texts:
In the Wikipedia article on the Modigliani--Miller theorem, it states two propositions. (It gives the cases of with and without taxes. Here I'll just focus on the case without taxes.)
The first proposition is that the value of an unlevered firm is the same as a levered firm. Given the assumptions, this is clear from the discussion:

  To see why this should be true, suppose an investor is considering buying one of the two firms U or L. Instead of purchasing the shares of the levered firm L, he could purchase the shares of firm U and borrow the same amount of money B that firm L does. The eventual returns to either of these investments would be the same. Therefore the price of L must be the same as the price of U minus the money borrowed B, which is the value of L's debt.

However, here I am asking about "Proposition II:"

  $$r_E(Levered) = r_E(Unlevered) + \frac DE (r_E(Unlevered) - r_D),$$
  where

  $r_E$ ''is the required rate of return on equity, or cost of equity,''
  $r_D$ ''is the required rate of return on borrowings, or cost of debt,''
  and $\frac{D}{E}$ ''is the debt-to-equity ratio.''

The article states that the "formula is derived from the theory of weighted average cost of capital (WACC)." (See a related question here.) My question is this: how can we arrive at this result from WACC?


texts: Single Peaked Preferences and Condorcet Cycles

texts: How can you prove the theorem that Single peaked preferences imply that there are no Condorcet cycles


texts:
I am curious what the typical breakdown of costs is for a soda bottler in the United States. I realize there are variations depending on region and brand. I am looking for ballpark estimates based on real knowledge (not guesses). The basic material costs I am looking for are:

plastic bottle stubs
labeling
caps
flavorant
sweetener (corn syrup)
all other costs (energy, wages, rents, taxes, etc)


texts: How does a country set an optimum minimum wage, i have went through loads of website but none of them give me a satisfied answer. For example, median of a country's income, percentage of GDP and such seem too shallow and unfair as a medium of calculation.


texts:
According to Bloomberg, the coupon rate on a 10-year UK government bond is 4.75%.

Bloomberg also states that the yield is currently 0.55%, and the market price £143.51.

But if the following formula is correct:

Then the yield should be $\frac{4.75}{143.51} \approx 3.31$%

Clearly this isn't the case. So what did I do wrong?


texts: Why do we need to "get the economy moving again"?

texts:
Sorry I have no background in economics but as a computer programmer, I specialise in building models out of simple math and logic, so I hope we can speak the same language without having to get into too much economic jargon.

Consider the following scenario:

Kate is a hairdresser and Alice owns a restaurant. Every month Kate goes to Alice's restaurant and spends \$50 on a meal, and Alice spends \$50 getting her hair cut at Kate's. This generates $100 of GDP. Now say there is a global pandemic which makes it dangerous to meet each other, Kate decides it's safer to cook her own dinner and Alice cuts her own hair. They are both in exactly the same financial position as they were before but no GDP has been generated. After a while the government announces that we all need to do our bit to "get the economy moving again" (which I interpret to mean "generate GDP") even if it means putting ourselves in danger.

I understand that the government wants economic activity because that's how they collect tax revenues, and I also understand that some people do jobs that are essential for the functioning of society. I also understand that going to work conveys other psychological benefits than simply earning money, but let's assume for the moment that there are at least some people people who would rather just stay at home and where there is reduced natural demand for their services.

It seems to me that all the money that hasn't been spent in restaurants and hairdressers during the COVID-19 pandemic hasn't gone anywhere, it's still sitting in the bank accounts of the people who would otherwise have spent it.

If we could find another way of redistributing that wealth from the people who's jobs are essential (and are therefore still getting paid but aren't going to restaurants) to people who's jobs are not essential (and therefore don't need to work during the pandemic), is there any harm with putting the economy on hold for an indefinite period until people decide they want to go back to work again?

Edit 8 June

Thanks for all the great responses, this has really helped my understanding but I don't think anyone has hit the nail on the head so I've added this note to try and clarify what I was after. I’ve tried not to move the goalposts to the extent that previous replies look stupid (I haven’t edited anything above this line).

Firstly just to clarify my original question, I wasn’t questioning the benefit of economic growth over stagnation under non-covid circumstances; I was questioning whether covid + economic stagnation might be better than covid + enforced economic activity.

Also one thing I maybe didn’t make clear enough is that I wasn’t talking about an enforced lockdown in cases where people would rather go to work; I was arguing that people who wanted to consume or produce less shouldn’t be obligated to consume and produce more, just to fuel the engines of capitalism.

The effect of covid has been to push the cost of goods upwards (because of the risk of contracting covid while producing them) and the benefit of consumption downwards (because of the risk of contracting covid whilst consuming). This will put some markets into a state of oversupply, even without an enforced lockdown.

So let’s say my widget supplier says “I’m no longer willing to supply that widget for \$50; I’d rather lose my job and get paid \$30 on welfare” and I say “I’m not willing to pay \$50 anymore; I’d rather live without it, even if it means I have to pay \$35 more in taxes”.

In this scenario we’re both happier than we would have been had we traded, and the government gets $5 to administer the welfare. The only people who aren't happy are those that have a vested interest in ever-increasing GDP, who in turn are often those in powerful positions and might try to use their influence to "get the economy moving again" to the detriment of the average citizen.


texts: Is there any good textbook for theoretical economics mathematical modelling?

texts: I am currently reading some theoretical economics books and, of course, many mathematical expressions appear. I kind of guess their meaning, but it takes a lot of time and, after all, my guesses are assumptions rather than certainties. Many times I find myself lost even in the easiest questions like: why use an exponent instead of a multiplication in this particular case? And even if I kind of guess their meaning, I struggle to understand the creation process of a model. I have looked for mathematical modelling textbooks but all I kind find are introductions to models for processing big data or data analysis. I would like to read a textbook that is fully focused on theoretical models. Also, the books I find for mathematical economics and such are books that teach how to solve specific problems rather than how to formulate models. Does anyone know any good textbook for someone like me? Thank you.


texts: With interest rates and inflation in the U.S. low and growth moderate, where is the money going?

texts:
Question is basically in the title. With interest rates so low for such a long period of time, I wonder where are that injected cash has gone?

I realize that the economy has definetly grown quite consistently for years now, but the middling growth and simulatenous near-zero interest rates would seem to indicate that the economic climate is so bad in the country that we basically have to ignite a nuclear bomb to boil a pot of water.

Is that the case? It doesn't seem so, and it seems worrying that maybe this cash from monetary policy is somehow disappearing into thin air as we create it or disappearing somewhere problematic


texts: Solvency and liquidity. How to understand them? Should Central Banks only lend to solvent but illiquid banks?

texts:
Solvency: Long-term liabilities are covered by assets(with value measured at maturity, not at market-to-market)

Liquidity: short-term liabilities are covered by assets which can be sold in the short-term.

Is this it?

Should CB lend to insolvent banks? or only to solvent but illiquid banks? This related to the problem of moral hazard, where if banks are being bailed out, more can think that their liability side is being covered by the CB/Government...


texts: Mathematical Notations that I Never Understand While Reading Articles or Dissertations

texts:
I have some problems when I reading mathematical notations. For example:
$$\mathrm{E}_{0}\left\{\sum_{\mathrm{t}=0}^{\infty} \beta^{t}\left[\mathrm{u}\left(\mathrm{C}_{\mathrm{t}}, \mathrm{M}_{\mathrm{t}} / \mathrm{P}_{\mathrm{t}} ; \xi_{\mathrm{t}}\right)-\int_{0}^{\mathrm{1}} \mathrm{v}\left(\mathrm{h}_{\mathrm{t}}(\mathrm{i}) ; \xi_{\mathrm{t}}\right) \mathrm{di}\right]\right\}$$
This is a optimization equation for representative agent in an economy. This problem here is maximizing this formula.
where
\begin{aligned}
&\mathrm{E}_{0}= \text{expected value in period 0} \\
&\mathrm{C}_{\mathrm{t}}= \text{ index of household consumption of goods supplied in period t}\\ &\mathrm{P}_{\mathrm{t}}= \text{index of prices of goods supplied in period t }\\
&\mathrm{M}_{\mathrm{t}}= \text{nominal money balances in period t }\\
&\mathrm{h}_{\mathrm{t}}(\mathrm{i})= \text{quantity of labour of type i supplied in period t}\\
&\xi_{t}=\text{ vector of aggregate shocks in period t}\\
&\mathrm{u}(.)=\text { utility in period } t\\
&\mathrm{v}(.)=\text { disutility in period } \mathrm{t}\\
&\beta^{\mathrm{t}}=\text { discount factor for period } \mathrm{t}
\end{aligned}
1- First of all, I don't understand the $\xi_{t}$ notation in $\mathrm{u}\left(\mathrm{C}_{\mathrm{t}}, \mathrm{M}_{\mathrm{t}} / \mathrm{P}_{\mathrm{t}} ; \xi_{\mathrm{t}}\right)$. Does semi colon here mean that this vector notation can affect the equation's behavior exceptionally, but the other variables affect it all the time?.  If there would be a positive or negative shock already, then u and v will be effected through the prices and wages. Why should we use this vector here?
2- Why do we need to take the integral of the disutility function, but don't need to take the integral of the utility function?
3- There are no enough explanations for newbies in articles in mathematical economics, and I can't find a textbook for this topic. I studied Varian's Intermediate Microeconomics, but there is no chapter for this. I looked up books that recommended here but again there is no chapter at all. Is there a book that covers all classical mathematical solutions and explains them in detail for economics?


texts: How to prove if production set Y satisfies free-disposal and CR of scale, then Y is convex, when there are only 2 commodities

texts:
Free-disposal and CR of scale can not imply convex production set.
But it is true for single-input and single-output model.
Therefore, I am wondering how to prove if production set Y satisfies free-disposal and constant returns of scale, then Y is convex when there are only 2 commodities.


texts: Constant Returns to Scale and Positive Marginal Products

texts:
In a simplified model in the search theory of unemployment, let $M=\mu{m(u,v)}$ be the matching function where $u$ and $v$ is unemployment and vacancies respectively. Given $m(u,v)$ has constant returns to scale and positive marginal products, how do we show that the job finding rate $f = M/u$ increases with labour market tightness $\theta=\frac{v}{u}$?

Given CRTS, I can rewrite $f$ as follows: $f=\mu{m(1,\theta)}=\mu{}m(\theta)$. How can you then show that given positive marginal products, we have $\frac{df}{d\theta}>0?$


texts: Is a 6% wealth tax a sustainable source of income?

texts:
Elizabeth Warren is planning to pay for various things with a 6% wealth tax on those with fortunes in excess of $1B USD.  Now, right or wrong, this seems to be an awfully big annual scoop from a bucket that one intends to be scooping from in perpetuity.  If the bucket gets low, then we'll have to find other as-yet-unknown sources of income to fund these various projects. Is the bucket filling up at a rate large enough to sustain such a 6% tax?

