texts: Maximising a partly concave and partly convex function

texts:
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable and strictly increasing function. Suppose that we are searching for the numbers $x_1$, ..., $x_n$ that maximise

$$\sum_{i=0}^{n}{f(x_i)}$$

subject to the constraints that $\sum_{i=0}^{n}{x_i}=\bar{x}$ and $x_i \geq 0$ for all $i$.

If $f$ is strictly concave everywhere, it is optimal to set $x_i = x_j$ for every $i$ and $j$ (so that $x_i^* = \bar{x}/n$ for all $i$). If $f$ is strictly convex everwhere, it is optimal to set $x_i=\bar{x}$ and $x_j=0$ for some arbitrary $i$ and all $j\neq i$. However, I am interested in the 'mixed' case where $f$ has at least one convex portion but is ultimately concave.

Specifically, suppose that $f$ is strictly concave for all $x \geq \hat{x}$. Does this imply that $x_i^* = x_j^*$ provided that $\bar{x}$ is 'large enough'? If so, what precisely is the assumption that we need to make about $\bar{x}$? If not, are there some additional assumptions we can make to ensure that $x_i^* = x_j^*$?

Many thanks in advance!

Edit 1: It has been pointed out that $f′(x_i^*)=f′(x_j^*)$ whenever $x_i^*>0$ and $x_j^*>0$. This might be a useful step towards an answer.

Edit 2: It has occurred to me that we will probably need to assume something like $f'(x) \rightarrow 0$ as $x \rightarrow \infty$ in order to ensure that $x_i^* = x_j^*$.


texts: Removing a degree of freedom from relative utilitarianism

texts:
Relative utilitarianism takes utilities as reported by agents, rescales them so that, for each agent, the alternatives have utility values between 0 and 1, and then chooses an alternative to maximize the (weighted) sum of the rescaled utilities. This forces an equality of sorts upon the agents as their utilities are all bounded on the same range. However, they can still express the degree to which they prefer A to B (relative to their preference of B over C) by making the gap between A and B larger (or smaller) than that between B and C.

Has anybody come across a mechanism like this except that, instead of rescaling reported utilities to a given range, we simply take the ordinal preferences expressed by the reported utilities and assign predetermined utility values (respecting the order).

That is, with relative utilitarianism:

$$ (10,4,2,0) \rightarrow (1,0.4,0.2,0) \text{ and } (100,9,1,0) \rightarrow
(1,0.09,0.01,0)$$

What I want to do is the following:

$$ (10,4,2,0) \rightarrow (10,7,5,2) \text{ and } (100,9,1,0) \rightarrow
(10,7,5,2)$$

The numbers in $(10,7,5,2)$ are irrelevant (they could be between 0 and 1) -- the point is just that they're the same across the two cases. Basically, I'm just extracting a preference order from the reported cardinal utilities and then slapping predetermined utility values on to them, respecting the order but not magnitudes in differences. Then, subsequently, I would choose an alternative to maximize the sum of utilities.

Two related questions:

Have you seen this done anywhere, either explicitly or implicitly?
Supposing you haven't, what would you call this?


texts: Are there multiple equilibria in the second price auction?

texts:
Suppose that $n\geq 2$ bidders compete in a second price auction. Each bidder $i$ knows their own valuation $v_i$, but only knows the distribution generating the valuations of the other players. Valuations are independently, continuously and symmetrically distributed. Define a (pure) strategy of a player as a function mapping from each valuation that they might have to a bid $b$; and define a (pure strategy) equilibrium as a set of (pure) strategies, one for each player, such that each player's strategy maximises their expected payoff given the strategies of the other players.

In this context, it is well known that it is weakly dominant for each player to bid their valuation, i.e. set $b(v_i) = v_i$. However, are there are other (pure strategy) equilibria of this game?

One point that perhaps should be clarified: in some discussion of second price auctions that I have seen, people define each player's strategy as their bid (a number) not their bidding functions. Here I am interested in the game obtained by defining strategies as functions.

Edit: in response to some helpful examples from @Giskard, we may wish to restrict attention to equilibria that (i) involve deviations from truthful bidding that occur with positive measure (ii) survive natural refinements that we might want to apply.


texts: Example of an economy where Equilibria may not be efficient, where one agent is altruistic

texts: I'm looking for a theoretic example of an economy where one agent is altruistic, while the others are not, that would make a walrasian equilibrium not efficient.


texts: What do interest rates tell us about the state of an economy?

texts:
I seem to have a misconception about what interest rates mean. On one hand, they signal how high a government's demand for money is, because if a government is ever in any serious need of money, they can sell bonds with a high enough coupon rate to ensure that investors will quickly buy them, which will have the knock on effect of raising interest rates. On the other hand, I hear that government will frequently increase/decrease interest rates in order to discourage/encourage consumer spending (although, frankly, I've got no idea how the governments go about changing these rates).

So, put bluntly, what do interest rates actually mean? If we take for example the UK, I've never heard anyone claim that the interest rates are low because the government is in no real need of money, but I have frequently heard that the interest rates are low because the government wants to encourage consumer spending. What should be read in to that?


texts: Liquidity puzzle in the representative household model

texts:
In a cash in advance representative household model, the nominal interest rate  may be determined by
$$\frac{1}{1 + i_t}= βE_t\left(\frac{M_t}{M_{t+1}}\right)$$
where $\beta$ is the discount rate.

I'm interpreting this model as if $M_t$ is known at time t. Is this a valid interpretation?
How from a temporary increase of the current money supply, which does not affect the expectation of the future money supply, can the impact on the nominal interest rate be given by $\frac{∂i_t}{∂M_t} = −\frac{1}{M_t E_t(M_t/M_{t+1})}< 0$
Assume that the growth rate of the money supply follows a linear ﬁrst-order, stationary autoregressive stochastic process of the form $$\ln(M_t/M_{t−1})= µ(1 − λ) + λ \ln(M_{t−1}/M_{t−2}) + ε_t$$, where $0 <λ<1$, and $ε_t$ is a white noise process. In this setting, how can a positive shock in $ε_t$ lead to an increase in $i_t$?

In the last two questions, I'm interested in the mathematical details. I understand the economic importance of this example. If what I ask in 3. is true, then we have an opposite effect from what we would expect (the liquidity effect = increase in the money supply, decrease in nominal interest rate) and hence the puzzle. However, the mathematics is escaping me, somehow... There's some assumptions I may not be considering that allows us to reach the conclusions above.
All this was taken from the book Dynamic Macroeconomics by Alogoskoufis (great book, has taught me much so far. It's just that I'm not a good economist, nor mathematician. =D).


texts: I calculated the HHI index for Chile exports and got values ranging from 0.09 and 0.13. We know that Chilean exports are very concentrated (around 40% of the exports are copper related goods) and the index might be misleading. I used HS 6 digits with the Customs data and Comtrade data. I am really puzzled and appreciate any help. Thanks.


texts: Does elasticity make sense for different levels of prices? If not, how can we fix that?

texts:
Let's say we know that our customers can't make sense of a raise in 5% of the price. It's too little for them to notice. However, an increase above 10% is easily noticed. If this is true, different level of prices impacts the customers in different ways and the formula we learned at college is not enough for real-world problems. Additionally, 10% of increase in something that costs 10 dollars is different than 10% of increase in something that costs 100 dollars, right?
So, how can we deal with this type of problem? How can we deal with price in real-world? How can we get elasticity in this situation?


texts: Could the Troika's economic plan work for Greece?

texts:
There are a number of things that are confusing me about the current Greek financial crisis.  The first is this.

  Is it plausible that if Greece did everything the Troika asked then
  the Greek economy would revert to high growth and high employment in a
  small number of years?


texts: What is the usefulness of approximating an optimal decision rule that close enough to steadystate in RBC model?

texts:
I'm reading understanding real business cycle by Plosser.

Here's my crude understanding: For a RBC model, the FOCs of lagrangian together with transversality condition usually forms a nonlinear difference equations system. The standard way of solving this system is by linearization in the neighbourhood of steadystate,  solve this problem as a linear difference equations system.

What insight can we get from this solution, except for gaining  some knowledge of whether the steadystate is locally stable?


texts: Can "invisible" investing by the Chinese govt. create bubbles in the stock market?

texts: In this link, they claim that the Chinese govt. secretly pumps money into the market as soon the market crashed due to Corona Virus. How is this different, in terms of long-term impact, from quantitative easing of Fed? Can this potentially create bubbles, as it hinders price discovery?


texts: What metrics can be used to distinguish between capitalistic and socialistic economies?

texts: What macroeconomic indicators are meaningful to distinguish whether a country leans towards socialism or capitalism (and where to find such data, specifically for european countries)?


texts: Is "$f(k,l)$ is decreasing return to scale $\Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$" always true?

texts:
For the productions $f(k,l) $ that are continuously differentiable, is the proposition  that

"$f(k,l)$ is decreasing return to scale $\Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$"

always true, I have checked for Cobb-Douglas functions and believe it will also hold for all Constant-Elasticity fuction, can someone give me some hints or show some counter-examples?

Here we define $f(k,l)$ to be decreasing return to scale if $ f(tk,tl)<tf(k,l)$ for $t>1$ for all $(k,l)$ in the domain.


texts: I want to make a grid [0,1] with 100 points but I want points to be concentrated at the edges close to 0 and 1. So I want 60-70% of the points to be in the intervals [0, 0.2] and [0.8, 1]. Any ideas on how I can do this?


texts:
I need the PMI time series for an econometic project but it seems I can't get it for free on the internet.

