a poisson rate of $r(t)$.

How can I compute the length $T$ such that with a probability of $P$ (for example, 0.99), at least one terrible thing has happened?

I know that for a constant rate $r(t) = \bar r$, the expected value is $1/\bar r$. How can I go on?


texts:
I am not familiar with economics but does anybody know any reference about cournot competition with strategic consumers?

In other words, is there any known competition where both producer and consumer can behave strategically and set the prices?


texts: Why do prices of consumer products seem to rise independent of their supply?

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For example, in my country, the price of coconuts steadily rises, despite the fact that we still have plenty of coconuts. The same with vegetables.

Is this caused primarily by an increase in the cost of labor as a factor input, or are other forces at play?


texts: Are expensive cities economically threatened by an inability to house low-income workers?

texts:
Cities like New York, San Francisco, and others enjoy booming local economies that support high-paying jobs in industries like finance and technology. This and other factors have driven the price tenants are willing to pay for rent to astronomical levels, pricing out lower-income workers who then have to make long commutes or take public transit to get to work.

Where I live, the average rent is $2,000, and both that figure and the area affected by inflated rent prices expands every year. As this progresses, help wanted signs and aggressive recruiting for low income jobs have become far more commonplace, indicating a labor shortage in these industries that is steadily increasing as the difficulty of commuting from areas with reasonably priced rent increases.

My city is by no means in a dire labor shortage situation, but I thought it might be interesting to consider a hypothetical city where the area of price-inflated rent becomes so large that basic upkeep from low-paying jobs that "make the world go 'round" is no longer feasible. Is this a real threat to the success of these cities? That is to say, is a labor market correction likely to drive wages up enough to sustain a workforce of extremely long-distance commuters?

Bonus:

Assuming this is a real threat, are rent regulation (San Francisco), high-quality public transit (New York), or anything else effective long term solutions?


texts: discount factor on rival and non-rival goods

texts:
I am asking to myself if we must use a different discount rate on rival and non rival goods. In standard Solow-Swann model, we use generally the discount factor $\rho$.

More formally, let's give the workhorse model used in environmental economics.

$$max \int_{0}^{\infty} u(c(t),s(t)) e^{-\rho t}$$

where $c(t)$ is consumption (rival good) and $s(t)$ is the environmental quality (or amenities) which is a non rival good by definition.

Let's say that $u(c(t),s(t))$ is an additive utility function which could be defined as

$$u(c,s)=\frac{c^{1-\sigma}}{1-\sigma}+\frac{s^{1-\phi}}{1-\phi}$$

where $\phi$ and $\sigma$ are elasticities. Also, to be complete, the constraint would be as

$$\dot{s}\left(t\right)=-c(t)$$

The question that I ask to myself is why an agent (or social planner) uses the same discount rate for a rival (consumption) and non rival (environmental quality.) ? For example, I have completely different preferences for consumption and environment for future. So, how can I use the same discount $\rho$ ?

There is an interesting paper of Endres et al. (2014) where authors use individual and social discount rates which are different.
In appendix B. (at page 631 of the paper), they define $A$ and $B$ where they say $A\neq B$ because they say each person treats differently rival and non rival goods.

So, is there a big caveat of growth models which contain rival and non rival goods in utility function ?

Thanks in advance for your hints.


texts:
Excuse me if this is not the site to ask this question but I read in meta that you have a accounting tag so here we go.

If I made a buy of an ETF in two different exchanges  with different currencies (same Isin, different currency see this question in personal money and finance exchange) and I'm valuing this securities at fair value. I have to take the ETF as the same or different security? (i.e. makes some difference the currency of the exchange)


texts: Impact of healthcare and college tuition on inflation

texts:
For as long as I can remember people in the US have complained about the high cost and trajectory of college tuition and healthcare expenditures. I've also read that inflation has been low for awhile now. How can these opposite trends occur at the same time? Reasons I can think of:

Inflation metrics do not account for healthcare and tuition or emphasize them less than other expenditures. Perhaps our current measures of inflation are somewhat inadequate
Rises in healthcare and college tuition are not as bad as the news would have you believe
The large costs of healthcare and tuition today are more to due slow but steady compounded growth over a long time, so their impact on inflation is less noticeable from year to year but more noticeable over 20-30 years


texts: how is new money actually introduced in the United States?

texts:
I'm aware that the fed controls the supply of money by contracting and expanding through permanent and temporary open market operations. Consisting of purchasing Treasury securities or through repos. These are sold primarily to primary dealers I  derstand but also to other organizations.