In other words, is the rate of wealth increase of Billionaires at least 6% on average?


texts: Does quasilinear preference contain rationality, monotonicity or other assumptions?

texts:
I have a question when I'm doing exercise 3.C.5(b) of MWG. The exercise asks to prove that a continuous preference on $(-\infty,\infty)\times R^{L-1}_+$ is quasilinear with respect to the first commodity iff it admits a utility function $u(x)$ of the form:
\begin{equation}
u(x)=x_1+\Phi(x_2,...,x_L)
\end{equation}
In the proof, the existence of the utility function needs to be shown, but I am not sure if the quasilinear preference is monotonic (and rational) since the definition of quasilinear preference only states about the numeraire commodity.

My  question: is the quasilinear preference relation naturally rational, monotonic and continuous, or we have to state the rationality, monotonicity and continuity additionally? Could you give some references?

Thanks a lot!


texts: According to North, Wallis, and Weingast (NWW), which states/societies have successfully made the transition to open access?

texts:
Weingast (2016) writes:

  The NWW framework redefines the process of economic and political development as the transition from a limited access order to an open access order. The transition is a difficult process, and NWW argue that only two or two and a half dozen states have successfully completed it.

Earlier, NWW (2009) had written:

  Perhaps 25 countries and 15 percent of the world’s population live in open access societies today

Have NWW ever explicitly stated what specifically these "two or two and a half dozen states" or "[p]erhaps 25 countries" are?

In NWW (2009), they have three subchapters (6.5, 6.6, and 6.7) specifically discussing the transition to open access in Britain, France, and the US. So these are three. What are the other 20+ states that in their opinion have also successfully made this transition?


texts: How does John Stuart Mill distinguish between "wealth" and "riches"?

texts:
JS Mill in his Principles (1848):

But though air is not wealth, mankind are much richer by obtaining it gratis, since the time and labour which would otherwise be required for supplying the most pressing of all wants, can be devoted to other purposes.

I am bewildered by the above sentence. Mill seems to be making a distinction between "riches" (or "being rich") and "wealth" (or "being wealthy"). But what is this distinction?


texts: Practical guide to Structural Equation Modeling

texts:
I am currently self-learning Structural Equation Modeling. I have studied some theory and also a bit about the software implementation, but not enough to practically conduct an SEM study.
I wanted to have a more detailed reading of the full practical implementation of Structural Equation Modeling.
For example, I have a theoretical model hypothesised for a phenomenon (with the latent and respective observed variables and their relations and the directions). How do I go next. What should be the sample size (10/observed variable?), how to practically make sure that I have chosen the right observable variables (which software, any rules of thumb that I must remember etc.), testing reliability and validity, any research design subtleties I need to take care of that might not be obvious from the theory, and then deriving the covariance matrix and hypothesis testing, what should be the practical steps to ensure their validity etc.
Any lecture/ video series, books, notes etc. or a list of resources that are comprehensive enough to be self-sufficient for a basic SEM study would be very helpful, especially those that are useful for self study.


texts: All else being equal, What is the value of job creation?

texts:
Job creation value
Just to clarify, I have no experience, academic background or deep understanding of economics. Apologies for such a basic question but I couldn't find a real answer.
I hear a lot about job creation:

"This will create X jobs"
"Losing jobs overseas"
Etc.

I have trouble understanding the inherent value of the current amount of jobs to society.  If jobs are lost together with the productivity they created then I get why there is a problem.  For example: A factory was destroyed in a fire, the workers lost their jobs, and society lost the productivity of the factory. But if all other things remain equal, what is the value of a job?  I'm going to add my very naïve analysis below to help illustrate my thinking.
Naïve interpretation
Let's say we have a country that has some people working right now. Suddenly 10,000 stopped working without affecting productivity. Maybe there was a temporary need that was filled or perhaps some technology made their jobs obsolete.
If current amount of jobs is an inherently positive thing, I should now be at a worse state than before. As I see it, I just got 10,000 potential workers. Modern humans, even not well trained ones, produce vastly more than they cost to support.
I can certainly understand that it can be traumatic to lose your job but that's an argument for job stability or something, not job creation.
The argument that all those people are not retrainable at all, seems a bit far-fetched. They can't all be 60 year olds who trained their entire life in this field and are uneducated in absolutely anything else. And if that was the case, it would be better treated as a surprising early retirement. Tragic for people who weren't prepared, yes, but a completely different problem.


texts: Endogenous Gentrification and Rates of Return to Education

texts:
Gentrification is, roughly speaking, the displacement or exclusion of poor people from areas with improved amenities due to higher rents and costs of living. The question I have is whether better educational facilities can have a dual effect. That is, if better schooling is an amenity for an area, but raises the wages of poor people by improving the rate of return on education, then will gentrification occur or not?

I've been struggling to find good literature on this topic. A few examples of papers I've found (Chicago citations):

Guerrieri, Veronica, Daniel Hartley, and Erik Hurst. "Endogenous gentrification and housing price dynamics." Journal of Public Economics 100 (2013): 45-60.

This paper talks about separating changes in housing prices as changes in housing demand shocks and gentrification. Education or labor demand is not the major point of endogeneity addressed here.

Baum-Snow, Nathaniel, and Daniel Hartley. "Gentrification and Changes in the Spatial Structure of Labor Demand." (2015).

This paper creates a model for spatial labor demand changes to better describe the nature of gentrification. Their paper would be very helpful, but it is unfinished.

Edlund, Lena, Cecilia Machado, and Maria Micaela Sviatschi. Bright minds, big rent: gentrification and the rising returns to skill. No. w21729. National Bureau of Economic Research, 2015.

This paper probably gets closest to what I'm looking for, focusing on returns to skill and gentrification. It doesn't exactly focus on education specifically, and though it controls for distance from city center, it doesn't control for things like quality of transportation services (as they admit).

My question is whether or not there is any literature that is related to the topic I am interested in, or if there isn't any, what previous literature may be relevant to look at during a review of the literature.


texts: Why are there base years for GDP in current prices (or Nominal GDP)?

texts:
I am looking at GDP in current prices for Indian states and there are multiple base years. This is confusing because GDP in current prices is supposed to be reported in the value of the currency for that particular year. So why are there multiple base years?

Here is an illustration of how the data are presented (this is coming from the Reserve Bank of India, source is Central Stats Office)

            Base Year: 2004-05

Year:  2011-12,    2012-13, 2013-14,        2014-15

GDP:  36224493, 41006812,   46418355,   52002992

            Base Year: 2011-12

Year:  2011-12,  2012-13,   2013-14,        2014-15

GDP:  37940203, 41140371,   46427154,   52646842

This is for norminal GDP. Again why is there base years when we are looking at nominal GDP (data for each year should use value of the currency for that particular year) Really appreciate any clarification.


texts: How do I adjust for heterogeneous labor markets when calculating the wage premium?

texts:
I have a dataset with mean and median wages for particular geographic areas around the United States. I am interested in calculating the wage premium between some areas. I can already do a simple version of that but I would like to adjust my model for heterogeneous labor markets because the dataset includes data split by industry group for each area. How would I go about doing that exactly?

Consider this example:

+------+-------------+--------------------+-------------------+
| Area | Industry    | Mean Annual Income | Number of Workers |
+------+-------------+--------------------+-------------------+
| IL   | Medical     | $100,000           | 50                |
+------+-------------+--------------------+-------------------+
| IL   | Natural Gas | $50,000            | 50                |
+------+-------------+--------------------+-------------------+
| NY   | Medical     | $150,000           | 60                |
+------+-------------+--------------------+-------------------+
| NY   | Natural Gas | $90,000            | 40                |
+------+-------------+--------------------+-------------------+

I could just calculate the wage premium in Natural Gas and Medical between IL and NY, then take a weighted average. But what should the weights be? The proportion of workers in each industry is different for the two areas here.

This looks very similar to textbook price index problems. Could I just calculate a chained price index?


texts: Panel econometrics for marketing mix analysis: how to include spending that affects all the individuals of a panel?

texts:
Dear stack exchangers,

in the course of an internship at a microfinance bank in Tajikistan, I have been tasked with assessing the efficiency of different marketing expenses.
I will try to expose the situation:

-I have monthly data (15 months)

-the individuals are cities (7 cities)

-as a regressand/dependent variable (called Y), I will be using the monthly variation in clients at the bank (three analyses: global, for deposit products, for loans. I may use the number of new clients, if it is avaible.

-my regressors/independent (called X) variables are the monthly expenses in one marketing tool (newspapers, billboard, leaflets, website ads, tv+radio), per city.

--> I'll have 105 observations to treat

My objective is to evaluate which media brings the most clients per Somoni spent.
To this end, using STATA, I will conduct a panel analysis, using errors ajusted for clustering, and a fixed  effect per city (the number of new customers per months may be affected, among other things, by the population of the sector).

The question that motivated this post is:
how could I include spending that is national (e.g. TV/radio) into my equations, and obtain a meaningful coefficient for it?

If I include the value of national spending in each equation, then the estimated  coefficient would give the average impact of national spending on Y at the city level.
But national spending has an impact on all cities at the same time.

Because the coefficient is an average, I guess multiplying it by 7 (as there are 7 cities) will give me the global impact of national spending on the number of customers.
What would be the problems with such a solution?
What alternatives are there?

I also have two subsidiary questions:

-A lot of Xs take the 0 value. And in a lot of cases, an observation has only one X different from 0. Does this pose a particular problem, apart from those of statistical significance? (I don't think so)

-Finally, I have a few questions concerning the design of my study.
Do you think that such a design will yield exploitable coefficients?

Is the exclusion of the interest rate variable a heavy problem? (I might not be able to obtain that data)

Should I worry about AR(1) problems? (maybe the number of new clients is affected by network effects, so Y(t) depends on Y(t-1))


texts: What is an equilibrium generated by replication?

texts:
Sorry this might be a little too rudimentary for you, but I'm not an Econ background. When I was doing exercises for MGW chapter 17 "Positive Existence of Equilibrium" I came across the following statement

  The consumers preferences are strictly convex, this implies that there is no equilibrium in the overall economy generated by replication.

What doe equilibrium generated by replication mean? I couldn't find it in the text.

Thanks in advance.


texts: Economic impact of employer ignorance to cliff effects?

texts:
Let's say an employee, Mike in Indiana, earns \$10.50 an hour. He gets a raise to \$13, but because he is no longer eligible for SNAP (food stamps), his net earnings actually go down. His wage has passed a certain eligibility criterion, and as a result there's a drop-off in benefits he's entitled to, and net income as a result. We call the situations that lead to these scenarios cliff effects, and a few examples as apply to Mike are shown in the graph below.