Does anyone know where can I download it for free?
Also a proxy for this series would be great.
The sample size: monthly, from 1960-70 to 2016


texts: Determining a variable from empirical results obtained from regression analysis

texts:
For context, I am trying to estimate the excess supply and demand in the Commercial Real Estate market and the rental price adjustment mechanism following the change in vacancy.
I found a paper titled "The Price Adjustment process and natural vacancy rate" that explores this rental price adjustment process for the housing market. Basically, the author estimates the demand, level of vacancy and supply stock in the market to construct an regression equation that attempts to explain the determinants of change in rental price (R).
Demand D, may be assumed to be a function of the rent per unit of housing services, R; the user cost of home- ownership, U; real income per household, Y; the price level, P; and demographic variables, Z, as set out in  D=d(R,U,Y,P,Z).
Vacancy V = Vacant units / Total Supply stock (Vacant units = Occupancy - Supply).
Then, the rate of change in rents (R) is a function of excess demand or supply in the market. This excess is the difference between long-run equilibrium vacancy (Vn) - V.
The results are obtained by assuming constant Vn and fitting regression equation R = b0 + b1.E - b2.V
From the results obtained, they estimate the long run equilibrium vacancy or the natural vacancy rate (Vn).
This is the part that I am not following. How is Vn calculated? Here's an excerpt from the paper:
"An estimate of the natural vacancy rate for each city can be determined from the empirical results in Table 1. If we assume the appropriate estimating specification of equation (4) would exclude an intercept, and that V' is constant over the estimating period for each city, then the intercept in estimating equation (5) for each city can be interpreted as bo = b2Vn, and the natural vacancy rate for each city is bo/b2. Assuming this specification, the last column in Table 1 sets out the estimated natural vacancy rate for each city. 1 "


texts:
There are a few papers that I have seen that publish insiginficant results, such as responses (see Easterly's response published in the AER to Burnside and Dollars World Bank paper titled 'Aid, Policies and Growth). The aim of these papers, however, is to negate a positive claim which they do by producing insignificant results (in the hypothesis testing sense) using the same idea as the original authors, but using new data.
However, I have yet to come across a major paper in its own right published in the top 5 journals that publishes results that are insignificant. This is a scary thought because when I do my own research, I always shudder before entering the regress y x command.   Are there well known papers that publish insignificant results?
Thanks!


texts: How do small firms survive in an oligopoly?

texts: How do small firms survive in an oligopoly if large firms already dominate a huge amount of market share in the market? in terms of the supermarket industry between large supermarkets and small grocery stores around the country.


texts: influence of growing foreign demand for local products on the net exports in a fixed exchange rate regime

texts:
Suppose we have a country $A$ with a fixed exchange rate regime.

Suppose that, suddenly, the foreign demand for $A$'s made products rose up.

What will happen to $X-IM$?

As far as I can tell $X$ grows and thus $GNP$ grows. Finally since $GNP$ grows and the exchange rate is fixed $IM$ grows. So, finally we can't say anything about $X-IM$?


texts: Difference between 'ideal variety' and 'love of variety' - International trade

texts: What really is the difference between the "ideal variety" (Lancaster) of a differentiated product approach and the "love of variety" (Dixit and Stiglitz) approach?


texts: Should coefficient on interaction term be positive or negative?

texts:
I have the following model for housing prices

price = $\beta_0$ + $\beta_1$ sqrft + $\beta_2$ bedrooms + $\beta_3$ sqrft $\times$ bedrooms + $\beta_4$ bathroom,

where sqrft is square feet.

I am confused regarding the interaction term. Should $\beta_3$ be positive or negative? I think that the effect of additional bedroom on house price is higher for larger houses. Is this correct?


texts: For a certain good, if there is a one-time fixed cost for a consumer to switch to a different firm, then this good is?

texts:
For a certain good, if there is a one-time fixed cost for a consumer to switch to a different firm in a later time, then we say this good is ____ (or has property ___). Examples include

Consumer: House renter
Firm: Landlord
Good: Stays in a house
One-time Cost: Moving cost

Consumer: Mobile phone user
Firm: Wireless carrier
Good: Uses of phone over a carrier network
One-time Cost: New account activation fee


texts: Will an increase in interest rate cause short run aggregate supply to shift?

texts: Most business borrow for financing their purchases of raw material and capital etc. Shouldn't a interest rate rise cause cost of production to increase, therefore shifting SRAS to left? Thanks in advance.


texts: Investment = Saving relation in an open economy

texts:
I am reading the book Macroeconomics by Olivier Blanchard.

It states that an alternative way of looking at an goods market equilibrium is investment = saving.  In an open economy it states the equilibrium condition is Net Exports = Saving (both private and public) - Investment.

I am struggling a little bit with the intuition of understanding this condition.  Would it be because the difference between saving and investment would contribute to the capital account aspect of the balance of payments in some way?

I would be very grateful if someone could help me to gain an understanding of this equilibrium condition.

Thankyou.


texts:
An urn contains equal number of green and red balls. Suppose you are playing the following game. You draw one ball at random from the urn and note its colour. The ball is then placed back in the urn, and the selection process is repeated. Each time a green ball is picked you get 1 Rupee. The first time you pick a red ball, you pay 1 Rupee and the game ends. Your expected income from this game is..

The answer given is 0 but shouldn't it be positive as the as the income rises if you consecutively draw the green ball? Please help me clarify this doubt.


texts: I am struggling understanding the concept of rational expectations. Can someone explain in simple words the concept of rational expectations? Does someone know a good (online) source explaining rational expectations?


texts: How technology will help economists to do better predictions?

texts:
Would technologies as AI, BI and Big Data help the economists to make better predictions and test models to solve problems like "What level of fiscal stimulus is better for a especific country?"

Is it something for the future or its already been used?


texts:
I would like to know if there exist a database where Value at risk of commercial banks are.

Beyond that if there is a connection between the rating from agency (as S&P, Fitch etc..) and the VaR of banks. And where I can find references of that.


texts: Why can't we use $R^2$ for different dependent variables?

texts:
Imagine we have a linear regression model with dependent variable $y$. We find its $R^2_y$. Now, we do another regression, but this time on $\log(y)$, and similarly find its $R^2_{\log(y)}$. Why can't I compare both $R^2$ to see which model is better suited?

Intuitively I would say that the log will decrease the variability, hence any model will improve once we 'add' the log transformation.

Is there another reason? Also is there a way to formalise this intuition?

Any help would be appreciated.


texts: Who exactly foots the bill if Greece defaults

texts: Apologies if the topic is not appropriate (economics newbie here) but I am curious as to who exactly would foot the bill if Greece defaults on the ~300 billion dollars it owes. It looks like most of the money is owed to EU, IMF and ECB but what does that really mean in layman terms? Does it mean that tax-payers in other (mostly EU) countries end up paying one way or the other.


texts:
I have a question related to IV methods. Suppose I have a regression

$Y = a + b_1 X_1 + b_2 X_2 + \epsilon$,

where $Y$ is a dependent variable and $X_1$ is an endogenous independent variable and $X_2$ is an exogenous one. I have found a variable $Z$ as the instrumental variable for $X$. The question is as follows. Suppose I now set up new variables such that $X_1^l(X_1^h) = 1(0)$ if $X_1 \leq(>) a_1$ and $X_2^l(X_2^h) = 1(0)$ if $X_2 \leq(>) a_2$. The my regression becomes

$Y = a + c_1 X_1^l X_2^l + c_2 X_1^l X_2^h + c_3 X_1^h X_2^l + c_4 X_1^h X_2^h + \epsilon$.

I want to know how to set up IV in this case. Thanks.


texts: How long are consumers willing to wait in order to find a bargain?

texts:
I have (what I believe to be) a microeconomics question that I'd like to explore:

  How long are consumers willing to wait to find a bargain on an item they'd like to purchase?

I believe the question is easy to understand, but I'm unsure of the methodology to collect proper and relevant data to solve the question.

The answer, I'm sure, is a bit complicated. Though I'm not completely certain, I suspect the relationship is such that time, $t$, is a function of the change in price, $\Delta P$, of a given item (i.e.,$\quad f:\Delta P \rightarrow t).$ The price change could be relative or absolute.

There might be a schedule of different coefficients, depending on the price bracket of different items. For example, one class would include items that many households could afford on a weekly basis (video games, books, t-shirts, etc.), while another class would include items that the average household doesn't buy every week or year (refrigerators, cars, overseas vacations, etc.), and another class would include luxurious items that only the top 2-5% percentile of income earners could afford (court-side tickets to a basketball game, a Ferrari, a bottle of Dom Perignon, etc).

So here's my question to the community here: does anyone know of any study or previous work that addresses this question? If not, does anyone know how I could go about researching this topic? I guess "SurveyMonkey" would be one route, but it seems like a daunting task, considering how many variables I might have to account for.


texts: Why didn't other oil pricing benchmarks such as Brent go negative?

texts:
This question is asking why the oil (in this case, WTI) price is  negative.

While I think I have broadly understood why WTI collapsed, I don't really understand why other oil pricing benchmarks didn't suffer the same fate. Brent oil, for example, to take the most famous one, suffered losses but was still around $20 per barrel.

What explains the fact that WTI and Brent acted in such different ways?
Is it that that Brent can be better stored? Transported? Refined?
Are the shut-in clauses or future contracts different?

What major factors explain why WTI went negative, while Brent did not?


texts: Erik Reinert's conclusions and experiments in economics

texts:
I have just read Erik Reinert's, "How Rich Countries Got Rich… and Why Poor Countries Stay Poor". Can anybody advise me some further reading on this topic? I wonder, in particular,

if there were investigations on the influence of the international specialization of labour on the migration processes?
if there were experiments in this field?

Thank you.


texts: Which regression technique is used for calculating price elasticity in practice

texts:
Since we need to consider 'Endogeneity' between price and quantity while calculating price elasticity and since linear regression cannot handle the phenomenon of endogeneity if objective of the model is to find causality, instrumental variable regression is used.

Since theory backs the idea of using IV regression, does this happens in real world? I mean corporations and governments use IV regression for price elasticity or do they use linear regression despite it's shortcomings in it's inablity to handle endogeneity?


texts: Does the current situation of excess reserve imply failure of QE?

texts:
Excess reserve @ Fed

In the past it was assumed that excess reserves should be kept around 0 and banks should be lending to each other as much as they are borrowing. The central banks would correct the negative or positive balance at the end of the day by lending or borrowing at premium rates, but that was only a short term solution.

Now we have 5 years of excess reserves at the Fed and a lot of articles about how banks don't care about cash deposits.

Is this the failure of QE? The money being lent and given frivolously circles right back into the Fed in the form of excess reserve it seems.

Is this making it categorically impossible to raise real interest rates? Maybe interest rates could go up if a devaluation process was launched and inflation started climbing, but I'm more interested in understanding what makes the real interest rate move.

Am I misunderstanding something or everything?


texts: How can lending be feasible on blockchain?

texts:
Given the fact that mostly all cryptocurrencies have a permanently set supply, they will invariably rise in value as cryptocurrency transactions rise. Even if cryptocurrency deflation cools off from where it is now, Crypto/fiat would still rise at a high rate due to population and economic growth.

So, I don't understand how loans would be feasible on blockchain.

Let's say I get a 1 BTC car loan at 1% interest that's amortized over 6 years, then the amount I would have to pay in dollars to cover the appreciation of BTC/USD along with the interest on the loan would probably be way above that on standard car loans.

To me, the only time it would be feasible to borrow BTC is when I am shorting BTC... Or am I missing something?


texts: Utility maximization in a 2-good scenario with an option to buy a combo of the two

texts:
I am solving the following question:

Suppose that we live in a two good world, books (x) and movies (y), with utility function given by $u(x,y)=min(x+2y,2x+y)$. Prices of books and movies are 25 and 10 respectively. Income is 1000.
Consider the following two schemes:

The person gets one movie free on each book they purchase.
In addition to buying books and movies separately you also get an option to buy a book with four movies combo pack for 50 only.