Can someone explain how the interest that is paid is set during auctions? Additionally it seems that the securities alone can not introduce money but through the interest paid on them?


texts: Could a tax on rental income that depends on price per square meter induce more housing with lower rents?

texts:
The background of this question is: In Germany rental income is generally taxed the same as regular business income. In some cities, there seem to be housing shortages across different incomes.
Are there countries where rental income is taxed by square meter/footage? Could it provide housing relief?

In the following tables there are three models of taxation shown. The first tries to model the current situation where the taxation is related to the gained income and not to the size and price of a flat. The following tables try to show the situation when taxation is based on price per m².


texts:
How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem?

In Duffie's book "Dynamic Asset Pricing," he outlines the "Martingale method" of solving stochastic control problems. I won't reproduce the whole outline or notation here, but the the essentials are given on p.217 of his third edition book:

After some discussion of a generalization, he mentions the following (p.221):

  Although this approach generates an explicit solution for the optimal-consumption
  policy up to an unknown scalar $\gamma$, it does not say much about the form of the optimal trading strategy, beyond its existence. The Notes cite sources in which an optimal strategy is represented in terms of the Malliavin calculus....

I know how to solve for the optimal trading strategy using the Hamilton-Jacobi-Bellman approach, but I would like to learn how to do this using the Malliavin calculus and the Clark-Ocone theorem. Duffie's book does not give directions on how to do this. Does anyone know (or can reproduce here) the way in which we would derive the optimal trading strategy this way? (For an easy, clean demonstration, it would be nice to assume, say,
$U(c) = E \int_0^\infty \frac{C^{1 - \gamma}}{1 - \gamma}$.)


texts:
What is the estimated propensity to consume out of wealth, and how does it depend on income levels?

To make sure we are talking about the same thing: I am asking what estimates we have on what percentage of their wealth people turn into spending (on pure consumption - not investment) annually. And I want to know how it depends on income levels. Do poor people have a higher percentage than others, since otherwise they'd starve? Do middle income people have a higher or lower percentage than high income people? And how big is that difference, if it exists?


texts: Editing formula for finding Marshallian Demand with Cobb-Douglas utility function

texts:
Suppose a utility function $u=x_1^ax_2^b$ with $a+b=1$. The following formula finds the values for $x$:

$x_1 = \frac{am}{p_1}\\
x_2 = \frac{bm}{p_2}$

But what if the utility function looks like $u=cx_1^adx_2^b$ so has additional factors bevore $x_i$? Can the formula above be edited accordingly?


texts:
Sorry i'm not really an economist but I don't know where else to ask.
I'm reading Ray Dalio's Big Debt Crises and he has several graphs for total US debt burdens
https://imgur.com/a/tPX3LuH
where it's about 350% of GDP in 2008, but when i can't seem to find source for total debt, only federal debt which seems to only be around 68% at the time
i'd like to find other countries total debt to GDP ratios too if possible. how do i go about this?
Thanks!


texts: Where does the Euler equation get its name from?

texts: The Euler equation, specifying the dynamical constraint for optimality of an intertemporal optimization problem, is widely used in modern economics. But where does it get its name from? What did Euler have to do with it?


texts:
Man has blue and red marbles. If he has more red marbles then blue one he wants to exchange one red for two blue($1R:2B$). If otherwise (more blue then red)he wants to exchange one blue for two red($1B:2R$). Are preferences of this man convex preferences?

My guess is that they are convex because linear combination of random bundles is worse than any chosen. Am i right?


texts: Why does Germany have such a small stock market, but very large powerful banks?


texts:
What is the difference between "aggregation" and a "representative agent?" I'm sorry if I'm not entirely clear on this question, but that's why I ask. It seems to me as if a representative agent is defined as a situation in which a competitive equilibrium can be reached by maximizing the utility of an object that can be interpreted as a "representative agent" whereas "aggregation" refers to a related situation where in competitive equilibrium prices don't depend on the distribution of an initial endowment. (Something to this effect.)