What I'm curious about is a rather specific question owing to the existence of cliff effects. Employees typically don't track earnings by employee after accounting for cliff effects, and so, what is the effect of their ignorance on the economics of the labor market? How does inability of employers to know about cliff effects experienced by their employees affect the market?


texts: Decreasing Costs, Increasing Returns to Scale, & C''(q)

texts: Given a profit-maximizing firm with production function $f(x_1,x_2)$, I understand that we can formulate a firm's cost function $C(q)$ by using the contingent demand functions $x_1^c$ and $x_2^c$. We can then use this cost function to see whether a firm has decreasing costs, namely if $C(tq)<tC(q)$. If the second derivative of the cost function, C''(q), is less than zero, does that also imply that this firm faces decreasing costs and thus increasing returns to scale?


texts:
Is there any application of the Heine-Borel theorem or the Bolzano-Weirstrass theorem to Economics?
Also where are the notions of compact sets and elementary Real Analysis used in Economics?


texts: What is the difference betwene a partial default and having debts partially written off?

texts:
From The Daily Telegraph:

  The new Syriza-led government has demanded some form debt write-off on the country's €317bn liabilities, two-thirds of which are owned to official creditors in the form of the EU and the IMF.

From BBC News:

  New Greek PM Alexis Tsipras says his country will not default on its debts.

A default is, according to Wikipedia:

  In finance, default is failure to meet the legal obligations (or conditions) of a loan, for example when a home buyer fails to make a mortgage payment, or when a corporation or government fails to pay a bond which has reached maturity.

Which leads me to the question:

What is the difference between some form of debt write-off (demanded by the Greek government) and a partial default (denied by the Greek government)?


texts: Calculating price in a pure exchange economy

texts:
The problem is simple, I'm not really sure of my answer though.

Consider an economy where there are two consumers and two goods:
$$U_1(x_{11}, x_{21}) = x_{11}$$
$$U_2(x_{12}, x_{22}) = x_{22}$$ $X_1 = X_2 = R_2^+$
; $e_i ≥ 0, i = 1, 2.$

For what values of endowments does an equilibrium exist? What are the prices in the cases where an equilibrium does exist?

Now we cant really use the tangency condition here to calculate the competitive allocation. Intuitively, it seems like there'd be an exchange of commodities. To me, it seems like there'd be different cases.

Case 1: Individual 1 has both $x_1$ and $x_2$, whereas individual 2 has only $x_2$. Since individual 1 only values $x_1$, the price of $x_1$ in this case would be 0, since he doesn't really need to trade. I'm not really sure how to calculate the price of $x_2$ though.

Case 2: Similarly, Individual 1 has some $x_1$ and no $x_2$. Individual 2 has some of both. In this case, price of $x_2$ should be zero, but again, not sure about the price for $x_1$. (I'm not really sure it matters though, since we usually always calculate relative prices)

Case 3: Both individuals have some quantity of both $x_1$ and $x_2$. In this case, the income from the excess of the commodity not required by the individual must be equal to the price of the commodity he needs to buy. The relative price in this case comes out to be $\frac{X-x_{11}}{x_{21}}$.

Does the answer make sense?


texts: $15 dollar minimum wage in the U.S. a good idea for the U.S. economy?

texts: After taking principles of micro and macro economics, both intro-level courses, I got the impression that price controls are generally not a good idea for a market economy. However, I continuously see controversy on social media and the news about raising the minimum wage. It's making me second guess myself. Is there anyone on here that can make a convincing case for or against the minimum wage? I would greatly appreciate it.


texts:
I know nothing about the 'economics of corruption' literature, whether in the medium(fluctuations) or long-run(growth)... Although I've found many surveys (mostly +5 years, and from journals I don't recognize), since I known nothing about this subject, I have no idea with which ones I should start,.
I'm looking for two pointers

One to a survey/literature review from a well-established journal (QJE, etc.)
A book on this subject, but similar in difficulty to those books for the general public like "Nudge", "Irrational Exuberance", "Trade Talks", "The Triumph of Injustice", etc.

Thanks in advance.


texts: Is this a total derivative - if yes, why minus

texts:
This is the beginning of the derivation of equation of motion from the Solow model (Romer, 2019):

My question is: is this the total derivative (w.r.t. ultimate source of change "t")? If yes, why there is a minus sign in front of the 2nd and 3rd term?
I assume because they are in the denominator. But I was not able find any rules for this on net. Everywhere are only "+" symbols. Thanks.
This is how I did it. Is it wrong? I did total derivative and got the same result as in the textbook:


texts:
Does the gravity model of trade apply equally for goods and services?

Naively it would seem that the more ephemeral services would be less impacted by it?


texts:
I have often heard the following argument against the antimonopoly/anticollusion law:

Whenever the entrepreneurs decide to enter into "illegal" collaboration, each one has an opportunity to gain profit through dumping. This will cause the price to fall to the desired free-market level.

Truth be told, I reckon this argument to be quite faulty. It works only when the entrepreneur aims at a short-term profit. Moreover, I cannot see how it works for trusts.
Yet, it got me thinking. Thinking of the last century, pretty much no collusions come to mind, just trusts: Standard Oil, Morgan's railroad monopoly, U. S. Steel (the US), the German Steel Trust (Germany), FIAT (Italy). Were there any decentralized monopolies? If not, did I underestimate the dumping argument? If not, what is the real reason behind it?

Edit: thanks to 1muflon1, who provided a very interesting link on collusions in the EU. It proves my ignorance in history (not knowing any cartels, that is). Besides, they pointed out that my terminology is a bit messed up. Sorry about that.


texts:
I'm studying financial economics/asset pricing and I often hear the terms cashflow risk and discount risk but I'm not sure what they mean? The Campbell/Shiller (1988) decomposition includes cashflows (future dividends) and discount rates (expected returns) and hence identifies both risks?
Apparently, the long run risk model from Bansal and Yaron (2004) and the duration model from Lettau and Wachter (2007) discuss cashflow risk whereas the external habit model from Campbell and Cochrane (1999) is about discount risk? The investment decision model from Berk Green and Naik (1999) apparently includes both? What about the simple CAPM and CCAPM?
Campbell and Vuolteenaho (2004) use an ICAPM set-up to decompose market beta in cashflow and discount component and show that value stocks have higher CF betas.


texts: Are there times when firms compete more with each other?

texts: I have the impression that sometimes firms are fiercely competing with each other, innovating and trying to gain market share and other times when firms are just hanging on. Are there any references about the timing of competition intensity?


texts:
The standard approaches for calculating GDP are:
$$
\text{GDP} = \text{Consumer Spending + Capital Investments + Govt. Spending + Net Exports}
$$
And
$$
\text{GDP} = \text{Total wages + Profits + Taxes + Return on Capital Investment}
$$
I have an issue in seeing the equivalence of these two approaches in different cases. Say we pay the government taxes. In the second approach that gets counted in "taxes", but in the first approach it doesn't get directly counted. Yes, the government spending usually comes out of tax revenue, but not all of tax revenue goes to government spending. So how does the "taxes" in the second approach get divided in the first approach. A good chunk of it goes to government spending, but what about the rest? Are we making an assumption that it's all spent? What if in a simple "two good economy", we have an individual/firm paying taxes but we don't add government spending. Does the tax money go "waste" here in our GDP calculation?

Secondly, we don't count wages in "capital investments" since we assume that the wages paid by firms (counted in the second approach) become consumer spending; but are we assuming that consumers spend ALL their income? How do we account for savings and simply models in which wages do not necessarily equal spending?


texts: Robust Standard Errors in Fixed Effects Model (using Stata)

texts:
I'm trying to figure out the commands necessary to replicate the following table in Stata. This table is taken from Chapter 11, p. 357 of Econometric Analysis of Cross Section and Panel Data, Second Edition by Jeffrey M Wooldridge. Here I'm specifically trying to figure out how to obtain the robust standard errors (shown in square brackets) in column (2). I'm trying to do this in Stata. I was able to to get the conventional standard errors using the command

xtreg lpassen lfare ldist ldistsq y98 y99 y00, i(id) fe

. I was able to get column (1) with

xtreg lpassen lfare ldist ldistsq y98 y99 y00, i(id)

and the corresponding standard errors with

xtreg lpassen lfare ldist ldistsq y98 y99 y00, i(id) vce(robust)

. However, the command

xtreg lpassen lfare ldist ldistsq y98 y99 y00, i(id) fe vce(robust)

does not work for column (2). It gives results that are different from the book. Could someone explain how to obtain these standard
errors in Stata?

Note that the data to go along with this question can be found here: https://mitpress.mit.edu/books/econometric-analysis-cross-section-and-panel-data
Alternatively, you can load it directly into Stata using

use http://www.stata.com/data/jwooldridge/eacsap/airfare, clear


texts:
When a country purchases foreign assets, does it change the Net Capital Outflow?
This was a discussion question in my class, and a lot ended up answering that NCO increases, but I'm not so sure.
Because when you look at the definition of Net Capital Outflow, which is
Purchase of Foreign Assets by Domestic Residents - Purchase of Domestic Assets by Foreign Residents,
The left term goes up because you bought foreign assets, but the right term also increases because the foreigners also received domestic assets (currency for instance) in exchange for giving away their assets. Therefore, the two terms should cancel each other out, and the NCO should remain constant.
In addition, since NCO = NX (Net Exports), and the activity above (purchasing foreign assets) doesn't affect the NX at all, making NX constant, the NCO should remain constant as well considering this equality, which means that the amount you gave (like currency) in order to purchase the foreign assets counts as foreigners purchasing domestic assets by giving away their assets right? So shouldn't the NCO remain constant?
This is what I thought, but the majority of the class somehow thinks that the NCO increases, so I'm confused. Could anyone tell me what the correct answer is, and how to correctly interpret this? Especially the right term. When a country purchases foreign assets, doesn't this also count as foreigners having purchased domestic assets since you traded assets with assets? And if this isn't the case and the NCO actually does increase, how do you explain why the NX remains constant while NCO increases when the two are supposed to be equal?
Thanks.


texts:
We often hear that the GDP grew 2 % the past quarter, or something like that.

But we are also told the GDP grows annually about 2-3 % every year.

How can both be true? If the GDP grows 2 %  in just one quarter, surely annual growth rate should be closer to 8-10 %?


texts:
The foundation of this question is a bit vague (based on something overheard at a conference) but I'm hoping someone here can provide some clarification.

I overheard a conversation between two people at a conference saying that signaling doesn't really make sense in zero-sum games. Unfortunately, I don't have much more context than that.

I have continued to think about this statement and really can't figure out why it ``doesn't really make sense.'' The zero-sum aspect only talks about the payoffs, where the signaling aspect is concerned with how information is revealed as a function of the players' actions. I don't see why a game being zero-sum should preclude signaling.

Question: Can signaling occur in zero-sum games? Please provide a link to a paper/example if so.


texts: Existence of nash equilibria in finite games

texts:
I was going through the proof of existence of a Nash Equilibria in finite normal form games (Proof via Brouwer’s theorem) and got a question regarding the requirement of finiteness for the number of actions a player can play. In particular, the proof hints at the update equations where players "compute" their payoffs/utility of playing a best response, before going deeper into Brouwer's. I would think that, in this framework, the number of actions needs to be finite otherwise it would be impossible to compute those "utility-updates"... but is it the main point? Or am I missing something?