Q1. What is the optimal consumption in scheme 1?

A. (40,40)
B. (0,100)
C. (10,75)
D. None of the above

Q2. What is the optimal consumption in scheme 2?
A. (0,100)
B. (10,75)
C. (10,80)
D. None of the above

My working:

For the first part I figured the following:
If I buy $x$ books, I only have to pay for $y-x$ movies, so therefore my budget constraint will look like this:

$$25x + 10(y-x) = 1000$$
$$\implies 15x + 10y = 1000$$

Now solving this budget constraint with the given utility function, I get the optimal consumption as $(40,40)$.

On to the next part, I apply the same logic as above. If I buy $z$ units of the combo for 50, I only have to pay for $x-z$ books and $y-4z$ movies. So therefore my budget constraint will look like this:

$$25(x-z) + 10(y-4z) + 50z = 1000$$
$$\implies 25x + 10y - 15z = 1000$$

My question here is two-fold:

Is my reasoning correct in the above two scenarios?
How do I solve for the optimal consumption in the second scheme, where I have the option to buy a combo?

Thanks!


texts:
First: for year 0, I do not know why the cash flow = $- 1000 / ( 1 + 0.10)^0 = 909.01$

Second: for year 1, if cash flow = $30,000-5000/(1+0.10)^1 = 25 454 $

How is "Cash Flow" column useful in getting the "Present Value" column?


texts:
I have started out reading seminal paper of Solow - Solow Growth model. It starts out with discussing weaknesses in Harrod Domar Model, a simple model of economic growth which featured prior to solow's work. You can read about Harrod model here

https://www.google.co.in/amp/s/sanaasaluja.wordpress.com/2015/08/05/the-harrod-domar-model-of-economic-growth/amp/

While discussing about Harrod Domar Model, Solow said it consistently uses short run tools for long run analysis (see the picture). But I don't understand why he called 'the multiplier' as a short run tool and 'margin(al) [product]' as a long run tool?


texts: Increase in the number of jobs in an economy: Central Bank raises interest rates?

texts:
For example since the August job report came out, which showed hundreds of thousands ob jobs created. This will inevitable lead to the Fed to increase interest rates, but what is the motive behind doing this?

Would this not simply lead to a decreased shift in consumption and be an attempt at stagnating the economy?


texts: Suitable terminology for the inverse elasticity?

texts:
In many microeconomic applications (e.g. monopoly price-setting) the inverse elasticity appears. Explaining such relations to laymen is often awkward because inverse proportionality is not as intuititve as direct proportionality.

In physics, there are often separate terms for inverses of important concepts (e.g. electrical resistance and conductance are each other's inverse).

Question: is there a commonly used term for the inverse elasticity? If not, what would be a suitable term that is easily grasped by laymen?


texts: preference convexity and existence of equilbria

texts:
Consider a production economy with $L$ goods, a single consumer and a single producer whose production set are given by $Y\subset R^L$. Question is to find the existence condition of equilibria of this economy.
I think the existence conditions are:

continuity and monotonicity for consumer preference

convexity for firm's technology.

Generally, convexity of consumer's preference seems to be required also for existence of equilibria. However, I cannot find the counter example that there is no equilibrium of this economy if consumer's preference is not convex and all other consumptions are satisfied.
Convexity of consumer's preference is really a condition of existence of equilibria in this one consumer-one producer economy?


texts: Should central bank raise interest rates during a condition of liquidity trap?

texts:
I was studying about liquidity traps and understood it fairly well that according to widespread beliefs the monetary policy turns out to be ineffective as nominal interest rates are close to zero and the public has deflationary expectations. Since nominal rates are close to zero nobody wants to hold financial assets and prefer cash instead.
My question here is that in such a condition when nobody is investing in bonds, should not the central bank raise interest rates to give higher incentive to bond holders. I know I am missing some point but can someone please explain this relationship between interest rates, inflation and bonds in the context of liquidity trap.


texts: Self-dual production functions that do not satisfy weak homothetic separability

texts:
I am looking for parametric production functions that do not satisfy weak homothetic separability (as first defined in Shephard, 1953), but that do allow for an analytical expression of the dual cost function to be derived from the cost minimization problem (they are self-dual). Do any exist?
For completeness, one can say a production function with variable inputs $M_{it}$, $L_{it}$ and fixed input $K_{it}$ is weakly homothetically separable if it is of the form,
\begin{equation}
    q_{it} = F\left( K_{it}, h( K_{it}, L_{it}, M_{it} ) \right),
\end{equation}
with $h( K_{it}, \cdot, \cdot )$ homogeneous of arbitrary degree for all $K_{it}$.
References
Shephard, Ronald W. COST AND PRODUCTION FUNCTIONS. PRINCETON UNIV NJ, 1953.


texts: How many cars are made in China by Chinese brands?

texts:
From the 25+ million cars made annually in China, many of them are German, American or Japanese brands.
How many of the cars made inside China are actually Chinese brands?


texts: Macroeconomics - Fiscal/Monetary Policy and the Price level

texts:
I was studying for my macroeconomics test by solving test banks and I came upon this question which has been really bugging me.

To decrease the price level

A.the Fed could buy bonds and the government could increase the
corporate profit tax.

B.A decrease in income tax and an increase in corporate profit
tax

C.the Fed could sell bonds and the government could lower the
corporate profit tax.

D.An increase in government spending and a decrease in the price
of raw material

Answer : C

I don't understand why the answer is C. If I take it answer by answer:

A) Expansionary monetary policy + contractionary fiscal policy = unknown result (Aggregate demand curve could shift to the left or to the right depending on which policy was more effective).

B) Either contractionary or expansionary fiscal policy depending on the values of increases/decreases. Employee income surpasses corporate profits income in most cases so I would consider this expansionary fiscal policy which raises the price level.

C) Contractionary monetary policy + expansionary fiscal policy. Why would they choose this as the right answer? It's as ambiguous as the others, the shift in the AD curve is unknown.

D) Expansionary fiscal policy (shift of the AD curve to the right) + shift of the AS curve to the right (which lowers the price level), again leads to an unknown result for the price level)

Am I approaching these questions badly or are they as ambiguous as I think they are? Also, when monetary policy and fiscal policy oppose each other, which one takes the lead on the shift of the AD curve? I feel like that it would solve a lot of problems to know that.


texts: In a problem set, I found a strange utility function: $U(c)=-1/2(c^* - c)^2$, where $c^* =$ positive constant level of consumption. Does this function have economic sense?


texts: Solow Model: Steady State v Balanced Growth Path

texts:
Okay, so I'm having real problems distinguishing between the Steady State concept and the balanced growth path in this model:

$$ Y = K^\beta (AL)^{1-\beta} $$

I have been asked to derive the steady state values for capital per effective worker:

$$ k^*=\left(\frac{s}{n+g+ \delta }\right)^{\frac{1}{1-\beta }} $$

As well as the steady state ratio of capital to output (K/Y):

$$ \frac{K^{SS}}{Y^{SS}} = \frac{s}{n+g+\delta } $$

I found both of these fine, but I have been also asked to find the "steady-state value of the marginal product of capital, dY/dK". Here is what I did:

$$ Y = K^\beta (AL)^{1-\beta} $$
$$ MPK = \frac{dY}{dK} = \beta K^{\beta -1}(AL)^{1-\beta } $$

Substituting in for K in the steady state (calculated when working out steady state for K/Y ratio above):

$$ K^{SS} = AL\left(\frac{s}{n+g+\delta }\right)^{\frac{1}{1-\beta }} $$

$$ MPK^{SS} = \beta (AL)^{1-\beta }\left[AL\left(\frac{s}{n+g+\delta }\right)^{\frac{1}{1-\beta }}\right]^{\beta -1} $$

$$ MPK^{SS} = \beta \left(\frac{s}{n+g+\delta }\right)^{\frac{\beta -1}{1-\beta }} $$

Firstly I need to know whether this calculation for the steady state value of MPK is correct?

Secondly, I have been asked to Sketch the time paths of the capital-output ratio and the marginal product of capital, for an economy that converges to its balanced growth path "from below".

I am having problems understanding exactly what the balanced growth path is, as opposed to the steady state, and how to use my calculations to figure out what these graphs should look like.

Sorry for the mammoth post, any help is greatly appreciated! Thanks in advance.


texts:
Mas-Colell, Whinston and Green, in Microeconomic Theory (third edition), postulate the concept of an index for an excess demand vector, which is later used in the Index Theorem:

A regular equilibrium of the economy is defined as the following:

$D$ denotes derivative (here, in respect to price), while $z$ denotes the excess demand matrix:

Where $p$ denotes price and $\omega$ denotes endowment.

What does the concept of index means?


texts: Why do so many models assume homothetic preferences?

texts:
...when Engels Law, backed by a good amount empirical evidence, demonstrates that overall consumer preferences are not homothetic.

See for example, Jorgenson (1997)


texts: How to show that GLS estimator is consistent in regression model?

texts:
$$\mathbf Y=\mathbf X\beta + \mathbf U$$
$$\mathbf E[\mathbf U\mathbf U']=\Omega $$

$$\hat \beta - \beta=(\mathbf X'\Omega^{-1}\mathbf X)^{-1}\mathbf X'\Omega^{-1}\mathbf U$$

let $\mathbf X^{*}=\Omega^{-0.5}\mathbf X$, and $\mathbf U^{*}=\Omega^{-0.5}\mathbf U$. it is obviously that $\mathbf u^{*}_i$,which is the i-th element of $\mathbf U^{*}$, is iid follows the standard normal distribution, if we assume that $\mathbf U$ follows normal distribution. But $x_i^{*'}$, the i-th row of $\mathbf X^{*}$ is not necessarily independent, for it is the linear combination of all rows in $\mathbf X$ (which is assumed iid for they stand for observations from the same distribution).

Thus the followings are not necessarily true under independent Law of Large number and Central limit theorem:

$plim\frac{\mathbf X'\Omega^{-1}\mathbf U}{n}=plim\frac{\mathbf X^{*'}\mathbf U^{*}}{n}= plim\frac{1}{n}\Sigma x_i^{*}u_i^{*} =0$
$\frac{\mathbf X'\Omega^{-1}\mathbf U}{\sqrt n}=\frac{\mathbf X^{*'}\mathbf U^{*}}{\sqrt n}= \frac{1}{\sqrt n}\Sigma x_i^{*}u_i^{*} $, converges to normal distribution

I understand that when $\mathbf \Omega $ is a diagonal matrix then $x_i^{*}$ is independent and it is not a problem, what if when $\mathbf \Omega $ is not a diagonal matrix? What kind of dependent LLN and CLT can be applied here? should we make other assumptions?


texts: Where can one find Beta values for stocks?

texts: Is there someplace specifically on the internet where one can find Beta values for stocks? I've been looking but apparently I'm looking in the wrong places. Tried WSJ stocks and Morningstar. Morningstar need to subscribe.


texts: Difference-in-Differences setup for policy evalution

texts:
I have a panel data set of housing prices from different neighborhoods in a city - and wish to test whether or not a policy has had an impact on the housing prices. The policy (treatment) is simply a sign signaling whether it is a good or bad neighborhood (based on parameters which are already known).
Initially I figured I could mirror the paper by Card and Krueger (1994) with a difference-in-differences estimation however what complicates my issue is that the policy enables neighborhoods to go from good-bad and bad-good over a span of 10 years. So they could potentially get a treatment multiple times.
Any suggestions into papers which has studied policies in a similar fashion or at methods which could be applied is greatly appreciated.


texts: Why did the internet price rise in the last 5 years in Germany?

texts:
5 years ago a casual internet connection with 10 Mbit and telephone connection cost about 20 € per month in Germany.