Could somebody clarify what these two concepts are and how they are related and/or different?


texts: Equation of exchange and inflation target

texts: The inflation target is $2$% and the equation of exchange states $MV=PQ$. Is the idea that we want to have greater money supply growth then real growth in general?


texts: Any information on a toy economy with 3 types of agents in it

texts:
I was thinking about a theoretical economy where there are 3 types of roles for the agents. They can be :

workers : produce good A
criminals : steal good A
cops : protects good A

without going into details, are they any theories around this type of economy and the different types of equilibrium that can be achieved, using different characteristics for agents, different rules etc...

This idea came from the fact that raising productivity could have perverse effects (raise criminality in this case) given certain conditions.

Also, do you have any tips on researching among existing economic theories for something that will describe an idea that you might have,


texts:
Trying to finding the internal rate of return R:

Net present value of costs is $\ Y(s)$

Net benefit is $\ Y(s+1)-Y(s)$ in every period t up to$\ \infty $

The answer is given as $\ R=\frac{Y(s+1)-Y(s)}{Y(s)} $
Is this the correct approach (NPV = 0)?:
$\ Y(s) = \sum_{t=1}^{\infty}\frac{Y(s+1)-Y(s)}{(1+R)^t} $


texts: Why would a central bank buy government bonds?

texts: E.g. the Bank of Japan buying Japanese government bonds.


texts:
Good day

In my Microeconomics course, we are handling the 4 imperfect competition models.

Currently we are discussing the Cournot Model, however I am unsure about a certain example. This is given as a lecture example (all information provided).

  Let us first assume that we start with a single firm (monopoly).

  This monopoly is the owner of a costless spring (and sells the water).

  I.e., MC = 0

  Start with our demand function:

Q = 120 – P
Now, determine the profit maximizing price/output combination.
MR = MC
MC = 0
Q = 120 – P (Demand function)
P = -Q + 120
Thus, MR = -2Q + 120
Thus -2Q + 120 = 0
Thus Q = 60
P = 60
Profits = 3600

I am familiar with the concept of calculating each firm's demand function, what confuses me is, in this example, we have a a single firm (monopoly) and when deriving its mariginal revenue function, one should end up with the following:

P = -Q + 120

d/dQ = P' = -1 (using chainrule for -Q => -1 and dQ of constant = 0)

thus MR = P' = -1

but in the example given, we arrive at:

MR = -2Q + 120

What am I missing or is this example incomplete (not all information given)?


texts: What's the relationship between Output elasticity and Returns to scale?

texts:
https://en.wikipedia.org/wiki/Output_elasticity

"If the production function contains only one input, then the output elasticity is also an indicator of the degree of returns to scale. If the coefficient of output elasticity is greater than 1, then production is experiencing increasing returns to scale. If the coefficient is less than 1, then production is experiencing decreasing returns to scale. If the coefficient is 1, then production is experiencing constant returns to scale. Note that returns to scale may change as the level of production changes."

So, the above is clear for 1 input. But what if the production function has two ore more inputs? Capital, labor, materials, etc? Can anyone show the proof?


texts: UK GDP accounts for profits on sale of home

texts:
A house is built and sold to a family as their primary residence for £1000 in 2000. The purchase price is included in GDP for 2000. In 2001 the house is sold for £2500. The seller pays solicitors' and agents' fees of £200. This is included in services part of GDP for 2001. He pockets £300 profit on the sale. Is this profit part of GDP?

I think not, but can find no authoritative answer.


texts: Expected Utility with expected value and variance

texts:
I'm having trouble with a question from Ariel Rubinstein's book, Lecture Notes in Microeconomic Theory. It's the problem 2 from Problem Set 7. Here's the question:

  Show that the utility function $u(L) = \mathbb E(L) - (\mathbb E(L))^2 - var(L)$ is consistent with vNM assumptions.