Edit: The proof I am looking at is: https://www.cs.ubc.ca/cgi-bin/tr/2007/TR-2007-25.pdf. The update rules are in "Theorem 23".


texts: Dynamic demand model in many good competitive markets and price optimization

texts:
This is a question about demand models, price optimization, dynamic pricing, big data, online learning, so I will cross-post in other communities.

$\mathbf{Background}$

I am interested in dynamic price optimization in the following situation:
* Let $q^d_t$ be the demand for product $d$ at time $t$. We model $q^d_t$ as a random process, which is observed at some random times $t_i$ at which the product $d$ is purchased.
* Let $p^d_t$ be the "ask price" of product $d$ at time $t$. A purchase of product $d$ at time $t$ would be made at this price.
* Let $c^d$ be the average cost of taking one unit of product $d$ to market. This includes production, storage and other fixed costs, delivery to the consumer, etc. In a first approximation we may assume that within the time horizon of the problem the costs are constant.

We can model the relationship between products demand and prices as
$$ q^d_i = \mathscr M(\mathbf p_i, \Theta^d, \mathbf{\epsilon}^q_i)  \tag{1} $$
where $\Theta^d$ is a list of parameter to be fitted, $\{\mathbf{\epsilon}^d_i \
\}_i$ are random unobserved errors, a norm (or size measure) of which we are set to minimize. The subindex $i$ is shorthand for $t_i$. Let $\mathscr M(\mathbf p_i, \hat\Theta^d, \mathbf{0}) $ be the fitted value of $q^d$ at present time.

I am working in a dynamic market, but I can assume the relation (1) changes slowly, so transaction data can be use to update $\Theta^d$ slowly.

The demand for product $d$ depends on not only on the price $p^d$ but on all other prices, i.e.: there price on some products may affect the demand of other products: some products can substitute for others, some products are "traffic drivers," etc.

The problem is to "learn" (in the data science sence) the realtionship (1), i.e.: the current "state of the market" as it pertains to product demand, and use it to set prices that maximize expected revenue:
$$ \sum_d ( p^d - c^d)*\mathscr M(\mathbf p, \hat\Theta^d,\mathbf 0 ). \tag{2} $$

There are two models of demand in terms of price that are well represented in the pricing literature, namely, the linear model and the log-linear model. Both of them are amenable to be learnt dynamically with, for example, stochastic gradient descent. Are there oher simple well represented models?

It seems reasonable to assume (2) is a concave function of prices, in which case the maximization of can be treateed within the convex optimization context. In the case of linear models of demand, the concavity of (2) reduces to verifying the matrix of price coefficients in the models induces a semiposive definite quadratic function, which suggest that a good way of guranting that is to restrict model (1) to those that will render (2) concave. My problem involves over 10^5 products (possibly over 10^6) , so computational complexity of imposing the concavity condition becomes a consideration.

The log-linear model (log(demand) = linear function of log(prices) + remainder)) for demand results in models for which verication of (2) seems untractable.

$\mathbf{Questions}$

1) Are there flexible models one can use in (1) for which (2) can be guarantied to be concave, or for which concavity can be verified with complexity less than $O(D^3)$ ? Here $D$= number of producs.
2) Is fitting those models and solving the optimization problem (2) computationally feasible in a dynamic context?

$\mathbf{Comments}$

1) Any flexible model for (1) is acceptable. My aim is to use dynamic learning. Interpretability is not an issue. Distributions of the remainders is not an issue.

2) To keep in the dynamic context, (2) need not be optimize at once. Since the relation (1) is not stationary, it would be enough to control prices dynamically to drive revenue upwards. This may relaxed the computational complexity of updating prices.

3) There are no supply constraints. Supply may be assume to be infinite.

4) Model (1) is a simplification, there are other obvious predictors of demand to be included, such as seasonality, etc.


texts: How can I obtain Leontief and Cobb-Douglas production function from CES function?

texts:
In most Microeconomics textbooks it is mentioned that the Constant Elasticity of Substitution (CES) production function,
$$Q=\gamma[a K^{-\rho} +(1-a) L^{-\rho}  ]^{-\frac{1}{\rho}}$$

(where the elasticity of substitution is $\sigma = \frac 1{1+\rho},\rho > -1$), has as its limits both the Leontief production function and the Cobb-Douglas one. Specifically,

$$\lim_{\rho\to \infty}Q= \gamma \min \left \{K , L\right\}$$

and

$$\lim_{\rho\to 0}Q= \gamma K^aL^{1-a}$$

But they never provide the mathematical proof for these results.

Can somebody please provide these proofs?

Moreover, the above CES function incorporates constant-returns-to-scale (homogeneity of degree one), due to the outside exponent being $-1/\rho$. If it was, say $-k/\rho$, then the degree of homogeneity would be $k$.

How are the limiting results affected if $k\neq 1$?


texts: Does Pareto-efficency take into account growth?

texts:
I'll try to state my question clearly:

For a given a "wealth" allocation Wt = (w1, w2, w3, ... ) for individuals I = (i1, i2, i3, ... ).

And a distribution of D= (w1/|W|, w2/|W|, w3/|W|, ... ), that is, as a percentage of the total.

Where Wt is Pareto Efficient at a given time frame  t , and W(t+1) is Pareto Efficient at  t+1 .

When there is growth such that     |W(t+1)| > |Wt|

Is Dt=D(t+1)?

If so, why? If not, how do you allocate say, capital, whose value is intrinsically linked to growth?

I understand many of my assumptions may be plain wrong or badly stated, I am still an undergrad. Sorry about that. And thanks in advance.

Further clarifications:

For each element  w  of Wt = (w1, w2, w3, ... ),

w= P * B

Where P is the price vector of a commodity bundle B.

I hope that my representation of growth as an increase in the magnitude of the W vector is correct. This is what has been bugging me the most. It's safe to assume that growth causes an increase in |W|, right?


texts: Why are elasticities defined as logarithmic derivatives?

texts:
In my economics class, we often compute the elasticity of $Y$ with respect to $X$,
$$\eta = \frac{\partial \log Y}{\partial \log X}.$$
You can compute this from the slope of a line fit to a log-log plot.

Why is it more natural to consider this quantity than the much simpler quantity
$$\eta' = \frac{\partial Y}{\partial X}$$
which is just as easy to measure? There seems to be some implicit assumption that $\eta$ is perhaps 'more applicable', maybe that it's less sensitive to the value of $X$ than $\eta'$ is, so it's more useful for extrapolation. For example, I've seen a demand curve extrapolated by assuming that $\eta$ is constant, yielding a power law. But why not assume $\eta'$ is constant, yielding a line? Neither seems particularly more natural to me.

Why is $\eta$ a more useful quantity than $\eta'$ in economics?


texts: Can banks maintain Euro accounts if the country they're in leaves the eurozone?

texts: If a country forcibly leaves the Eurozone, is it possible for banks within this country to maintain existing euro deposits?  Or does leaving the eurozone mean those deposits are automatically converted?


texts: Intuition behind the positive slope of LM curve : 'Income must increase'?

texts:
Source: by John Floyd PhD  (in Economics; U Chicago)

  The intuition behind the positive slope of LM is as follows:
  An increase in the interest rate reduces the demand for money
  and an increase
  in income increases it [the demand for money].
  To [...] [equalize] the demand for money equal to a constant money supply
   as the interest rate rises
  and we move along the LM curve,
  the level of income must increase.

Would someone please explain the bolded? It sounds too imperious and presumptuous:
how MUST a rise in interest rate increase consumers' level of income?
Eg, employers can still refuse to increase salary. Then income would NOT increase?


texts: A government running like a literal business

texts: Hopefully this doesn't get partisan, but I wanted to see where a thought experiment would go where a government stopped collecting taxes and instead fund itself by running businesses (selling products and services) alongside other private businesses out in the free market.


texts: Risk Premium in the Expected Utility Theory

texts:
Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have

$$ Eu(w+x) = u(w+E(x)-R). $$

The classical derivation of the risk premium is as follows:

A Taylor series expansion of order 2 in the neighborhood of $(\omega + E(x))$ of the left-hand side (LHS) gives

$$u(\omega+x) \approx u[\omega+E(x)] + u'[x-E(x)] + \frac{1}{2} u''[x-E(x)]^2,$$

A Taylor series expansion of order 1 in the neighborhood of  $(\omega + E(x) - R)$ of the right hand side (RHS) gives

$$u(\omega + E(x)-R)  \approx  u(\omega+E(x)) - u'R.$$

Taking expectation of the first series expansion and combining the results of the two series with the definition of the risk premium yields

$$u(\omega + E(x)) + u'E[x-E(x)] + \frac{1}{2} u''E[x-E(x)]^2  \approx   u(\omega+E(x)) - u'R.$$

This implies

$$R \approx - \frac{1}{2} \frac{u''}{u'} E[x-E(x)]^2.$$

My understanding of this derivation is that we can take a 2- or higher-order expansion of the LHS if we want the risk premium to be related not only to the variance of $R$ but also to higher moments of $R$.

However, is there any (economic) rational for the first-order expansion of the RHS? And for its different neighborhood evaluation?


texts:
My understanding is that standard models in economics assume the firm is a capitalistic firm, in the sense that it pay workers a wage but no profits. (is that right?)

I am interested in modeling cooperatives, where workers own profits and distribute them. But profits seem hard to model explicitly. Any idea how to model this? Perhaps a reference to the literature?


texts: Economic models failing to predict inflation

texts: In this video here Warren Mosler states that all economic models fail to predict inflation ("All their models show it's indeterminate"). I am looking for some references to support that claim... Or is Warren plain wrong?


texts: Correct Equation for Pooled OLS Regression (with Time Dummies and Interaction Terms)

texts:
I have a question regarding a pooled OLS regression. Basically, I’m not sure I’m writing out the equation properly.

The data is on feature films released between 2006 and 2016 (11 years); box office revenue is the dependent variable. What I’m interested in is the coefficient of the variable CritSentiment and if it increases over time (CritSentiment is a binary variable that takes the value 1 if critical reception for a film is positive and 0 otherwise).

So aside from a bunch of film-specific controls (such as production budget), I’m including yearly time dummies to control for any trend-effects, as well as interaction terms between these time dummies and CritSentiment. The coefficients of these interaction terms should measure the estimated difference between the coefficient of CritSentiment in year t and the coefficient in the (omitted) base year.

$$\textit{Revenue}_{it} = \alpha + \beta_1 \textit{Budget}_{it} + \ ... \ + \beta_{15} CritSentiment_{it} \ + \sum_{t=1}^{11-1} \gamma_t Year_t \ + \sum_{t=1}^{11-1} \delta_{t} Year_{it} CritSentiment_{it} \ + \epsilon_{it}$$

What I’m unsure about is basically just whether the above equation correctly assigns the i and t subscripts, which I find a bit confusing (especially when it comes to the intercept and interaction terms).