Today, the chepest contract that I could find in Germany is an internet connections with 16 Mbit and telephone flat for landline, which costs monthly 30 €.

Why did the price rise about 50%? The infrastructure has already been build and the difference between 16 Mbit and 10 Mbit isn't that big.


texts: Instrumental Variable Paper for Minimum Wage

texts: I am trying to write a paper dealing with minimum wages and employment.  I understand there is simultaneity bias between these two variables so I must come up with an instrument.  Does anyone have any ideas for instruments?  I am also wondering if it is feasible to do a cross-sectional study instead of a time-series one in this scenario.  *Note:  The class requires using IVs and I am open to suggestions for other topics.


texts: I'm third year economics student and all econometrics we had so far and basically all empirical studies in economic subjects we had so far are linear regression. Is there any alternative, can anyone suggest any reading material or direction in which I can explore?


texts: Should we expect more structural technological unemployment if growth becomes more limited by natural resources and less by labour?

texts:
Technological unemployment, where unemployment arises from (with some oversimplification) workers being replaced by machines, has so far been temporary as new jobs were created that replaced the old jobs.  Structural unemployment has been predicted many times in the past and the present, but has not (yet) occurred.

Historical increases in productivity have led to an increase in overall production.  Physicist Timothy Garrett models the economy as a heat engine, with more details in papers linked from Garretts personal page:

  In each of the past 40 years for which records are available, a continuous 7.1 Watts has been required to maintain every one thousand inflation-adjusted 2005 dollars of historically accumulated economic wealth (not yearly economic output or GDP). As of 2010, civilization was powered by about 17 trillion Watts of power which supported about 2352 trillion dollars of collective global wealth. In 1970, both quantities were less than half this. In the interim, energy consumption and wealth grew equally rapidly in the interim at an average rate of 1.9% per year.

Dr. Garrett is not an economist by training, and I don't know how his models are received by mainstream economists.

How do contemporary forecasts on technological unemployment take into account an economy that is increasingly limited not by the availability of (sufficiently skilled) labour, but rather by the availability of resources?

To illustrate it further: some speculate that in the next years and decades, self-driving cars will displace professional drivers (taxi drivers, lorry drivers, etc.).  This will initially increase unemployment, but it would also lower the labour component of the price of many goods.  Historically, civilization has responded to such events more with an increase in production than with an overall decrease in hours worked.  However, production cannot be increased arbitrarily; resources become increasingly scarce. Therefore, those prices will go up.  That means that perhaps this time around, the feedback preventing structural, technological unemployment does not apply...  hence my question.

I welcome answers that do and answers that do not take into account externalized costs such as damage to natural ecosystems, pollution, and anthropogenic climate change.


texts: How can foreign protectionism affect local FDI

texts:
I am citing an article here:
In a speech at the G-20 in Istanbul, TİM’s Mehmet Büyükekşi said, “Protectionism is increasing in every market around the world and it is affecting not only Turkish exports, but also Foreign Direct Investment [FDI] in Turkey.

I really can't see a link between protectionism in another country and FDI in Turkey. What is the link here? Also, he later says that devaluation of euro against the dollar affected total FDI value. That makes a little more sense to me, because it can be that amount in euros prepared for some investment in Turkey suddenly became less valuable. I hope that is correct, but I don't get the protectionism part?


texts: Greece default and why are US States not seen defaulting?

texts:
Reading various articles, it is clear that Greece is in the situation simply due to the fact that they have indulged in overspending on their national budget for over a decade, and with the 2008 financial crisis this have have worsen as they have lost additional revenue.

Every US state and city is also responsible for their own budgets, and making sure that they are kept in balance -- while a handful of US cities have gone bankrupt, there have not been any news about US state getting into a crisis of the same scale as Greece has.

Is there a difference between how a national budget is run in the Euro Zone versus how a US State budget is run with respect to oversight where a US State cannot get insolvent to the same degree as Greece before the US Fed steps in?

What are the lessons from the US model which would need to be implemented in the Euro Zone to prevent another Euro Zone member to end up in a similar situation?

EDIT

Specifically; Are there any specific laws in the US which allows the Feds to step in before a state defaults?


texts: Recommended tests do detect breaks in time series

texts: What tests do you recommend for finding breaks in the following time series: log of inward FDI, log of nominal GDP, log of outward FDI from 1980 to 2012?


texts: Papers on Game Theory and the Housing Market

texts:
Professor George Fallis in his book "Housing Economics" writes:
(Chapter 4 pg. 78)

The (home)owners will establish a pricing strategy depending on how they believe demanders are behaving; and the search strategy of demanders will depend upon the pricing behaviour of the (home)owners. The elegant separation of the demand side and the supply side is no longer possible. The modelling of such a market will be extremely complex, and the idea of equilibrium will have to be rethought.

This being said there is one thing that comes to mind when wanting to model house pricing based on this reality: Game Theory.
My Question:
Is there any (famous or otherwise) papers which discuss the nature of Game Theory in the housing market?
(Papers with computer simulations of the housing market are additionally helpful!)


texts: Cost function from an easy CES production function

texts:
How can I find the cost function c(w,p) given that the production is
$f(x) = x_1+x_2$
I did Lagrangien's method but my problem is that I got no $x_1$ and no $x_2$ after taking the derivate.
So I would like to know how can I derive a cost function?
Thanks in advance !


texts: Value of money (incomes) question - what is the "r" here?

texts:
I would like some help with a fairly basic "value of money" question. (I'm very much a beginner in this field so please bear with me.)

I'm writing about income changes throughout a decade (2010-2019). And I would like to convert a bunch of random incomes (lump sums) from different years to their "2020" value.

I found the formula for the present and future value calculations. My problem is that I do not know what to put in place of the "r" and if I'm using the right formula.

Suppose that I have an amount of $3000, and this amount is an income in the year 2011. Now do I understand it correctly that I need to use the FV formula if I want to know its value for the current year (2020)?

So it would look something like: FV = 3000 x (1+r1) x (1+r2) ... x (1+r9), right? (9 because 2020-2011 = 9, that's why I wrote 9, correct me if I'm wrong please)

Similarly, with another example, would $5000 from 2019 look like this for 2020: FV = 5000 x (1+r1) ? So just one r.

But what exactly is r? Is it simply the inflation for each year? Do I just take the yearly inflation rate of my country in each year from 2011 to 2019 and use it as r1, r2, r3 etc.?  Or from 2012 to 2020? IF it really is just the inflation rate, then for r1 do I start with the inflation rate of 2011 or 2012? If I'd like to see the value of a 2011 lump sum for 2020, then r1 should be the inflation rate of 2012? Or what do I put in the place of r if not this?

OR do I have to do something entirely different to get the results I need?

Thanks in advance, any help is very much appreciated!!


texts: In auction theory, why is my own valuation a random variable?

texts:
Auction theory typically (always?) begins by assuming that each bidder's valuation is a random variable. Now, it might seem reasonable (at least from a Bayesian perspective) for you to treat other people's valuations as random variables. After all, you don't know their valuations! However, what justification can there be for treating your own valuation as a random variable when deciding on how to bid? And are there any approaches which do not begin with this assumption?

Edit: Here's another way of posing the question. In the context of auction theory, people normally seem to define a strategy as a function mapping from my (random) valuation to my bid. But assuming that I know my valuation, why not simply define my strategy as my bid?


texts: How do I find out which form of utility function is being used?

texts:
Can someone tell my how i can figure out which type of utility function the following maximization problem has. It is for an overlapping generations model.

$$\underset{x'}{\max} x'\big(E_t (P_{t+1}+δ_{t+1})-(1+r^f)P_t\big) - \tfrac{\gamma}{2} x'Ωx $$
Where:
$x'=$ portfolio of shares

$E_t (P_{t+1}+δ_{t+1}) =$ expected future payoff

$\gamma =$ agent i risk aversion

$Ω=$ covariance matrix


texts: Literature Recommendation: Advanced Undergraduate Economics

texts:
I come from a strong quantitative background and am going to law school in the fall. I'm interested in financial product regulation and competition law. I have taken an introductory course in economics, but my exposure to economics stopped there.

I was wondering if you had reading suggestions in micro, macro, and financial markets. Although I don't have an issue with calculus, lin alg, or probability, I tend to prefer learning by the use of examples, e.g. "too many chefs in the kitchen" to explain diminishing returns.

I really don't like jargon and so far I seem to come across a lot of online resources (especially regarding financial products) that seem to use a lot of jargon with little reference to basic concrete examples. I tend to be very detailed oriented, so I prefer texts that lay out their variables and constants clearly. Something lighter and shorter tailored for independent study would be best.


texts:
Currently reading David Adler's text on distributional weights in benefit-cost analysis (https://scholarship.law.duke.edu/faculty_scholarship/3110/), I cannot manage to fully grasp the definition of the anonymity axiom.

The isoelastic/Atkinson social welfare function (SWF) allows for an inequality aversion parameter; greater weight is put on changes affecting worse-off individuals. Adler states that this function satisfies the anonymity/impartiality axiom, defined here as "meaning indifference between any given utility vectora and all rearrangements of component numbers". I understand this, broadly, as meaning that the levels of utility, and not the persons enjoying those levels, are what counts.

I can't manage to reconcile the fact that the "anonymity/impartial SWFs focus only on the patern of well-being, and not on the identities of the people who end up at particular well-being levels" (page 267 of the text) with the use of an inequality aversion parameter, which, by definition, treats individuals differently. Would this not mean focusing "on the identities of the people who end up at particular well-being levels"?

What am I missing ?

Any links towards readings on this subject would be much appreciated as well.

Many thanks.


texts: Will inflation rise or fall when the Fed increase their interest rate?

texts:
When the Fed lower the interest rate, there will be a rise in GDP and thus a decline in unemployment, which in turn cause the inflation to go up according to the Phillips curve. But Fisher’s equation tells me that real interest rate = interest rate - inflation. So if real interest rate does not change, an increase in interest rate should also cause a increase in inflation, a contradiction.