Where $\mathbb E(L)$ and $var(L)$ are the expected value and the variance of the lotteries, respectively.

So here's what I thought: we know the following set of implications
$$\text{Function is linear} \implies \text{Has the expected utility form} \implies \succsim \text{satisfies vNM assumptions.}$$

So, it suffices to show that $u(L)$ is linear. As we know that $var(L) = \mathbb E(L^2) - (\mathbb E(L))^2$, let's rewrite our utility function.

$$u(L) = \mathbb E(L) - (\mathbb E(L))^2 - (\mathbb E(L^2) - (\mathbb E(L))^2) = \mathbb E(L) - \mathbb E(L^2).$$

Take two lotteries, $L$, $M$. We should have that

$$U(\alpha L + (1 - \alpha)M) = \alpha U(L) + (1-\alpha ) U(M) \qquad \alpha \in [0,1].$$

So, $$U(\alpha L + (1 - \alpha)M) = \mathbb E(\alpha L + (1 - \alpha)M) - \mathbb E((\alpha L + (1 - \alpha)M)^2) = \alpha \mathbb E(L) + (1-\alpha)\mathbb E(M) - \alpha^2 \mathbb E(L^2) - 2\alpha (1 - \alpha)\mathbb E(LM) - (1 - \alpha)^2 \mathbb E(M^2).$$

But the above isn't equal to $$\alpha U(L) + (1-\alpha ) U(M) = \alpha (\mathbb E(L) - (\mathbb E(L))^2) + (1 - \alpha)(\mathbb E(M) - (\mathbb E(M))^2).$$

Can you guys help me to see where I got it wrong?


texts: What do you call a game that is both simultaneous and sequential?

texts: Is there a standard term for a game that has both simultaneous and sequential parts? Is it a mixed game? A combined game?


texts: What are the fundamental economic proofs

texts: We had a question on this site for  Fundamental equations in economics. What I'd like to know is what are the most important proofs needed in economics?


texts: Question about an interpretation of the MRS

texts:
Given the marginal rate of substitution of $x$ for $y$ : $\frac{u'(x)}{u'(y)} $
I know one can interpret this as the amount of $y$ one is willing to give up for an additional unit of $x$, or the amount of $y$ that has to be given to compensate the consumer for a loss of $x$.
But mathematically, is it saying, how much the consumer values the next unit of $x$, in terms of the next unit of $y$? or the marginal valuation of $x$ in terms of additional units of $y$?


texts: What is the government's ideal rate of growth for property prices?

texts:
If property prices raise too quickly, it can price people out of the market, cause mortgage stress and financial hardship and create a property bubble.

If property prices fall too quickly, it can be devastating to the economy as property investors have investments worth less than their loan.

So ideally, does the government want property prices to go up or to go down and at what rate?


texts: Is there a name for goods/services/rights/etc. for which the "direction" of payment in a transaction could vary based on circumstances?

texts:
For example, consider Amazon Hub Lockers, order pick-up boxes usually located in 3rd party retail venues such as drug/convenience stores, etc. Amazon benefits by reducing last mile delivery costs and expanding its customer base beyond those already having safe delivery locations, all without paying for dedicated locker space. The retail venues benefit from the incremental sales accompanying increased foot traffic. Depending on the relative value of these benefits, competing options available to the parties, etc. it seems reasonable that the net cash exchange could go in either direction.
This same scenario exists (at least hypothetically) for music licensing. A well-known artist knows that a film, Youtube video, etc. will benefit from use of her song, and she doesn't benefit much from the incremental exposure (or might even be hurt by overexposure). So, she can demand a significant fee for the song's use. On the other hand, a relatively unknown artist might rationally pay a film's producers to include her song due to the much needed exposure provided.
The transfer of ownership of large goods like boats also falls into this category. The owner of a desirable boat will be paid by the new owner. However, the owner of a large, unsalvageable boat likely will have to pay someone to take title due to the cost of disposal.
Labor rates for internships can be positive or negative. It's unheard of for tech companies to have unpaid software interns, but I understand it common for internships at talent agencies, PR firms, etc. to be unpaid. I've read that high school kids from wealthy families sometimes pay for the right to go to a 3rd world country and perform "volunteer" work for a couple weeks as a way to pad college applications. The variance in these labor rates is due to the difference in the benefit to the laborer vs. the value provided by the labor coupled with the relative supply/demand of laborers/jobs in each category.
Is there a name for goods/services/rights for which prices might reasonably be paid in either direction? A macroeconomic example might be interest rates, but I'm happy to limit the scope to microeconomics.
Is it relevant that the examples I've cited all are composites of individual goods/services, none of which having prices likely to vary in direction? The deal between Amazon and a retailer involves two services: (1) the retailer leasing space to Amazon for a locker and (2) Amazon providing the retailer with a stream of incremental foot traffic. It is only that the values of these two components can vary relative to each other that results in a composite price with varying net cash direction.
It also strikes me that all transactions might theoretically have this property, although with varying likelihoods. For example, every item in my home either has value if sold on eBay/Craigslist or is worth so little that I would have to pay the trash hauler to take it away. Perhaps the term I am seeking expresses a matter of degree vs. kind?


