texts:
As per my calculations, the derivative of the MR curve is given by:
$MR'(q)=2p'(q)+qp''(q)$, where $p(q)$ is the inverse demand curve. Therefore,for a downward sloping demand curve, if the second derivative is large and positive, MR should actually be increasing.
However, intuitively, if demand falls, then marginal revenue should fall as well, and by a greater amount than demand. The two don't seem to match up, and that's my concern.


texts: I bought a house on a mortgage. If its price changes later, how will it affect the ease of repaying the loan?

texts:
I had some difficulty in understanding this paragraph in an article explaining the movie, 'The Big Short':

  Most of us when buying a house take out a loan (mortgage) and pay back
  the purchase price over time. We also usually hope that the value of
  the house we buy will go up not down. In the US, many people had
  come to assume that house prices would always rise, because they’d
  risen without fail for many years. This attitude saw mortgage lenders
  offering riskier and riskier loans to people who’d only be able to
  make payments if the price of their house continued to increase.

https://www.ecnmy.org/engage/the-big-short/


texts: Annual data VS Monthly data VS Quarterly data for a VAR model

texts:
I have read blogs posts that say one should use monthly, quarterly or annual data depending on whether you want to predict monthly, quarterly or annual outcome respectively.
So I guess the same applies to studying the dynamics of two or more variables using a VAR model. For example, the response of $y_t$ to a shock in $x_t$ should be expected to be different at monthly, quarterly and annual frequencies, right? It appears so in my experiment in the attached figure.
So saying that "the response of $y_t$ to a shock in $x_t$ is positive" is incomplete, I guess. Perhaps, it is better to say, "the response of $y_t$ to a shock in $x_t$ is positive at annual frequency, negative at quarterly frequency, and so on".
Or it is that the results should be similar irrespective of the frequency of the data?


texts: Business agreement design - is there science behind this?

texts:
I am working on schemas how advertisement space is sold to the ad agencies, ad networks and individual customers. There are lot of questions involved how to design the business agreement. E.g. one can agree about predefined budget and minimum rating level. In other case one can agree about predefined rating level and free floating budget to achieve. In the third case one can pack ad space and sell it in packages, maybe using some kind of auction.

The question is - is there science behind decision what type of agreement, what kind of agreement conditions the company should choose and present to the customer? What arguments are used in such decisions? One can say, that the key argument is optimization of profit, but how one can decide that scheme 1 bring greater profit thatn scheme 2? And profit is not the sole argument, because customer can decide not to agree with some kind of schema. Then negotiation process starts (it may be even automatic) and there should be found some common ground - e.g. maximal utilisation of resources, there should be compromise between the possibly contradictory goals of maximizing the profits of each company.

So - is there such kind of science as design of business agreements, design of sale conditions?

I have heard about mechanism design and auction design, maybe there is agreement design as well?

Thanks of any suggestions! I am technical person, but sometimes I feel that I should know the business side as well. And there should be "first principles", some optimization criteria that can form the basis for business agreements, proposals and negotiations.

Added: I have heard about contract theory - maybe that is the direction where I should look? Maybe my question is about unexplored area?


texts: How to control for population in Difference-in-Difference?

texts:
Random example, but let's say I'm examining the effect of a health program on influenza cases in India. They just randomly start the program in 7 of the 29 states. I have data on the number of flu cases in every state for a few years before and after the program was initiated. So I can run a diff-in-diff:

F = B0 + B1(Post*Treat),

where F is the # of flu cases, and B1 is the treatment effect, and I find B1 to be neg and significant. But what if the underlying population changed during these years? If untreated states' population grew relative to treated states, that might explain the difference rather than an effective program. So how do I control for population? I've read that using the rate instead of total number of cases is problematic (denominator of the outcome would be pop, which causes issues in the regression as I understand), but I don't think I can just do:

F = B0 + B1(Post*Treat) + B3(logPop),

where logPop is log population (obviously), right? Assume I have the data of population for each state for every year.

Thank you for all help!

P.S. I use R, so any answers that put it in terms of R would be a plus


texts: How infinite Nash equilibria are possible in a game?

texts:
I was studying games when one of the players seems to be indifferent between two or more pure strategies because he gets the same payoff with each strategy. We say that there are infinite Nash equillibria in the game but I am unable to calculate it and get an intuitive idea of how is it happening.
For example in the following game
$$\begin{array}{c|a|c} & L_2 & R_2& \\ \hline L_1 & (3,1) & (0,1) \\ \hline R_1 & (0,1) & (4,1) \\ \hline \end{array}$$

Seemingly, P2 should not even bother about anything even if he is playing pure strategy or randomizing. But here if we assume that P2 plays L with probability q and P1 plays L with probability p then making them indifferent we see that we cannot calculate p but q comes out to be 4/7. How is it possible or what is the interpretation ? If I am doing it wrong then what is the correct way to determine equilibria in this case ?

Another example is

$$\begin{array}{c|a|c} & L_2 & R_2& \\ \hline L_1 & (1,1) & (0,0) \\ \hline R_1 & (0,0) & (0,0) \\ \hline \end{array}$$

How many Nash's equilibria are possible in this ?


texts: Fact-checking Dan Ariely (2008) on Duke basketball tickets story

texts:
In Predictably Irrational (2008, pp. 127-133), Dan Ariely describes the Krzyzewskiville phenomenon (Duke students camp for weeks to get basketball tickets), and how he and Ziv Camron used it to study the WTP-WTA discrepancy. This is all very interesting — the only problem is that what's written in that book is completely different from the analyses done in the original academic paper Camron & Ariely (2000). (See summaries below.)
So my question is this: Which version is correct (if any) — the one in Predictably Irrational or the one in Camron & Ariely (2000)?  Which facts/results are actually correct? Or did they just make up most of it?

Summary of version in Predictably Irrational:

Duke students queue up in tents for weeks or even months.
Those at the front of a line don't get tickets to the game. Instead, they merely get a lottery number that gives them a chance to win the game.
Camron & Ariely then personally called up "more than 100 students". For the lottery winners, they asked for their WTA (minimum price at which they were willing to sell a ticket). For the lottery losers, they asked for their  WTP (maximum price at which they were willing to buy a ticket).

Findings:

In general, the students who did not own a ticket were willing to pay around \$170 for one. ... Those who owned a ticket, on the other hand, demanded about \$2,400 for it.

Conclusion:

From a rational perspective, both the ticket holders and the non-ticket holders should have thought of the game in exactly the same way. After all, the anticipated atmosphere at the game and the enjoyment one could expect from the experience should not depend on winning a lottery. Then how could a random lottery drawing have changed the students' view of the game—and the value of the tickets—so dramatically?

Summary of version in Camron & Ariely (2000):
In their "Study 1", their subjects are students who signed up for a lottery. However, there is no mention that these students had to queue or camp for tickets. More importantly, contrary to what's stated in Predictably Irrational, Study 1 contains no analysis that compares lottery winners to the lottery losers. Instead:

A hundred names of potential subjects were randomly drawn from a list of students, who had signed up for a lottery determining who would be eligible to purchase a ticket to the tournament. Ninety-three respondents (those we were able to locate) were interviewed over the phone by research assistants who were unaware of the study’s hypotheses. ...
Participants were first asked to indicate their selling and buying prices. The buying-price question asked for the highest price the respondent would pay for a ticket (to the NCAA Final Four basketball tournament), assuming s/he did not have a ticket. The selling-price question asked for the lowest price at which the respondent would agree to sell a ticket assuming s/he had one

Table 1 (which I presume is where the \$170 and \$2,400 figures quoted above come from):

It is only in their "Study 2" that there is any mention of campers being recruited as study subjects. Here however, there is no mention whatsoever of these campers entering any sort of lottery. There is certainly also no analysis comparing lottery winners and losers. There is also no hint of the \$170 and \$2,400 figures in the results here.


texts: In economics what is "total of pre-tax income of all citizens" called?

texts: What terminology is used in economics/finance to refer to the total of pre-tax income of all citizens of a country? And where to find that information


texts:
I have two very basic questions about second order stochastic dominance (SOSD):

Am I right in thinking that this is only a partial order, i.e. you can find a pair of lotteries such that neither SOSD the other?
Could it be that, if we only consider lotteries with equal means, SOSD is then a complete order? [I suspect not...]


texts:
Let's consider a Mundell-Fleming model for the short-run, with flexible exchange rates. Now, if we have a monetary contraction (or expansion), the exchange rate path will differ whether we're in the presence of rational expectations or not, and if the goods market adjust slowly.

Realistically, there are empirical evidence that the goods markets adjust slowly. In this case, if the agents are not forward-looking, then there's a slow adjustment of the exchange rate until there's an equilibrium. But when the agents are rational, the expected exchange rate is immediately the equilibrium exchange rate, and with a slow adjustment from goods market, there will be an overshoot(difference between the actual exchange rate and equilibrium one) for some periods, before reaching the equilibrium.  With a rapid adjustment in the goods market, the output would go immediately to equilibrium.

My question is what implications have a bigger or smaller period of overshooting/adjustment for the equilibrium exchange rate?
Are there also some empirical studies on this?

Any help would be appreciated.


texts:
$u(x_1,x_2)=|x_1 −2|+x_2$

Is this function continuous?

PS: The continuity theorem I use is this: Whenever for any $x^n$, $n \in N$ with $x^n \to x$ (i.e. $\lim_{n \to \infty} x^n = x$) and for any $y^n$, $n \in N$ with $y^n \to y$ with the property that $x^n$ is weakly preferred to $y^n$ for all $n \in N$, it must be that $x$ is weakly preferred to $y$.


texts: About gross domestic product at factor cost

texts:
GDP at factor cost= Net value added + Depreciation. Here my question is why depreciation added to Net value added? I am confused here: Net value added = Gross value added - depreciation; so the above formula becomes GDP at factor cost= Gross value added - depreciation + Depreciation. Here depreciation get cancelled and finally becomes GDP at factor cost= Gross value added.
Source: http://www.economicsdiscussion.net/national-income/components-national-income/top-17-components-of-national-income/18793


texts: Can perfect behavior be proved in a game of incomplete information?

texts:
Assumption: We have a machine that plays games perfectly.

The machine plays a game of Chess. Chess is a game of perfect information and complete information. We (assuming we have enough computational power for that) build the complete game tree for a game of chess and show that every move the machine made was minimizing the possible loss for the worst case scenario (comparison to minimax) and as a result, prove that it was playing perfectly.

The machine plays a game of Backgammon. Backgammon is a game of imperfect information, but still complete information since both players have the same amount of information available to them. We do the same thing as with chess, including the dice rolls and probabilities for every possible outcome and show that every move that the machine made was, once again, minimizing the possible loss for the worst case scenario (comparison to expectiminimax) and as a result, prove that it was playing perfectly.

Now the machine plays a game of Poker. Poker is a game of imperfect information and also incomplete information. Once we're reviewing the game, can we mathematically prove that the moves the machine made were perfect? Or is the fact that bluffing as a concept exists already means that it's sometimes impossible to compare two moves with each other and decide if there was anything better that could've been done?