Any help or comment is appreciated.


texts: Envelope theorem for discrete choice sets?

texts:
If we have a function
$$f(x)=\max_yg(x,y)$$

Then we can find the derivative $d/dx \ f(x)$ by realizing that
$$(1): \quad \frac {\partial }{\partial y}g(x,y^*)=0$$
because of the first order condition for maximization.

We can use this by recognizing that $$\frac d {dx}f(x)=\frac d {dx}g(x,y^*(x))=\frac \partial {\partial x}g(x,y^*)+\frac \partial {\partial y}g(x,y^*)\frac {dy^*(x)} {dx}=\frac \partial {\partial x}g(x,y^*)$$
Where the last equality follows because of result $(1)$.

However, my question is, what if $y$ can only take a discrete number of values? such as $0$ or $1$? We can of course say:

$$f'(x)=\begin{cases}
g_x(x,0) \quad \text { if } g(x,0) > g(x,1)\\
g_x(x,1) \quad \text { if } g(x,0) < g(x,1)
\end{cases}$$

However, I am wondering if there is a kind of "envelope theorem for discrete choice sets", that would allow us to simplify this (especially if the choice set is discrete but large).


texts:
In a mixed economy like the UK to what extent are wages a function of Government policy?

Presumably at the bottom of the pay scale the minimum wage could be said to be a function of Government. And the rate of wage increase up the skills ladder could be related to the availability of cheap/low-skilled labour, which could be said to be function of migration policy.

But presumably the market itself remains an important (the most important) element in wages?


texts: Ex post evaluation of conservation projects - accounting for time in cost calculations

texts:
I'm looking at differences in the cost-effectiveness of two alternative conservation strategies (treatments). The analysis will compare benefit-cost ratios between the two treatments. Projects vary in age (number of years since undertaken eg. trees planted) within and between treatments, from 20 to 7 years. I have several projects as replicates for each of the two treatments. I have field data (birds) for my measure of effectiveness, measured in one year. I have calculated a total cost using input costs from an established pricing structure, giving a total cost for each project in dollars equivalent to the same year as the bird data. I do not have access to the original (actual) cost for the year undertaken. Note the costs were one-off in the year of implementation, not ongoing.
My question relates to the estimation of costs and the different ages of the projects. My concern is that similar projects will have the same cost, despite one being twice the age. Should the costs account for different ages of the projects, and if so how to approach it? The literature commonly focusses on calculating present value using discounting for projects to occur in the future; I can find less regarding past costs.


texts: Compensating variation versus change in value of goods consumed?

texts:
I study an economy with two goods ($x$ and $y$) and two consumers ($A$ and $B$). First there is no trade between $A$ and $B$, so they consume their endowments $e^A_x$ and $e^B_x$ and reach utility levels $u^A_1$ and $u^B_1$. Thereafter, trade develops between $A$ and $B$ and they reach utility levels $u^A_2$ and $u^B_2$.

I now want to find how much better off each consumer has become due to trade. I understand that looking at the increase in utility does not give any meaning, since the utility function is an ordinal function. From what I can gather, the correct way of doing this is to calculate the compensating variation $CV$ - how much more of the nominal good they need in autarchy in order to reach $u^A_2$ and $u^B_2$, respectively.

However, whouldn't comparing the value of each consumer's endowments (i.e. their autarchy consumption) and the value of the goods they end up consuming after trade also tell us how much better off they are after trade?


texts: Do the donated NFL losing team shirts destroy local economies?

texts: I've recently become aware of the fact that the NFL prints both championship teams' shirts in advance to satiate incredible demand -- but instead of destroying the losing teams' shirts like they used to, they instead donate them to developing countries. But the thought of flooding these local economies with free shirts, which doesn't create jobs, GDP, and hurts local clothing business, seems like it would be terrible for the economy. Is this indeed the case?


texts: Competitive prices, tax and lump sum cash transfer in case of externalities

texts:
An economy is made up of two people. The utility functions are
$$u_1(x_{11},x_{12}) = x_{11}x_{12}$$
$$u_2(x_{21},x_{22}) = 2x_{21} + 2x_{22} −x_{11}$$

The initial endowments are $ω_1 = (1,0)$ and $ω_2 = (0,1)$.

(a) Calculate a competitive equilibrium. Draw an Edgeworth box diagram to illustrate your answer.

(b) Find the locus of interior Pareto optimal points.

(c) Calculate prices $p_1$ and $p_2$, a per unit subsidy $s$ or tax $t$, and lump sum cash transfers $T_1$ and $T_2$ to bring the economy to the allocation $x_1 = (\frac{1}{3} , \frac{1}{2} )$, $x_2 = (\frac{2}{3} , \frac{1}{2})$

I am having trouble with the 3rd part. Here is how I tried doing it:
It can be seen from utility that increased consumption of $x_1$ by 1st consumer results in less utility of 2nd consumer. So, I charged a tax $t$ on consumption of good 1 by 1st consumer and gave a lump sum payment $T$ to compensate for it.
So the budget constraint became
$(P_1+t)x_{11} + x_{12} = p_1+ T_1$ (normalising $p_2=1$)

After maximizing the utility I got two equations with three variables $p_1$, $T_1$ and $t$:

$$\frac{1}{3}P+T_1-\frac{2t}{3} =0 $$

$$P_1 + T_1 = 1$$

Now, since it's given that for consumer 2 the two goods are demanded in positive quantities so it must mean that $p_1=1$.
( $p_2 =1$)
Incorporating it into the first two equations I got $T_1=0$ and $t=\frac{1}{2}$ and then using 2nd's BL I got $T_2= -\frac{1}{6}$.

Now, a negative transfer for cons. 2 seems a bit absurd. So, could someone please tell me where I could be going wrong.


texts: Nash equilibrium for Bertrand Model with Spatial Differentiation

texts:
Consider a town with consumers represented by a closed interval $[0,2]$ with the consumers spread continuously and uniformly. There are two stores, $A$ and $B$ who sell the same product at $p_A$ and $p_B$ at no cost.

A consumer has a gross utility of 4 from having the product which is reduced by price paid and travel costs, which is determined as distance traveled. Each consumer only buys 1 unit of the product, and if the consumer does not buy from either store, he has a utility of 0. For example, if a consumer is located at $x=1.5$ and buys from store B at $p_B=1$ which is located at $x_B=2$, then his utility is $4-1-|2-1.5| = 2.5$.

Suppose that $A$ is located at $x_A=0$ and $B$ is located at $x_B=2$. Also, suppose stores much charge at $p \le 4$.

Suppose stores are profit maximizers. What are the equilibrium prices, quantities, and profits for both stores?

My initial thoughts are that, in this scenario, the profit functions for each store is denoted as:

$$ \pi_A=p_A+p_A(\frac{p_B-p_A}{2}) $$

$$ \pi_B=p_B-p_B(\frac{p_B-p_A}{2}) $$

We can take the first order condition for each, to get the maximizing profit.

$$ \frac{\partial \pi_A}{p_A} = 1 + \frac{p_B}{2} - p_A = 0 \implies p_A = \frac{p_B}{2} + 1 $$

$$ \frac{\partial \pi_B}{p_B} = 1 - p_B + \frac{p_A}{2} = 0 \implies p_B = 1 + \frac{p_A}{2} $$

By substituting one into the other, we have that $p_A=p_B=2$, $q_A=q_B=1$ and $\pi_A=\pi_B=2$.

I'm not very sure about this solution or the direction I took to solve it. Any advice here would be appreciated on what other direction I should try.


texts:
This question is also regarding Aiyagari and Gertler (1985). We have the governments flow budget contraint:

$\frac{B_{t-1}}{p_{t}} + \bar{g}w = \tau_{y}(t)+\tau_{o}(t) + \frac{M_{t}-M_{t-1}}{p_{t}} + \frac{B_{t}}{(1+i_{t})p_{t}}$

Each period the government consumes the fraction $\bar{g}$ of the total endowment. $\bar{g}$ is i.i.d with mean $\bar{g}$. The government's expenditures are financed  by lump-sum taxes, money and one-period discount bonds. $M_{t}$ and $B_{t}$ are the supplies of money and nominal bonds at the end of period $t$.

$\tau_{i}(t)$ is the lump-sum tax where $i$ is either the old or young generation.

The authors then describe a fiscal policy rule:

  Assume taxes are levied only to meet the obligation
  on the debt. Further, let $(1 - \delta)$ be the fraction of the obligation which is backed by direct taxation, where $0 \leq \delta \leq 1$. That is, the present value of the
  stream of direct tax levies equals $(1 - \delta)$ times $\frac{B_{t-1}}{p_{t}}$

In and of itself I don't have any problem understanding this. However, they then define a time-stationary tax policy which satisfies:

$\tau_{y}(t)+\tau_{o}(t) = (1-\delta)[\frac{i_{t}}{(1+i_{t})}\frac{B_{t}}{p_{t}}-\frac{B_{t}-B_{t-1}}{p_{t}}]$ (2.8)

They describe this as:

  The policy requires that, each period, tax levies equal $(1 - \delta)$ times the
  difference between the present value of the current interest obligation on
  the debt and a term which corrects for the adjustment in the value of the
  obligation.

This I don't quite understand but I re-arranged the term inside the brackets and obtained $[\frac{B_{t-1}}{p_{t}} - \frac{B_{t}}{(1+i_{t})p_{t}}]$

This makes somewhat more sense to me because I interpret it as: Each period taxes have to back $(1-\delta)$ the value of the outstanding real debt minus the present value of the future debt (I don't quite understand why the present value of next periods debt is subtracted...)

The next part is in regards to difference equations (I think). They define the expected present value of discounted taxes as $T_{t}$ where $T_{t}$ must satisfy:

$T_{t} = \tau_{y}(t)+\tau_{o}(t) + \frac{E_{t}(T_{t+1})}{(1+i_{t})E_{t}(p_{t}/p_{t+1})}$

I understand what the equation is saying but since I have barely done any dynamic programming at university yet I can't seem to solve it. The authors say:

  In view of (2.8) it is clear that $T_{t} = (1-\delta) \frac{B_{t-1}}{p_{t}}$.

I understand why this must be true (given the definition of the fiscal policy) but I cannot show this from the difference equation above.

I know one method of solving difference equations is to 'iterate forward' but I don't think I am doing it correctly.

So my question is regarding how to solve equations like the one above. And what should I read in order to get a better grasp at difference equations. I have heard Sargent and Ljungqvist is a good place to start. And some clarification regarding what the time-stationary policy means intuitively, would be greatly appreciated.


texts: Why was Modigliani-Miller so relevant and innovative when it came out?

texts:
The Modigliani-Miller theorem*, a foundation of modern corporate finance, basically states that, in a no-frictions world, two identical firms have the same enterprise value, regardless of their financial structure.