Thanks a lot in advance.


texts: Is it worth while to get a master's in math (or applied math) before pursuing phd in economic theory?

texts:
I'm planning to apply to phd programs in economics and I'm hoping to eventually work in academic research on economic theory, social choice theory, welfare economics or related areas. I'm wondering if doing a masters in math before applying to an economics phd would be worthwhile? Seems like it might be nice to have the math stuff down really solid, so I can focus on economics in grad school.

By the time I finish undergrad (in U.S.), I will have taken the following math courses (one semester each): Multivariable calc, linear algebra, abstract algebra, real analysis, topology, optimization, probability-statistics, basic numerical analysis with matlab, differential equations.
Econ courses that I'll have taken: year of micro, year of macro, year of econometrics, year of graduate micro.

Edit: My undergrad major is philosophy and also a joint major math-economics.


texts: Since 1980, in which years has the US debt-to-GDP declined and why?

texts: In other words, what were the factors in the reduction of the debt-to-GDP ratio?  Why did the ratio decrease during some booms and not others?


texts: Intuition for effect of interest rate changes in New Keynesian model

texts:
I am trying to understand the intuition behind the effect of an interest rate change in a simple New Keynesian model (or really in any sticky price model).
As a simple example, I take (roughly) the model in https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxnYXV0aWVnZ2VydHNzb258Z3g6MTA1YTg1NTljNjE4ZjJhNg. In this model, a fraction $\gamma$ of firms sets their price optimally for that period, and the remaining firms index their price to last period. I have the following (log-linearised) equations:

Euler equation: $\hat{c}_t = E_t\hat{c}_{t+1} - \frac{1}{\sigma}\left(\hat{i}_t - E_t\hat{\pi}_{t+1}\right)$
Labour supply: $\hat{n}_t =\frac{1}{\phi}\left(\hat{w}_t - \hat{p}_t - \sigma \hat{c}_t\right)$
Optimal pricing: $\hat{p}_t^*-\hat{p}_t = \left(\hat{w}_t-\hat{p}_t\right) - \hat{a}_t$
Inflation: $\hat{\pi}_t = \frac{\gamma}{1-\gamma}\left(\hat{p}_t^* - \hat{p}_t\right)$
Output: $\hat{y}_t = \hat{a}_t + \hat{n}_t$
Goods market clearing: $\hat{y}_t = \hat{c}_t$

There is some redundancy because I am looking for intuition. The solution to this system is
$$
x_t = E_t x_{t+1} - \frac{1}{\sigma}\left(\hat{i}_t - E_t\hat{\pi}_{t+1} - r_t^n\right) \\
\hat{\pi}_t = \kappa x_t
$$
where $x_t = \hat{y}_t - \hat{y}_t^n$ is the output gap, $\hat{y}_t^n = \frac{1+\phi}{\sigma + \phi}\hat{a}_t$ is the natural level of output, $r_t^n = -\sigma\left(\hat{y}_t - E_t\hat{y}_t^n\right)$ is the natural rate of interest, and $\kappa = \frac{\gamma}{1-\gamma}\left(\sigma + \phi\right)$.
Now suppose the central bank reduces the nominal interest rate. Assume also that there is no change to the net supply of government bonds (which are the vehicle for borrowing and saving). I know that the outcome will be a positive output gap and increased inflation. I am trying to understand how that occurs.
The standard story is that there is consumption demand by the Euler equation, so firms have to increase output, which raises their costs. The firms that can do so will raise their prices. As a consequence, there is inflation and a positive output gap.
If this is the correct intuition, where does the increased demand faced by firms actually come from? Individuals do want to consume more (Euler eq, 1), but they cannot all borrow and they are already at their optimal intratemporal margin (labour supply, 2). Individuals can't actually consume more until their incomes/output is higher. They won't work more unless real wages rise. Firms won't increase output, wages, or prices unless there is more demand. What is the mechanism?
Thanks!
Edit - I clarified that individuals borrow and save via trading in government bonds, and that the net supply of government bonds is held constant.


texts: How to prove dynamic inefficiency in the Solow model?

texts:
I know that if capital is below the golden rule level in the Solow model, then we are dynamically efficient, and vice versa.

How is that proven?


texts: Demand function for partially subsumable products

texts:
I am struggling with this question that should be simple for economists (I am not an economist at all):
There is a market with a limited number of (heterogenous) consumers with two firms, each offering a product. The two products are ‘partially’ substitutable. I am looking for demand functions to show how the two products interplay in terms of price and demand.
I remember there were some traditional models in microeconomics showing something like this:
d1= a1 – b1.p1 + c1.p2
d2= a2 + b2.p1 – c2.p2
where d and d2 show the demands and p1 and p2 denote prices of products 1 and 2 respectively.
The issues with these functions are that:

They include many unknown parameters (i.e., a1, b1, c1, a2, b2, c2);
They do not directly consider ‘partial’ substitutability;
They include prices identified by the firms, but ideally, I would also like to include ‘values’ of products (v1 and v2) identified by consumers regardless of their prices (perhaps, this is similar to what utility functions consider).

Is there any way to solve these issues by using stronger functions?
Thank you


texts:
Suppose you are given 2 models.
Model of 1 has $y$ as the dependent variable and $x$ as the independent:
$$y = \beta_0  + \beta_1 x + \epsilon$$
Model 2 has $w$ as the dependent variable and $x$ as the independent variable
$$w = \lambda_0 + \lambda_1 x + u,$$
such that both models have their own disturbance term.
Then you are given a fitted model in which $y$ is dependent on $w$.
$$y = \phi_0 + b w + e$$
Now the question is to find plim of $\hat{b}$.
I tried making $x$ the subject from model 1, plugged the $x$ in model 2 and then plugged $w$ (model 2) in fitted. Now when I took $Cov(xy)$ after all this substitution my fitted model $y$ doesn't have and $x$. I can't further solve for $plim$.


texts: Utility function must be continuous for $V(p, e(p,u) )$ to hold?

texts: Most utility functions we work with are already continuous, so I thought it was understood that it must continuous. But how would I show that if the utility function is discontinuous the identity V(p, e(p,u))=u might not hold?


texts:
Question: Represent the extensive form of the game:

Suppose, Nature chooses either Up or Down with probabilities 0.5 and 0.5, respectively.

Then Player 1 chooses either Right or Left and does not observe nature's choice.

Finally, Player 2 chooses either G or H. Unlike Player 1, Player 2 observes the choice of Player 1 prior to making his choice. Player 2 also observes nature's choice if Player 1 has chosen Right but does not observe nature's choice if Player 1 has chosen Left.

My take:

Is this correct? I am not really sure about the instructions in bold.


texts: Can anyone help me understand the budget constraint of an investor in complete market?

texts:
In the problem below, u is a utility function; $\beta$ is a discount factor; pc(s) is the price for a contingent claim for state s. c is initial consumption and and y is initial wealth. s represents a specific state.
$$max \ u(c) + \Sigma_s\beta\pi(s)u[c(s)]$$
$$ s.t. \ c + \Sigma_s pc(s) c(s) = y + \Sigma_s pc(s)y(s)$$

Can anyone help me understand the budget constraint?


texts: Factoring Technology into Economics models

texts: There has been tremendous improvement in technologies in recent years. My question is: have economists been able to properly evaluate and factor the values of recent innovations in the technology sector? We often hear about various economics indicators such has Manufacturing PMI and industrial productions, but these indicators often fail to mention technology related jobs or the values of recent innovations. Can anyone help me understand how technology is valued?


texts: How can you find all parameter estimates are statistically significant but without performing any sophisticated calculations?

texts: I have a question that contains a list of parameter estimates and their related standard errors. It then goes on to ask that I explain how I know all parameter estimates are statistically significant at a 5% significance level, but without performing any 'sophisticated calculations'. Does this mean I have to compare the standard errors to the estimators or do I find their t-values?


texts:
Does stock picking work? Why/why not? What does the research say about it?

(I was expecting that this should already have been asked and looked quite extensively for such a question but couldn't find anything)


texts: Imperfect Substitutes and Utility Funcitions

texts: The utility function for perfect substitutes is defined as U(X,Y) = aX + bY. If the two goods X&Y are imperfect substitutes what would be their utility function?


texts: Inflationary recession vs Deflationary recession

texts: I heard the terms deflationary recession & inflationary recession in a podcast and would like to understand what it means, what causes them and past examples.


texts: own and cross elasticity for many products

texts:
This publication uses this formula to fit a model to predict the demand of a product A:

Log_Demand_A = constant + b1*log_Price_A + b2*log_Price_B + b3*Promo_1 + b4*Promo_2 + b5*log_Price_A*Promo_1 + b6*log_Price_A*Promo_2

I have 2 questions.

What is done in practise when businesses sell hundreds of products? Could one fit several models for product A (e.g. own for own elasticity and let's say we have 2 other products B and C, another one for the interaction A->B and another one for the interaction A->C and the combine the demand prediction using some kensemble method).
Are the 2 promos in the above formula specific to product A (i.e. do not necesaarily apply to product B)?


texts: Intuition for why $EV>CV$ for a normal good

texts:
I understand the mathematical proof and the graphical illustration behind this property ($EV>CV$ for the variation in the price of a normal good), but I still do not understand the economic intuition. Can anyone explain, in intuitive terms, why the comparison between $EV$ and $CV$ is given by the sign of the wealth effects?

Edit: there seems to be different definitions of $EV$ and $CV$. Here are the ones that I use. Following a change in price from $p^{0}$ to $p^{1}$, the income being fixed at $w$, $EV$ is defined by
\begin{equation*}
v(p^{0},w+EV) = v(p^{1},w)
\end{equation*}
whereas $CV$ is defined by
\begin{equation*}
v(p^{0},w) = v(p^{1},w-CV).
\end{equation*}
For these definitions, if I am not mistaken, if the good is normal, then $EV>CV>0$ for a price decrease and $0>EV>CV$ for a price increase.


texts: Does working abroad cause less unemployment? Or is it actually harmful (directly or opportunity cost)?

texts:
This question is from subjective origins but is (supposed to be) objective.
The context of this question arises from people in third world countries going abroad to work. Often they are seen as money-hungry people who don't 'love' their country (unless they are, say, physicists who do research abroad due to poor facilities or engineers or financiers simply looking for higher salary or something like that).
I was thinking that those people help their country through foreign remittances. I later additionally thought another help done is that whatever job they would have done in the country is likely ('likely' is probably the key word here) going to be replaced by someone else who would otherwise have been unemployed or underemployed would have that job which in turn likely (hooray key words) means that someone else who would otherwise have been unemployed or underemployed would have that job, etc.

If the answer is no (working abroad necessarily causes less unemployment), under what kinds of situations might this be the case?
If the answer is no (again, working abroad necessarily causes less unemployment) due to geographical variations, you may consider third world countries.