If not, does that also mean that the assumption is wrong and it's impossible to play perfectly with incomplete information?


texts: How do low interest rates negatively impact bank earnings?

texts:
A lot of Banks are focused on bread and butter lending to small businesses and consumers. Many of those are putting aside provisions for loan losses in the wake of the Covid-19 pandemic. Headlines point to the drastic impact of lower rates on banks.
Assuming banks lend at certain rate + spread/margin,  are they not supposed to have hedged the interest rate move (E.g. with interest rate swaps or derivatives) ?
Are bank earnings tied to the interest rate level? How exactly ?


texts: Preference for consumption smoothing and actual smoothing

texts:
The typical dynamic consumption-saving under certainty model can be written as:

$$
\max V(c)=\sum_{t=1}^{T} \beta^{t-1}\; u(c_t)
$$
Subject to the intertemporal budget constraint
$$
\sum_{t=1}^{T}\frac{y_t}{1+r}=\sum_{t=1}^{T}\frac{c_t}{1+r}
$$

Where $T\leq \infty$ (finite or infinite horizon), $\beta \in (0,1)$ is the subjective discount factor, $y_t$ is the individual's income and $c_t$ is the individual's consumption in every time period. Finally, $u(\cdot)$ is the agent's subutility function, with $u^{\prime}>0$ whose concavity is usually related to the agent's preference for consumption smoothing. The argument is equivalent to the one justifying that an individual will reveal risk aversion iff his utility function over wealth is strictly concave.
The argument that leads to consumption smoothing is the following:
The first order condition for the problem is the well known Euler equation

$$
\frac{u^{\prime}(c_t)}{u^{\prime}(c_{t+1})}=\beta \; (1+r)
$$
It is assumed that $\beta^{-1}=(1+r)$ so that
$$
u^{\prime}(c_t)=u^{\prime}(c_{t+1}) \quad \Rightarrow \text{by strict concavity of} \; u \quad c_t=c_{t+1}
$$

I have two questions regarding this argument which are somehow related:

The result of consumption smoothing seems to be independent of the preference for such smoothing: one needs the condition $\beta =(1+r)$ to hold in orther to obtain the result.
It seems to me that the implication
$$
u^{\prime}(c_t)=u^{\prime}(c_{t+1}) \quad \Rightarrow c_t=c_{t+1}
$$

Would still hold for a strictly convex utility function, as one needs a much general condition to the implication to hold, namely that the derivatives of the utility function will be unique for any increasing utility function.. it seems to be that the uniqueness of $u^{\prime}$ (i.e $u^{\prime}(a)=u^{\prime}(b) \quad \Rightarrow a=b$) will hold irrespective of the sign of $u^{\prime \prime}$ provided it is not equal to zero.

If my thinking is correct this would imply that the desire for smoothing doesn't play any role on what the individual does at the end, as this possibility is open only when $\beta =(1+r)$ holds, and furthermore, it would be optimal to smooth out consumption even to an agent with a strictly convex utility function.


texts: What can we conclude from the overdetermined equity premium puzzle?

texts:
The equity premium: A puzzle (Mehra and Prescott (1985)) lays out the basic problem with equity returns:

  Restrictions that a class of general equilibrium models place upon the
  average returns of equity and Treasury bills are found to be strongly
  violated by the U.S. data in the 1889–1978 period. This result is
  robust to model specification and measurement problems. We conclude
  that, most likely, an equilibrium model which is not an Arrow-Debreu
  economy will be the one that simultaneously rationalizes both
  historically observed large average equity return and the small
  average risk-free return.
  ...Historically the average return on equity has far exceeded the
  average return on short-term virtually default-free debt. Over the
  ninety-year period 1889-1978 the average real annual yield on the
  Standard and Poor 500 Index was seven percent, while the average yield
  on short-term debt was less than one percent. The question addressed
  in this paper is whether this large differential in average yields can
  be accounted for by models that abstract from transactions costs,
  liquidity constraints and other frictions absent in the Ar~ow-Debreu
  set-up. Our finding is that it cannot be, at least not for the class
  of economies considered. Our conclusion is that most likely some
  equilibrium model with a friction will be the one that successfully accounts for the
  large average equity premium.

I've summarized this for my grandmother by saying that the most basic economic models explain the high equity premium by saying people are very risk adverse but if they are that risk adverse, other things make no sense, like how much people charge to do dangerous jobs.

In the 30 years since, much ink has been spilled on the subject of just what is causing the equity premiums in the historical record. Indeed, there is a huge book, the
 Handbook of the Equity Risk Premium that just summarizes these results. I've read much of this book and I've come away a bit confused. There are so many explanations each capable of explaining much of the puzzle that the puzzle itself appears overdetermined. That is, if all the (or even several popular ) explanations are true, the question isn't "why is the premium is so large?" but rather "why is the premium so small?".

What are we to conclude about this? All the explanations jointly can't be true, some are contradictory. For example, the peso and reverse-peso explanation says long run returns are likely lower than historical returns in the USA, while preference based explanations of the equity premium need an actual premium to explain. However, once we've eliminated the contradictory explanations, what then? What does one conclude about the individual explanations, the literature as a whole, and the underlying phenomenon?


texts: Why is the income effect zero for quasilinear utility functions?

texts:
Suppose I have the utility function $$U(x,y) = \sqrt{x} + y$$
subject to budget constraint
$$p_x x + p_y y = m$$
Then
$$x_M =\frac{p_y^2}{4 p_x^2}$$
$$y_M = \frac{m}{p_y} - \frac{p_y}{4 p_x}$$

where $M$ denotes Marshallian.

Now suppose I increase $p_x$ to $p_x'$.

Why is the income effect zero?


texts: Why do many economists believe that money is neutral in the long run?

texts:
If a central bank carried out monetary policy that consisted of multiplying each person's wealth by a common factor, I would find it plausible that all prices would get multiplied by the same factor and there would be approximately no real effects.

However, this is not how central banks carry out monetary policy. They print money and engage in market transactions that target certain prices. To me it does not seem plausible that this has no real effects, in the long run or the short run.

My question is, why do many economists believe that money is neutral in the long run? Do they take the quantity theory of money as proof that money is neutral in the long run? Is there particular empirical evidence, or influential papers that have convinced many economists that money is neutral in the long run?


texts:
During the last decades there has been an increase of anti-capitalistic movements around the world which are fundamentally different from those of the XIX-th and XX-th centuries in the sense that they do not belong to a "working class", but rather to a "middle class" who has had high levels of education.

By capitalism I mean any exchange market economy (with private property, one currency, representative democracy, competitive markets,...), i.e. in a broad sense and not referring to regional particularities (for example US vs Europe).


texts: How can a government save, if it has deficit?

texts:
I am reading an IMF paper about China's debt (link) which says:
❝ Despite a large augmented fiscal deficit of 10 percent, fiscal savings remain higher than other countries, resulting from the biased composition of spending towards investment ❞
How can a government have deficit and at the same time have positive savings?


texts:
Could price floors improve worker safety in the meat cutting industry?
My question is inspired by the Future Perfect podcast https://www.vox.com/future-perfect/21502225/chicken-meatpacking-plant-future-perfect-podcast which discusses the poor worker safety record of the meat cutting industry.
My thoughts are that if a price floor is binding that meat companies might compete on product quality including production practices like worker safety. Also, companies that take worker safety seriously could also enter the market since the price floor could support the higher costs of improved worker safety.


texts: How do EMH proponents explain Black Monday (1987)?

texts:
On Black Monday (19 Oct 1987), the Dow Jones Industrial Average fell by 22.6%. How do proponents of the Efficient Markets Hypothesis (EMH) explain this event?
Do they actually claim that the intrinsic value of the DJIA fell by 22.6% that day? Or do they have some other explanation?


texts: In fisher equation, Should I use "expected inflation" not "actual inflation"?

texts:
In fisher equation,
 real interest rate = nominal interest rate - expected inflation rate

During calculating real interest rate, I've question that whether I can use actual inflation rate instead of expected inflation rate.

so, is it make sense?
 real interest rate = nominal interest rate - actual inflation rate


texts: "Elasticity of marginal utility of consumption ( μ ) with respect to utility." (Green Book quote)?

texts:
In the Green Book (page 97) it is stated "the elasticity of marginal utility of consumption (μ) with respect to utility".

What is it? Is it an error ? I always heard of the elasticity of the marginal utility with respect to consumption...


texts:
How does one really compute inflation? I just now quickly looked up how the real GDP was computed. It is using the base year price to multiply the number of products traded. Is that meaningful? Is a ten year inflation computed on the base of the zeroth year price? The change in demand and supply would have made a huge change in the price when there is no inflation. The Motorola flip cell phone price now must be less than 1/100 of the price when it first came out. Does that mean there is severe deflation? On the other hand, the price for it could explode because it could have become a collector item. What about the price of a quantum computer --- the real one, or just something akin to DWave --- when it comes out? Are we going to compare its price against Von Neumann's Maniac or Allan Turing's Bombe or Intel 40386? This is nonsense and absurd. One rescue I can come up with right now, is we divide a finite time interval into multiple periods and computing recursively. We must assume the inflation speed is faster than the change of the supply and demand in each interval. I do not even know if that makes mathematical sense. Is there a proof of legitimacy for this or any other remedies, at least mathematically?

luchonacho has provided some sources below in his answer, particularly hedonic regression, for estimating the inflation. I have expressed my doubt over the efficacy of method. Here I would like to criticize the method further on the technicality.

The hedonic regression does not answer my question for distinguishing the change in supply and demand including that caused by the technological change. It seems the proponents of hedonic regression claim that it could make the distinction. Hedonic regression assumes the price of a good as the linear function of its attributes. Suppose the attributes have not changed over the period under consideration. However, the supply and demand for this good have changed due to, say, technological innovation that either has made the good obsolete or more valued or made useful in completely different ways than before, as well as inflation. Unless one already know extraneous information either on the change in supply and demand or the inflation, there is no way one can distinguish inflation from the change in supply and demand.


texts: Savage's subjective probabilities applied to Allais paradox

texts:
I've been reading up on the von-Neumann and Savage proofs for the existence of an expected utility representation.  I've also been reading critiques of the expected utility hypothesis, especially the Allais paradox.

Its obvious that the Allais paradox "disproves" von-Neumann: this can be shown numerically using commonly used utility functions such as log-utility.  However, I'm less sure why Allais and Savage are inconsistent with each other.  Its easy to find "subjective" probabilities that resolve the Allais paradox while still retaining the expected utility form.  To see this, consider the outcomes of the Allais paradox:

$$M^T=\begin{bmatrix}
1 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 \\
1 & 5 & 0 & 0 \\
1 & 0 & 1 & 0 \\
1 & 1 & 1 & 0 \\
1 & 5 & 1 & 0 \\
1 & 0 & 0 & 5 \\
1 & 1 & 0 & 5 \\
1 & 5 & 0 & 5 \\
1 & 0 & 1 & 5 \\
1 & 1 & 1 & 5 \\
1 & 5 & 1 & 5
\end{bmatrix}$$

Where each column represents one of the four gambles.