Given a firm A, whose liabilities are 50% equity, and 50% debt, and a firm B which is financed 100% by equity, the value of firm A and the value of firm B are the same.

Isn't it just obvious? What am I missing?

* -
Modigliani, F.; Miller, M. (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment". American Economic Review 48 (3): 261–297. JSTOR 1809766.


texts: Euler's Homogenous Function Theorem with elasticity

texts:
I'm currently reviewing my prof's slides in preparation for an exam. In one of them, he talks about Euler's Homogenous Function Theorem:

  Let $f(x_1, x_2, ..., x_n)$ be a function homogenous in degree $\rho$.

  $$\rho f(x)=\sum_{i=1}^n x_if_i(x)$$
  Where $f_i(x)$ is the partial derivative with respect to $x_i$

In the next slide, the following consequence is stated (the slides clearly state that the result is obtained by applying Euler's theorem to Marshallian demand):

  $$\sum_{j=1}^n e_{i,p_j}+e_{i,I}=0$$

I assume that this is a case where the function is homogenous in degree 0, as the same slide states that, if a demand function is homogenous in degree 0, then there is no monetary illusion. However, I have no idea how this result was derived using Euler's theorem.


texts:
When I was in college, a classmate of mine working two jobs mentioned that his/her job working at at a local fast food restaurant was causing undue stress and dissatisfaction.

My response was to ask "What is your price on Happiness?"

If your income from the other job can satisfy your basic needs (rent, food, clothing, etc.) and the income from your fast food job was 'extra' aren't you valuing your happiness at $10/hr?

In a short time I learned that my classmate decided to quit the fast-food position. But in hindsight, I never gave much thought as to my advice.

With this said, can it be realistically said that a price can be put onto happiness?


texts: maximizing leontief-type utility function

texts:
How do I maximize the utility function:
$ U(x,y)= max(ax,ay)+min(x,y) $ , where $ 0<a<1 $ with respect to prices $ p_{x}, p_{y} $ respectively and income $ m $.

I know leontief-type utility functions are solved by graphing and not by using Lagrangians, buy how do I graph this function?. ( I know there would be kinks on the graph, but how do I find those kinks)


texts: How would banking in UK change if minimum required capital to open own bank would be £100k instead of €5m?

texts:
DIRECTIVE 2013/36/EU

  Article 12

  Initial capital

  Without prejudice to other general conditions laid down in national law, the competent authorities shall refuse authorisation to
  commence the activity of a credit institution where a credit
  institution does not hold separate own funds or where its initial
  capital is less than EUR 5 million.

Assumption

Let's assume that at some point people realized how great the banking profession is and a lot of entrepreneurs were willing to take the burden off the bankers by starting their own bank. The only problem they had was lack of required capital, which for the UK, or any bank in an EU member state, was about €5m. In the following parliamentary election people voted for a liberal (not just by name) party that promised to lower the minimum required capital to £100k, so that banking would no longer be a privilege of the super rich. Every middle class entrepreneur can now easily gather the required capital and start competing in the free market of banking services.

I know that there is an exception to the minimum required capital for particular categories of credit institutions which the UK used for building societies but let's focus on fully-fledged banks exclusively.

  Member States may grant authorisation to particular categories of credit institutions the initial capital of which is less than that
  specified in paragraph 1, subject to the following conditions: (a) the
  initial capital is no less than EUR 1 million; (b) the Member States
  concerned notify the Commission and EBA of their reasons for
  exercising that option.

Question

Given that banking, Fractional Reserve Banking especially, heavily relies on support from taxpayers, mostly through Deposit Guarantee Schemes (DGS) without which we can safely assume that FRB wouldn't be possible, banks would have to find other ways to build trust than simply rely on always-solvent taxpayers, and the fact that the minimum capital to open one's own bank in the UK is €5m, what can we reasonably expect to happen if that minimum required capital was lowered to, say, £100k?

In other words, is there any justification, other than we are a cartel go away, that banking, or FRB in particular whose biggest asset is taxpayers guarantees through DGS, be restricted to super rich people that can afford the €5m minimum required capital?
Why can't we have real competition in the banking sector by allowing for creation of micro banks?

My own prediction

Competition in the banking sector would take an unprecedented turn and, as with every liberalisation of market rules, quality of the services would rise.
Regular as sine wave financial crises would then be occurring with higher frequency but a lot smaller amplitude.
No bank will be too big to fail as small banks would take a substantial part of the market.

Community bank

An example of small lending company which is not a bank in regulatory terms but despite its micro capital it successfully competes with big banks on the lending market -
Burnley Savings and Loans. Not directly the kind of changes that I am requesting but it shows that it is possible for a small company to succeed on the lending market.

References

http://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32013L0036
http://www.fsa.gov.uk/pages/doing/how/deposit_taking/index.shtml
http://www.bankofengland.co.uk/publications/Documents/joint/barriers.pdf
http://www.fsa.gov.uk/
https://en.wikipedia.org/wiki/Capital_requirement
https://en.wikipedia.org/wiki/Capital_Requirements_Directive


texts: How a country is categorized as developed or developing?

texts: Can you share an official source or reference of definition of a developed and developing country? some IMF or World Bank definition with link would be preferred. I need to write the reference in my thesis. Thanks


texts: Is product opportunity frontier the same as PPF?

texts:
In CFA level 1 reading 14, they have this term called Production Opportunity frontier and it is defined as

Curve describing the maximum number of units of one good a company can produce, for any given number of the other good that it chooses to manufacture.

The graph is a straight line

Is it the same thing as what is commonly known Production Possibility Frontier with the curved line?


texts: Price elasticity and optimal pricing in a monopoly with zero marginal cost

texts:
I am having trouble understanding how to calculate the optimal price P for a good and understand the optimal price elasticity of demand in the following condition:

The firm is a monopoly seeking to maximise profit.
It also has a zero marginal cost (MR = 0).
The firm can only produce/sell an upper limit/number of the good (I am not sure if this changes anything in the analysis)

I found a lot of documentation on the web regarding price elasticity, but I did not find (enough) details about the conditions described above. My understanding is that, even in the above conditions, the optimal price elasticity of demand is at unit elastic (E= -1) [is this correct?], but I have no clue how to calculate the optimal price of the good [is there any formula for it?].
Apologies if my questions is a bit broad, I am very new to this area of study and any help (or reference to a worked solution) is appreciated.


texts: Best way to learn econometrics for application?

texts: I am very interested in the subject, but want to gain understanding on application that can be useful on the job.


texts: What are the effects of a 12 month sudden stop/shutdown of a capitalistic economy like the US?

texts:
Consider a scenario where consumer confidence remains low until a virus such as COVID-19 is contained. In this scenario, containment is defined as being achieved once a vaccine is manufactured and distributed in 12-18 months after shutdown. Assume the following criteria:

A synchronous eradication effort amongst all states/countries in a system is highly unlikely.
Countries remain in a long-term suppression phase - a metaphorical game of "whack-a-mole" as researcher Ed Yong describes, where the threat of spread continues to pop up in various regions due to the virus's novel ability to remain undetected in many carriers, new strains arriving seasonally, duration of immunity remains unknown, etc. rendering "easing" of lockdown restrictions a non-option.

What are the effects on a sudden economic shutdown in a capitalistic system for a prolonged period of time like 12 months? 18 months?


texts: Are supply and demand always (with arbitrary dimensions but still) linear?

texts:
I have economics knowledge of high school level (and basic economics from my engineering degree), and I always noticed that supply and demand functions are linear (in 4+ dimensions).

It is -in practice, in real life- always the case? If not: What counterexamples (with theoretical models) do exist?


texts: Are there studies on the impact of the closing of military bases on islands, especially Okinawa

texts:
According to a study in the Journal of Defense and Peace Economics on the economic impact of base closures "base adjustments have only a marginal impact on the local community in which the bases are located." However, that same study goes on to state that:

  [E]vidence obtained from this line of research [case studies] can hardly be generalizable by design. An indication of this is the varied conclusions that these studies have reached. While a few found substantial negative impacts of the base closures, others have indicated that the local communities have been quick to adapt to the change in economic landscape.

I am interested in possible economic impacts on Okinawa from US base closures. From the economy section of the Wikipedia article on Okinawa:

  The 34 US military installations on Okinawa are financially supported by the U.S. and Japan. The bases provide jobs for Okinawans, both directly and indirectly; In 2011, the U.S. military employed over 9,800 Japanese workers in Okinawa. As of 2012 the bases accounted for 4 or 5% of the economy. However, Koji Taira argued in 1997 that because the U.S. bases occupy around 20% of Okinawa's land, they impose a deadweight loss of 15% on the Okinawan economy. The Tokyo government also pays the prefectural government around ¥10 billion per year in compensation for the American presence, including, for instance, rent paid by the Japanese government to the Okinawans on whose land American bases are situated. A 2005 report by the U.S. Forces Japan Okinawa Area Field Office estimated that in 2003 the combined U.S. and Japanese base-related spending contributed $1.9 billion to the local economy. On January 13, 2015, In response to the citizens electing governor Takeshi Onaga, the national government announced that Okinawa's funding will be cut, due to the governor's stance on removing the US military bases from Okinawa, which the national government doesn't want happening.

Are there any studies of the potential impact of base closures on Okinawa, or at least other islands which would be more similar to Okinawa than non-island Germany? If there aren't, are there newspaper articles?


texts: Some confusions about instrumental variable (econometrics)

texts:
As the title says, I have some confusions about instrumental variable.

According to my lecture note (which is supposed to be reliable), instrumental variable has two big properties:

Validity: an instrumental variable and error term are not correlated and it implies that the instrumental variable does not directly lead to changes in dependent variable.
Relevance: an instrumental variable and endogenous variable are correlated.

So here is my confusion. (let's denote z is an instrumental variable)

Endogenous variables are correlated with the error terms and z is correlated with endogenous variable.

Doesn't this imply that z is correlated with error terms? If so, it violates the Validity (mentioned above).

In case my question isn't clear enough. Here is the case where I am stuck: $$
score_i = \beta_0 + \beta_1 course_i + u_i
$$
where $course_i$ is a binary variable of taking a preparatory course and $u_i$ is an error term.

Quite obviously, $course_i$ is correlated with $u_i$ since the parental income is one of the unobserved variables (so in $u_i$) and $course_i$ and parental income are correlated (I think this is also quite obvious).

So far we know that parental income (I think this is an instrumental variable) is correlated with $course_i$. But since parental income was belonged to error term, it violates Validity.

Any help is welcome.


texts: Why would overemployment mean that labor is used inefficiently?

texts:
If labor is being used efficiently, there is no excess unemployment
  or over employment.

