texts: Signalling models and out of equilibrium beliefs

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Consider the simplest version of the Spence signalling model. There are two types of worker, with either productivity $\theta_H$ or instead productivity $\theta_H < \theta_L$. The proportions of the workers are $p_H$ (share of high types) and $1 - p_H$ respectively. Risk-neutral and competitive firms pay wages that may depend on a worker's education level $e \in \{0, 1 \}$. Finally, getting education ($e = 1$) costs $c_H$ for the high types and $c_L > c_H$ for the low types.
My question is simple:

What are the possible wage schedules that sustain a pooling
equilibrium? In particular, can a pooling equilibrium wage schedule specify a wage of
zero following $e = 1$?

I will briefly elaborate on my understanding of the problem and what is unclear to me. In any pooling equilibrium, workers must be paid their expected productivity. So following $e = 0$, the specified wage must be
$$
w(e = 0) = \mathbb{E}(\theta) = p_H \theta_H + (1 - p_H)\theta_L
$$
Furthermore, to ensure that nobody wants to deviate (by getting education), we only need to ensure that the high types won't deviate. (If they won't want to deviate, then neither will the low types). This requires that
$$
w(e = 1) - c_H \leq w(e = 0) = p_H \theta_H + (1 - p_H)\theta_L
$$
So the wage following $e = 0$ is uniquely determined in the pooling equilibrium (the equation). Moreover, the wage following $e = 1$ must be sufficiently low to ensure that nobody gets education (the inequality). I am wondering if there are any additional constraints that the wage schedule in a pooling equilibrium must satisfy, or whether any wage schedule satisfying these constraints will sustain pooling (as a PBE).
To make the issue a bit more salient, suppose that we propose some wage $w(e = 1) < \theta_L$. For example, suppose you make the wage for those who get education zero. Clearly, nobody will choose education, i.e. the inequality holds. Moreover, wages don't need to be set optimally following $e = 1$ since this happens with zero probability in equilibrium. On the other hand, no possible type could have a productivity of zero, so this wage schedule does not follow from any possible firm beliefs. This suggests that the wage following zero education needs to also satisfy
$$
w(e = 1) \in [\theta_L, \theta_H]
$$
Is this indeed a further constraint (in any pooling equilibrium where both types choose $e = 0$)?


texts: How would one go about modelling the effectiveness of public transportation? More specifically how does one go about comparing two transit systems in terms of their ability to move a larger numbers of people and how fast they move them.


texts:
An important result in auction theory is Milgrom & Weber's linkage principle, which, roughly, holds that the expected revenue from an auction is higher is the seller commits ex ante to reveal as much information about the good for sale as possible.

I am trying to understand why this should be true even if bidders are risk-neutral and care only about the expected difference between their value and the price paid.

Is anyone able to provide some intuition for this result?


texts:
Consider the following regression model:

$y_{i1}=\beta_1 +u_{i1}$
$y_{i2}=\beta_{21}+\beta_{22}x_i+u_{i2}$.

If $E(x_i' u_{i1})\neq 0$ and $E(x_i' u_{i2})=0$, will we get consistent estimators for $\beta_1$ and $\beta_{21}$ using GLS?
I think we will not get consistent estimators for both, because the assumption $E(x_i\otimes u_i)=0$ is violated. Please correct me if I am wrong. Thanks in advance!


texts: Private and Social Optimum with externality in this example

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Firstly, I wanted to know if we may be consider as an externality, a situation such that a customer A bought a bike to a seller B, not properly checked - and which may provoke some accidents.

Obviously there is some damage here, not fixed by the price, because otherwise the bike would have been cheaper I guess, but is it not just an asymmetry information ? I am really hesitating.

Then, my two other questions are related to practical exercise:

If I have a function such that $U(x_1,x_2)= C\ln(x_1-10)+D\ln(x_2)$. Can we agree on the fact that the function is NOT a Cobb-Douglas one? I thought that because if I take the exponential then I have something like $(x_1-10)^C(x_2)^D$ and although $C=D=1/2$, if I can increase by two $x_1$ and $x_2$ I don't double my utility. But don't know if that is enough to prove it.
Then in the second part, it's about how to internalize the social cost of an externality in order to reach the optimum. The context is quite basic: I pollute the environment in order to produce something, that I sell to: $p$. The cost of polluting is $2q^2$. The individual inverse demand function is $p=-q +100$. I did the calculation in order to find in private optimum how much good will be produced, found the how much good will be produced in social optimum if we take in account the social cost of 10$ per unit.

Basically, I found that with private optimum we produce 20 and with social one, 18. Then, I don't manage to find if we may reach 18 (by computing the damage on the seller, we will receive for every product 10 dollars less) - the social preferred level of production - by creating a tax? I guess a pigouvian one. I know that implementing a tax is not always the best solution because sometimes the externalities can be internalize by one of the two sides less costly, but I'm quite lost.


texts: How does the U.S agriculture subsidy not constitute export subsidies under the WTO?

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The WTO explicitly prohibits subsidies on export goods to prevent dumping and market distortion but the United States spends $2.4 Billion annually on corn subsidies and has a trade surplus of $19.5 billion in agricultural goods.

How does this subsidy not constitute dumping under the WTO guidelines?


texts: Influence of a TTIP on the GDP of a european country

texts:
So my question is simple but what I would like to know is if my method of calculating something like that plausible or not.
So it goes like this : the formula we took at lecture for calculating is

  GDP = C + I + G + (X-Z)

With :

  C= consumption , I = investment, G = government spending (army defense, etc...), X = exportations, Z = importations

If a TTIP is put in place between Europe and USA, creating a free trade zone following theory exportations will rise causing the economic growth of European countrys, this will also cause our consumption (C) to grow, I will not explain why to not have to go into any details but this will cause our importations (z) to also grow.
So my question lies here, can I assume that exportations and importations are going to grow by the same quantity thus creating a balance and that the GDP will rise because of the rise in consumption or would that be an invalid theory? Will exportations and importations meet a certain equivalence at some point?

Sorry for my English I am studying in french so it is kind of hard to explain.


texts: Are there some examples of theoretical models that discuss pandemics?

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I am looking for some papers/references that showcase theoretical economic models that incorporate pandemics. Most work seem to be purely empirical. Does anyone know of some papers that try to model effect of pandemics on economy/economic behavior analytically?

Update:
Some of the theoretical papers that I managed to find with helpful suggestion of kurtosis to include SIR & SEIR in search include:
Daron Acemoglu et al (2020), Optimal Targeted Lockdowns In A Multi-Group SIR Model
Eichenbaum, Martin S., Sergio Rebelo, and Mathias Trabandt. The macroeconomics of epidemics.
Any further suggestions are still welcome


texts:
What are the possible problems/issues of regressing smooth time series with almost no fluctuation?
Here is a specific example.

Is there anything I have to pay attention to when interpreting coefficients? Or is there no proper way to regress time series like these? If so, what are the reasons?


texts:
When some entity takes advantage of an arbitrage opportunity, who is losing money? For example, when there are price differences across cryptocurrency exchanges and someone exploits an arbitrage opportunity, who is losing out?

A vaguer question: what are the microeconomic implications of arbitrage?


texts: How to Show That, on a Balanced Growth Path, Two Variables Grow at the Same Rate

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If we are given that a variable is on a balanced growth path (for sake of argument we shall assume consumption), how do we show that another variable related to consumption (like capital or wealth) should grow at the same constant rate as consumption? I tried giving the verbal explanation below, but I was marked off for not being rigorous enough.

My verbal explanation was the following (in the problem there were only two variables, consumption and wealth and we were given that consumption was on a balanced growth path):

If consumption grows at a constant rate, wealth must also grow at the same constant rate. If the growth rate for wealth is greater than that of consumption, we will have positive wealth during the last time period, so we could not have been maximizing utility (because the agent gets no utility from holding wealth). If the growth rate for wealth is less than that of consumption, then a constant growth rate of consumption would not be sustainable over an infinite time horizon because the agent would eventually have less wealth than is necessary for the level of consumption prescribed by optimality.

My professor said that I could use FOC's to show that they must grow at the same rate, but I'm not sure how I would do so. Can anyone help me understand?

$\textbf{Edit:}$
The specific model for which I used this argument is the one laid out in the following question:
Solution Method for Infinite-Horizon Maximization Problem. We end up getting steady state consumption (which is a form of a balanced growth path with the growth rate being 1). He said it was correct in this model that steady state consumption implied steady state wealth, but that my explanation was not rigorous enough.


texts: USD/CAD fx: What's the difference between Buying USD and Selling CAD?

texts:
Beginner question here.
I'm Canadian, and my investement account is, by default, in CAD currency.
Recently I wanted by buy a US stock so I had to convert some of my CAD money in USD money.