Edited to add: Also my concern is understanding whether or not like: are the ones going abroad necessarily like money-hungry people who do not 'love' their country or something? If you choose to work in your country, then do you necessarily 'love' your country more or 'serve' your countrypeople more than if you didn't work in your country? Of course 'love' and 'serve' are subjective, but it's like I wanna understand if somehow working abroad is like more beneficial to the individual but harmful to the country or something. To me, it seems like going abroad benefits everyone at least from 3rd to 1st world.


texts: Are there any drawbacks to a hypothetical climate policy?- Carbon tax for reducing Income tax

texts:
Disclaimer: I do not have a formal education in economics

Here is the idea of my hypothetical policy: graduated over a period, say about 10 years or longer, the income tax is phased out and a carbon tax is implemented, such that the revenue lost from the income tax is gained by the carbon tax.

Possible strengths:

Increased consumption
Increased incentive for the public to invest in renewable energy
Increasing the weight of the penalty of wasted fuel.

Possible weaknesses

Reduction of the tax base
Unequal tax burden on oil companies, and those that rely heavily on oil
The potential that the graduated increase in carbon tax and decrease in income tax will not be fulfilled (non-cooperation).

Are there any weaknesses, that I, in my limited economic understanding, have overlooked?


texts: Economic and Statistical Significance Of Coefficient

texts:
I want to know If I am comprehending these terms correctly
Summarizing the difference between economic and statistical significance of coefficients (Describing the terms, process of assessing each with formulas)
Statistical Significance is driven from a large estimate or small standard error where we look at t-tests or p-values to determine whether or not to reject a null hypothesis. While Economic significance looks more at the magnitude and sign of the estimated coefficient, if the numbers turn out to be so small then the x variables do not really affect the y variable.
The process of assessing with formulas For Statistical significance wouldn't assessing the process with formulas just include the formulas to calculate t-test and p-values to determine if we can or cant reject the null. Such as the t*, critical values, p-value
For Economic significance isn't it =0+11+....+. and dealing with 2?
Question 2 Why one does not necessarily mean the other?
(For Whoever marked my last one as a duplicate I don't see why, My question asks about Statistical Significance and Economic while the other one just talked about economic, and I looked at his question and feel maybe it could answer 10% of my question) If whoever first commented could respond again, the answer was so helpful I wanted to show my friends but got burdened this morning waking up to seeing the post was gone.
The previous question got "duplicated" by this "Is there any standard measure of economic significance?" post.


texts: Why is devaluing your currency good for exports?

texts:
I have the typical answer:

"A cheaper currency means exports will go up because it's cheaper to buy from us!"

Yeah, sure, but that's obviously full of holes.

Let's have a simple situation:

We have China (yuan) and America (\$).
America needs 100 "item" from China every year.
One "item" costs 1 yuan.

Now, let's say currently (situation A):

The rate is 1\$:1yuan
That means America pays \$100 every year.

In situation B, we devalue the Yuan:

The rate is 1\$:2yuan
That means America now does one of the following:

Only pays 50\$ and still gets the same 100 items.

China basically just lost 50\$ a year. China loses.

Still pays 100$ but now gets 200 items instead:

China gets the same 100\$ but is now giving out 200 items instead. China loses.

So, how exactly would China ever benefit from devaluing its currency? It doesn't make any sense to me, you're literally just giving more exports, you are not getting anything more in return.

The only reason I could think of, is that they actually do think that, in order to stay competitive, they need to sell 2 items for 1$ instead of only 1 i.e. they do think it should be that cheap and they don't want the floating currency price to interfere with what they think should be the correct price for their products.


texts:
If X is finite, define this function $u : X \rightarrow  \mathbb{R}$ by $u(x) = |\{z\in X:z \prec x \}|$. Prove that $u$ is a utility function for $\succsim$.

Is it sufficient to prove that the relation is transitive and complete?
By Lemma:  If $\succsim$ has a utility function, then it is transitive and complete.


texts: For a paper I was using the micEconCES package to estimate the CES production function for a country at the aggregate. For a two-input function with capital and labour I used for the variables the Perpetual Inventory Method to construct aggregate capital, labour hours and GDP for output. I used methods provided in the package to do the estimation. But now I am kind of unsure, what I have to check the data for f.e. autocorrelation, multicollinearity etc. or do I even have to check for that?


texts: How could the Euro zone be broken up in an ordered way?

texts:
Let’s assume that the members of Euro zone all agreed that it would end in 18 months time with each country getting its own currency.

What process could be put in place to allow this to happen without causing of lots instability?


texts: Can I draw a smaller sample from one treatment group?

texts:
in an RCT, I have 3 different treatment groups and one control group. The size of the control group is around 1000 while the size of other groups are just above 300.

To test balance I used ANOVA and Welch test, which show that several variables are unbalanced. Can I draw a smaller random sample (400) from the control group so that the sizes of all groups are relatively equal?

Actually after doing that only one variable is unbalanced. So would it cause any problems if I want to draw a smaller sample just for more balance? Thanks!


texts:
Suppose I have two teachers: Adam and Bob. Suppose Adam takes 20 hours to lecture and 30 hours to grade, while Bob takes 100 hours to lecture and 60 hours to grade.

In absolute terms, Adam is clearly a better teacher because he does the same work in less time. But supposedly they could still benefit from trade and specialization of labor.

Why does only relative price and not absolute price matter in international trade models?


texts: Macroeconomic formulas for global limited raw material economy exist?

texts:
Macroeconomics basic formulas are referring to a model in which the raw material are unlimited.
Also the efficiency of production is a consequence of the pressure done by consumers (that buy the most cheap product, between the ones with the same level of quality).

exist formulas that try to model an economic system that "expand" toward the maximization of efficiency in using the limited quantity of raw resources?

(provided that we can describe the actual basic model like one that "expand" toward the maximization of quantity of production and quantity of selling, by total units or by total revenue).


texts:
I've searched around the web for awhile now and I'm beginning to think this might be an unanswerable question. I want to know if there is a theoretical way to determine the worth of a particular good, either cash or item, independently of average purchase price (ideal selling so exactly whoever wants one and can pay for it at the price will get it).

The specific case is a virtual economy such as a video game, where there might be no way to get real world cash into or out of the game, but you want to determine if the value of SuperSwords is right to buy and what those swords are likely to be worth in the future. Is there a general formula for this situation?

A secondary case that I also wish to know about is setting the price (in-game stores) of such items. While this may push the topic more towards video game design rather than economics, I think that the basis of a price is more heavily in the modeling an economy area than a game area. What will be the best way to adjust the pricing? The four factors controlled are price sold by the store, price paid by the store, how many the store can buy and how many the store can sell.


texts: Markov decision processes, contractions and value iteration

texts:
I am reviewing Markov decision processes (MDP) and there is something I am missing with respect to the contraction argument. I am pretty sure it is a silly mistake somewhere (maybe computational), but anyways, I cannot figure it out. Here it goes.

Consider a simple MDP with two states and two actions defined as follows.

$$ r(s,a) = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix},$$

$$ P(s,s',1) = \begin{pmatrix} 1 & 0 \\ 1 & 0 \end{pmatrix},$$

$$ P(s,s',2) = \begin{pmatrix} 0.5 & 0.5 \\ 0.5 & 0.5 \end{pmatrix},$$

$$ \beta \in (0,1). $$

Now suppose we start with two guesses for the value function

$$ V_1 (s) = \begin{pmatrix} 100 \\ 0 \end{pmatrix}, $$

and

$$ V_2 (s) = \begin{pmatrix} 0 \\ 1 \end{pmatrix}. $$

If we iterate on these approximate value functions using the Bellman operator we get

$$ T(V_1) = \begin{pmatrix} \max_a \begin{cases} 1 +  100\beta, \qquad \text{ if }  a = 1, \\
                                                 1 +  50\beta,  \qquad \text{ if }  a = 2.                                               \end{cases}\\
                             \max_a \begin{cases} 1 +  100\beta, \qquad \text{ if }  a = 1, \\
                                                 1 +  50\beta,  \qquad \text{ if }  a = 2.                                               \end{cases} \end{pmatrix} =
\begin{pmatrix} 1 + \beta 100 \\ 1+ \beta 100 \end{pmatrix}$$

and

$$ T(V_2) = \begin{pmatrix} \max_a \begin{cases} 1 +  0\beta, \qquad \text{ if }  a = 1, \\
                                                 1 +  0.5\beta,  \qquad \text{ if }  a = 2.                                               \end{cases}\\
                             \max_a \begin{cases} 1 +  0\beta, \qquad \text{ if }  a = 1, \\
                                                 1 +  0.5\beta,  \qquad \text{ if }  a = 2.                                               \end{cases} \end{pmatrix} =
\begin{pmatrix} 1 + \beta 0.5 \\ 1+ \beta 0.5 \end{pmatrix}$$

But then for $\beta$ close enough to $1$ and taking for instance the Manhattan norm, we have

$$ d(V_1(s),V_2(s)) \approx 101,$$

and

$$ d(T(V_1(s)),T(V_2(s))) \approx 199.$$

Now that sounds weird to me because I thought $T$ was supposed to be a contraction mapping. Where did I screw up? Is there a mistake in my computation? I am forgetting to apply an important hypothesis? Or am I misunderstanding something about contraction mappings?


texts:
I'm reading a book about the economic development of South Korea during the 'miracle' period.

One of the points the author makes is the following:

  A major source of industrial disputes was delayed wages, a mechanism
  whereby companies attempted to pass the burden of slack business on to
  their workers by withholding wages (just as [they] passed the slack on
  to dependent sub-contractors by delaying payments).

I get that slack is unused inputs, which would in this case be the wage laborers and the capital that the sub-contractors produce. But what's the point of withholding wages in response in having excess productive capacity? If it matters, the companies of interest here are the Chaebol conglomerates.

(the book is The Politics of Economic Reform in South Korea: A Fragile Miracle)


texts: Marginal Utility with Supply and Demand Curves

texts:
Can someone explain how the equilibrium points in the image below (source: The Foundations of Econometric Analysis) represent marginal utilities.  I have read about the relationship between the marginal rate of substitution and the ratio of marginal utilities in terms of the theory of consumer behavior but have not seen marginal utility in this context.  I imagine this use is similar but my logic is failing me.