These gambles have the following corresponding "physical" probabilities:

$$ p=\begin{bmatrix}
0.008 \\
0.713 \\
0.080 \\
0.001 \\
0.088 \\
0.001 \\
0.001 \\
0.079 \\
0.009 \\
0.000 \\
0.010 \\
0.001
\end{bmatrix} $$

Using a log utility with initial wealth of $100,000, I get 13.911 "utils" for the sure million; 14.040 utils for the 89% chance for 1 million, 1 percent for 0, and 10% chance for 5 million; 11.777 utils for the 89% chance of 0 and 11% chance for 1 million; and 11.906 utils for the 90% chance of 1 million and 1% chance of 5 million.  Clearly this violates Allais' paradox.

However, consider the following subjective probabilities:

$$q=\begin{bmatrix}
0.04 \\
0.16 \\
0.02 \\
0.04 \\
0.07 \\
0.18 \\
0.01 \\
0.13 \\
0.07 \\
0.18 \\
0.03 \\
0.07
\end{bmatrix}$$

Using these probabilities, I get 13.911 "utils" for the sure million; 13.785 utils for the 89% chance for 1 million, 1 percent for 0, and 10% chance for 5 million; 12.880 utils for the 89% chance of 0 and 11% chance for 1 million; and 13.440 utils for the 90% chance of 1 million and 1% chance of 5 million.  This provides probabilities that are consistent with Allais' paradox.

How or why is Savage's proof inconsistent with Allais' paradox?


texts: Find utility function given indifference curve?

texts:
Given an indifference curve, how do you go about finding a utility function?

For example, given $z= \frac{k^\frac{1}{\delta}}{x^\frac{\alpha}{\delta}y^\frac{\beta}{\delta}}$ (defined by $U(\cdot) = k$), find a utility function. To do this, would I have to assign an arbitrary number for the utility and rewrite the function? I'm confused about what to do and can't find anything in my textbook about it. Thanks


texts:
Guvenen et al look at earnings shocks over time, and try to argue whether these are compatible with standard career-ladder models with normal shocks.

However, their data is no real shocks, it is time differences in labor earnings. We do not know which part of these were expected. What are things to consider if one tries to take into account for the fact that these income changes are - to some extent - expected ex ante?

My first guess would be that since people expect future rise in income, correcting the "shocks" for that would mean that the unexpected part of the shocks is to the left of their yearly changes in wage income. That is, there are more shocks downwards than upwards.


texts: Why high levels of inflation doesn't leads to high levels of employment?

texts:
According to the original Phillips curve $\pi=(\mu+z)-u$ there's a negative relation between inflation and unemployment.
That being said, if there were a really high level of inflation, then there would be plenty of employment, and this would be awesome for the economics agents. This would also mean that firms would be producing (so they must be selling a lot, so having a high demand) a lot, this would increase GDP, and therefore the quality of life of all of us.
However in real life, this doesn't seems to work like that, for example take Venezuela.
So what is the problem?
What happens?
Thank you in advance.


texts: Is the amount of tax that consumers pay the same as the amount producers pay?

texts:
I am confused about the amount of tax producers and consumers pay.

On this diagram, I can see that the supply curve increases by twenty dollars, as the tax is 20 dollars. The consumers have to pay 10 dollars more from what they previously had to pay.

This confuses me a bit. Don't producers and consumers pay the same amount of tax? When I look at this, it seems like they pay a different amount. The consumers pay 10 dollars more, but the producers don't pay $10 more.


texts: just economic interpretation: Is every steady state a golden rule steady state?

texts:
Is every steady state a golden rule steady state in solow model?

I know this question’s exact answer. I only want to ask for the following,

When know that at steady state $\dot{k}=0$

And in solow swan model $$\dot{k}= sk_t^a-(\delta + n+g)k_t$$

Since this equation is zero, I obtain the $$k_{ss}=(\frac{s}{\delta + n+ g})^{1/1-a}$$

When I maximize $$c_{ss}=f(k_{ss})-(\delta + n+g)k_{ss}$$ with respect to $k_{ss}$

I obtain the golden rule level $k_{gr}=(\frac{a}{\delta + n+ g})^{1/1-a}$

So,

$$k_{gr}=k_{ss} \iff a=s$$

That’s, saving rate is equal to capital share of income.

Otherwise, under different conditions, they are not the same.

What i want to ask that to what extent such a expression in the view of an economist is logical? This is true in terms of mathematical expression, but is it logical in terms of economic intuition  as well? If correct, What does this result say to me intuitively?


texts: Data Set of Bourguignon and Morrison 2002 AER

texts:
This question is about the following paper:

F. Bourguignon and C. Morrison "Inequality among World Citizens: 1820-1992", American Economic Review, Vol. 92, No. 4. (Sep., 2002), pp. 727-744.

On p.730, the authors say that

  The data, data sources, and assumptions behind them are available at:
  (http://www.delta.ens.fr/XIX).

But the link is dead.

Does anyone know where their data can be accessed /downloaded?

P.S. I am interested in data which were used in calculating Gini and other indices reported in the paper.


texts: What is the relation between the USD Swaps Rates and US treasuries?

texts:
I understand a swap rate is the fixed leg on a IRS (source), and a swap spread is the difference between a swap rate and the interest rate of a US treasury of the same/similar maturity. (source)
I also came across these charts of USD Swap Rates like for example here: link
If I understand correctly, if I am paying a floating rate like the 10y UST rate, I could get into IRS contract with a bank so they would pay the floating rate and then I would pay the swap rate associated to the 10y UST according to the chart in the provided link, is this correct?
This means that I would start at a loss if the USD swap rate is higher than the corresponding UST yield and at a gain if it is lower. Is this correct?
First I was under the impression that in an IRS both legs started with the same value and the floating leg would move up or down but if that was the case there would not be a need for USD swap rates because they would be the same as the UST yield, am I wrong?
Follow up questions:
How are the USD swap rates determined? Is it determined by supply and demand of the fixed and floating legs? (so that if there is more demand on the fixed leg the swap rates would be positive and in the opposite case they would be negative)
Mainly I want to check if my understanding is correct or not.


texts:
Different assets have different motivations and components for price determination. For example, an equity stock price might be considered to be include the value of underlying company, its potential for future growth, and its value as a store of wealth (kind of like a Yap stone).

The price of a currency would seem to be largely determined by the balance of trade with the country or countries involved. For example, if there is a net interest in buying the products of a country, then its currency will be in demand and the price will decrease, but if the citizens of the country are net buyers of foreign goods, then the price will tend to decrease. Thus, it is self balancing, because as long as the net buying of foreign goods continues, the value of the currency will decline reducing the amount they can buy, until it becomes so low that the country is forced to become a net seller, and the value of the currency begins to increase again.

Is there an econometric method for valuing currencies that takes such factors into account?


texts: Why are Massachusetts electricity costs so high?

texts: Massachusetts has the third highest electricity cost in the US (after Hawaii and Connecticut). Why is this?


texts:
Hope this isn't too simple a question.

I read an article that stated  that the UK government and EU have reached a draft agreement for a Brexit deal, leading to the following market movements after the announcement.

1) GBP rose against USD
2) Yields increased for 10-year British government bonds (i.e bond prices fell)

The first point seems fairly predictable, but why would seemingly less investment risk lead to a decline in bond prices? Could this be more about British  equities becoming more attractive relative to bonds due to less perceived risk?


texts: Help with a choice under uncertainty exercise

texts:
Let $u$ and $v$ be utility functions (not necessarily VNM) representing $\succsim$ on $\mathcal{G}$. Show that $v$ is a positive affine transformation of $u$ if and only if for all gambles $g^1, g^2, g^3$ in $\mathcal{G}$, with no two indifferent, we have:

$\frac{u(g^1)-u(g^2)}{u(g^2)-u(g^3)} =\frac{v(g^1)-v(g^2)}{v(g^2)-v(g^3)}$

I have tried to figure it out, but I am not sure where to start. Anyone who got a hint for me?


texts: Is there any paper/data source on price dispersion that contains coefficients of variation for US commodity prices like gas, bananas, or the like? I would like to get a sense of the distribution of CVs for homogenous good.


texts: What is the different between a Sales Tax and a Value Added Tax?

texts:
The USA has a sales tax which is applied at the point of sale, in states which have a sales tax. During the Democratic Party primaries, one of the candidates, Andrew Yang, proposed moving to a Value Added Tax (VAT), which his platform claims to be in place in 160 countries.
It terms of process, it seems that with a VAT, companies must charge the end tax even when selling to other companies, but only pay the tax collection agency the difference in what was collected and what was owed. With a sale tax, it seems that companies do not collect any tax when selling to other companies
Hence, what is the difference between a sales tax and a VAT in terms of the amount of taxes collected? It seems that in both cases, the taxes are only applied to the end consumer.


texts: Two different notations of the limit distribution of the trace test

texts:
I have seen two different versions of the limit distribution of trace test.

If $B_u$ is a standard Brownian motion, then I have seen

$tr\left\{\int_0^1(dB)B'\left[\int_0^1BB'du\right]\int_0^1B(dB')\right\} $ from 'Likelihood-Based Inference in Cointegrated Vector Autoregressive Models' by Søren Johansen

and $tr\left\{\left(\int_0^1B'(dB)\right)'\left[\int_0^1BB'du\right]\int_0^1B(dB')\right\} $ from 'New Introduction to Multiple Time Series Analysis' by Helmut Lütkepohl.

I don't understand why they are equal. I guess that $\int_0^1(dB)B'=\left(\int_0^1B'(dB)\right)'$, but I don't see why.

Any help is really appreciated.


texts: Am I correct that cyclical unemployment can be negative?

texts:
Let's start with stating and emphasizing some truths that we will need later.
Overall unemployment rate=Frictional unemployment + Structural unemployment + Cyclical unemployment. Also, Natural rate of unemployment = Frictional unemployment + Structural unemployment. From this we can see that Cyclical unemployment would need to be equal to zero in order to our economy to have natural rate of unemployment.

But suppose we have overall level of unemployment that in LOWER than the natural rate of unemployment. Now things get interesting. We can't get overall level unemployment become lower than the natural rate of unemployment by decreasing frictional and/or stuctural unemployment. Fortunately, there is the third component of overall unemployment, namely cyclical unemployment. If we agree that cyclical unemployment can be negative, then this way we can allow overall unemployment to be under the natural rate of unemployment.

It looks reasonable mathematically, but I have some doubts because I have never heard that unemployment can be negative. Is my reasoning correct, can we have negative cyclical unemployment?

And if I'm NOT correct, if cyclical unemployment can NOT be negative, then HOW do we get overall unemployment below the natural rate of unemployment?


texts:
Given the company's production function $f(L,K)=L^{1/3}K^{3/4}$, find slope of the isoquant passing through $(L,K)=(20,40)$ is equal to $-4/5$ (K is on the vertical axis).