There would have been other ways, but this led me to use an FX tool. The interface was similar to this:

Action: [ ] Buy [ ] Sell

Currency: [ ] CAD [ ] USD

So basically, in order to do what I wanted to do (convert CAD to USD), I had 2 options:

A) Buy USD

B) Sell CAD

What's the difference between both actions ?


texts: I have been trying to model a Pay What you Want scheme. Now, for a monopoly it is clear that monopoly will have more profit by setting monopoly pricing assuming all players are selfish. But consider a scenario of 2 sellers one posting a fix price and other a PWYW strategy. In a market of selfish players the PWYW will make huge losses and market would move on to the fix price seller who can now act as a monopoly. So does this imply that there is an incentive for the selfish players to keep PWYW firm in market ? Also, how do I extend this idea to more than 2 firms ?


texts: Can someone please explain how personal savings and fiscal deficit are related in this context?

texts: The lines which i have highlighted is what I want to be explained to me. This is with reference to indian economy


texts:
I am looking for papers on Dutch disease. Especially interested in Venezuela, UK, Colombia, Norway.
Thank you in advance.


texts:
I have a problem understanding the market clearing condition for aggregated equilibrium in the Ramsey model.

Market clearing implies that all resources are used up, hence: $Y_t=C_t+I_t$ , where $Y_t$ is defined as aggregated output, $$Y_t=\int_{0}^1 Y_{jt} dj\qquad (1)$$.

Also both factor markets labour and capital clear: $$N_t=\int_{0}^1 N_{jt} dj=1 \qquad (2)$$.

And accumulated capital of households $$K_t=\int_{0}^1 K_{jt} dj\qquad (3)$$.

So, can someone tell me why (1) can be interpreted as the average of $Y_t$.(2) is equal to 1 and why (3) is not equal to 1?

Thanks!


texts: Financing U.S. government budget deficits, and their impact on interest rates

texts:
I have two questions. The first is about how exactly the U.S. government finances a budget deficit. The second is about the effects of budget deficits on financial markets and interest rates.

Q1. We say that deficits are financed by the sale of government bonds. But I don't understand exactly what this means. Government bonds are always available for purchase, regardless of whether Congress passes a balanced budget in a particular fiscal year -- right? So it is not that the government issues bonds only in years that run a deficit. So what exactly do we mean when we say deficits are financed by the sale of government bonds? A priori, I could make several guesses. It could mean that if Congress passes a budget deficit in a certain fiscal year, the Treasury issues more attractive securities that fiscal year -- e.g. with higher interest rates -- to incentivize more bond sales that year. (This doesn't seem like it could be true for all Treasury securities, because, e.g. I-bond fixed rates have been virtually zero in recent years despite the huge deficits the last eight years.) Alternatively, it could simply mean that funds accrued from the sale of bonds in earlier fiscal years, stored in some Treasury account, are withdrawn to cover the deficit. I know these are naive questions, and I suspect both are too simple to tell the whole truth, if there's any truth to them. But I'd like to have a better idea of what exactly we mean when we say deficits are financed by the sale of bonds, partly because the answer to this question could matter for the second question.
Q2. In macro 101 we are taught the following toy model. The bond sales used to finance a budget deficit crowd out private investment, since funds spent on government bonds are no longer available for loan to private institutions. This reduction in the supply of loanable funds, in turn, is supposed to drive up interest rates, as financial institutions try to incentivize more investment. But we haven't seen an increase in interest rates in the U.S. despite big deficits over the last several years. Why? What does the toy model get wrong? Is the point that the upward pressure on interest rates predicted by the toy theory can be mitigated by low Fed rates?

If it's easier to point me to an intermediate reference on this material rather than provide an answer, please do so. I'm looking for much more detail than can be found in mainstream elementary macroeconomics books (e.g. Mankiw).


texts: Doubt regarding Walrasian equilibrium with complements for both agents

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There are two goods $1,2$ and two agents $ 1,2 $. Both have the utility function $ u_{i}=\min({x_{1i},x_{2i}}) $ for agent $i$ .The endowments are $(1,3)$ and $(3,1)$ for agent $1$ and $2$ respectively. I have to solve for the Walrasian equilibrium.

I found out the demand for $x_{1}$ for both agents and at this point I tried to clear the market for $x_{1}$:
(setting $p_{1}=1$ and $p_{2}=p$, I get)
$\frac{1+3p}{1+p}+\frac{3+p}{1+p} = 4$
 At this point I generally try to solve for the equilibrium price $p$.
But In this case, Its a trivial equation. What does this mean ? What is the equilibrium price?

Sorry if I am not seeing the obvious. I am new to this and dont know much.


texts: Selection of functional form for utility function in theoretical model

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I am starting to work on an IO model and I am puzzled in front of the choice of the appropriate utility function. Since the concept of utility is so abstract, and one cannot directly refer to empirical articles on what factors should the decision be based on?
Is it exclusively on the basis of what the assumptions on marginal effects of the variables taken into account are? Isn't this prone to subjective reasoning that may bring researchers to forge their result based on a particular specification?
An example of this may be the results one obtain in Hotelling models depending on the transportation cost functions, how do you choose?
Thanks, and sorry if the question seems to vague.


texts: How Does Adding Regressors Affect Standard Errors and Existing Coefficients?

texts:
(First off, bonus points if you can write my question title more clearly)

My project right now is to research citizenship status and income.

At first my regression was like this:

$$ INCOME = \beta0 + \beta1STATUS $$

Now, I am going to do one with control variables like this:
$$ INCOME = \beta0 + \beta1STATUS + \beta2EDUCATION + \beta3ZIPCODE$$
When I'm looking at the coefficient and standard error for immigration status, what does the regression of earnings on immigration status and all my control variables tell me compared to a regression of just earnings on immigration status? Generally in regressions, how does adding more variables change standard errors and coefficients?


texts: Which capital accumulation is right? $K_t = (1-\delta)K_{t-1} +I_t$ or $K_t = (1-\delta)K_{t-1}+I_{t-1}$?

texts:
In a lot of models with capital, I find different variants of capital accumulation formula as follows:
$K_t = (1-\delta)K_{t-1} +I_t$ or

$K_t = (1-\delta)K_{t-1}+I_{t-1}$

Which one is more economics-sound formula?


texts: Can someone help explain the passage here? I'm rusty with my linear algebra so the derivate of these transpose matrices isn't making any sense to me. A detailed explanation would be very much appreciated. What happens to the 1/2, and that whole second term in general?


texts: What is the difference between average cost and marginal cost?

texts:
$$AC(q) = \frac {C(q)}{q}$$
$$MC(q) = \frac{\partial C(q)}{\partial q}$$

These are the definitions. But I don't understand what the difference is.

Is the average cost the cost per unit while the marginal cost is about infinitesimals?


texts: Is there any reason deflation would reduce profit?

texts: Profits are the difference between input and output prices. Is there any reason deflation would cause profits to decline generally rather than in those industries where output prices fell faster?


texts: Constructing a game of coordination failure

texts:
I was reading the following paper:
https://www.econ.nyu.edu/user/debraj/Papers/AdseraRay.pdf
It is a short piece and the intuition sounds very clear to me. But my mathematical incompetence is preventing me from coming up with a simple example of how this works. I was wondering if anyone could enlighten me on this.
Here is the basic setting. Suppose there are $\bar{K}$ capitalists in a country. The economy is divided between old sector $A$ and new sector $B$. At the beginning all are in $A$. Among $\bar{K}$, $K$ goes to $B$, and the rest $\bar{K}-K$ remains at the old sector $A$. The rate of return at $A$ a fixed rate of return of zero. The return in $B$ is higher when more people migrate to the new sector $B$, i.e., $r=f(K)$ where $f(0)<0<f(\bar{K})$. $f(K)$ could be thought of as a long-run level return.
It is optimal for all $\bar{K}$ to move to $B$, but there is a time lag for the return to be realized. In other words,
$\dot{r}(t)=g(f(K(t))-r(t))$ where $g$ is an increasing function, $g(0)=0$, and $r(0)=f(K(0))$
Let's assume that initially all capital is in $A$. The authors say that if there is no congestion costs for moving to $B$, then the initial condition prevails such that all capital remains in $A$. If there is a congestion cost, e.g. moving later will incur higher cost, or if there is a subsidy for moving earlier, then $B$ is the equilibrium.
To construct an example of this game, I suppose $\bar{K}=1$ and $f(K)=K-0.5$. Then $f(0)=-0.5<0<0.5=f(\bar{K})$. I think about discrete time $t=1,2,3,\cdots$.
If a capitalist remains in $A$, then the return will be zero forever. Suppose on the other hand that all capitalists move to $B$. To account for time lag, I assume that the return in $f(K(1))=-0.1$ and $f(K(t>1))=0.5$.
I am not considering congestion costs here, but what is preventing capitalists from migrating to the new sector? If we account for the sum of all returns, wouldn't it still make sense for capitalists to enter into a new sector $B$? I think I am having trouble with understanding the very basic concept of economics.


texts: Where can I find quarterly/monthly medicare/medicaid state level drug utilization data

texts:
I read a paper titled 'State generic substitution laws can lower drug outlays under
medicaid'. It uses quarterly state level medicaid drug utilization data. However, I could only find yearly data at the state level. Has anyone has experience in this data set.