texts: Characterising utilitarianism and altruism in economics

texts: This question is a quantitative analogy to this question on philosophy.SE.  Within the framework of economic decision-theory using utility functions, how do you characterise the moral principles of utilitarianism and altruism, and how do they relate?  (Please ignore uncertainty in the outcome of actions, since I don't want to complicate the question unnecessarily.)


texts: How do I figure out whether the ICs are convex or concave?

texts:
Question: Randy Ratpack hates studying both economics and history. The more time he spends studying either subject, the less happy he is. But Randy has strictly convex preferences.
(a) Sketch an indifference curve for Randy where the two commodities are hours per week spent studying economics and hours per week spent studying history. Will the slope of an indifference curve be positive or negative?
(b) Do Randy’s indifference curves get steeper or flatter as you move from left to right along one of them?

My attempt: Since he hates studying both economics and history and the more time he spends studying either subject, the less happy he is, his marginal utilities for economics and history are negative each. Therefore the slope of the ICs will be negative ($\frac{dy}{dx}=-\frac{U_x}{U_y}$). I cannot figure out whether the indifference curve is convex or concave. $\frac{d^2y}{dx^2}=\frac{d(-\frac{U_x}{U_y})}{dx}=-\frac{U_{xx}Uy-U_xU_{yx}}{U_y^2}$. How do I determine the sign of this expression. I do not know what the signs of $U_{xx}$ and $U_{yx}$ are.


texts: How successful is the Islamic banking model?

texts:
Under Islamic law (Sharia), any interest is considered usury and is prohibited. This makes banking in Islamic ruled countries difficult as the normal way for banks to create profit is through lending money at a rate of interest. Rather, Islamic banks work by profit sharing or buy-sell method (e.g. when asking for a mortgage, the bank buys a house and sells back to the borrower at a higher price).

My question is: how successful is this model of Islamic banking? Does it make more money? Are there any advantages that this model gives not present in the regular banking doctrine?


texts: What impact would introducing 15 times more soy worldwide do to the price of soy?

texts:
Soy is a commodity and the main export of Argentina. It is said Argentina has 40 million of hectares of arable land and it produces food for 400 million persons and that potentially could make food for 600 millions. I can't confirm this is true but it's said by the president of one of the main agrarian organizations of Argentina, probably with statistics made by them and/or data of the national institute of agrarian technology.

Africa it's said to have 600 million hectares of arable land, which is 15 times the arable land of Argentina. What would happen to the prices of soy related commodities if Africa proportionally introduces 15 times more soy related products to the world? Take any soy product you want for the answer, soy bean if you want for example. Can this be calculated? I've heard of prices simulations predictions for other commodities when introduced or retrieved from the market, such as oil, so I suppose this can be calculated.


texts: Can CPI and real GDP have high correlation?

texts: I have historical data where the CPI and GDP are correlated. Does this make sense? If not, how do I test for it?


texts: Confusion on Strategy Sets in a simultaneous move game

texts:
I have a confusion on how to define strategy sets;

I understand that in dynamic games strategy sets are defined as $\textbf{sets of functions}$ - see for example my previous post, link below:

Define and characterize equilibria of the following game

However I cannot square this with what would be a strategy set in a simultaneous move game; as an illustration consider the following simple game:

There are two players competing for a prize of $1$. Each player $i$ choses effort level $x_i \in \mathbb{R}$. When the efforts levels are $(x_1,x_2)$, the probability that player 1 wins the prize is given by $p(x_1,x_2)$ and the probability that player 2 wins the prize is given by $1-p(x_1,x_2)$. Player $i$'s cost of exerting effort $x_i$ is equal to $x_i$.