I need to state whether the statement above is true or false. In my opinion that is true because i need to calculate $MRTS_{LK}$ which is obviously equal to $-4/5$, but the answer in my textbook is: $-8/9$. Thus my question is am i doing something wrong or just the answer in my textbook is wrong?


texts: What is the impact of fracking on oil prices?

texts:
I read an article about the recent fall of gas prices in the US claiming that the fall in gas prices was due to the expansion of fracking within the US.  The article said that, over the past few months, the oil harvested from fracking had come onto the market reducing the price of gas at road-vehicle refueling stations.

Obviously, I realize that an increase of supply with a constant demand will decrease prices.  But, is there any way to validate the article and conclude that the decrease in oil prices was due to fracking?  The article I read did not go into detail on how they reached their conclusion.


texts: Why do we spread knowledge across nations?

texts:
We have access to lots of knowledge on paper sharing platforms, open course platforms, open-source platforms and question asking platforms and etc, and Tesla opened all its electric car patents in 2014 starting from which year XPeng and FF and many others in China and other countries were founded.
I don't know why we are not afraid of the backfires of knowledge sharing or the late-mover advantage? Does a company need the often mentioned technical barrier to be competitive? In China there was a saying "师夷长技以制夷" which means literally "learn from foreigners to compete with them", then I thought those platforms are very dangerous to be utilized by enemies/competitors.
I am sorry if I asked this in the wrong place again(if so, please kindly let me know where I can post this question). I asked this question somewhere else on StackExchange and somebody suggested that I should consider comparative advantage and I learned the term here but cannot still get my head around how to answer my question using that. Any suggestions? Thanks in advance.


texts:
Is there any sort of recognised standard (e.g. ISO) for grouping jobs into job sectors e.g. 'technology', 'emergency services'?

I asked this on StackOverflow here and they suggested this SE.

Would this be as close as I'm likely to get?


texts: Does Direct Benefit Transfers make an economy poorer?

texts:
Printing money and giving to the poor causes inflation.
Increases demand and hikes prices. This is basically certain.

But on the contrary, a paper titled Debunking the Stereotype of the Lazy Welfare Recipient:
Evidence from Cash Transfer Programs1 by Nobel Laureate Abhijit Banerjee ,MIT stresses that directly giving out monetary benefit does not make workers lazy and increases productivity with experimental proof from 7 programs.

Is this not in direct conflict with this concept that handling out money to poor,when goods and services are limited would cause inflation.
It turns out this is even being implemented in my home state post a cyclone amidst the pandemic, so I'm confused as to which outcome is possible given they are in direct conflict with each other ?


texts: Does a price on the demand curve represent the highest or lowest price the consumer is willing to pay?

texts:
My question comes out of the context of the explanation for quotas in the textbook Macroeconomics, 4th edition by Paul Krugman. The explanation is for what could've happened had a quota on cab rides not been placed. In this explanation, the price of $5.50 is apparently the minimum price consumers are willing to offer:

  Looking back at Figure 4-8, you can see that starting at the quota
  limit of 8 million rides, New Yorkers would be willing to pay at least
  $5.50 per ride when 9 million rides are offered.

In the next paragraph, there is another reference to the price as being the minimum that people were willing to pay:

  The same is true for the next 1 million riders: New Yorkers would be
  willing to pay at least $5 per ride when the quantity of rides is
  increased from 9 to 10 million...

Shouldn't this price be the maximum price that consumers are willing to pay for, instead of the minimum price, as the book suggests? Why would a consumer not want to pay less that $5.50$ dollars per ride, at $5.30$ dollars for example, if the same quantity of rides (9 million) is offered?

I have included a copy of the diagram that is referenced, which I redrew. The x axis is quantity of cab rides per year, in millions of rides. The y axis is the fare price per ride. The green, orange and red lines are the demand, supply and quota restriction lines respectively. Please click to enlarge image.


texts: Why does nation's total debt matter and not NIIP?

texts:
Most people in the media talk about how the total debt level of a nation relative to its GDP is a measure of how "screwed" the country is. For example, see this: http://www.zerohedge.com/news/goldmans-sigma-x-hints-who-next-contagion-target

It seems to imply that UK is in bad shape but nobody seems to pay attention to it?
Japan also not looking good.

However, look at the Net International Investment Position (NIIP) of these countries:
UK: about 0% of GDP (equal amount of debt and assets)
Japan: >50% of GDP (Japan holds more assets than debt)

"A country's external debt includes both its government debt and private debt, and similarly its public and privately held (by its legal residents) external assets are also taken into account when calculating its NIIP"

If Japan needed to pay back its debt, couldn't it just sell some of the assets it holds and repay that way?

Is there something I'm missing here? Which is the right way to look at things?


texts: Why does the US government not invest in the stock market?

texts: We often talk about the huge public debt of the US government. Why does it not invest in the stock market (at least in index funds) instead of issuing debt? Can they not reduce the debt that way?


texts:
I want to interpret the output of a fixed effects regression and need help with interpreting the country-fixed effects.
The regression is the following:
pm.alldata <- pdata.frame(alldata , index = c("country", "year") )
a.fixedtwo <- plm(log(production) ~ log(temp) + log(rain) + drought + flood + storm + log(labour) + log(fertilizer) +log(capital) +log(area) , data = pm.alldata, model = "within", effect = "twoways")

The dependent variable is agricultural production. I want to look at how temperature and precipitation affect agricultural production (although this is rather irrelevant to the question I have). The country fixed effects refer to 28 countries. The county-fixed effects are as follows:
As I understand it, we can say that country 5 (Ecuador) has an unobservable negative effect (-5,99469) on agricultural production. Am I right?
Now I come to my main question:
I have divided these 28 countries into two subgroups (poor and rich countries).
If I regress only the 14 poor countries, the coefficients of the country-fixed effects change to the following:

Now the effect of country 5 (Ecuador) is suddenly positive (7.5768). This would mean that Ecuador has positive unobservable effects on agricultural production. Is it normal for the signs to change when this is subdivided into a subgroup?Which of the two values of Ecuador should I use for interpretation when comparing the value of Ecuador with the value of a rich country (e.g. Argentina)?


texts: Interpretation of a differenced regression

texts:
I'm experimenting with some data in R and I've found that though there is statistical significance between two variables, however their changes are not statistically significant.

I first ran a standard regression of revenue on price, adding a quadratic term to account for diminishing returns from increase in price. Giving us the formula:

$$y_{Revenue}=\beta_0+\beta_1Price+\beta_2Price^2$$

The results which were produced are:

> summary(lm(Wage~Price+I(Price^2)))

Call:
lm(formula = Wage ~ Price+ I(Price^2))

Residuals:
Min      1Q  Median      3Q     Max
-131.87  -87.77  -27.60   44.15  244.66

Coefficients:
           Estimate Std. Error t value Pr(>|t|)
(Intercept)  -1.650e+03  2.645e+02  -6.238 5.44e-06 ***
Price         3.640e-01  3.640e-02   9.999 5.28e-09 ***
I(Price^2)   -1.026e-05  1.129e-06  -9.086 2.41e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 116.9 on 19 degrees of freedom
  (7 observations deleted due to missingness)
Multiple R-squared:  0.8816,    Adjusted R-squared:  0.8691
F-statistic: 70.72 on 2 and 19 DF,  p-value: 1.577e-09

The second regression I ran was a regression of the change in revenue on change in price. Giving the formula:
$$\Delta y_{Revenue}=\alpha_0+\alpha_1 \Delta Price+\alpha_2 \Delta Price^2$$

Call:
lm(formula = diff(Revenue) ~ diff(Price) + diff(I(Price^2)))

Residuals:
   Min     1Q Median     3Q    Max
-82.52 -42.55 -11.98  19.20 142.36

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)
(Intercept)         5.093e+01  2.649e+01   1.923  0.07046 .
diff(Price)         1.343e-01  7.165e-02   1.874  0.07727 .
diff(I(Price^2))   -4.987e-06  1.691e-06  -2.950  0.00857 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 62.29 on 18 degrees of freedom
  (7 observations deleted due to missingness)
Multiple R-squared:  0.4521,    Adjusted R-squared:  0.3912
F-statistic: 7.426 on 2 and 18 DF,  p-value: 0.004449

Why do these variables lose their degree of  statistical significance while in the regular regression they are significant on the 1% level and how do you interpret such results economically?


texts: General mathematical model of incomplete contracts?

texts:
I have read various articles about incomplete contracts, like Hart's papers and Milgrom's papers.

But I have not found a paper that defines mathematically, in the most general way possible, what an contract is, and how a contract can be more, or less, "incomplete".

Is there a general model that has as special cases the incomplete contracts studied in the literature (e.g. by Hart, Incomplete Contracts and the Theory of the Firm, and others), and perhaps also as special case the complete contracts?

Note: I am not necessarily asking for a general model that can include all the reasons for incomplete contracts (thought that would be nice too). Just a model that can be used to state how (in)complete a particular contract is, whatever the reason.


texts: Do countries invest in the country's own stock market?

texts: For  example can the government of the UK invest in some company with shares in the FTSE 100? Or can Russia take the opportunity now that the shares of oil companies are low to buy them?


texts: Is the Trans Pacific Partnership good or bad for the U.S?

texts:
I've explored a number of different articles and some say it's good because american consumers/business aren't impacted by the tarrifs, however some other sources say we barely export anything to the counteries part of the TPP and hence we're giving them too much benefit for nothing.

I have found plenty of sources saying it's 'good' or 'bad' and they cite numbers such as '50000' added jobs, 5% increase in gdp, etc but there is no actual discussion of how they came up with these estimates.


texts: Data Reduction using Principal Component Analysis

texts:
I have performed PCA over a data set containing 25 items (variables). PCA was performed in a view to reduce the number of items (variables) from the data set, so as to move forward with analysis. Opting for Varimax rotation. The rotated component matrix is shown below
. The Communalities is show below  the question is which Items (variables) should i reject from the data set and why based on the output.


texts:
I quote the first few paras. of this Reddit comment:

  [1.] Imagine you had a business selling lollipops at school. Since you can
  buy a bag of 100 for \$10, you can sell them for 25¢ a piece for a
  profit.

  [2.] But you don't have \$10. But there is profit to be made for all if
  people give you the money. So you ask your friends to invest. They
  each give you \$1 and you give them (and yourself) some stock in
  the venture - a promise to split the profit. You guys buy a bag,
  and in one week, you sell all your lollipops for 25¢ each.

  [3.] So now you have 0 lollipops and 25¢ x 100 = \$25 Awesome!  Maybe you
  pay yourself a market rate for your job in the venture as salesman
  (you're also an employee since you sold the pops) - say \$5 So you have
  \$20 to split 10 ways. Everybody makes \$2 from their \$1 investment -
  everybody wins. you could pay them back their \$1 investment and
  another \$1 profit - this extra is called a dividend.