texts: need help from theorists: proof in Cole, Mailath, and Postlewaite (2001)

texts:
I have one question in the proof for section 4.1. in Cole, Mailath, and Postlewaite (2001).
$$\lim_{\varepsilon \to 0}\frac{1}{2\varepsilon}\int_{\overline{l}-\varepsilon}^{\overline{l}+\varepsilon} v(\beta(i) + \delta, \sigma(i+\beta^{-1}(\beta(i) +\delta) - \overline{l}-\varepsilon))-v(\beta(i), s(i))di$$

They say the above limit is equal to :
$$v(\beta(\overline{l}+\delta, \sigma(\tilde{l}))-v(\beta(\overline{l}, s(\overline{l})),$$ for $\tilde{l} = \beta^{-1}(\beta(\overline{l})+\delta).$

I am not sure how do they this. I think if $\varepsilon \to 0$, the term inside the integral goes to 0. But, the answer they give us is to substitute $\overline{l}$ for $i$ in the integral. I appreciate if you give some help to figure this out.


texts: Regression Optimization problem under constraints

texts:
To estimate a simple linear regression:
$$ y = \beta_0 + \beta_1 x + \epsilon $$
I have the assumptions that a researcher $A$ can only sample individuals with a value $y < y^A$. Similarly, a researcher $B$ can sample individuals with a value $y <y^B$, with $y^B < y^A$. I also know that $\beta_1 < 0$.

Are the estimates from the researchers $A$, $B$ going to be biased?
If so, which one is likely to be more biased?
How can I illustrate that graphically?

What I have tried so far, is to assume that $y^A = (\hat{\beta_0} + \hat{\beta_1}x)^A$ and then I tried to derive the OLS for this model instead but I stumble upon calculations, i.e.
$$  \partial{(SSR)}/\partial{\beta_0}  = -2A \sum{\left( y_i - (\beta_0 + \beta_1 x_i)^A\right) \left(  \beta_0 + \beta_1 x_i\right)^{A-1}} = 0$$
How do I get along from here? I have some intuition that I should use a logarithmic approach?


texts: Revealed preference if we know that the decisionmaker is rational?

texts:
In standard revealed preference, we don't assume that the agent has rational preferences over a choice set $X$, and we can then ask: under what conditions can $X$ be rationalized by a rational preference relation?

One answer turns out to be: if the choice set $\mathcal C$ contains all    subsets $C\subset X$ of 3 elements or less, and the weak axiom of revealed preference is satisfied.

But now, what if we already know from the outset that the preference relation of the decisionmaker is rational, and we just want to pinpoint uniquely which preference relation this is? Then at the very least, we only need every 2-element subset of $X$, but it seems that this can be imporved. Is there work on this?

EDIT: Let me state the question more clearly: What are minimal conditions on a choice collection $\mathcal C\subseteq \mathcal P(X)$ such that for any preference relation that generates choices $c(C)$, that preference relation is the unique rationalization of those choices?


texts: How to calculate equilibrium income given a certain level of unemployment?

texts:
I need help with this question. I do know the procedure to calculate the equilibrium income and can solve the following question without taking the employment factors in mind. However, I just can't get how the employment factor figures in the equilibrium calculations.

Suppose labour and capital are used in fixed proportions in the production of output in a closed economy. Suppose the existing capital equipment is utilised fully but a quarter of the labor force is unemployed. Let $Y$,$C$ and $I$ represent aggregate levels of income, consumption, and investment expenditure in the economy in dollars at constant prices. Let $C=100+0.6Y, I=500, G=200$

Calculate the level of income in the economy.
If the government raises its nominal expenditure to 400, then what is the increase in real income in the economy?
If the government raises its nominal expenditure to 400, then what is the fall in the percentage of unemployed in the economy?

This is how I've solved it :
Y=C+I+G = 800+0.6 Y So Y = 2000
With 400 as government expenditure, the new equilibrium income will be 2500. So the increase in the income is 500.
I think this will be solved using Okun's law:

$$\Delta u_{t}=0.4(g_{y_{t}}-3)$$

But I'm not sure how to proceed.


texts: How to distinguish Full-time (FT) employment and Part-time (PT) employment when calculating employment rate?

texts:
Which of the following is true for the Canadian labour force data for June, 2015, for unemployment, Full-time (FT) employment, and Part-time (PT) employment?

A)  Unemployment fell because FT employment rose more than PT employment fell

B)  Unemployment fell because PT employment rose more than FT employment fell

C)  Unemployment rose because FT employment rose less than PT employment fell

D)  Unemployment rose because PT employment rose less than FT employment fell

E)  Unemployment rose because FT employment and PT employment fell

The answer is A). This question indicates that PT and FT has mutual relationship. But I think we don't normally count PT when calculating unemployment rate. So how does the choice A) work?


texts: Which diagnostic tests are suitable for Measuring Total Factor Productivity (TFP)?

texts: I did the TFP estimation with Levinsohn Petrin (in R) but I have doubts about the diagnostic tests e.g. I know that the estimation of autocorrelation in residuals has to be done (it would be very helpful if the library to be used can be stata or R) I also read if there are constant returns to scale.


texts: Why does entitlements leads to lower US productivity?

texts:
In a recent Bloomberg interview, Alan Greenspan suggested that entitlements leads to lower productivity, can you please explain it?

What does 'capital stocks' mean?

Does he means that because we are spending a lot on health we don't have money to invest in other things?

Thank you

  ALAN GREENSPAN:  Well, it's unfortunately very simple but not a good story.  It's turning out that we're using more and more people at the
  margin to produce less and less.  Productivity, which is output for
  man hours as we conventionally measure it, is running at a very low
  rate of increase.  And that's the critical variable in the economy
  over both the short-term and the long-term.

  So what we are confronted with right now is a very serious problem
  caused by the fact that capital investment is falling far short of the
  requirements necessary to keep the capital stock growing, and
  therefore productivity.  It is not working.

  LIU:  So how do we reverse that?  What exactly is behind that,
  Chairman?

  GREENSPAN:  Well, I've on many occasions indicated that the best way
  to standard this is to track it backwards.  There's a very tight
  relationship between the stock of nonresidential, private stock and
  output per hour.  They move together parallel all the time for very
  good reasons.  But that capital stock requires capital investment.
  And capital investment, in turn, is being crowded out by a very
  substantial increase in government expenditures.  Basically,
  entitlements -- because both parties, both the Republicans and the
  Democrats, don't want to talk about it largely because it is
  considered the third rail of American politics.  You touch it and you
  lose.

  LIU:  Well, so that makes perfect sense.  So it might come down to
  cutting some costs, right, to cost controls, Chairman.  Top of your
  list, I know you've mentioned entitlement spending.  You know, you've
  got Medicare, Social Security.  The No. 1 thing that you think that we
  need to cut our costs on is what?

  GREENSPAN:  Well, the basic issue is the entitlements and the reason
  it's a problem is that people put money in their own funds and their
  employers' funds plus interest and that is what they perceive they et
  back , and therefore they are entitled to it because it is their
  money.

  The only problem is that's not what we are doing.  We're not creating
  enough funding for the Social Security trust funds, and the same thing
  goes for Medicare Part A.  And we're not funding this.  So long as we
  are not funding this, we are dollar for dollar crowding out capital
  investment.


texts: Do US 501(c)(3) non-profits have to divulge their investments?

texts: Do US non-profit organizations with tax exemption under Section 501(c)(3) of its Internal Revenue Code which have investments (such as university endowment funds) have to divulge these investments in any sort of filings? If so, are these required to be available to the public?


texts: How can a positive relationship between capital per effective worker and technological change be explained?

texts:
I'll get to the point: so, in the context of theories of long-run economic growth, I understand at a basic level that, in the Solow model, there is a negative relationship between capital per effective worker (K/AL) and technological change () - higher amounts of technological change means it is harder for firms to keep with up new innovations in capital terms.

In contrast, there is, supposedly (speaking in very simplified terms) a Schumpeterian-type ('market for inventions') model, where there is a positive relationship between K/AL and technological change, because technological change is determined, in part, by K/AL, as this increases the supply of 'innovations'.

I do not understand how an increase in K/AL would increase the supply of innovations within this model - would someone please explain for me why this relationship might hold true?


texts:
Assume, using the following equation
$Y=[((A_1L)^\alpha K^\beta)^\sigma+ (A_2X^\gamma)^\sigma]^{1/\sigma}$, we back out (obtain) the evolution of $A_1$ & $A_2$. Can we interpret $A_1$ as labour-saving technical change index since it augments labour in the model?


texts: Macroeconomics, the circular flow of income and profits

texts:
I'm really confused about the concept of the circular flow of income. Specifically, I'm confused about the following situation:

Imagine a simple economy where households don't save their income, so they spend it entirely on goods/services.

Now imagine there is only one firm in the economy producing a single good, say chocolates. Let's assume the firm has $5000 in total at first (obtained from all households, none of whom have any income at the moment).

Let's say the firm buys raw materials from households and pays households their wages, and let's assume altogether it costs the firm all \$5000. And now the firm decides to sell all chocolates produced at a price such that in total, the prices add up to \$6000, so that the firm earns \$1000 in profit.