Players choose their effort levels simultaneously.

Now looking standard textbooks I suspect that the strategy sets of both players would be defined as:
$S_1 = \mathbb{R}$, $S_2 = \mathbb{R}$
Since both players will choose an effort level $x\in \mathbb{R}$.

However given that a $\textbf{strategy}$ for player $i$ is defined as a complete contingent plan, it would be natural for me to define a strategy as a function:
$s_i: \mathbb{R} \to \mathbb{R}$,

that is for each possible effort level $x_j \in \mathbb{R}$ that player $j$ chooses, player $i$ will choose an effort level $x_i \in \mathbb{R}$.
But then since $S_i$ is the $\textbf{set of}$ strategies it would appropriate to define the strategy set of this game for player i as:

$S_i = \{s_i : \mathbb{R} \to \mathbb{R}\}$ , that is the set of all possible functions $s_i$.

But then this definition would conflict with the original one I gave at the beginning.

So which of the two (if any) would be the correct "strategy set" of this simultaneous move game?
Thank You!


texts: Making predictions with a distributed lag model

texts:
I have a question regarding making predictions from distributed lag models. Suppose, I have a simple linear distributed lag model of the form:

$$y\left(t\right)= \sum^{k}_{i=0}\beta_{i}x\left(t-i\right) + \epsilon\left(t\right)$$

Assuming co-linearity is not an issue. Suppose, I have many data points along the temporal and spatial domain for the explanatory variable $x$. However, I only have data for one time instance for the response variable but I have many data points in a spatial domain. Assume that there is homogeneity in the spatial domain.

The variables have a spatial domain; however, I am ignoring this and assuming homogeneity int the spatial domain for both $x$ and $y$. Also, many values of $y$ can correspond to a single value of $x$.

Is it possible to use the model for prediction? In the sense that one could take the lag coefficients and say at the initial time the only effect of the explanatory variable on the response variable is $\beta_{o}$ and at some time in the future, $t=n$, the only effect of the explanatory variable on the response variable is $\beta_{n}$.

Thanks in advance for you time and consideration.


texts: Errata for Wooldridge graduate econometrics book

texts:
Does anyone know where I can find an errata to the 2nd edition (2010) of «Econometric Analysis of Cross-Section and Panel Data» by Wooldridge? I've tried the accompanying website, but I could not find it.

Any help would be appreciated


texts: Fixed Effects: Identifying coefficient for interaction term with a constant

texts:
Suppose I have a regression of the form:
$$
Y_{it}=\beta X_{it}+\beta_{2}X_{it}\times D_{i}+\alpha_{i}+\epsilon_{it}
$$
 In the above, we have information by country-year on $Y_{it}$ and
two regressors: $X_{it}$ and $D_{i}$. $X_{it}$ is time varying,
but $D_{i}$ is fixed for each country over time. $\alpha_{i}$ measures
the country fixed effect.

My question is: can $\beta_{2}$ be identified?
As a fixed effects procedure uses only within-country variation, and
as $D_{i}$ does not vary over time, how is $\beta_{2}$ separately
identified from $\beta?$ I ran the regression and did find that
it was identified. Am I missing something?


texts: Search terms to find a menu of currency exchange mechanisms?

texts:
I'm look to find a good source for comparing mechanism designs for simple currency exchanges.
Is there a name for a category of game (e.g. Stackelberg game) that encapsulates the operation of an exchange?
What search terms should I use (the above terms don't seem to work) to find mechanism designs for simple currency exchanges?
Is there a good source text book that would cover this?


texts: Why can high variance help you in Heckman (1998) but not Aigner and Cain (1977)?

texts:
Heckman (1998) argues that, if the bar for acceptance is high (so most applicants are rejected), then belonging to a group who quality has high variance tends to help you. The argument is something like this: if employers only hire people whose quality exceeds a certain cutoff, but most people fail the cutoff, then if your group's distribution of quality has higher variance it will have more mass above the cutoff.