  [4.] Now, would your investors go in again next week? Sure! You're doubling
  their money. And you ran out of lollipops right? So maybe get everyone
  together to vote and we all agree at a shareholder meeting to skip
  the dividend and turn the venture into a business that reinvests
  the profit into 2 bags of lollipops and make money even faster.

  [5.] Next week you sell out again. Since you're just one sales guy, you
  still only cost \$5 and your profit margin has risen. You can now
  buy 4.5 bags of lollipops each week. Your business is growing!

See para. 5:

how has my profit margin risen? The profit is the same in the sales in 1 and 4?
why can I "buy 4.5 bags of lollipops each week"? Is the author just postulating this? Or does this follow from my 2 sales?


texts: Why did it take so much QE by the ECB to raise the Eurozone inflation to 2%?

texts:
From 2015 to 2018 the ECB increased the money supply by around 20% (around 6% y/y), with a GDP increase rate under 1%. Yet the inflation rate remained under 2%. A back-of-the-envelope calculation would expect a much larger inflation rate (around 5% or more). What happened?

UPDATE: here is my calculation: using a quantity of money model: $Y P = v M$
where $Y$ is the GDP, $P$ is the price level, $v$ is the money velocity and $M$ is the money supply, then the inflation (rate of variation of $P$) is the rate of variation of $M$ less the variation of $Y$, that is about 6% - 1% = 5%


texts: Estimates of magnitude of externalities generated by education?

texts:
It is standard to claim that education generates positive externalities.

For example, Mankiw (2017, Principles of Economics, p. 193):

  education also yields positive externalities. One externality is that a more educated population leads to more informed voters, which means better government for everyone. Another externality is that a more educated population tends to result in lower crime rates. A third externality is that a more educated population may encourage the development and dissemination of technological advances, leading to higher productivity and wages for everyone. Because of these three positive externalities, a person may prefer to have neighbors who are well educated.

But do economists (or anyone else) actually have any estimates of the magnitudes of the externalities generated by education?

(For example, Mankiw's "more education leads to better government for everyone" sounds plausible. But has anyone ever tried quantifying this? And if they did, is the effect positive and large? Or might it be near zero or even negative?)


texts:
I have this utility  function:
$$u(c,l)=c-\frac{\eta}{\eta+1}(24-l)^{\frac{\eta+1}{\eta}}$$
where c is consumption and l is sparetime.
Then I also think we must have the condition: $$pc+wl=24w$$ where p is the price and w is
the wage. An income tax is then introduced t, 0<t<1 so the
the consumer's hourly wage is $w(1-t)$.
Then I have to find the highest tax revenue the state can get is?
I think I will use Lagrange. I have proof that I got monotonic convex preferences. Then if I use
condition together with the utility  function I think I get the Lagrange problem:
$$L=max_l  \frac{24(w(1-t))}{p}-c-\frac{(w(1-t))l}{p}+(c-\frac{\eta}{\eta+1}(24-l)^{\frac{\eta+1}{\eta}})$$
Then I get the first-order condition:
$$\frac{\partial L}{\partial l}=0 <=> -\frac{w\cdot (1-t)}{p}+(24-l)^{\frac{1}{\eta}}=0$$
But I can't see how I can find the highest tax revenue that the state can get. If I
isolate t is it probably the tax rate I find, or what?  Can someone help me?


texts:
In contract theory and mechanism design, if the agents have one-dimensional characteristics, then they are usually considered as a contiuum on $\mathbb R$; if they have n-dimensional type, then they are in a contiuum on $\mathbb R^n$.

Naturally, if those (n-dimensional) types have some sort of correlations, then we could have a manifold of agents!

Or, if "n" is infinite, then we have agents on the infinite dimensional vector space.

Are there any research considered a manifold of agents?


texts: The Difference between investment and savings in CA identity

texts:
Mathematically speaking the current account is defined as:
$$\text{CA}=S-I$$

where $S$ is savings and $I$ is investment.

We know for a closed economy $S=I$ so $CA=0$. practically speaking for an open economy what is the difference between these two terms?


texts: Consumer surplus from a Hicksian demand curve: what is it?

texts:
A Hicksian demand curve indicates how much of a good will be demanded given price holding level of overall utility fixed.

When in equilibrium with a supply curve we end up with this area we would call consumer surplus, however we can no longer interpret it as "income saved by the consumer with respect to his actual demand" which is an appropriate interpretation when marshallian demands are used.

How exactly do we interpret this type of consumer surplus?


texts: Where is the money that was in the economy pre-lockdown?

texts:
Countries are in lockdown, companies have no customers and thus no income.

They have to lay off staff which in turn means ex-staff have no income. Everyone simultaneously and quickly depletes any savings so they can no longer buy goods and services.

Where is the money that was circulating in the economy before lockdown?


texts: Can supply and demand curves be used in electricity modelling?

texts: Can the (Supply and Demand) curves be implemented in electricity modelling for a country ? How can this be modelled and how can the user set the interaction point between supply and demand?


texts: Is the trade deficit driven by lack of domestic savings?

texts:
NYU Prof Joseph Foudy said the US trade deficit was caused by a lack of domestic savings and that tariffs on China would just shift the deficit to other countries. Zacks says

  A country’s trade balance (current account balance) is the difference between the value of exports of goods and services and the value of imports of goods and services. Through national accounting identities, the trade balance can also be expressed as the difference between national (both public and private) savings and investment.

So isn't Foudy really saying we have a deficit because we import more than we export? In other words isn't the lack of domestic savings identical to the deficit rather than its cause?


texts: How to derive the Indirect Utility Function from the Marshallian Demand Function?

texts:
I have been trying to derive the indirect utility function $(V(p,y))$, where $p$ is price and $w$ is wage, given the Marshallian demand functions $x(p,y)$ with the help of Roy’s identity (the utility function is not known. We only know the Marshallian Demand functions)

I would need to take the integral of the marshallian demand to obtain V. But this seems rather complicated to me.

If Roy’s Identity is:

$$ x(p,y) = - \frac{\partial V(p,y)/ \partial p}{\partial V(p,y)/ \partial y}$$

So if I know $x$ how can I derive $V$?

I have been thinking about this and trying some equations, but unfortunately I could not come up with a solution.

Thank you for your help!


texts: Banking Regulatory Frameworks, between the 1973 collapse of Bretton Woods and the introduction of the Basel Accords in 1988?

texts: Does anyone know of any work on banking system behaviour, and in particular the governing regulatory frameworks that applied between the 1973 collapse of the gold standard based Bretton Woods system and the introduction of the Basel Accords and capital regulation beginning in 1988?


texts: Gale-Shapley Follow-up Literature and General Questions

texts:
The Gale-Shapley Algorithm is a way of matchmaking between two different entities of people. It guarantees that every individual player is matched and that the matches are stable.

What sort of literature has been done building off of this? How does social welfare change when the two entities do not have the same number of individuals in them, so that not everyone can be matched? Are there faster ways to match individuals with each other (lower runtime?). And most importantly, what sort of applications does the Gale-Shapley algorithm have in economics?

It seems like a very weird game theoretic model just because when I read the proof for the validity of the algorithm, it doesn't seem like the problem is "discrete"; that is, optimizing who gets matched with who and finding a Pareto efficient result can't be solved through maximizing a continuous function. (As a side question, is the Gale-Shapley allocation Pareto efficient?)

Edit I meant to say, in the second paragraph, "it seems like the problem IS "discrete". So my apologies there.


texts:
i have a rather methodological question. I have a theoretical model and to test it I run some simulations. Because some parametervalues are not entirely clear or are up for debate I want to do a sensitivity analysis.

For this I use a one-at-a-time sensitivity analysis and change only one variable at a time. My question is the following:

When running such a sensitivity analysis is it acceptable to show the "boundaries" of the model parameters, i. e. as the question "For which values are the results of the model in line with empirical research and for which values do I get unrealistic results?"

And my second question (I use an example to make things clear): In my base Model I use a interest elasticity of -0.25 which is based on an empirical study by Chrinko et al. 1999. I know that there are a lot of studies on interest elasticity with results ranging between 0 and -1. Should I use the entire range of this results for my sensitivity analysis and is it bad if I show that my model works for some data (i. e. for -0.25 and -1 but not for 0?)


texts: NE equilibrium with lobbying of cournot producers

texts:
I have had an exam (exam is now past and submitted, but I want to now understand the solution without waiting) with the following questions:

GAME

Consider two firms playing the following two-stage game:

Firm face the following inverse demand:

$$
P(Q) = \frac{S+s_1 + s_2}{(Q+k)^{\alpha}}, Q=q_1 + q_2.
$$

in the first stage, firms can simultaneously lobby to ease trade restrictions by increasing $s_i$, for each unit of $s_i$ each firm pays $\frac{s_i^3}{9}$.

In the second stage they observe each other lobbying choice and set quantity simultaneously. Production costs are zero.

Let $\alpha = 3$ and $k=1$. Show that there is a NE with $S+s_1 +s_2 > S + s_1^{spne} + s_2^{spne}$ and explain why this is NOT a subgame perfect.

SPNE

SPNE is easy to find by backward induction, we know that in the second stage firms profits are

$$\pi_i = \frac{S'}{(Q+k)^{\alpha}}q_i - \frac{s_i^3}{9},$$

$S'$ is a fixed constant at this stage, so by differentiating we find the best responses and the optimal quantities

$$
q_1 = (q_2 + k)/(\alpha-1)\to  q^*_i = \frac{k}{\alpha-1}.
$$.

Anticipating this, at stage one, firm will want to maximize

$$\pi_i = \frac{S'}{(Q^*+k)^{\alpha}}q^*_i - \frac{s_i^3}{9},$$

deriving in $s_i$ we find the solution to be

$$
s^*_i = \sqrt{\frac{3q^*_i}{(Q^* +k)^{\alpha}}}
$$

Another SPNE?

I have tried finding an NE, but could not. Only thing I can find is what I think is another SPNE in which strategies are:

Both play $(\hat{s}, q_i^*)$ where $\hat{s} > s_i^*$ . If the other player deviates in the first stage, then the other will punish the other in the second stage by producing some

$$ q^p $$

such that $$\pi_1(\hat{s},s_2^* ,q^p,q_2^*) = \pi^{spne}$$ while
$$\pi_2(\hat{s},s_2^* ,q^p,q_2^*) < \pi_2(\hat{s},\hat{s} ,q_1^* ,q_2^*) $$ This should be -- assuming there is such a $q^p$ -- a credible threat since the player can get the same as the previous SPNE payoff and effective since it lowers player 2 profits by lowering the demand it receives.