But here I find a problem: no one can buy all \$6000 worth of chocolates because only \$5000 is in the economy at the moment. So firms can only sell a total of \$5000 worth of chocolates and thus never earn any profit.

Where did I go wrong? Did I go wrong? I'm assuming I did because to me the result I got is nonsensical.


texts: How yield rates influence the "cost of borrowing" for borrowers

texts:
I am currently learning about quantitative easing, and I am having trouble understanding yield rates and how that influences the "cost of borrowing".

This is the resource I am using.

The lecturer says something along the lines of "the yield of bonds reflects the cost of borrowing for the issuer. If the yield for these bonds reduces it means accessing finance is cheaper. They can raise finance but now at a lower cost to them" (he is referring to both government and corporate bonds).

I am a bit confused about some things here. When he says that "the yield of [corporate] bonds reflects the cost of borrowing for the issuer, so for banks who issue corporate bonds, if the yield on the bonds decreases it is cheaper to access finance", is this simply referring to how much the company has to pay back  for the bond or is it referring to how much it costs banks to borrow from the central bank - and are corporate bonds only referring to banks or are they referring to all corporations? And when they say "the yield of these bonds reduces ... they can raise finance at a lower cost to them", is that referring banks borrowing from other banks or something?

Sorry if this is confusing I'm just having trouble piecing this together.

Thank you


texts: Lagrangian: How to understand the No-Ponzi Condition

texts:
In http://www.uni-hamburg.de/fachbereiche-einrichtungen/fb03/iwwt/makro/slides2.pdf page 8, lagrangian is written as follow: $$L = E_0 \sum_{t=0}^{\infty}\beta^t\{U(C_t,N_t) + \lambda_t(P_tC_t + Q_tB_t - B_{t-1}-W_tN_t+T_t)+\psi_t(\lim_{T \to \infty} B_T)\}$$
where bond $B_t$ has solvency condition $\lim_{T \to \infty} B_T \geq 0$.

In page 9 then all first-order conditions are derived, but I don't see anything related to $\psi_t$ and solvency condition. Why can the first-order condition relating to $\psi_t$ be dropped?


texts: Rawlsian SWF and Arrow Impossibilty Theorem

texts:
given Arrow impossibility theorem the only social welfare function that satisfies unrestricted domain, pareto and the independence of irrelevant alternatives is Dictatorship. However I was wondering which one of these criteria the Rawlsian SWF fails. I was suspecting Independence of irrelevant alternatives, however I can't come up with a proof.
Thanks in advance for your help.


texts: What is the upper limit of circulating money on earth?

texts:
I've come up with this question while discussing the topic of customer-perceived value with coworker.

Is there a theoretical upper limit to all circulating money in this world?

To avoid inflation or the simple answer "just print more money", let's use the current USD as the 'standard money' in this question. (I'm simply going to go off 'value of USD' from Google [if someone has a more precise way, then any suggestions would be much appreciated] where 1USD = .91 euro at the time of writing this).

According to Business Insider:

  according to the CIA, the total amount is $80 trillion if you include
  "broad money.

In my mind, assuming that all first-world counties' standard of living stay the same or get better, if third-world countries were to, all of a sudden, become first world countries in 2020, that would mean there is more money circulating in the world (more GDP per capita in the third-world country, thus more GDP per capita in the world).

And as the economies of third-world countries get better, they would create more value in their products/services that the people of their country produces.

So in an ideal world, if everyone lived as millionaires (aka, everyone drives $100,000+ cars, million-dollar homes etc.), due to the economy in every country flourishing, wouldn't that mean there is no upper limit to all circulating money in the world?

But as a counter, that's only in an ideal world - not reality.

Let's say you can buy a car for 50,000 USD. The manufacturer is  not going to create that car if it takes them $50,000 to make it. Where's the profit?

So then let's say there is a company that creates the rubber for the tire, another company creates the seats for the the car, so on and so forth. All those companies are not going to create their product without profit, because where's the incentive to do so without it?

If that's true, then someone at the bottom of the chain will be doing the work for minimal profit, which makes me think that the cars that are sold to people only exist because people at the bottom of the chain - which leads to, first world countries only exist due to third world countries (why do you think a t-shirt at GAP costs 3 dollars? Gap is selling you the shirt for 3 dollars because they only paid 1.50 dollars to make it, which someone did, most likely in a third world country), which means the upper limit of circulating money in the world would more or less look like y = ln(x) image of y = ln(x) because as first-world countries get wealtier, there is only so much they can grow because they're bounded to the work in third-world countries.

Disclaimer: My counter argument is simply a hypothesis and I have no grounds of proof. I'd be happy to debate/have someone shed some light if I am entirely wrong. The only reason why I mentioned it is because I wanted to provide a counter reason as to why there is an upper limit to all the circulating money in the world.

Clarification: What I am not asking is all the value in the world. I could create a painting and say it's worth 900 trillion dollars and that would 'increase' all the monetary value in the world to 980 trillion (assuming that we currently have $80 trillion in circulation). What I am asking is strictly circulating money.


texts: From MMT viewpoint, how do taxes make sense?

texts:
I understand this part of MMT: From 100 USD that the Fed prints, the state can get back (or destroy) 10 - 90 USD back in taxes. But what is the effect of taxes on the economy:

A household buys food for 50 USD incl. 10% tax - what is the effect of the tax here?
A private person buys a luxury item of 80 USD with 25% tax - what is the effect of the tax then?
A foreigner buys the same luxury item of 80 USD but requests tax free discount (as he has an account on the Bahamas ) - how does tax discount and avoidance show up in MMT ?


texts: Understanding the impact of Subprime Mortgages crisis on investment banking

texts:
I'm interested to know the exact magnitude of impact of Subprime Mortgages crisis on major players in investment banking.

In particular, how can I find data for percentage of revenue from Subprime Mortgages in total revenue for major banks, like Goldman Sachs, Morgen Stanley, The Bear Stearns and  Lehman Brothers?


texts: Is equity value is the same as stockholders equity? I have been given liabilities and stockholders equity total also and I need to calculate the leverage ratio, but I not sure what numbers should I use and whether I need to calculate the equity value using asset value and etc. or I could just plug in the number.


texts: Is money mostly created (out of nothing) by banks making loans?

texts:
In the Bank of England's Quarterly Bulletin, 2014 Q1, McLeay, Radia, & Thomas write a pair of articles titled:

"Money in the modern economy: an introduction" and
"Money creation in the modern economy".

I believe they subscribe to what Werner (2014) calls the credit creation theory of banking. From their Overview:

In the modern economy, most money takes the form of bank deposits. But how those bank deposits are created is often misunderstood: the principal way is through commercial banks making loans. Whenever a bank makes a loan, it simultaneously creates a matching deposit in the borrower’s bank account, thereby creating new money.
The reality of how money is created today differs from the description found in some economics textbooks:
• Rather than banks receiving deposits when households save and then lending them out, bank lending creates deposits.
• In normal times, the central bank does not fix the amount of money in circulation, nor is central bank money ‘multiplied up’ into more loans and deposits.

These two articles were published in the BoE's Quarterly Bulletin, so I had initially assumed that what they were saying was the mainstream/widely-accepted/orthodox view. On further reading (e.g. of Werner, 2014), I discovered though that this might not be so and am now slightly confused as to what, if any, the mainstream view is.
My main question is this: Is the above description of money creation largely accurate?
Follow-up questions: Does this description differ from what is written in most textbooks and academic papers and books? (And if so, why? Is it because the above description is a relatively recent development? Or the above description has been true for a long time now, but has simply not been incorporated into textbooks and economists' models?)


texts:
Suppose a Decision Maker (DM) has willingness to pay (WTP) of 100, and her actual elicited willingness to accept (WTA) is 110, can this DM be a standard rational agent? Why or why not?

My thinking is that if the DM is a standard rational agent, then her WTA should also be 100. Is this correct?


texts:
I was reading the ISO 10962 (the 2015 version) which classifies financial instruments.

In the Collective Invesment Vehicle (CIVs) they separe them in:

Standard Funds
Hedge Funds
REIT
ETF
Pension Funds
Fund of Funds
Private Equity Fund

In the fourth attribute of each one of that CIVs is "Security type and investors restrictions" and the possible values are:

Shares
Units

Question: What is the difference between both?

Investopedia

Mutual fund units, or shares, can typically be purchased or redeemed as needed at the fund's current net asset value (NAV) per share, which is sometimes expressed as NAVPS. A fund's NAV is derived by dividing the total value of the securities in the portfolio by the total amount of shares outstanding.

Open-end fund (wiki)

An open-end fund is equitably divided into shares which vary in price in direct proportion to the variation in value of the fund's net asset value. Each time money is invested, new shares or units are created to match the prevailing share price; each time shares are redeemed, the assets sold match the prevailing share price. In this way there is no supply or demand created for shares and they remain a direct reflection of the underlying assets.