The figure represents a demand curve progressively shifting to the right with a lagging supply.


texts: Why is sugar cane still harvested manually in Brazil?

texts:
I read that up to 70% of Brazil's sugar cane in the Sao Paulo area is still harvested manually. Some workers are paid $1.50 per tonne. Why is it still being cut manually? Some possibilities:

(1) farm owners lack the capital to buy mechanical harvesters

(2) human labor is cheaper

(3) regulatory or legal obstacles are blocking the use of harvesters


texts: I have some doubt regarding gdp sector, while measuring gdp by income approach, we add depreciation. My doubt is: does the cost of goods that go into replacement of existing worn out capital is only treated as depreciation? Or do we also add the depreciation expense of all existing and serving goods, which have not worn out?


texts: Market clearing condition with Walras law

texts:
I have a diamond overlapping model

The question is as follows

  Let us consider an infinitely lived production economy populated at time t by $N_t$ identical and perfectly competitive adult individuals. Each agent is born from a single adult parent and lives for two periods. Each youth is part of his parent consumption and each adult is endowed with 1 unit of time that can be allocated between child rearing and market activity. At time t, the budget constraint of the representative adult individual can be written as:
  $$c_t\le d_t +w_t e_t$$
  where e denotes the time allocated to work, w stands for the real wage, d represents the real dividend income that corresponds to a fraction 1/N of the aggregate profit $\pi$, and c is the consumption level. Under the assumption that the cost or raising each child is a fraction $\tau$ of the parental time endowment, the time constraint faced by the representative household at time t is:
  $$\tau n_t + e_t=1$$
  where n denotes the number of children born at time t. The preferences of an adult individual at time t can be described by a logarithmic utility function U which depends on his consumption level and the number of children:$$u(c_t, n_t)=ln c_t + \gamma ln n_t$$ where γ>0. Let us assume that there is a single perfectly competitive firm using the following
  Cobb-Douglas production function at every time t: $$ Y_t= AX_t^{1-\epsilon}L_t^{\epsilon}$$
  where ε∈(0,1) stands for the output elasticity with respect to the land input, A>0 denotes a productivity parameter and Y represents the aggregate output. The stock of land is fixed: $\bar{}$ = $_t$ and the labour input $_t$ is defined as the aggregate amount of time allocated to work. The law of motion of the adult population from time t to t+1 is given by:
  $$N_{t+1}=n_tN_t$$
  The question asks to write down the utility maximization problems for both adults and firm and I need to derive both competitive labor supply and labor demand sechedules respectively.

My answers are respectively:

$d_t$ is dividend income and $d_t=\pi/N$
For agent problem:

$$max [ln c_t + \gamma ln n_t]$$

Subject to $ c_t\le d_t+ w_t (1-\tau n_t)$

Lagrangian $L= ln c_t + \gamma ln n_t +\lambda [c_t- d_t- w_t (1-\tau n_t)]$

FOCs

(1) W.r.t $c_t$:  $(1/c_t)+\lambda =0$

(2) w.r.t $n_t$: $\gamma / n_t +\lambda w_t \tau =0$

(3) w.r.t. $c_t-d_t-w_t+w_t \tau n_t=0$

By (1) and (2):

$$\frac{(1/c_t)}{\gamma / n_t }=\frac{\lambda}{\lambda w_t \tau}$$

So, $c_t= n_t\tau w_t$    …(4)

When substitute (4) into (3)

$n_t\tau w_t-d_t-w_t+w_t \tau n_t=0$

$$n_t=\frac{\pi /N+w_t}{2\tau w_t}$$

which is labor supply schedule.

For firm’s maximization problem

$$max [Y_t-w_tL_t-X_tr_t]$$

$$max [Y_t= A\bar{X}^{1-\epsilon}L_t^{\epsilon}—w_tL_t-\bar{X}r_t]$$

By FOC w.r.t. $L_t$

$\epsilon A\bar{X}^{1-\epsilon}L_t^{\epsilon -1}-w_t=0$$

Then $$L_t= (W_t / \epsilon A)^{1/(1-\epsilon )}$$
which is labor demand sechedule.

————

So far, I have written all question with my answers in order to give information about the general framework of the question. And I will be glad if you let me know when see any mistakes so far. But my actual question is posted below:

    how can I write the equilibrium conditions on the goods’ market at time t and how can I show that it is equivalent to the labor market clearing conditions according to the Walras law?

I do that

For labor market clearing: $N_{t+1}=L_t$

Then, $$N_{t+1}/N_t= L_t/N_t$$

$n_t=e_t={Nw_t-\tau \over 2N}$

But after that, I cannot proceed my solution. Help me to do this part?

Thank you.


texts: $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$, then the preference is linear?

texts:
$x,y,a$ are vectors in $\mathbb R^n$

We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero.

We want to prove (or disprove by counterexample) that:

Suppose $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$,

Then the preference is linear.

One definition of linear preference is that $x\sim y$ implies $x+a\sim y+a$ for any $x,y,a$.


texts: Price Synchronization in the Calvo Model

texts:
In the paper Gorodnichenko, Sheremirov and Talavera (2014) the authors compute empirically the degree of price synchronization across different goods. In a nutshell their definition of synchronization is given by:
\begin{equation}
sync^h_i = \frac{(A− 1)}{(B − 1)} \text{ provided $A > 0$ and $B > 1$}
\end{equation}
where $A$ is the number of sellers of good $i$ that change their prices and $B$ is the total number of sellers of good $i$. The measure is computed over an horizon $h$ in weeks.

They then compare this empirical measure with what would be implied by the Calvo (1983) model of price adjustment. In page 16 they argue that the degree of synchronization at horizon $h$ in the Calvo (1983) model is given by:

\begin{equation}
sync_{calvo} = 1 - (1 - \bar{f})^{h+1}
\end{equation}

where $\bar{f}$ is the median frequency of price adjustment. I have two questions regarding the last equation:

1) Why does the calvo model imply this degree of price synchronization?
2) What should be the frequency at which $\bar{f}$ is computed? Is it annual? Weekly? Something tells me it should be a daily measure of the frequency of price adjustment ... But if that is the case the figure 2 on their paper below, implies that a 0 week horizon, $\bar{f}$ should be 0.2. I have no idea where this number comes from (definitely does not seem consistent with their estimates of price adjustment in table 5).


texts: Competitive equilibrium in an exchange economy with lexicographic preferences

texts:
I am really stuck with this problem and not able to approach it. Any help will be much appreciated.

I tried to draw edgeworth box with initial endowment point. I do know that for competitive equilibrium, tangency condition must be met such that both utility curves are tangent at equilibrium point. But here, i am not able to identify utility curves. Please help.

Consider an exchange economy with two agents,1 and 2 and two goods X and Y. Agent 1's endowment is (0,10) and Agents 2's endowment is (11,0). Agent 1 strictly prefers bundle (a,b) to (c,d) if,either a>c or {a=c and b>d}. Agent 2 strictly prefers bundle (a,b) to (c,d) if min{a,b} > min{c,d}. For both agents, we say that bundle (a,b) is indifferent to bundle (c,d) if, neither (a,b) nor (c,d) is strictly preferred to each other.

Q. This exchange economy has:
a)one competitive equilibrium allocation.
b)two competitive equilibrium allocations.
c)infinite number of equilibrium allocations.
d) no competitive equilibrium allocations.

Answer : a


texts:
This is a question related to the question: Kuhn-Tucker optimization problem and game theory .The question is: Some cultures emphasize more social interaction more than others. Is there a role for culture in the model?

My solution is:

Maximization of the social function with respect to $t_{12}$ and $t_{21}$

max aln( T - $t_{12}$+ $t_{12}$$t_{21}$) + (1-a)ln (w(T-$t_{12}$)) +aln( T - $t_{21}$+ $t_{12}$$t_{21}$) + (1-a)ln (w(T-$t_{21}$))

and the FOCs are:

a($t_{21}$-1)/(T -$t_{21}$ +$t_{12}$$t_{21}$) + a$t_{21}$/(T -$t_{12}$ +$t_{12}$$t_{21}$)=(1-a)/(T - $t_{21}$)

and

a($t_{12}$)/(T -$t_{21}$ +$t_{12}$$t_{21}$) + a(-1 +$t_{12})$/(T -$t_{12}$ +$t_{12}$$t_{21}$)=(1-a)/(T - $t_{12}$)

But I cannot find the optimal solutions. Please share your ideas with me.


texts: Comparative statics question with an application

texts:
In the state of Mexas, two politicians (Mr. BO, or "Politician 1" and Mr. TC, or "Politician 2") are competing intensely for a senate seat. The two politicians spend on advertising to increase the number of supporters. A political consultant finds that the optimal advertising expenditure of Mr. BO, $S_{1}$, depends on the spending $S_{2}$ by Mr. TC and a "likability" parameter $\alpha$ that influences the popularity of Mr. BO in Mexas: $$\text{Equation 1:  }S_{1} = f\left ( S_{2}, \alpha \right ),$$
where $f:\mathbb{R}_{+}^{2}\rightarrow \mathbb{R}$ is twice continuously differentiable, $0<\frac{\partial f\left ( S_{2}, \alpha \right )}{\partial S}<1$ and $0<\frac{\partial f\left ( S_{2}, \alpha \right )}{\partial \alpha}<1$ for all $S_{2} \geq 0$ and all $\alpha \geq 0$.

The optimal expenditure of politician 2 depends on the spending $S_{1}$ of politician 1 and a "redness" parameter $\beta$, which influences how many people would stick to Mr. TC: $$\text{Equation 2:  }S_{2} = g\left ( S_{1}, \beta \right ),$$
where $g:\mathbb{R}_{+}^{2}\rightarrow \mathbb{R}$ is twice continuously differentiable, $0<\frac{\partial g\left ( S_{1}, \alpha \right )}{\partial S}<1$ and $0<\frac{\partial g\left ( S_{1}, \alpha \right )}{\partial \alpha}<1$ for all $S_{1} \geq 0$ and all $\beta \geq 0$.

The equilibrium values of $S_{1}$ and $S_{2}$ are given by the solution of the simultaneous equations (1) and (2). Suppose that there is a unique solution $S_{1}^{*}>0$ and $S_{2}^{*}>0$.

Does an increase in $\alpha$(holding $\beta$ constant) necessarily increase or necessarily decrease $S_{1}^{*}$? Explain.

My attempt: Here I have used Implicit Function Theorem to answer the question, as we are essentially looking for the comparative statics of $\frac{\mathrm{d} S_{1}^{*} }{\mathrm{d} \alpha }$.

Since from equation 2, $S_{2}^{*} = g\left ( S_{1}^{*}, \beta \right )$, I substituted $S_{2}^{*}$ in equation to obtain $$S_{1}^{*} = f\left ( g\left ( S^{*}_{1}, \beta \right ), \alpha \right ).$$ Then since $$S_{1}^{*} - f\left ( g\left ( S^{*}_{1}, \beta \right ), \alpha \right ) = 0 \equiv F,$$
I can apply the Implicit Function Theorem (IFT) to derive $\frac{\mathrm{d} S_{1}^{*} }{\mathrm{d} \alpha }$.

So $$\frac{\mathrm{d} S_{1}^{*} }{\mathrm{d} \alpha } = - \frac{\frac{\partial F}{\partial \alpha}}{\frac{\partial F}{\partial S_{1}}} = - \frac{\frac{\partial f\left (  \right )}{\partial \alpha}}{1 - \frac{\partial f \left (  \right )}{\partial g} \frac{\partial g \left (  \right )}{\partial S_{1}^{*}}} \frac{>}{<} 0.$$

Since we do not know the sign of the derivative $\frac{\partial f \left (  \right )}{\partial g}$, the effect of $\alpha$ on $S^{*}_{1}$ is ambiguous.