Is this is an equilibrium at all and is it an SPNE or just a NE?


texts: Prove relation between expected utility and utility of the mean

texts:
Assume $U(x)$ is a concave, monotonically increasing function. If we know that

$$U\left[E(p)\right] > U\left[E(q)\right]$$

where $p$ and $q$ are probability distributions, how can we prove that

$$E(U_p) > E(U_q)$$


texts: Practical advice for calculating optimal prices

texts:
The company I work for is interested in making the pricing for its products more quantitative.  I researched the topic and I found some theory for calculating optimal pricing in Microeconomics texts and the "Pricing and Revenue Optimization" text by Phillips.
I have an engineering background and the theory makes sense to me, but I can't find any good material about how to implement these calculations in practice.
Here are some more specific questions

Calculating the optimal price requires a price-response function (seems very similar to a demand curve) associating price with demand.  The material I've read assumes that this function is known, but I can't find any good material about how to fit a price-response function in practice.  I've found some vague advice about using survey data, but it doesn't seem that practical or specific to me.  Are there some more specific and established methods for fitting a price-response function?  Maybe from historical transaction data?

Calculating the optimal price requires a cost function associating production quantity with cost.  I can imagine calculating this by accounting for raw material and labor costs in the manufacturing plant, but would appreciate if there's a more formal way to do this.  Maybe a complete tally of the costs I can sum up.

I imagine that any estimates of the price-response function and the cost function will have error.  Is there an established way to quantify the error and its impact on my pricing calculations?  This isn't addressed by the resources I've found.  Pricing of my company's products will have a large impact on revenue and I don't want to just fly by the seat of my pants.

Are there established methods for simultaneously optimizing the prices of a portfolio of products given a manufacturing quantity constraint?  The plants are constrained by the quantity of product they can produce.  The Phillips text has some theory on constrained pricing for one product, but not a portfolio of products.

Any advice is greatly appreciated!  Or even simply some insight as to whether optimal pricing theory is useful in practice, or sharing any war stories of actually implementing optimal pricing.


texts: What does the area defined by two different values for quantity under a supply curve represent?

texts: Assume that a and b (b is greater than a) indicate the quantity of supply on a linearly increasing supply curve. How can be the area formed by those two points under the supply curve interpreted? The interpretation should be made independent of a demand curve. That means no equilibrium price and producer surplus to account for. Could that be the difference between production costs for the given range of quantity?


texts: A professor at my college (I'm a rising sophomore) expressed interest in me working for him as an RA as I have had previous research experience prior to coming to college and I did well my freshman year. He told me that he has projects that he is working on, but what he would enjoy more is for me to come to him with an interesting project idea and then he will just pay me to go loose on the work and come to him when I get stuck. In all my prior research experience I've always been assigned a research question or topic and from experience with open-ended classroom assignments I always struggle with finding a good topic and having that topic satiate my interest for a long time. I was wondering if you guys had any pointers as to how to come up with an interesting problem or research question. Furthermore, I want to do some work in financial trading, or quantitative finance or some field that utilizes heavy amounts of modeling and programming so if you know of any open research problems in those fields, feel free!


texts: What's the role of money multiplier in the banking system?

texts:
On the internet , there are lots of people claming that the banking system has an immense power because it can multiply money obtained by deposits ( 'make money out of thin air' ) and then lend this money just with the provision of the reserve ratio , according to the theory of money multiplier.

They say that asking a real collateral for money without any previous existence is a fraud. It gives a disproportionate power to banks.

However, they seem not to consider that when the banks multiply money they gain a liability towards the depositor , and every time they multiply money is always a new liability due to deposits , so in the end the only profit for the banks ,say in a mortgage , should be the charged interest and not the entire mortgage (if the creation hadn't a liability it would be true) as they claim.

Are my considerations good? Can someone underline other relevant factors? Is this theory a total nonsense?


texts: I have 25 quarterly observations and I want to estimate price elasticity of demand. I intented to use GMM-IV estimator. However, I read that it is not good for small samples. What can you suggest me? Please keep in mind that I am not econometrician by profession.


texts: How does reverse repo rate affect money supply?

texts: What is the impact of increase/ decrease of reverse repo rate on Monetary Base, Money multiplier and therefore, overall money supply?


texts: Is it feasible for another country to attack the US dollar via counterfeiting?

texts:
Assuming, for the sake of the question, that a well-resourced adversary (another country, most likely) had the means and motive to conduct economic warfare against the United States through large-scale counterfeiting, what would be the scope of the impact?
For example, if shipping containers full of $100 notes that were indistinguishable from genuine US currency were distributed around the world, would that be enough to destabilize the US dollar domestically, or would it be just a drop in the bucket relative to the amount of dollars available globally?


texts: In this 3-way currency exchange, who loses, and by how much?

texts:
Let's say, hypothetically, we have the following imbalanced exchange rates:

1USD = 1.2EUR

1.2EUR = 1000 JPY

1000 JPY = 1.5 USD

Let's say person A starts off with 1 USD, buys 1.2 EUR from B, then buys 1000 JPY from C with the 1.2 EUR, then finally buys 1.5 USD from D with the 1000 JPY.

Person A now has .5 more USD than they started with. Where did the .5 USD come from? Who lost that equivalent amount? Does it depend on the exchange rates before and after this imbalance happens?


texts: Estimation of a Non-linear production function with Non-linear least squares

texts: Suppose that you have to estimate a Non-linear production function (for instance a Cobb-Douglas or a CES) by using Non-linear LS (and hence without log-linearization). You have just aggregate time series on GDP at constant prices, the Capital stock at constant prices and the level of Employment. What kind of adjustment should be done to the variable in order to obtain consistent estimation of the parameters?


texts: Need a math help for the Cagan's model in macroeconomics

texts:
From the appendix after the chapter 4 in Macroeconomics 7th edition by Gregory Mankiw.

  To keep the math as simple as possible, we posit a money demand function that is linear in the natural logarithms of all the variables. The money demand function is

  $m_t − p_t = −\gamma( p_{t+1} − p_t)$,

  where $m_t$ is the log of the quantity of money at time t, $p_t$ is the log of the price level at time t, and $\gamma$ is a parameter that governs the sensitivity of money demand to the rate of inflation. By the property of logarithms, $m_t − p_t$ is the log of real money balances, and $p_{t+1} − p_t$ is the inflation rate between period t and period t+1. This equation states that if inflation goes up by 1 percentage point, real money balances fall by $\gamma$ percent.

Shouldn't $(p_{t+1} - p_t)$ be the log of inflation rate? Why it says just "the inflation rate"?

  This equation states that if inflation goes up by 1 percentage point, real money balances fall by $\gamma$ percent.

My math level is like that of a high school. Would anyone be so nice and explain this for me? To me, it doesn't make sense at all.

$\ln \frac{M}{P} = \ln (\frac{p_{t+1}}{p_t})^{-\gamma} \rightarrow \frac{M}{P} = (\frac{p_{t+1}}{p_t})^{-\gamma}$

So, if the $(p_{t+1} - p_t)$ is just the log of inflation rate, then $\frac{p_{t+1}}{p_t}$ is the inflation rate and,

  inflation goes up by 1 percentage point

would mean $\frac{p_{t+1}}{p_t}$ is going to get +1, right? But I couldn't possibly think it would result the fall of $\frac{M}{P}$ by the $\gamma$ point. What am I missing?

And secondly, if the $(p_{t+1} - p_t)$ is just the inflation rate,(not the log of any) then it bugs me more than the former. So, +1 change to the inflation rate is like nothing but that we would get "$−\gamma(1 + p_{t+1} − p_t)$" at the right side, right? How could this be the case?


texts: Difference between the International Dollar and PPP

texts:
This may be a very rudimentary question but I am trying to discern the difference between purchasing power parity and the international dollar.

I am starting to work on a project where we are trying to look at infant mortality rates and their relation to GDP along with some other indicators from different countries. I have started to look for different data through GapMinder.

Reading some of the variable descriptions they claim to have the GDP in PPP and then some other reference GDP PPP in international dollars.

So I then took to the internet looking for the difference. The Wikipedia artilce on the Geary–Khamis dollar is leading me to believe they are the same thing if i am using USD as my base dollar unit?

So my question ultimately would be: What is the difference between the international dollar and PPP?


texts: Is there a difference between buying a currency and selling the currency to be converted to?

texts:
I'm not an economist. I'm looking to exchange my CAD to EUR. I watched the rates on a exchange office, and I found something strange:

We buy:                   We sell:
1 EUR = 1,4946 CAD (1)    1 EUR = 1,3280 CAD (2)
1 CAD = 0,6691 EUR (3)    1 CAD = 0,7530 EUR (4)

How can there be 4 different rates? I understand why CAD -> EUR is different of EUR -> CAD with the supply and demand. When the exchange office buys 1 CAD, it sells EUR too. I supposed it was to make things easier, so I checked it:

1 EUR = 1,3280 CAD (2)
=> 1,3280 CAD = 1 EUR

1 CAD = 0,6691 EUR (3)
1,3280 * 1 CAD = 1,3280 * 0,6691 EUR
=> 1,3280 CAD = 0.8886 EUR

Here, we found that it's indeed, more interesting for the customer to accept a sell than buying (from the office point of view for the words buy/sell).
But is the difference, normal? And why?


texts: Why did John Keynes believe that monetary policy to be less effective than fiscal policy?

texts:
So why did John Keynes believe that monetary policy to be less effective than fiscal policy for stabilising the level of economic activity, particularly in a recession?
Lowering markets' interest rate encourages borrowing and reduce the incentive to save, which to me it seems that it produces similar economic benefits to fiscal? But I guess that it takes time for the effects of low interest rate to flow through the transmission channels?
I suppose the reason why he favoured fiscal is tied to the time period he lived in?


texts:
Is there a term for a game whose pareto optimal solutions and nash equilibria are disjoint?

(e.g. prisoner's dilemma)


texts: How to derive consumer expenditures in EMEA 14.2.5

texts:
I am working on a problem 14.2.5 from EMEA by Sydsaeter, Hammond and Strom.