This phrase from Khan Academy struck me as quite strange. Why on Earth would over employment mean that labor is NOT used efficiently? Labor is a resource. And if we can use more of a resource without increasing its size, then it would seem that we are using it more efficiently, we are using bigger share of it.

For an example, land is recourse. If we will drain swamps we will be able to use more of land for commerical purposes, meaning that we will use land more efficiently. I believe that similiar reasoning can be applied to labor.

P.S. What I understood from comments: Overemployment is inefficient because it happens due to sticky wages/prices in short run equalibrium. Sticky prices/wages create inefficiency in the market, thus it should be nothing suprising that overemployment caused by sticky wages/prices leads to inefficient use of labor.


texts:
I recently came across a utility function with min written at the start. I assumed that it was a case of a leontief utility function, and only after going ahead with the problem I found out that it is a case of perfect substitutes. Until then, I didn't even know that perfect substitutes could take this form. How do I identify various utility functions accurately? Are there other such confusing cases which I need to be aware of?

The example I have mentioned above looks something like this:
      U = Min [2x + y, x + 2y]


texts: An $n$-player prisoner's dilemma where a coalition of 2 players is better off defecting

texts:
I'm interested in a game kind of like the prisoner's dilemma. The important thing about the 2x2 prisoner's dilemma is that it is efficient if all cooperate, but this is not an equilibrium, because both players have a dominant strategy to defect.

I have in mind a variant. Suppose $n$ players can choose to cooperate or defect. It is group efficient if all cooperate, but any player would like to defect from that. Further, any coalition of 2 (more generally $k$) players would prefer to defect together. So we could imagine payoffs $u(\text{all defect})=0$, and switching to cooperate increases all individual payoffs by 1, but at a private cost of $2+\epsilon$ (more generally $k+\epsilon<n$). So, it is always better for the group if someone cooperates, but only for a large enough group.

Is there a name for this kind of thing? Are there any papers or other resources that explore how this differs than the classic prisoner's dilemma?


texts: What is the difference between order driven and quote driven markets? Is there any theoretical microstructure book that gives the intuition behind the types of markets with respect to the orders that traders give to the market makers to buy or sell an asset or a security?


texts:
The formula for today's consumption is defined as:

$$C = Y - T -S^P $$

That being said the consumption of tomorrow is:

$$C' = Y' - T' + S^P(1+r)$$

Could anyone possibly explain to me why the saving becomes positive in tomorrow's consumption formula?

Thank you very much for your help


texts: Shouldn't national Stock Indices proportional to GDP of the country?

texts:
I was looking at Japan: Japan's GDP trajectory and Nikkei 225.
It seems from 2011 - 2015 the GDP contracted but the Nikkei has gone up. Would there be a good explanation for this ?


texts: Auctions and finding nash equilibrium of a dynamic game

texts:
Suppose we have a sequential version of an Auction game:
• Player 1 places a bid.
• Player 2 observes player 1’s bid, then places a bid.
• The player with the highest bid wins the item at auction.
• In case of a tie, the winner is determined randomly (with equal probability among
those tied).
• The winning player pays his bid.
Two players bid for a rare bottle of Scotch. This is an auction in which they
can bid any amount in $\Bbb R_+$. Suppose the two players both value the item at £500.
Find all pure-strategy Nash equilibria of this game.
The answer provided didn't seem too intuitive:

Player 1’s strategy is to bid 500.
At the information set following 1 bidding 500, Player 2’s bid is in [0, 500].
At all information sets where 1 bids any x1 below 500, Player 2 bid is in (x1, $\infty$).
At all information sets where 1 bids above 500, Player 2 bids anything in $\Bbb R_+$.

I somehow get that we do NOT need to consider sequential rationality, but how does point 4 follow i.e P2 bids anything in $\Bbb R_+$?
Any help will be greatly appreciated.


texts: Relationship between IRS and Competitive equilibrium

texts: If there are increasing returns to scale in both sectors (in a 2x2x2x2) production and consumption economy, then a profit maximizing allocation most likely involves the economy producing only one type of good?


texts:
Let's destroy the USD dollar: I am the government of a small, economically and geopolitically unimportant country that has its own currency and a local central bank. I order the local central bank (at gun point, if need be) to lend me dollars. Is there a technical problem to do this? No, this is just an exchange of papers and electronic messages -we can write on them anything we want, especially with a gun in our head. We can attach to these electronic records any three-letter code we want, so why not "USD"?

Now I have a bank account with a balance of gazillions and gazillions of dollars- and USD ones, the heavy stuff.

I can pay off my public debt, make every citizen rich (or just those that I like), import all the luxuries in the world, buy as much energy as I want, whatever. After all, I will be paying in USD dollars right? I will be wire-transferring from a bank account, an electronic signal that will contain some digits and the code "USD" attached.

So let's hear it from the experts: what kind of checks has the international community in place in order to effectively avoid such a situation?

And what if, as the most long-lasting counterfeiters know, we were to do this modestly, just a little at the time to help a tad with the local government budget, but without "showing-off riches" to the rest of the world??


texts: Ramsey growth model - per capita vs aggregate variables

texts:
I am reading a paper Okuguchi,1981 with a Ramsey growth model. There is a constant population growth $n$ such as $L(t)=e^{nt}$. The way he writes the Hamiltonian is quite interesting (equation 5 on page 658.)

$$H=e^{-(\rho+n\left(1-\sigma\right))t}\left[\frac{C^{1-\sigma}}{1-\sigma}+\psi AG+\phi\left(Q-C\right)\right]+\lambda R$$

where capital letters represent the aggregate variables and not per capita variables. $\lambda$ is constant in the model.

In fact, the author does not deal with per capita variables but aggregate variables. Of course, he takes into account the population growth since $n$ appears in co-state dynamics. However, I can not understand how he puts the exponential term $e^{-(\rho+n\left(1-\sigma\right))t}$ in the Hamiltonian in this way.
I would really appreciate if you give me some hints or suggestions.

In the same fashion, is it correct to write something like

$$H=e^{-(\rho-n)t}\left[U\left(C\right)+\lambda\left(AK-C\right)+\mu\left(\left(1-S\right)S-\gamma AK\right)\right]$$


texts: Why hasn't the huge increase in supply provided by Airbnb decreased prices?

texts:
Simple supply and demand economics would suggest that the huge increase in the supply of rooms to rent by Airbnb should have reduced the price of rental significantly in those cities where Airbnb is most popular. However, this appears not to have happened. Why is that?

There are, for example, ~80,000 airbnb listings in London alone and only ~1500 hotels with ~146,000 hotel rooms.

In fact, it is argued that Airbnb increases prices!

  Our empirical results show that the overall causal impact of Airbnb on
  property values can be large. For example, in areas within 5km of Los
  Angeles’s central business district the price increase has been 14%.
  Within 2.5km of beaches, the price increase due to Airbnb has been
  almost 10%.

How can this be?


texts: Combining functions that satisfy the Inada conditions

texts:
Suppose $f: \mathbb{R} \to \mathbb{R}$ and $h: \mathbb{R}^n \to \mathbb{R}$ are functions that satisfy the Inada conditions, and also
$$
\forall i:
\lim_{x_i \to \infty} h(\mathbf{x}) = \infty.
$$

Does the function $f(h(\mathbf{x}))$ also satisfy the conditions?


texts:
Is homogeneity of degree zero necessary in proposition 2.F.1?
It seems like the proof does not assume homogeneity of degree zero to establish the proposition.
If this is true, it seems that homogeneity is not required to establish that the Slutsky matrix is negative semidefinite (only required assumptions are differentiability and Walras' law?)

Thank you so much for your help!


texts:
Imagine that there are 3 firms in a monopolistic market, F1, F2 and F3. Firms 1 and 2 are incumbent firms and act simultaneously whereas Firm 3 observes the actions of both firms before deciding whether to enter.

All firms face a market price of $P(Q) = 16-q_1-q_2-q_3$. Incumbent firms face a production cost of $C_i (q_i) = 4q_i$ for $i= 1,2$. Firm 3 faces a production cost of $C_3(q_3) = 4 + 4q_3$. Find both firm 3 and firm 1's payoff.

I understand that I need to take firm 3's best response function which is
$$0.5  (12-q_2-q_1)$$
but I am not sure where to go from there. Do I substitute this back into the price equation? I tried doing this but it wouldn't yield any definitive answers. Thanks!


texts: Can anyone give me some reference on Mundell-Fleming model estimated empirically?

texts:
In virtually all texts of intermediate Macroeconomics$^1$ the Mundell-Fleming model is taught. But his estimate is not addressed in the classical texts of econometrics. I've always wanted to read some reference, but my searches have not worked

1: "Most open macroeconomy models in the textbooks are variations of the Mundell-Fleming model." Ohno Lecture notes: Mundell-Fleming Model with a Floating Exchange Rate


texts: Utility function of a representative agent with quasilinear utility

texts:
Consider an economy with $n$ consumers with an identical utility function, which is quasilinear in $x$:

$$ u_i(x,y) = x+u(y) $$

If we want to represent all consumers by a single representative consumer, what would his utility function look like?

Here is my current solution.

For every consumer, the demand for $y$ depends only on the price. It is determined by the equality:

$$ u'(y_i) = p_y $$

so:

$$ y_i(p, m_i) = (u')^{-1}(p) $$
(where $m_i$ is the income of consumer $i$).

Hence, the aggregate demand is:

$$ Y(p, M) = n \cdot (u')^{-1}(p) $$
(where $M$ is the aggregate income of all consumers).

Let's assume that a representative consumer has utility function $U$, which is also quasilinear in $x$:

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

Then, his demand will be:

$$ Y(p, M) = (U')^{-1}(p) $$

Equating the above expressions for the aggregate demand gives:

$$ (U')^{-1}(p) = n \cdot (u')^{-1}(p) $$

$$ U'(y) = u'({y \over n}) $$

$$ U(y) = n\cdot u({y \over n}) $$

So, the utility function of the rep. agent is:

$$ U(x,y) = x + n\cdot u({y \over n}) $$

Is this calculation correct?


texts:
I am doing a project on technological change in the job market, that is the substitution of routine occupations and increasing demand for high-skilled jobs.
I have done some research on this and now I am seeking extra sources of advice. I was wondering if anyone could recommend me a model which would be applicable to present technological change or job-market flows with?
Thank you in advance!


texts: Violation of completeness axiom (simple everyday examples)

texts:
Simple everyday examples of violations of transitivity are not difficult to come up with, but I'm having trouble thinking of some for the completeness axiom.
One possible formulation of the completeness axiom in plain English:

Given any two alternatives A and B, exactly one of the following is true: (1) I strictly prefer A to B; (2) I strictly prefer B to A; (3) I am indifferent between A and B.