Unit or share class (wiki)

Many collective investment vehicles split the fund into multiple classes of shares or units. The underlying assets of each class are effectively pooled for the purposes of investment management, but classes typically differ in the fees and expenses paid out of the fund's assets.


texts: Let the utility function $U = a + b \min\{x,y\}$. Are $x$ and $y$ perfect complements?

texts: It is possible to have a monotonic transformation on this type of utility function, but what about $a$ and $b$? Usually a function with perfect complements is $U(x_1, x_2) = \min \{a x_1, b x_2 \}$


texts:
Is there a statistic that describes the “churn” in the unemployment rate i.e. how many became unemployed compared to how many found work?

I’ve heard of unemployment volatility (https://www.emeraldinsight.com/doi/abs/10.1108/03068291211224937) but never could find any stat for it in the U.S.

For a better idea of what I’m talking about, here is an article written about it in India: https://www.cmie.com/kommon/bin/sr.php?kall=warticle&dt=2017-10-31%2009:43:08&msec=273

Does the BoLS track this metric?


texts: Incentive Compatibility Construction Rule

texts:
Suppose we are interested in constructing an incentive compatibility constraint for an agent to announce his state truthfully.

Consider a simple case of the state space being $S=\{H,L\}$ and his payoffs to be $\pi_L,\pi_H$.

For the player to announce the state and payoff truthfully, is it correct to set the IC as:

$$\pi_H\leq\pi_L.$$

If it is correct, why is it so, and if it isn't, what is the correct way of setting up the IC and why? Is there a general rule of thumb in constructing an IC? Any reference would be also helpful.


texts:
I have several macroeconomic models (eg two DSGEs and a VAR). They each produce forecasts for GDP, inflation and unemployment, and I have data to test them on, going back years.
How can I say which model has the "best" overall performance?
I realise this is vague, so here's more detail:
Assume that model X performs better than model Y on GDP, but worse on inflation.
If I'm just looking at GDP, I could just ask something like "which model has the smallest mean square error?" (predicted GDP - actual GDP, squared)
Similarly, if I only care about inflation, I could do the same thing.
But I actually care about forecast accuracy over all three variables (GDP/inf/unemployment).
Is there a way to assess accuracy over all three variables, without just assigning weights to each MSE value and adding them up?
Thanks for your help!


texts: Rationalizable action profiles in nice symmetric games

texts:
Suppose we have a nice symmetric game with $n$ players, i.e. each player's action space is the same compact interval of the real line. I am tasked with identifying all of the rationalizable action profiles, and I am wondering if this set of action profiles will include profiles other than the unique symmetric Nash equilibrium. I know that there are often more rationalizable action profiles than there are Nash equilibria, but I'm specifically interested in nice symmetric games.

Starting with the initial action set for player $i$, denoted $A_i$, I have iterated the rationalization operator twice so far, and as expected, the set of available actions shrinks, and always includes the Nash equilibrium action. Is there some point when iterating the rationalization operator will cease to reduce the set of available actions?


texts: Can econometrics test for correlation or causality between prices and corruption?

texts: This week there was news that some prices are rising. I heard that in some countries where corruption is high the prices are also higher. I wonder if there is causaility or just both at same. It would be interesting to find some material to support if the claim is true. Is there some study e.g. comparing prices levels for energy and testing whether corruption levels in an economy (bribing, black market, unregulated markets) influences prices?


texts: Why is it that the "right" inflation is positive?

texts:
I have read in several places that inflation should be positive, at about 2%-3%. The most recent example was in this answer from another stack exchange site.

How is this value obtained and under what assumptions?


texts: Marxist Economics: Understanding Capitalist Exploitation through "speed up" or increase in intensity

texts:
I have been studying Marxist economics for a little over 3 months now and have been really trying hard to understand the arguments made.

Right now I'm watching Dr. Stephen Resnick's course on Marxist Economics and am having difficulty understanding the Matematics behind the concept of capitalist exploitation through "speed up" or increase in intensity.

He presents the following formula:
$$\text{I}=\frac{SV+V}{lh}$$

where
-$\text{I}$ is intensity
-$SV$ is surplus value
-$V$ is variable capital/ value added by workers
-$l$ is number of laborers
-$h$ is the number of hours each laborer works

he argues that there exists a way to increase surplus if we hold l and h fixed. Mathematically im not sure how this is done.

It cant be from a change in machinery/capital stoc as noted in a previous video of Dr. Resnick since this would decrease the capitalists level of surplus1.

So if there is no change in hours worked, number of workers and machinery- How is this increase in surplus value occurring?

1. this is based on the equation:

$$r=\frac{SV}{V}\left(1-\frac{C}{V+C}\right)$$

where:

-$r$ is the rate of profit

-$\frac{S}{V}$ is the rate of exploitation/rate of surplus value

-$\frac{C}{C+V}$ is the index of mechanization/rate of mechanization, where $C$ is value of machinery.


texts: In this scenario, which coin is more valuable?

texts:
There are two coins, Coin A and Coin B. You can transfer Coin A for Coin B or Coin B for Coin A only in the two following ways:

Give 100 Coin A for 10 Coin B

Or

Give 10 Coin B for 50 Coin A

In this situation, which of the coins is worth a higher value? A friend of mine presented this problem and we were unable to find a solution. Any thought?


texts: Dynamic Optimization : Resource Stock as a Sink

texts:
I think about a dynamic problem where social planner maximizes the following utility ;

$$\underset{c\left(t\right)}{max}\int_{0}^{\infty}u\left(c\left(t\right)\right)e^{-\rho t}$$

subject to two constraints

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

$$\dot{S}\left(t\right)=\left(1-S\left(t\right)\right)S\left(t\right)-\gamma AK\left(t\right)$$

where $S(t)$ and $K(t)$ hold for natural capital (seas, lakes, forests etc.) and physical capital respectively. $c(t)$ represents consumption.

In this $AK$ model, physical capital generates some wastes which are harmful to natural resource stock with a constant parameter $\gamma$.
This feature is close to Wirl (2004) in environmental economics literature.

The Hamiltonian of the problem is

$$\mathcal{H}=u\left(c\left(t\right)\right)+\lambda\left(t\right)\left(AK\left(t\right)-c\left(t\right)\right)+\mu\left(t\right)\left(\left(1-S\left(t\right)\right)S\left(t\right)-\gamma AK\left(t\right)\right)$$

$\lambda$ and $\mu$ are co-state variables for physical and natural capital.

Dynamics of co-state variables are

$$\dot{\lambda}=\rho\lambda+\mu\gamma A-\lambda A$$

$$\dot{\mu}=\rho\mu-\mu\left(1-2S\right)$$

In fact, in this model, it is easy to remark that natural capital don't have any amenity value don't provide any positive utility and it is just like a "sink".

As the social planner just takes into account the negative effect of capital accumulation (it creates wastes), I think natural capital enters in this model as a "cost".

Then, is it possible to say that $\mu$ could take a negative value as natural capital represents a cost for capital accumulation ?


texts: Bayes Nash Equilibrium in a game with continuous actions

texts:
I am attempting to think through a particular type of game with continuous strategies, with Bayes Nash equilibrium as the solution concept. I first describe the game below, followed by questions.

Game

Consider the following game between two agents: A and B.

Agent A draws a cost $k$ from a distribution $F(k)$, which has support on $[0,\overline{k}]$. Knowing this cost, she chooses an action $x\in [0,\infty]$ and thereby incurs a cost $k\cdot x$.
The choice of $x$ produces a benefit $R(x)$ for agent B, with $R(0)=0$, $R^\prime(x)>0$ and $R^{\prime\prime}(x)<0$.
$R(x)$ is not observed until the game is completed. Instead, A is paid by B for her effort based on a noisy but strictly informative signal $\xi(x)$. Higher $\xi$ always indicates higher $x$ on average.
Specifically, B has a prior distribution $\pi (x)$ over $x$ and observes $\xi(x)$. B always pays A her expected product $E(R(x)|\pi,\xi)$ so that B expects a payoff of zero for any value of the signal.
Finally, in Bayes Nash equilibrium, we require that $\pi (x)$ is "correct": i.e., given the distribution of costs $F(k)$ and the expected payments as a function of $x$ and $\pi (x)$, actions $x$ actually do have the distribution $\pi(x)$.

Questions

There appears to always be an equilibrium to this game with a degenerate prior $\pi(x)$ that has all its mass on zero. In this case, $E(R(x)|\pi,\xi)=0$ for all $x$, and A would never choose $x>0$, confirming the prior. Do you agree?
What are some non-trivial sufficient conditions for there to be additional equilibria in pure strategies (i.e., with $x>0$ in some states of the world)?
How would one characterize these other equilibria if they exist? For example, how would the set of equilibria change if the benefit function increased from $R(x)$ to $\hat{R}(x)$ = $c\cdot R(x)$ where c is a constant greater than one?