Does my answer make sense?


texts: I cannot find for this Simple shared effort level game

texts:
Each player can contribute to the project with non-negative effort.

Player 1's utility is $u_1=e_1(1+e_2-s\cdot e_1)$ where $s\in [0,1]$.

Player 2's utility is $u_2=e_2(1+e_1-e_2)$

For case 1, each player contributes to the project simultaneously.

For case 2, player 1 moves first then play 2 moves next

I cannot find a Nash equilibria (SPNE for case 2) if $s$ is less than  $1/4$.

If I draw best a response diagram, the two best response functions do not intersect. But I don't think that $e_1=0$, $e_2=0$ is a Nash equilibrium, since they have would have an incentive to exert more than $0$ effort.

Can $e_1=\infty$, $e_2=\infty$ be a nash equilibrium?


texts:
My setting is the following.

I have a sequence of  games $\lbrace G_n \rbrace$ in which the strategy space is $S=[0,1]^2$, there are two players $(I=\lbrace 1,2 \rbrace)$, and payoff functions are given by the continuous (no other restrictions so far) functions $U_i^n(x_1,x_2)$ for each player $i=1,2$. That is, each game is  defined by $G_n = (U^n, S,I)$.

Now, I know that the payoff functions $U_i^n$ converge pointwise to a (discontinuous) limit $U_i$. I therefore write down the 'limit game' $G = (U,S,I). $ We can write down a correspondence that maps a game to its nash equilibria. Call that correspondence $EQ$, and we define, for a particular game $G_n$, that $EQ(G_n) = \lbrace (s_{n1}^*, s_{n2}^*), (s_{n1}^{**},s_{n2}^{**}) \dots\rbrace $ where the right hand side is the set of (potentially infiite) nash equilibria for the game $G_n$ and, generically, we allow each equilibrium strategy $s_{ni}$ to be a mixed strategy. That is, a probability measure over $[0,1].$

I then analysed the limit game, and have found a unique mixed strategy nash equilibria in that game. That is, $EQ(G) = \lbrace (s_1^*, s_2^*) \rbrace$.

I do not have closed form solutions for the equilibria, $\lbrace (s_{n1}^*, s_{n2}^*), (s_{n1}^{**},s_{n2}^{**}) \dots\rbrace $, of the games in the sequence $\lbrace G_n \rbrace$. Naturally, though, I would like to say something about how the equilibria converge to the equilibrium of the limit game.

My questions are (to start) as follows.

Given the pointwise convergence of payoff functions $U^n \rightarrow U$, in what sense can I say the games $\lbrace G_n \rbrace $ converge to the limit game $G$?
What conditions do I need on the equilibrium correspondence $EQ$ so that I can say something about the convergence of the equilibrium strategies? That is, am I able, with some argument, to establish that there exists a sequence of equilibria that converges to the equilibrium of the limit game in some sense. That is, $\lbrace (s_{n1}^*, s_{n2}^*)\rbrace_{n=1}^\infty \rightarrow \lbrace (s_{1}^*, s_{2}^*)\rbrace$, perhaps in the weak sense, perhaps in the strong sense, or perhaps in some other sense.

Any help or references are greatly appreciated.

Edit: clarified the notation and question.


texts: Principal Components Analysis in Economic analysis

texts:
I have a data set of annual prices of various energy carriers over several decades. I want to estimate a model of output using these price series - I guess, I will do a co-integration analysis. There appears to be a high positive correlation among the price series.

Would it be appropriate to do a PCA and use the first component as an
explanatory variable assuming it captures most of the variation among
the price series?
How well is the application of PCA accepted in
empirical research in economics?


texts: How much is someone willing to pay to own a monopoly?

texts:
I'm currently working on a problem from Intermediate Microeconomics Workouts by Varian and I've become stuck on a particular question to do with monopolies.

We are given the demand curve for a monopolist:

$$ q = 160-2p $$

and the total daily costs:

$$C = 2000 + 10q$$

From this, I've found the profit-maximising price, quantity and daily profit which are as follows:

$$p* = 45$$
$$q* = 70$$
$$\pi* = 450 \text{ per day}$$

Now, the question I'm stuck on is: If the interest rate is 10% per year, how much will someone be willing to pay to own the monopoly?

My first approach was to simply multiply the total profits per day times 365 days times 1.1 to get the yearly profits with interest, but apparently that's incorrect.


texts: Advice for finding literature for thesis

texts: I have to write my bachelor thesis in the coming months and I was planning on replicating one of the leading papers of the last years in the field of macro economics. Problem is that I am insufficiently acquainted with the literature and my supervisor does not want to help me in any way with regards to the topic/research question. My hope is that the community could advise me on what the most important/influential papers have been the last 5 or so years in the field. Any help is appreciated.


texts: What does it mean that households provide the four factors of production?

texts:
I've learned that the factors of production are Labor, Land, Capital and Entrepreneurship. I've also learned that households, or units of people living under one roof, supply these resources.
But I'm confused because I can only understand how a household can provide Labor and Entrepreneurship. When does a firm ever pay rent to a household for the use of land? Don't they pay other firms?
Doesn't capital usually come from other firms as well? If a publishing company invests in computers, they get them from Microsoft--not any household, right?


texts: Does stronger regulation of economic activity impede economic growth in constitutional democracies with basic constitutional rights?

texts:
Given similar democratic constitutions and basic constitutional rights such as property rights, freedom of speech, freedom of press etc and the definition of regulation according to OECD:

Regulation is broadly defined as imposition of rules by government, backed by the use of penalties that are intended specifically to modify the economic behaviour of individuals and firms in the private sector.

Is there a relationsship between regulation of economic activity and economic growth? Are there any reviews / meta analysis?


texts: Why are Americans at the top of nearly every field?

texts:
I live in India, and having spent several years in America before returning, I noticed that Americans dominate in nearly every sphere of human activity. For example, the US seems to be blessed with the best musicians, the best sportsmen and sportswomen, the best scientists, and so on.
The significant difference between the two countries, economically speaking, is that the USA is strongly free-market, while in India has had socialist leanings for most of her history.
I don't want to broadly compare the two systems or the two countries right now, or even talk about brain drain. I merely want to know if there is any theory in the free-market framework that says that people with niche talents will have their abilities put to fuller use in a market economy. Is there any logic to the market economy that makes such a thing likely, or even inevitable? I suspect Adam Smith might have something to say regarding this phenomenon.


texts: Possible regression models for a dependent variable that is a proportion

texts:
I am writing an applied econometrics paper. The dependent variable is a percentage of people who answered in the affirmative to a survey question asked in 60 different countries.

One possible model is a beta regression model for proportional dependent variables.

What are some other methods that are suitable for proportional dependent variable regression analysis?


texts:
This question isn't about asymmetric information per se but rather one of the assumptions. Consider a market for second hand cars; there are lemons (low-quality cars) and plums (high-quality cars).

For lemons, the valuations are: $V_{b} = 1500 $ and  $V_{s} = 1000$. The subscripts denote buyer (b) and seller (s).

For plums: $V_{b} = 4000$ and $V_{s} = 3000$

The buyer knows that there is an equal amount of each car (i.e., the probability of the car being high or low quality is 50%) but she doesn't observe the quality. This results in market failure because the buyer is willing to pay

$\frac{1}{2}(1500 + 4000) = 2750$

Therefore the sellers of plums leave the market because $2750 < 3000$ and only sellers of lemons remain. And now the buyer is only willing to pay 1500, therefore only lemons will be traded.

What is confusing me is that it seems like we are assuming that the buyer knows the sellers valuations. I.e., the buyer knows that because the seller values plums at 3000, and the buyers expected valuation is below this, those sellers will leave the market. Am I misunderstanding something or is this the actual assumption in this case?


texts: Why labour, capital, and output levels cannot be pinned down in perfect competition?

texts:
Consider a firm producing with the following technology:

\begin{equation}
 Y = AL^{\alpha}K^{\beta}
\end{equation}

Assuming that factors are paid their marginal contribution to output, it can be shown that the optimal factor choice for this firm is:

\begin{equation}\label{eq:k-l ratio}
 \frac{L^*}{K^*} = \frac{\alpha}{\beta}\frac{r}{w}
\end{equation}

(this comes from finding each factor's payment, and combining them)

Thus, the furthest we can go in terms of characterising the equilibrium in this economy/firm relates to the optimal capital-labour ratio. In effect, nothing can be said about the level of inputs and outputs, $L^*$, $K^*$, or $Y^*$.

This is not the case if there is just one input. For instance, if $Y=AL^\alpha$, then

$$L^*=\left(\alpha A\frac{p}{w}\right)^{1-\alpha}$$

The reason is not related to the degree of returns to scale, as this is not constrained. It is not related to elasticity of substitution either, as in the case of a CES, it is also the capital-labour ratio which is solved for. Here, the solution is

$$ \frac{L^*}{K^*} = \left(\frac{\alpha}{1-\alpha}\frac{r}{w}\right)^\sigma $$

So, the question is, why can we not pin down the level of optimal inputs and output? Is this because we have treated factor prices as exogenous, so we are missing the supply side of each factor market?


texts: Monetary policy takes medium run time to take effect. Why study it in short run?

texts:
Well I'm reading a book on the IS-LM model.
At the end of the chapter, page 125 in my edition, the author presents one paper showing some graphs where the monetary policy (monetary contraction - increasing 1% of the federal funds rate) influencing output, but with its greatest impact only being felt after 4 quarters, and continues well into the 8th quarter.
At the same time, when the impact of the monetary policy is the greatest, is when the price level also begins to noticeably change.

According to the author, since in the IS-LM model we've assumed that the price level is given, the fact that the price level only begins changes at 4th quarter, is a good support for our assumption.

Well, my question then is, why should we study the monetary policy as if it had the same time to impact as fiscal policy in the short-run, when the graphs support more the medium-run impact? Or is it a matter of magnitude of the policy at hand?(The Central Bank can move the interest rate with a lot more leeway than just a 1%)


texts: What would be the economic effect of widespread instances of individuals paying off consumer debt?

texts:
In light of the economic impact of the recent shutdowns in response to COVID-19, the Australian Government is considering bringing forward planned tax cuts, that were do to be implemented gradually over the next five years. The tax cuts themselves aren't too large compared to other economic stimuli currently in action, but I read the following statement on a Guardian article:

The Australia Institute paper, by senior economist Matt Grudnoff, concluded that bringing forward the income tax cuts was an “ineffective stimulus”.
He cited the “simple fact of economics that high income earners are more likely to save or pay down debt with the tax cuts, rather than spend the extra funds to help stimulate the domestic economy”.
“A more effective way to stimulate the economy would be to invest heavily in direct employment programs or focus on supporting those who are doing it tough by maintaining or increasing the current rate of the jobseeker supplement.”

This left me wondering what happens to the wider economy when people decide en masse rather than spending their disposable income on consumer goods/services, to instead  pay down their debt and save/invest?