Aigner and Cain (1977) also discuss variance based discrimination. Assuming that you send a signal equal to your group's mean, the only effect of higher variance is to dissuade risk averse employers to hire you. There is no Heckman style mechanism where high variance can help you if most people get rejected.

I would be very grateful if someone could explain what leads to this contrast.

My (possibly confused) thoughts on this: the Heckman model makes sense if employers decide whether to grant an interview based on whether the probability that someone's quality is above a certain level exceeds a certain cutoff. But that is a crazy hiring rule! Instead, they should just look at whether expected quality exceeds a certain cutoff (to be fair to Heckman, this is supposed to be the hiring rule.)

OK suppose that this is the hiring rule: can high variance still help you (in the context of an audit/correspondence study)? Well, I can see how this works if the researcher perfectly controls on one dimension (e.g. what the auditors say) but doesn't control on another (e.g. attractiveness), and one group has higher variance on that second dimension, which means more of them get over the bar. But that logic totally breaks down in correspondence studies (supposedly also a target). Here the employer does not get to see some realisation from a distribution of quality that is unobserved by the researcher. At best, the employer can say: that group's high variance, so more likely to exceed the cutoff. But that brings us back to the crazy hiring strategy already discussed.


texts: Finding demand function given a utility min(x,y) function

texts:
I am confused about a particular point regarding finding a demand function. All the problems in this practice set I am doing have involved applying the method of Lagrangian multipliers. But I am uncertain if it applies here for this problem.

Problem Setup

Consider a consumer with utility function $u(x,y) = \min\lbrace x,y\rbrace$. Suppose we are given wealth $w$ and prices $p_x = 1, p_y = \frac{1}{2}$.

My Work

Not much to do yet. All I did was set up a budget constraint $w = xp_x +  yp_y = x + \frac{1}{2} y$.

My Confusion

I was all set to setup a Lagrangian multiplier equation when suddenly I realized that my utility function is a $\min$ function. At first, I thought this function wasn't differentiable. Now, I am thinking it is not differentiable but it is partially differentiable. I am still unsure.

My Guess

I suspect yes $\min$ is partially differentiable based on this thread

https://math.stackexchange.com/questions/150960/derivative-of-the-fx-y-minx-y

But I suspect my answer will need a piecewise component or something.

My Question

Are Lagrangian multipliers applicable here? If so, how do I define the Lagrangian in piecewise terms as I think I will need to do?  If it is not differentiable, how does one derive a demand function given a $\min$ or a $\max$ function?


texts: What is a number estimated as a Tornqvist Index?

texts: In the Solow growth model, to compute economic output $Y$, you need variable $A$ being total factor productivity. I found some data about my country's TFP but it's estimated as a Tornqvist Index. What does it mean? Can I simply use that number in the equation to calculate $Y$?


texts: Global games: How to derive posterior with uniform prior and signal

texts:
I have access to some lecture notes on Global games (following the model of Carlsson and van Damme (1993)) showing how to derive the players posterior beliefs. But I don't really grasp how players with uniform priors and uniform signals derive their posterior.

I have the following information:

Ex ante each state $x \in [-1,5]$ is equally likely, so $x \sim U(-1,5)$. Where $x$ is a payoff.

Then player $i$ draw an iid signal from $U(x-\varepsilon, x+\varepsilon)$, where $\varepsilon$ is a (small) number.

The posterior is then given by $p(x | x_i) = \frac{p(x_i | x) p(x)}{p(x_i)} =
\begin{cases}
0 \quad &\text{if } x_i \notin [x - \varepsilon, x + \varepsilon] \\
\frac{5 * 1/6}{5 * 2 \varepsilon / 6} = \frac{1}{2 \varepsilon} \quad &\text{else}
\end{cases}$

Can someone explain how to derive the relevant expressions for $p(x_i | x)$ and $p(x_i)$?