Additional Notes

I am aware of examples of this kind of game with discrete actions $x$. These are comparatively easy to analyze. What I am struggling with here is how to think about equilibria with continuous actions and therefore also a continuous prior $\pi(x)$. The fixed point problem seems much trickier in this case.
EDIT: It seems the way to think about this may be with continuous-state markov chains, though I am not completely sure how to write this problem in that form. Even assuming I am on the right track here, I can so far only find sufficient conditions for the existence of a unique stationary distribution, but no theorems that guarantee non-uniqueness or that suggest a way to do comparative statics on the set of equilibria.
Aside from that, feel free to make further assumptions or introduce new notation if it helps.
This is the first question I have posted. So constructive feedback is welcome.


texts:
do you know any book/manual dealing specifically with monetary unions ? I know economics of monetary union of De Grauwe, but I'm looking for other references.
Thank you


texts: Is the world economy highly-dependent on the United States of America?

texts:
How dependent is the economy of the world on the United States?

Can US policies have disastrous impacts on other superpowers in the world such as Germany?

For example, take into account countries such as Iran and Turkey which were hit by US sanctions and their economy soon deteriorated.

I want to know if the same can happen to a country like Germany, UK, or Japan if at some point in time US decides to impose similar measures on such countries or even decide to stop doing business with them?

In brief, can German economy, as an example, survive without the United States? Are they heavily-dependent on the US?


texts: Models with Learning by Doing and Knowledge Spillovers - Barro, Sala-i-Martin (2003)

texts:
Consider the model of endogenous growth with learning by doing and knowledge spillovers presented in Barro & Sala-i-Martin (2003), chapter 4, section 4.3, starting in page 212. In equilibrium, the growth rate of consumption in the decentralized economy is given by:
$$ \frac{\dot{c}}{c} = \left(\frac{1}{\theta} \right) \cdot \left( \underbrace{f(L) - L \cdot f'(L)}_{\phi_0} - \delta - \rho\right) $$
where $c$ is per capita consumption, $\theta$ is the inverse of intertemporal elasticity of substitution, $L$ is the size of the labor force ($\frac{\dot{L}}{L} = n$ is assumed to be equal to $0$), $\delta$ is the depreciation rate, $\rho$ is the subjective discount rate and $\phi_0$ is the marginal product of the capital.
If we now consider a central planner, the following expression from the growth rate of $c$ can be obtained:
$$ \frac{\dot{c}}{c}\bigg\vert_{\text{planner}} = \left( \frac{1}{\theta} \right) \cdot (\underbrace{f(L)}_{\phi_1} - \delta - \rho) $$
where $\phi_1 = f(L)$ is the average product of the capital.
The authors then go on to present an example using a Cobb-Douglas production given by:
$$ Y_i = A \cdot (K_i)^\alpha \cdot (KL_i)^{1-\alpha}, \quad 0 < \alpha < 1 $$
where the index $i$ corresponds to the firm $i$, i.e., $Y_i$ is the output of firm $i$.
Under the assumptions of the model, if we substitute $y_i = \frac{Y_i}{L_i}, k_i = \frac{K_i}{L_i}$ and $k = \frac{K}{L}$, and then set $y_i = y$ and $k_i = k$, the average product of the capital is:
$$ \frac{y}{k} = f(L) = A \cdot L^{1-\alpha} $$
and the marginal product of capital is
$$ f(L) - L \cdot f'(L) = A \cdot \alpha \cdot L^{1-\alpha} $$
and, therefore,
\begin{align*} \frac{\dot{c}}{c} &= \left(\frac{1}{\theta} \right) \cdot \left(A \cdot \alpha \cdot L^{1-\alpha} - \delta - \rho\right) \\ \frac{\dot{c}}{c}\bigg\vert_{\text{planner}} &= \left( \frac{1}{\theta} \right) \cdot (A \cdot L^{1-\alpha} - \delta - \rho) \end{align*}
Since $0 < \alpha < 1$, the growth rate of the decentralized economy is lower than that of the economy with a central planner.
Continuing, the authors write the following and I quote:

The social optimum can be attained in the decentralized economy by introducing an
investment-tax credit at the rate $(1-\alpha)$ and financing it with a lump-sum tax. If buyers
of capital pay only the fraction $\alpha$ of the cost, the private return on capital corresponds
to the social return. We can then show that the decentralized choices coincide with those
of the social planner. Alternatively, the government could generate the same outcome by
subsidizing production at the rate $ \frac{(1-\alpha)}{\alpha} $

I can't understand how the tax and subsidy could make the decentralized economy achieve a socially optimum level of growth rate. Intuitively, I can see how that might work but I cannot see how the math behind it would work in this case.
If anyone could explain that to me or point me in the right direction I'd appreciate it. Let me know if I need to add more details to the question.


texts: Are Open Market Operations a Gift to the .1%?

texts:
My Background
I was an Economics major a long time ago and I don't work in a related field.  I have this question that's been nagging me.  I hope somebody can answer the questions at the bottom.

Background Information
During Open Market Operations, the Fed buys or sells Treasuries in order to effect certain desired results such as changing the interest rate or changing the money supply.

To pump more money into the economy, the Fed will buy tons of Treasuries.  In other words, banks and other entities will give their Treasury papers to the Fed and in return, the Fed gives cash to the banks.  Then, this cash eventually finds its way into the local economy, spurring economic activity.

My Questions

When the Fed sells and buys Treasuries from banks, aren't the banks getting an enormous gift?  When I say gift, I mean that it's almost like free money.  When the Fed buys Treasuries, it announces what it will do and then buy in massive quantities which will inevitably drive up the value of Treasuries.  Banks are now selling their Treasuries for much higher prices than it was just a few days ago.  Isn't this a great deal for them?  How can they say no?
The second largest beneficiaries of the Fed's purchase of Treasuries aren't the common masses but are the large institutional investors who have a lot of money to begin with.  They are suddenly getting loans at extremely attractive rates and terms.  Is this preferential treatment (aka gift) very fair?  Can't we create a different system of loans so it's not so skewed towards the wealthiest .1%?

I strongly believe that Open Market Operations are absolutely an indispensable tool for the Fed to manage the economy.  But, that's not point though.  My point is that although it's necessary, doesn't Open Market Operations extremely favor the financially wealthy?  Trickle-down economics may work here but history has told us repeatedly that it's not very even-handed.  The money that flows to the average American is much less than what the people at the top get.

Is my description of this process correct?  Are Open Market Operations a large gift to the banks and the large investors that receive the initial loans?


texts: Heckscher-Ohlin with non homothetic preferences

texts:
Can someone tell me how I can show with an example that the Heckscher-Ohlin result does not necessarily hold when preferences are not homothetic.
I was asked if it similar as a case in which the preference are heterogeneous, but that would obviously be a different type of preference.

Would anyone know how to proceed?

Cheers,
James


texts: In classical macroeconomics, why Labor supply responds to real wages and not money wages?

texts:
real wages =  money wages/price(P).
what are the assumptions here?
why labor doesn't respond to money wages ?


texts: Is there a class of demand functions that deliver equal surplus to consumers and a monopolist?

texts:
Consider a market with a monopolist firm that has zero marginal cost and faces demand $D(p;\mathbf{a})$, where $\mathbf{a}$ is a vector of parameters and $p$ is the price. The monopolist maximizes profit by solving $$\max_p D(p;\mathbf{a})p,$$
so that the optimal price, $p^*$, satisfies $$D_1(p^*;\mathbf{a})p^*+D(p^*;\mathbf{a})=0.$$

This optimal price, $p^*$, results in consumer surplus $$\text{CS}=\int_{p^*}^\infty\!D(p;\mathbf{a})\,dp,$$
and producer surplus
$$\text{PS}=D(p^*,\mathbf{a})p^*.$$

My question is: is there a family of demand functions, $D(p;\mathbf{a})$, such that $\text{CS}=\text{PS}$ always holds at $p^*$, and if so what does the functional form look like?


texts: If Trump's economic policies are destructive, why is the US economy so healthy?

texts:
One doesn't have to look very hard to find suggestions that Trump's economic policies are damaging to the US economy. Example, example, example, example. In fact I barely recall reading any articles in the mainstream media that said that Trump's policies are beneficial.

However all indications are (example from just earlier this month) that the US economy is extremely healthy.

Why is there a disconnect? Are the economics theories wrong? Is this a case of the economy being too complicated to model, and the results in this case turned out to be incorrect? Are the economists who made those predictions politically biased? Are the indicators imperfect and conceal hidden weakness? I notice that economists also predicted that Erdogan's policies will be destructive for the Turkish economy, and that panned out; I'm wondering why the predictions evidently aren't working for the US economy.

I'm not an economist and know little about the topic, so would prefer an elementary explanation.


texts: Is there a comprehensive list of all market failures ever discovered?

texts:
I'm looking for a complete run down of all different kinds of market failures;

Wikipedia has a list but I'm not sure if there might some obscure kinds of market failures that Wikipedia is missing. Are there types of Market failures that are not mentioned in this the standard textbooks/wikipedia?

Wikipedia: "Market failures are often associated with time-inconsistent preferences, information asymmetries, non-competitive markets, principal–agent problems, externalities, or public goods."


texts: Are the goods in additively separable utility functions normal goods?

texts:
Inspired by this answer.