Consider the consumer demand problem:
$$ \max_{x,y} U(x,y) = \alpha \ln(x-a) + \beta \ln(y-b) \text{ s.t. } px+qy=m \tag{*} $$
where $\alpha, \beta, a, b, p, q$ and $m$ are positive constants with $\alpha + \beta =1 $, and moreover, with $m>ap+bq$. Show that if $x^*, y^*$ solve problem (*),  then expenditure on the two goods is given by the two linear functions:
$$ px^*= \alpha m+ pa -\alpha(pa+qb), qy^* = \beta m+ qb - \beta (pa + qb)$$

My attempt:
I set up Lagrangian:
$$ L= \alpha \ln(x-a) + \beta \ln(y-b) - \lambda (px+qy-m) $$
and get FOCs:
$$ \frac{\alpha}{x-1} = p \lambda$$
$$ \frac{\beta}{y-1} = q \lambda$$
$$ px+qy = m$$
I tried to solve the system above and then my plan was to multiply $x^*,y^*$ with $p$ and $q$ but that gives me different consumption function. Book has a hint that I should solve for $px$ and $qy$:
$$px = pa + \frac{\alpha}{\lambda}$$
$$qy = qb + \frac{\beta}{\lambda}$$
Then the book hints I should use budget constraint to eliminate lambda so I plug it there:|
$$ pa + \frac{\alpha}{\lambda} + qb + \frac{\beta}{\lambda}  = m $$
$$ \lambda = \frac{\alpha + \beta}{m- pa - qb} $$
When I plug the solution for lambda back to equation for $px$ I just get:
$$ px^* = pa + \frac{\alpha m - \alpha pa - \alpha bq}{\alpha +\beta} $$
And this is again not the consumption expenditure function the textbook says I should get. I don't get why I can't end with the same consumption expenditure as the book. Does anyone know how to solve this?


texts: Why is every action considered to be in the support while calculating mixed strategy equilibrium?

texts:
While evaluating the mixed strategy equilibrium, in most of the cases, we consider that all actions of a player are in the support of the equilibrium.Is it always so?
I was going through a problem (36.1, Chapter 3 in Ariel Rubinstein’s A Course in Game Theory) where the mixed strategy equilibrium was calculated by considering all the possible actions in the support of the probability distribution. I was able to reach to this solution using the basic theory, but I cannot prove that every action will be in the support.
Here I am borrowing the definition of support from Ariel Rubinstein’s A Course in Game Theory.


texts:
Assume a clothing store needs a 100,000 line of credit (LOC) to
  manage its operating cash flow each month. The store plans to use the
  LOC to make inventory purchases at the beginning of the month, and
  then pay down the balance as the store generates sales. The bank
  agrees to charge a lower interest rate on the LOC if the clothing
  store deposits a $30,000 compensating balance. The bank loans the
  clothing store’s compensating balance to other borrowers, and profits
  on the difference between the interest earned and the lower rate of
  interest paid to the clothing store.

From https://www.investopedia.com/terms/c/compensating-balance.asp

Why can't the bank provide only 70,000 loan to the clothing company at an adjusted equivalent interest rate?

I can't see the value of compensating balance.


texts: How Does Land Value Tax (e.g. Georgism) Decouple Lease Transfer From Improvement Transfer?

texts:
In theory, a land value tax (e.g. Georgist single tax), works by the government replacing property taxes with leases on land, as an incentive to invest in property improvements.  This obviously works when the owner of the improvement is the holder of the lease on the improved land. However, if the land value increases, and the rent on the lease does not, the holder of the lease, in effect, privatizes the positive network externalities of others' improvements.  Therefore, it is necessary that the lease not fix the rent payments for the duration of the lease and, instead, dynamically adjust them to collect (thence distribute as a social good) the increased land value.

At some point a lease holder may be unable or unwilling to pay the rent, causing a lease transfer.  If his improvements are mobile, he can pull up stakes and move them.  However buildings are typically fixed improvements. Hence there can occur a decoupling of ownership of a fixed improvement from the ownership of the lease on the underlying land.  This would appear to be a theoretic problem with the LVT, since the new owner of the lease's right to improve the property would be constrained by the prior owner's use of the land in the form of fixed improvements.

How does LVT theory deal with this decoupling of land lease from improvement ownership with land lease transfer in the absence of improvement ownership transfer?


texts: What economics aggregate(s) could suggest an imminent change in exchange rates?

texts: I have read articles about the Swiss Franc breaking its peg with the dollar and I would like to understand what indicators people look at to determine whether a currency break/depegging is imminent. More which of these useful economic aggregates are most important in determining a currency peg break?


texts: Effect of changing Non Labor Income on Consumption-Leisure problem

texts:
Given a Utility function $U(c,l) = c - \frac{1}{2}l^2$ , where $c$ is the consumption and $l$ is the number of hours of labour. Let $L$ be the maximum amount of labor, so the amount of leisure is $L - l$. The wage rate is $w$.

Assume a linear tax rate $r$, where $0 < r < 1$. Also, there is a fixed transfer of $R > 0$ to every individual that is irrespective of labor supply choice. Solve for labor supply l that maximises utility.

My solution:

$c = (1-r)wl + R$ therefore we maximise $U(l) = (1-r)wl + R - \frac{1}{2}l^2$.

Differentiating $U$ w.r.t $l$ we get $(1-r)w - l = 0$; therefore $l = (1-r)w$. So this shows that $R$ has no relation to $l$. However, it should make a difference due to the income effect, so I'm not sure what I'm doing wrong :/

Thanks!


texts: What is the difference in estimation between A, B, and C? They seem very similar

texts: This is a question in our econometrics class, and we're unsure of how to deal with the additional z2 and z3 in part B and part C.


texts: Total Differential of a Utility Function Subject to a Budget Constraint

texts:
I am trying to fully understand the process of maximizing a utility function subject to a budget constraint while utilizing the Substitution Method (as opposed to the Lagrangian Method). I am following the work of Henderson and Quandt's Microeconomic Theory (1956).

My confusion lies with obtaining the total differential of the generalized utility function after substituting in the budget constraint. For example, suppose you have the following utility function:

$$U=f(q_1,q_2)$$
Subject to:
$$y^0=p_1q_1+p_2q_2$$

The total differential of this utility function is:

$$dU=f_{q_1}dq_1+f_{q_2}dq_2$$

where $f_{q_1}$ and $f_{q_2}$ are the partial derivatives of $U$ with respect to $q_1$ and $q_2$, and $dq_1$ and $dq_2$ are the changes in $q_1$ and $q_2$.

Substituting the budget constraint into the utility function results in:
$$U=f(q_1,\frac{y^0-p_1q_1}{p_2})$$

I am struggling to calculate the total differential of the above function. Would the total differential just be the partial derivative of $U$ with respect to $q_1$ multiplied by the change in $q_1$? Below is my attempt:

$$U=f(q_1,\frac{y^0}{p_2}-\frac{p_1}{p_2}q_1)$$
$$dU=f_{q_1}dq_1-\frac{p_1}{p_2}dq_1$$

The next step in the book (after skipping the above total differential) is:
$$\frac{dU}{dq_1}=f_1+f_2(-\frac{p_1}{p_2})=0$$

Obviously, my intermediate calculation is incorrect (probably in multiple ways). Can someone identify and clarify my mistakes in progressing from the substituted utility function to the above equation? I understand that this process is used to equate the marginal rate of substitution to the goods price ratio and I am aware of its interpretation. My question lies simply with the mathematical derivation.


texts: How to understand share value vs real worth of the company

texts:
When read in the news articles for stock market price, I learned that the share value of a company changes in a year.  My question is does the share value really reflect if the company is doing good or not?

Example: In the recent aPIGEE article it says,  the company in a 52 week duration share value ranged from \$5.45 to \$16.34 .


texts: How do I calculate the cost per usage of a machine?

texts:
If you buy a machine for 10.000 dollars, which costs as a yearly write-off 2000 dollars, how do I calculate the cost per usage of a machine? Do you just divide the the yearly write-off by the times you use it per year? Or do you divide the yearly write-off by the times you potentially could use it per year?
How do you take into account the wear and tear/loss of value of using it?
Or is there some other way?

The machine is used in diagnostic medicine. I'm trying to calculate how much 1 test costs.

Is it just 2000/(Number of times used per year)?


texts:
Is the following graph possible?

I've attempted to sketch the TC/TR curves for it but they don't seem to be able to satisfy the following two properties at the same time:

1) Slope of Total Cost (TC) being less than the slope of Total Revenue (TR) until q=b, that is until quantity is at the zero marginal profit level.

2) TC being lesser than TR at first but going on to be greater than it after q=a, that is after quantity is at the zero economic profit level.


texts: Can someone tell me how to find the 'delivery price' on a futures exchange? This is the one detail I cannot find on a real futures exchange.


texts:
I have the following question to answer in my macroeconomics textbook. Steel producer makes steel worth 4000 out of which 0.25 is sold to machines producer and 0.75 of steel is being sold to the car producer. Machines are being sold to car producer for 2000. Car producer also buys tires from tires producer for 500. In effect he produces cars worth 5000 out of which 1/5 is being exported. Calculate GDP by three different methods.
And below in my textbook there is a table to calculate transaction value, value added, final goods expenditures etc. But how out of those data calculate GDP by three different methods? I know the equation GDP=C+I+G+NX, but how does it help?


texts: Sustainability of Collusion in a finite Bertrand competition with N > 2 firms

texts:
In a infinitely repeated Bertrand competition, collusion is sustainable if, and only, if, the following inequality is satisfied,
$\frac{\pi}{N(1-\delta)}\geq\pi$
Where $\pi$ is equilibrium profits, and $0 < \delta < 1$ is the discount factor. If the game is finite, I make the following claim:
Collusion is not sustainable, as each firm has an incentive to deviate from collusion in the last stage of the game. However, how would I go ahead and prove this claim?
My initial attempt, was to setup the following inequality,
$\frac{1-\delta^T}{1-\delta}$ $\frac{\pi}{N}$+$\pi_{\varepsilon}$ $\delta^{T-1}$ $\geq$ $\pi$,
where $\pi_{\varepsilon} < \pi$, and is given to the deviating firm. Is this a valid approach, or should I change my approach?


texts: No Ponzi game condition and transversality condition are the same?

texts:
Given the following non-stochastic planning problem with finite horizon,
\begin{align}
&\max_{\{k_{t+1}\}}\sum^T_{t=0}\beta^tU[f(k_t-k_{t+1})] \\
\text{s.t. } & 0\leq k_{t+1}\leq f(k_t)\\
& k_0 >0 \text{ (given)}.
\end{align}
I found that in order to make the first order conditions necessary and sufficient I have to add the so called no Ponzi game condition, i.e.
\begin{gather}
\lim_{T \rightarrow \infty} \frac{k_{T+1}}{R_{T+1}} \geq 0
\end{gather}

When written with the equal sign, this condition can be interpreted as the willingness of not keeping any capital at the end of life. And this is the same interpretation of the so called transversality condition.

Thus, is it right to interpret the no Ponzi game condition as a finite horizon version of the transversality condition? If not, which is the difference between them?


texts: How do we find pareto optimal points in a 2 goods simple exhange economy?

texts:
Suppose there are 2 individuals in a simple exchange economy with utilities $U_{1}= ax_{1} + x_{2}$ and $U_{2}= y_{1}y_{2}$.

Endowments are $(x_{1},x_{2})=(4,0)$ and $(y_{1},y_{2})=(1,5)$.

We are asked the values of $a$ such that the above allocation is pareto optimal.

The answer as given is $MRS_{A} \ge MRS_{B}$ implies pareto optimal.

How did we arrive here?

URL for reference: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34

URL for actual problem: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34


texts: How do you read currency exchange rates in terms of domestic and foreign currency?

texts:
I am having some issues understanding how to read exchange rates.
E is the exchange rate

I read online that if we have for example E\$/€, then the base currency in this case is the dollar and the quote currency is the euro . In this case , if E\$/€ = 1.50, this would mean that 1$ would buy 1.50€.

However, in my textbook i am having some miss understandings.
In my textbook , the domestic currency is the EURO and the foreign currency is the DOLLAR.

It states :
The exchange rate can be defined in two ways, the first one being

1) The price of the domestic currency (euro) in terms of the foreign currency (dollar). If 1€ =$1.50 , then E=\$/1€=1.50.