Carlson and van Damme “Global Games and Equilibrium Selection”, Econometrica, Vol. 61, No. 5 (Sep., 1993), pp. 989-1018


texts:
By definition,vectors are quantities having magnitude as well as direction ,especially as determining the position of one point in space relative to another

We study consumption bundles by taking them as vectors.My question is why can't we think of them as scalar quantities to study them.Why do we think of consumption bundles as locations in commodity space.What is its use?

In real world, whenever we think of commodities , only their quantities come to our mind.And when we compare two commodity bundles, we only compare their quantities.Then,why do we have to bring in the concept of vectors here...are there any cases in the real world where we are concerned about the displacement of the commodity bundles.I am unable to understand this.

Thanks.


texts:
I was wondering if there is a way to account for daily inflation data. I have daily short-term interest rates, and I would like to convert them to real short-term interest rates.

Can I just average the monthly CPI over the days of that month to calculate the real rate with the Fisher equation?

Any help is greatly appreciated!


texts: $1.25 PPP per day poverty threshold - What precisely does it mean?

texts:
As Wikipedia states:

  In 2008, the World Bank came out with a revised figure of $1.25 at 2005 purchasing-power parity (PPP).

(Update: In 2015, this was updated to $\$1.90$ at 2015 PPP.)

Wikipedia cites Ravallion, Chen, & Sangraula. "Dollar a Day Revisited", 2009.

Of course, there will always be difficulties with measurement.

But conceptually, what precisely is this $\$1.25$ figure meant to capture?

Does it mean the equivalent of someone having to pay for absolutely everything (food, water, shelter, utilities, transport, education, etc.) with just $\$1.25$ a day, in a place where prices are similar to those of the US average in 2005? Or something else?


texts: Why is real investment included in GDP?  I thought GDP is only supposed to measure final goods produced?  I thought capital is an intermediate good but I guess I am wrong. An intermediate good is sold eventually to the customer so prevent double counting we don’t count it. But I guess with capital it is not sold to other firms. Am I correct"


texts: Show that First order conditions are necessary and sufficient for utility maximization

texts:
I have a budget set
$$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$
where $y>0$ is income.
Assuming the preferences are strictly monotonic and convex, I want to show that first order conditions are necessary and sufficient for an interior solution to the utility maximization problem
**My solution **
First step : I maximize utility subject to the given budget set
Second step: I calculate first order conditions
Third step : I use hessian matrix.
If the determinant of this hessian matrix H is negative, then I can say that the FOCs are necessary is sufficient. (Is this true?)
My solution is like that
where $$u_{11}={\partial^2 u(x_1, u_2)\over \partial x_1^2}$$
$$u_{22}={\partial^2 u(x_1, u_2)\over \partial x_2^2}$$
$$u_{12}={\partial^2 u(x_1, u_2)\over \partial x_1 \partial x_2}$$
$$u_{21}={\partial^2 u(x_1, u_2)\over \partial x_1 \partial x_2}$$
I don’t know this answer is enough and correct. Because this solution seems not to be sufficient. Please share me your ideas about my solution.
Thanks a lot.


texts: How to prove a generalised function is quasiconcave?

texts:
I have a question I have been asked to solve:
Given that $(a_1, a_2,...,a_n)\in R_{++}^n$ and $(x_1, x_2,...,x_n)\in R_{++}^n$, and $A>0, \mu >0, p \neq 0$, if there is a function $f(x)=A(a_1x_1^p+a_2x_2^p+...+a_nx_n^p)^\frac{\mu}{p} \space \space \forall x \in R_{++}^n$, show that function $f$ is a quasiconcave function over $R_{++}^n$ when $p \in (0,1]$.
I understand that to show a function is quasiconcave, it needs to satisfy this definition:
$f:_+^→$ is quasiconcave on $_+^$ if and only if $∀,∈_+^$ and for all $\in(0,1)$
$f(+(1−))≥\{f(),f()\}$
I am wondering how I would use this definition to show that a generalised function $f$ is quasiconcave, or if I should be approaching this from another concept/definition.