To make it a bit more precise, by normal good I mean demand is (not necessarily strictly) increasing in income, and by additively separable utility function I mean that a monotone transformation exists for which
$$
U(x_1,x_2,\dots) = f_1(x_1) + f_2(x_2) + \dots
$$
(Also assume $U$ is increasing in all variables.)
Given a linear budget constraint and a utility maximizing consumer, do these goods $x_i$ exhibit normal behavior for all income levels?


texts: How does the Fed choose its asset purchase rate in an ample reserves era?

texts:
The St. Louis Fed's article "A New Frontier: Monetary Policy with Ample Reserves" states that the Fed now uses the IOER and ON RRP rates to set the FFR, instead of open market operations, which are no longer capable of influencing interest rates.

But the Fed just indicated it will resume treasury rollovers and net asset purchases next month, given the ongoing rate collapse (since December).  Before 2009, it purchased/sold assets continuously to alter the money supply to clamp the effective FFR within its target range.  How does the Fed choose its asset purchase rate now?


texts: What determines the outcome of a price war, and why isn't that outcome reached instantaneously?

texts:
Mary is making a hefty profit manufacturing and selling widgets. Jim has some money laying around and he is trying to figure out if he shouldn't start manufacturing some widgets too.

In this example assume that the marginal cost to produce a widget is zero (time, money, etc are all close enough to zero to be indistinguishable), but the cost of making a widget manufacturing plant is quite high.

Also assume that the market for widgets is fairly centralized. There are two bins with widgets in them and consumers can purchase their widgets from either bin. They cannot be resold, however. There are laws against that for whatever reason, and they are ruthlessly enforced. You may only sell widgets that you manufacture yourself.

What does Jim decide? And if he decides to enter the widget business, what is the eventual price per widget and how long does it take to reach that price?

More (but not too) formally:
Our situation can be modeled by a few different games,

Case 1: assume the rules of the price war are

players take turns setting a new, lower price from $\mathbb R$ or passing. When both players pass, the prices are locked and the market is allowed to run for t.

in this case the optimal strategy to set your price to whatever price your opponent sets, if the prices are already equal, then pass.

Case 2:

The market is allowed to run for time t after each player sets a (lesser or equal) price, they take turns setting prices, and they choose prices from $\Bbb Z$.

Here the optimal strategy is in fact no different. if the price starts at $p1$, and the sharing strategy is $S$, then there exists some $t$ such that for all $t'$>$t$ $$EV(S,S,t)=\frac{t*p}{2} >tk(p-1) > EV(S,S',t)$$ for all $p,k,S'$

Case 3:

Both players set prices in each timestep t without the information of the price their opponent sets in that time step, and the market is run.

In this case, no pure strategy is guaranteed to exist, because the information is not perfect. I don't know what the Nash equilibrium would end up being, nor do I know that there is any reason to suspect that it converges (as t -> 0) to the same price as the previous two cases, despite the game seeming to do so.

So I guess the question becomes, why does competition even exist at all in this market, and since all of these scenarios seem to converge towards the reality. ?


texts: Arellano and Bond (1991) or Blundell and Bond (1998) in R estimation

texts:
I have the following problem with the Arellano and Bond (1991) or Blundell and Bond (1998) estimators in R using the plm package. I receive the following problem when trying to run the needed regression:

The dataset could be found here: https://drive.google.com/file/d/1WUCrMCi7bJmhYbzZxNuXDpFIwXJTqdh3/view?usp=sharing
My code is the following, it seems that I do everything correctly, the formula I need to be estimated is the following:
remove(list=ls())

library(plm)
library(dplyr)
library(ggplot2)
library(prodest)
library(estprod)
library(broom)
library(pdynmc)

pckg<-c("plm","readxl","dplyr","ggplot2", "broom","prodest", "estprod")
#install.packages(c("plm","readxl","dplyr","ggplot2", "broom","prodest", "estprod"))
lapply(pckg, require, character.only = TRUE)

# Set the working directory
setwd("C:/Users/vadya/Desktop/baka")

# Downloading the survey data
Data <- read.csv("test.csv", header=TRUE, sep=",")
str(Data)

Data$ID<-as.numeric(as.factor(Data$ID))

summary(Data)

DataA11 <- Data %>%
  filter(NACE == 'A' & Year < 2013) %>%
  filter(VA > 0, L > 0, FA > 0, M > 0, Turn > 0, TA > 0) %>%
  mutate(ID = ID,
         Year = Year,
         l = log(L),
         va = log(VA),
         fa = log(FA),
         m = log(M),
         turn = log(Turn),
         ta = log(TA),
         ff1 = (LTD + STD)/TA,
         ff2 = lag(Cash),
         ff4 = FA/Sales,
         ff5 = TFA/TA)

####################################################################################

mod2LP <- prodest::prodestLP(DataA11$turn, fX = DataA11$l, sX = DataA11$fa, pX = DataA11$m, idvar = DataA11$ID, timevar = DataA11$Year,
                             R = 100, cX = NULL, opt = "optim", theta0 = NULL, cluster = NULL, tol = 1e-100, exit = FALSE)
mod2LP
omegaLP <- prodest::omega(mod2LP)
summary(mod2LP)
summary(omegaLP)

DataA11$omega <- prodest::omega(mod2LP)

######################################################################################

DataA11 <- DataA11 %>%
  arrange(ID, Year) %>%
  group_by(ID) %>%
  mutate(domega = omega - dplyr::lag(omega),
         debt = LTD + STD,
         ddebt = debt - dplyr::lag(debt),
         dsales = Sales - dplyr::lag(Sales)) %>%
  ungroup

PDataA11 <- pdata.frame(DataA11, index = c("ID","Year"))

pdim(PData)
pvar(PData)

z1 <- pgmm(domega ~ lag(domega, 1:2) + ddebt + ff1 + ff1:ddebt + Age + ta + dsales | lag(domega, 2:99),
           data = PDataA11, effect = "twoways", model = "twosteps")
summary(z1, robust = TRUE)

ALSO! It would be perfect if you provide any information on that package and also what I do incorrectly + would be great if you said how to add fixed effects to this pgmm function.
Thanks a lot to each of you in advance!!!:)
UPDATE:
data("EmplUK", package = "plm")

## Arellano and Bond (1991), table 4 col. b
emp.gmm <- pgmm(log(emp)~lag(log(emp), 1:2)+lag(log(wage), 0:1)+log(capital)+
                  lag(log(output), 0:1)|lag(log(emp), 2:99),
                data = EmplUK, effect = "twoways", model = "twosteps")
summary(emp.gmm)

I run this code, that is provided here: https://rdrr.io/cran/plm/man/pgmm.html
and I get the following message:


texts:
Someone was saying: "Why is credit so important? Because when a borrower receives credit (loan), he's able to increase spending. Spending drives the economy. This is because one person's spending is another person's income ".

I think he didn't look at the lender's prospective. When a lender gives his money to someone else, his spending will decrease. So the economy is balanced and this will not drive the economy. The same amount is spent just by a different person.

Am I right?  What am I missing?


texts:
I am trying to prove the existence of at least one stable steady state in a situation where I am given properties of the production function but not an explicit functional form. I have the following (implicit) first order difference equation for the evolution of capital (comes from an overlapping generations model with no uncertainty):

$$ (1+n)k_{t+1}(k_t)=s(w_t,R_{t+1}) $$
Where $k$ is per capita capital, $n$ is population growth, $s$ is savings, $w$ is wages (the problem assumes that labor is inelastically supplied), and $R$ is rental rate on capital, with the appropriate time subscripts. From the firm's problem, and the assumption that the production function is CRS, this can be re-written as:
$$ (1+n)k_{t+1}(k_t)=s(f(k_t)-k_tf'(k_t), f'(k_t)-\delta)$$
Where $\delta$ is depreciation. We are given standard assumptions on $f(k)$: $f(0)=0, f'(k)>0, f''(k)<0$, Inada conditions: $ \lim\limits_{k \to \infty}f'(k)=0,\lim\limits_{k \to 0}f'(k)=\infty$

I have been able to prove that

1) $k_{t+1}(0)=0$

2) $\lim\limits_{k \to \infty} \frac{k_{t+1}}{k_t}=0 $, implying that at some point, $k_{t+1}$ lies below the $45^\text{o}$ line

3) Solving for the derivative of $k_{t+1}$ with respect to $k_t$:
$$ k_{t+1}^{'}(k_t)= \frac{-\frac{\partial s}{\partial w_t}k_tf''(k_t)}{1+n-\frac{\partial s}{\partial R_{t+1}}f''(k_{t+1})} $$

Making some additional assumptions on the derivatives of savings with respect to wages and interest (that aren't relevant to my question), I have that this is positive.

However, in order to show that there exists at least one stable steady state, I need to show that $k_{t+1}$ crosses the $45^\text{o}$ line from above. This is where I am stuck. My professor says that this follows from the Inada conditions on $f(k)$, but I'm not seeing it. If I can show that $\lim\limits_{k \to 0}k_{t+1}^{'}(k_t)=\infty$, then I think I'm set. And this will hold if $\lim\limits_{k \to 0}k_tf''(k_t)=\infty$ (I think). But the Inada conditions are on $f'(k_t)$, not $f''(k_t)$, so I don't know how to get what I need.