If i look at E=\$/1€=1.50  , i see E\$/€.

This implies how in this case, the base currency , orelse 1€, is written as a
the second currency , and E\$/€= 1.50 . With one euro you can buy 1.50 dollars.

2) The second way of writing the exchange rate is the price of the foreign currency in terms of the domestic currency . In this case E=€/\$= €0.65 .
In this case, the base currency is also written as the second currency , with 1 dollar being able to buy 0.65 euros.

Then my questions is that i'm not sure why there are different ways of writing the exxhange rate. On internet E\$/€=1.50 means that with one dollar you can buy 1.50 euros. In my textbook, E=\$/1€=1.50.  , which i assume is the same thing as E=\$/€= 1.50 means that with 1 euro you can buy 1.50 dollars.

What am i misenterpeting ?


texts: Is it possible to eliminate the U.S. national debt?

texts: A political science teacher of mine has said that the U.S. national debt has grown way beyond reach and is now just a political talking point with no real value.  He says that there is no point in trying to pay it back and that it should be left alone since all the money is fiat, thus "imaginary".  What's your take on this?  Is it still possible to pay off the debt in 'x' amount of years without experiencing hyperinflation?


texts: Simplex Lp interpretation of dual problem´s solution

texts:
I am wondering whether my interpretation of my simplex dual problem result is correct.
The primal problem is:
                                M1  M2  M3  M4
    materialdemand for 1 kg P1  0   2   1   4
    materialdemand for 1 kg P2  3   2   2   0
    materialdemand for 1 kg P3  1   2   1   1
    constraint          (kg)    220 295 240 120

*Mi = material; Pi = product

    Z= 2,3X1 + 2,3X2 + 2X3 --> max

Constraints:

3X2 +   X3 <= 220
2X1 + 2X2 + 2X3 <= 295
X1 + 2X2 +  X3  <=240
4X1 + X3 <=120
X1;X2;X3 >= 0

the dual problem is the as follows:
V = 220w1 + 295w2 + 240w3 + 120w4 --> min

Constraints:

2W2 +   W3 + 4W4 >= 2,3
3W1 + 2W2 + 2W3 >= 2,3
W1 + 2W2 +   W3 +   W4  >=2
W1;W2;W3;W4 >= 0

I interpret w1 in my final tableau being the opportunity costs of M1, W2 of M2, W3 of M3 and W4 of M4.
I would appreciate if you could help :-)


texts: Calibration of utility function parameters controlling labor disutility

texts:
Consider the very basic utility function

$$ u(c, n) = \log (c) - \alpha \frac{n^{1 + \frac{1}{\nu}}}{1 + \frac{1}{\nu}}$$

Where $c$ is consumption and $n$ is working hours. As the Frisch elasticity here is given by $\nu$, I would calibrate $\nu$ to be between 0.5 and 1.

However, I'm wondering what to do with $\alpha$: What do I calibrate that against?


texts: Epstein zin and resolution of uncertainty

texts:
I'm reading Simon Gilchrist's notes here. I understood everything until and including page 14, where it reads
$$\frac{W_h^{1-\rho} + W_l^{1-\rho}}{2} \geq \frac{c_h^{1-\rho} + c_l^{1-\rho}}{2} $$
and that's supposed to show that the certainty equivalent of lottery A is higher than the CE of lottery B. However, the CE of the two lotteries, according to page 12, are $(\frac{1}{2} c_h^{1-\alpha} + \frac{1}{2} c_l^{1-\alpha})^{ 1/(1-\alpha)}$ and $(\frac{1}{2} W_h^{1-\alpha} + \frac{1}{2} W_l^{1-\alpha})^{ 1/(1-\alpha)}$.
I know that we are supposed to assume $\rho > \alpha$, but I'm not sure how that helps.


texts: First Order Stochastic Domination and lottery preferences

texts:
Let $L$,$L'$ be two lotteries over the real numbers. Let $u$ be an increasing Bernoulli utility function. Let $F_L$, $F_{L'}$ be the CDFs of the two lotteries. We wish to show that
$$L \succ_{FOSD} L' \iff \mathbb E(u(L))\geq \mathbb E(u(L')).$$
I am able to prove the necessity. I am not able to prove sufficiency. I get an expression like $\int u'(x) f_L dx \leq \int u'(x) f_{L'} dx$ after integrating by parts, but am unable to proceed after that.
This is not a homework problem.


texts: Compute the inverse of a conditional quantile regression output

texts:
Short Clarification :
This question was asked at the Cross Validated SE (Question at CV) but one highlighted in the comments, that this might be more applicable to this SE due to its economic topic. Feel free to migrate the question (if possible) to this SE. On the other hand, there is a related question at CV SE which focuses just on the estimation technique. Feel free to go there if some things in this question need clarification, which I hope is not the case. (Question about Control Variate QR )
Please excuse me for this long introduction.
Brunello et al (2009) show that extended compulsory schooling leads to increased wages respectivly to the individual gender. Their empirical model first uses quantile regression to show the impact of compulsory schooling years (ycomp,
defined as the instrument variable z) on actual years of education (s). Afterwards they subtract those fitted values of the regression from s to get the ability of a person of a specific quantile.(2)
They claim that their model is exactly identified to do so.(3)
In the end they come up with a quantile regression aproach which is augmented by the control variate computed in (2). But if I understand them correctly they compute the inverse of the $\tau$ - quantiles of distribution $a$ and $u$. (4)
If I got that right, could somenone help me to show how this is done? I suspect some kind of Monte-Carlo Method, e.g. importance sampling, but I'm unsure. A solution with R-code is appreciated but not necessary.
Simplfying the question : How do one calculate $G_{a}^{-1}\left(\tau_{a}\right)$ and $G_{u}^{-1}\left(\tau_{u}\right)$?

(2):First, we estimate the conditional quantile functions of schooling $s$
and compute the control variate $$
 a\left(\tau_{a}\right)=s-\bar{Q}\left( \tau_{a} \mid X, z \right) $$

(3): Omitting subscripts for simplicity, the earnings-cum-education model
presented above can be written in the format of an exactly identified
triangular model, as in Chesher's approach $$ \begin{array}{c} \ln(w)=\beta s+s(\lambda a+\phi u)+\gamma_{w} X+a+u  &(6)\\ s=\gamma_{s} X+\pi
 z+\xi a &(7)\end{array} $$

(4): Define $\tau_{a}=G_{a}\left(a_{\tau_{a}}\right) \text { and } \tau_{u}=G_{u}\left(u_{\tau_{u}}\right)$, where $a_{\tau_{a}}$ and
$u_{\tau_{u}}$ are the $\tau-$ quantiles of the distributions of $a$
and $u,$ respectively. Furthermore define $Q_{w}\left(\tau_{u} \mid s,
 X, z\right)$ and $Q_{s}\left(\tau_{a} \mid X, z\right)$ as the
conditional quantile functions corresponding to log wages and years of
education. Ma and Koenker (2006) show that recursive conditioning
yields the following model $$ \begin{array}{c} Q_{w}\left[\tau_{u}
 \mid Q_s\left(\tau_{a} \mid X, z\right), X, z\right]=Q_s\left(\tau_{a}
 \mid X, z\right) \Pi\left(\tau_{a}, \tau_{u}\right)+\gamma_{w}
 X+G_{a}^{-1}\left(\tau_{a}\right)+G_{u}^{-1}\left(\tau_{u}\right)& (8) \\
 Q_{s}\left(\tau_{a} \mid X, z\right)=\gamma_{s} X+\pi z+\xi
 G_{a}^{-1}\left(\tau_{a}\right) & (9)\end{array} $$ Given the restrictions
imposed by (6) and $(7),$ the key parameter of interest
$\Pi\left(\tau_{a} \tau_{u}\right)$ is a matrix with the following
structure $$ \begin{array}{c} \Pi\left(\tau_{a},
 \tau_{u}\right)=\beta+\lambda G_{a}^{-1}\left(\tau_{a}\right)+\phi
 G_{u}^{-1}\left(\tau_{u}\right) \quad \end{array} $$

Metatopic : I really think that this topic would benefit if there would be a specific quantile-regression tag. Since there is none and my reputation is too low to create a new one, I will go with just the regression tag.


texts: How much is currently invested in artificial general intelligence research and development?

texts:
Glossary: Artificial general intelligence (AGI) is the name given to an upcoming technology that would be able to solve all sorts of problems, like a human, and unlike more specialized existing artificial intelligence (AI). In a sense, AGI is closer to depiction of AI in movies and in the public's mind.
Originally my question was about valuation but I was told this is not allowed here. So I am only asking about existing investments in artificial general intelligence.
Company or VC names are optional.
The main point is to get more information about artificial general intelligence economics.


texts:
I have bond yields for Indian G-Sec. For short term yields the proxy are (15-91 days) , (92-182 days) , (183-364 days). For long term yields the proxy are 5,10 & 15 years. Data ranges from 1996 - 2016.
But the yield values for 15 years bonds are unavailable from 1996 to 1999. So in order to have a complete data-set, i need to compute the 15 year bonds yield those 3 years on monthly basis.

Please check the below link for data file.
https://spaces.hightail.com/space/9wrYy


texts: Constant Elasticity of Substitution- profit maximization vs cost minimization

texts:
Consider the following production function:
$$
Y=A\left[\alpha K^{\rho}+\left(1-\alpha\right)L^{\rho}\right]^{\frac{1}{\rho}}
$$
In the above, $\rho$ is the substitution parameter, and $\sigma=\frac{1}{1-\rho}$
is the elasticity of substitution. One definition of the elasticity
of substitution is that this parameter is defined as the substitution
of $K/L$ with respect to $MRS_{K,L}$ holding output constant. In other words:
$$
\sigma=\frac{d\text{log}\left(K^{*}/L^{*}\right)}{d\text{log}\left(F_{L^{*}}/F_{K^{*}}\right)}
$$
 Notice, that the optimal choice on part of the firm implies that
$F_{L}/F_{K}=w/r$ . As such:
$$
\sigma=\frac{d\text{log}\left(K^{*}/L^{*}\right)}{d\text{log}\left(w/r\right)}
$$

My question is as follows: how important is the fact that we hold
output constant? I understand that if we consider the problem of the
firm in two stages, i.e. in the first stage as a cost minimization
problem (choosing optimal $K^{*}$ and $L^{*}$ for a given level
of output), and in the second stage, choosing an output level to maximize
profits, then if relative prices change, it is not necessary that
the profit maximizing output stays the same. In other words, if relative
prices change, we shift to a different isoquant, and this definition
of $\sigma$ is not the correct one.


texts: Does the value of a pure strategy Nash equilibrium(if exists) equal the value of the mix strategy Nash equilibrium in two-person zero-sum game?

texts:
Given a two-person zero-sum game, a mixed strategy Nash equilibrium always exists and all such equilibria have the same value. A pure strategy Nash equilibrium, however, may not exist.

My question is: suppose that a pure strategy Nash equilibrium exists, does the value of it equal the value of the mixed strategy Nash equilibrium?