One example that I was hoping could work (but didn't) came from the book/movie Sophie's Choice, where Sophie is made to choose between the following two alternatives:

A: Send her son to the gas chambers (and her daughter to the children's camp).
B: Send her daughter to the gas chambers (and her son to the children's camp).

She is initially very reluctant to express a preference for either alternative. So one possible interpretation is that she is exactly indifferent between A and B. Another is that she does not obey the completeness axiom.
However, she is then pressed further and told that if she doesn't choose, she'll simply be given alternative C: "Send both children to the gas chambers."
Faced with this alternative C that is clearly inferior to both alternatives A and B, she then does indeed choose one of the alternatives (B: Send her daughter to the gas chambers), hence strongly suggesting that she does indeed obey the completeness axiom.
The above is of course merely my interpretation of the story in Sophie's Choice. Maybe someone can give an alternative interpretation where the above turns out to be an example of the completeness axiom being violated.
(One possibility might be along these lines: Sophie's preference relation is incomplete over {A,B}. When faced only with A and B, she doesn't prefer A to B, doesn't prefer B to A, and isn't indifferent between A and B. However, when given an additional option C that is vastly inferior to A or B and which she must default to in the absence of a choice, she now prefers B to A.)

For those who seem to believe the completeness axiom is inviolable and are  unaware that "within economic theory, criticism of the axioms of transitivity and completeness have quite a long history" (Putnam, 2002, p. 163), please see the following three examples of economists criticizing the axiom of completeness:
Von Neumann and Morgenstern (1953, Theory of Games and Economic Behavior, 3rd edition, p. 630):

The axiom (3:A)—or, more specifically, (3:A:a)—expresses the completeness of the ordering of all utilities, i.e. the completeness of the individual's system of preferences. It is very dubious, whether the idealization of reality which treats this postulate as a valid one, is appropriate or even convenient.

Aumann (1962, p. 446):

Of all the axioms of utility theory, the completeness axiom is perhaps the
most questionable. Like others of the axioms, it is inaccurate as a description of real life; but unlike them, we find it hard to accept even from the normative viewpoint.

Anand (1987, p. 190):

Whilst completeness is one of the first assumptions used in any" formal"
theory of rational choice, it is probably less acceptable as an axiom of
rationality than either transitivity or independence.


texts: When big companies invest on a new idea/product?

texts:
I am graduated in AI field. I love robotics and intelligent systems, so I worked on some new products by myself at home that have new ideas and are interesting(at least me and my friends think!). I decided to apply for a accelerator or incubator, bu I faced whit a question like this in those forms:

  Who are your largest competitors and why? Differentiators? How can you
  defend your business model?

And when I thought about it, there is no competitor at the moment(because of new idea and product), but the large companies like google,apple,microsoft,sony,samsung,etc would become our competitor at AI(Artificial Intelligence) field! And I think they can remove me from the market very soon and very easy!

So, I don't know what should I do? Should I forget my AI field ideas and make a company in that field because of those huge companies?

Is it possible to find that, when does companies enter to a business? Or is it possible to make a deal with them to have our individual company? Or I must try to become their employee and just this(Actually if the accept me :) )?


texts: Confusion about the effect of an increased expected inflation on the price level

texts:
In Mankiw's Macroeconomics 7th edition, on page 99, there is the following equation, which states that "the price level depends not only on today’s money supply but also on the money supply expected in the future":

$$M/P=L(r+E_{\pi},Y)$$

where $L$ stands for the demand for real money balances and $r$ for the real interest rate. The author then poses the following thought experiment:

  Suppose the Fed announces that it will increase the money supply in
  the future, but it does not change the money supply today. This
  announcement causes people to expect higher money growth and higher
  inflation. Through the Fisher effect, this increase in expected
  inflation raises the nominal interest rate. The higher nominal
  interest rate increases the cost of holding money and therefore
  reduces the demand for real money balances. Because the Fed has not
  changed the quantity of money available today, the reduced demand for
  real money balances leads to a higher price level.

My question is: I understand that, by the above equation, considering that $M$ is fixed, a decrease in the demand for real balances should lead to an increase in $P$. However, what exactly happens in the real world that causes the price level to rise as a result of people trying to get rid of the excess money they are holding? I can see that, if they were spending those "extra" balances on consumption, that would increase the demand for goods and services, which in turn would lead to higher prices. But since the reduction in $L$ was motivated by a rise in the interest rate, it is savings that is increasing, and not consumption. So, what is going on here? Thanks in advance.


texts: Have the Greek bailouts been included in state budgets Eurozone members?

texts:
A lot of people (mainly journalists and politicians) say that Eurozone taxpayers pay for the Greek bailouts. On the other hand, a lot of economists say that those money have not been added in the yearly state budgets of the Eurozone members because they are not physical money coming from the tax payers.

Contrary, most of the Greek bailout funds are given in the form of intergovernmental guarantees for which Greece pays actual real interests. Additionally, the bailouts not being bond-like give the creditors as the Eurozone countries the right to ask back the value of these guarantees whenever they like.

Can someone objectively clarify the situation? Specifically, can you give some details on the form of these intergovernmental guarantees?


texts: Signalling Model (How to solve a differential equation?)

texts:
I'm currently reading "SAVING RATES AND POVERTY: THE ROLE OF CONSPICUOUS CONSUMPTION AND HUMAN CAPITAL" by Omer Moav and Zvika Neeman, and I encounter some problem deriving one of the equations.

Utility function, where $y$ is income, $\widetilde y$ is the belief of $y$ based on $x$ and human capital $h$, $x$ is the product of interest:

$$u(y,x) = (y-x)^{1-\lambda} \widetilde y(h,x)^\lambda$$

Differentiate with respect to $x$:

$$\frac{\lambda}{1-\lambda} \frac{y-x}{\widetilde y(h,x)} =
\frac{1}{d \widetilde y (h,x) / d x}$$

This is the confusing part, how do I get this from above knowing that $y=\widetilde y(h,x)$?

Given this $\underline y$, the lowest possible income an individual of $h$ can have ($\pi$ is an uncertain component of income that is not observed and has mean zero):

$$\underline y (h) \equiv h + \underline \pi (h)$$

$$\widetilde y (h,x)^{1/(1-\lambda)} - \frac{x}{\lambda} \widetilde y (h,x)^{\lambda / (1-\lambda)} = \underline y (h)^{1/(1-\lambda)}$$

I think it's something to do with utility being indifferent for the marginal person who consume $x>0$ and $x=0$, but I don't know how to work it out to get the equation shown above.

Thanks!!


texts: Consumer Theory (Finding demand functions)

texts:
Suppose that Sally’s preferences over baskets containing food (good $x$), and clothing (good $y$), are described by the utility function $u (x, y) = \sqrt{x} + y$. Sally’s corresponding marginal utilities are,
1
MU$_x=\frac{1}{2\sqrt{x}}$ and MU$_y=1$.
Use $p_x$ to represent the price of food, $p_y$ to represent the price of clothing, and $I$ to represent Sally’s income.

Question 1: Find Sally’s food demand function, and Sally’s clothing demand function. For the purposes of this question you should assume that $I/p_y \geq p_y/(4p_x)$.

I'm having a really tough time working out how to solve this problem and any kind of help would be much appreciated.


texts: What are the statistical tests I need to perform before I regress GDP on multiple variables?

texts:
I'm using data over 10 countries for the period 1975 to 2010. My objective is to check if the chosen regressors have significant effect on GDP.
I have very basic knowledge of econometrics which I learnt in my first year of college. I was introduced to simple linear regression model with k variable which involved estimation of OLS, calculations of standard error, hypothesis testing for the slope coefficients. All of these were done with the assumptions of no perfect multicollinearity and the random disturbance term U follows normal distribution with constant variance. I have read a few papers on similar topic and they perform tests like unit root and Granger causality but I don't understand them.
So what are the topics I need to learn to be able to perform a test of significance for a panel data? Also, what would be an easy to understand book with stata examples for the suggested topics?


texts: Does 'infinitely elastic' and 'inelastic' pertain to same meaning? What is the difference between them? Please explain in brief.


texts: Where can I find real-time indicators of economic activity?

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In this paper, they are using Canadian debit card dataset. I am not sure where to get such a dataset.

http://www.cirano.qc.ca/pdf/publication/2009s-23.pdf

My broad question is what kind of indicator can I use that indicates real-time economic activity of the people? Something that indicates how much people are buying on an hourly basis for an example. I am willing to look at unconventional datasets or willing to scrape information from scratch.

I thought about using Amazon review timestamps for example, but I know want to when people are buying something. Specially over the United States or smaller.


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Every night, all 60 inhabitants of a tiny village visit one of the village’s taverns (not necessarily the same tavern) and an average of 75 strangers do the same. Both the villagers and the strangers are willing to pay up to $3 for a drink, and no one ever buys more than one. But, whereas the strangers pick any tavern at random, the villagers compare prices and go to the cheapest. The market is in free-entry equilibrium and each tavern’s costs of providing q drinks a night are C(q) = 36.75 +0.1q +0.03q^2. What do the taverns charge for a drink?

I have solved this question but couldn't understand why in the end there were 3 low price and 2 high price taverns? How do I figure out how many low price and high price taverns there is? Is there a method?


texts: Does the government ever pay back its debt from the OMO to the Fed?

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I'm getting confused about how exactly does money being created by the Fed.

From investopidia.com:

The Fed could initiate open market operations (OMO), where it buys and sells Treasurys to inject or absorb money.

If the Fed holds the Treasurys until maturity doesn't it need to be paid back the par? So how exactly does extra money being created?

Thanks


texts: Aggregation theorems hold if endowments are endogenous?

texts:
I have a specific question about considering a representative agent. According to Rubinstein 1974, in an inter-temporal economy with $N$ individuals each one with initial endowment $e_i$ and everything else homogeneous. The intertemporal constraints of the investor are:
$c_{0i}=e_{0i}-\eta_i p$
$c_{1i}=e_{1i}+\eta_i X$
Where $e_{0i},e_{1i}$ are present and future endownments, $c_{0i}, c_{1i}$ represents present and future consumption, $p$ is the price of the investment technology, and $\eta_i$ is the number of units bought. Finally $X$ is the payoff of the investment technology.

Assuming investors differ only on their endowments, we can solve for the equilibrium using a representative agent with the average endowment $\bar{e}=\frac{\sum e_i}{N}$.

Suppose now that the present endowment of each agent depends on how many units he/she decides to buy.
$c_{0i}=e^i(\eta_i)-\eta_i p$

The function $e^i(\eta_i)$ is not necessarily the same for all investors.

My question is: Can we solve for the equilibrium using a representative agent with endowment
$\bar{e(\eta)}=\frac{\sum e^i (\eta)}{N}$ ?

Thank you

Reference: Rubinstein, M., 1974. An aggregation theorem for securities markets. Journal of Financial
Economics 1, 225-244.