Thanks very much in advance for the help!!


texts: Has the assumption that individuals' tastes do not change over time been rigorously challenged?

texts:
In their seminal paper De Gustibus non est Disputandum, Stigler and Becker (1977) surveyed four classes of phenomena widely believed to be inconsistent with the stability of tastes: addiction, habitual behavior, advertising, and fashions, and in each case offered an alternative explanation.

All these explanations are based on the assumption that individual tastes are stable over time. They compare tastes to the Rocky Mountains: "both are there, will be there next year, too, and are the same to all men.”

Question: I am wondering if the assumption that individual's tastes do not change over time has been rigorously challenged. And how?

Note: I added rigorously because their argument is subtle and very persuasive. For example, the role of experience and addiction can be explained with stable preferences. As a consumer gains experience with a good, it becomes easier to use. Thus the cost of using it goes down as use goes up, resulting in higher marginal profit. As the marginal utility diminishes with usage, equilibrium is reached when the diminishing marginal utility gains match the reduction in cost obtained by increases usage.

Update: I found a nice related survey on Endogenous Preferences by Samuel Bowles.


texts: Constrained optimization for $u(x_1,x_2,x_3,x_4)=\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \}$

texts:
Suppose preferences are represented by the following utility function

\begin{equation}
u(x_1,x_2,x_3,x_4)=\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \}
\end{equation}

Write the

Walrasian demand functions
Hicksian demand functions
Indirect utility function
Expenditure function

Remark

I come from a math background and my only experience with economics are (so far) the first three chapters of the book Microeconomic Theory by Mas-Colell, Whinston, and Green. Following their approach, I want to solve the following
utility maximization problem

\begin{equation}
\max_{\vec{\mathbf{x}}\in \mathbb{R}^4} \{u(\vec{\mathbf{x}})\} = \max_{x_1,x_2,x_3,x_4} \{\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \} \}
\end{equation}

s.t. $p_1 x_1 + p_2 x_2 = w$

to get the Walrasian demand functions $x_i(\vec{\mathbf{p}},w)=x_i(p_1,p_2,p_3,p_4,w)$. Then I could get the indirect utility function by substituting these solutions into the utility function:
\begin{equation*}
v(\vec{\mathbf{p}},w)=u(x_1^*(\vec{\mathbf{p}},w),x_2^*(\vec{\mathbf{p}},w),x_3^*(\vec{\mathbf{p}},w),x_4^*(\vec{\mathbf{p}},w))
\end{equation*}
Similarly, to get the Hicksian demand functions $h_i(p_1,p_2,p_3,p_4,u)$, I would solve the expenditure minimization problem
\begin{equation*}
\min_{\vec{\mathbf{x}}} \{\vec{\mathbf{p}} \cdot \vec{\mathbf{x}}\}
=\min_{x_1,x_2,x_3,x_4} \{p_1x_1+p_2x_2+p_3x_3+p_4x_4\}
\end{equation*}
and then get the expenditure function by multiplying
\begin{align*}
e(\vec{\mathbf{p}},u)
&=\vec{\mathbf{p}} \cdot \vec{\mathbf{h}}^*(\vec{\mathbf{p}},u)
 \\
&=p_1 h_1^*(\vec{\mathbf{p}},u) +p_2 h_2^*(\vec{\mathbf{p}},u)+p_3 h_3^*(\vec{\mathbf{p}},u) + p_4 h_4^*(\vec{\mathbf{p}},u)
\end{align*}
Although I can visualize the entire process, I'm stuck at the beginning - solving the constrained utility maximization and expenditure minimization problems. Starting with the utility maximization problem, I want to write the Lagrangian
\begin{equation*}
\mathcal{L}(x_1,x_2,x_3,\lambda)=\alpha \min\{a x_1, b x_2 \} + \beta \min \{c x_3, d x_4\}+\lambda(w-p_1x_1-p_2x_2)
\end{equation*}
and take the first order conditions
\begin{equation*}
\frac{\partial u(x_1,x_2,x_3,x_4)}{\partial x_i}=\lambda p_i
\end{equation*}
however I don't know how, mathematically, to take the above first order conditions with respect to $x_i$ since $\min$ isn't everywhere differentiable. (However, as this answer points out, the partial derivatives of our objective function exist almost everywhere.)

This is my first experience with solving for demand functions, aside from the Cobb-Douglas example provided in the book Microeconomic Theory. Could anyone help me complete this example?


texts:
Hey there! Can anyone help me with this? I am able to arrive to expression (3) from (2) by using the lagged variable and make the variation from $Y_t$ and then divide to the right such that $\beta_0 = \alpha_0 /(1-\alpha_1)$. But I cannot arrive to (4) any help?
Thanks a lot in advance!


texts: Showing existence of a Nash equilibrium in pure strategy

texts:
Consider a game with $N$ players, each indexed by $i=1,...,N$. Every player $i$ has to choose a $J\times 1$ vector of actions $a_i\equiv (a_{i,1},...,a_{i,J})$ where each $a_{i,j}$ can be zero or one. For each player $i$, let $a_{-i}$ denote the actions of the other players.
The payoff of each player $i$ is
$$
u_i(a_i, a_{-i}; \theta)+v_i(a_i; \delta)
$$
where $u_i$ and $v_i$ are some parametric functions of the parameters $\theta$ and $\delta$. Moreover $v_i$ is monotone decreasing in $\sum_{j=1}^J a_{i,j}$.
A pure strategy Nash equilibrium (PSNE) of the game is $a^*\equiv (a_1^*,...,a_N^*)$ solving
$$
 a_i^*\in \arg\max_{a_i\in \{0,1\}^J} u_i(a_i, a^*_{-i}; \theta)+v_i(a_i; \delta) \quad \forall i=1,...,N
$$
Question: Suppose that I'm able to show that a PSNE exists for $\theta=\theta_0$ and $\delta=\delta_0$ where $\theta_0$ and $\delta_0$ are some specific real values of the parameters $\theta$ and $\delta$. Can I conclude that a PSNE exists for $\theta=\theta_0$ and any value of $\delta$?
In particular, here, I'm wondering whether the claim may follow from the fact that $v_i(a_i; \delta)$ enters additively, does not depend on $a_{-i}$, and it is monotone.


texts: Can integrals be interpreted simultaneously as aggregates and averages? (Mas-Colell et al. 1995, Proposition 4.C.4)

texts:
I'm currently reading chapter 4 of Mas-Colell, Whinston, and Green (1995).
I have a problem with the way integrals are treated. For instance, Proposition 4.C.4 (p.113) states that when wealth is uniformly distributed on $[0,W]$, the aggregate and the average demand function are:
$$x(p) = \int_0^W x(p,w) dw $$

Where $x(p,w)$ is an individual demand (every individual has the same preferences, their demands only differ in the amount of wealth).

However, I think the right way to write the average would be:
$$x(p) = \int_0^W \frac1W x(p,w) dw $$
because this is the definition of the expected value.

Am I wrong? When using integrals, can I just assume that averages are equal to aggregates?
This a big problem to me because in exercise 4.C.10 it is asked to prove that $$C(p,w)=\int_0^W S(p,w)dw - S(p,W)=-D_w x(p).x^T(p)+\int_0^WD_w x(p,w).x^T(p,w)dw$$ is positive definite, where $S(p,w)$ are individual Slutsky matrices, and $S(p,W)$ is the Slutsky matrix of aggregate demand.

I thought to define $w=aW$ with $a$ uniformly distributed on some interval. Therefore, I could re-define $x(p)=x(p,W)$ and differentiate $x(p)=x(p,W)$ and $x(p,w)=x(p,aW)$ with respect to $W$. However, I'm not sure how to define an interval for $a$ such that average wealth is equal to aggregate wealth using $w=aW$.

Note: Proposition 4.C.4 is based on an example given by Hildebrand (1983) ("On the Law of Demand"). I read the article and he assumes wealth is distributed on $[0,1]$. With this interval, aggregate demand is equal to average demand. Does this mean Proposition 4.C.4 is misspelled? If it is so, I still have a problem with exercise 4.C.10 because I need an interval for a such that aggregate wealth is equal to average wealth.


texts: Doesn't the Pareto-extension rule invalidate Eliaz's (2004) unified theorem of social choice?

texts:
Eliaz (2004) uses social aggregators to provide a unique "meta-theorem" from which Arrow and Gibbard-Satterthwaite follow as corollaries. He defines social aggregators as follows. Let $\mathcal{P}$ denote the set of all n-tuples of linear (thus strict) orderings over the elements of set $X$, where $|X| \geq 3$, and $\mathbf{R}$ a set of binary relations on $X$. A social aggregator is a function $F: \mathcal{P} \rightarrow \mathbf{R}$. A social welfare function is a social aggregator satisfying acyclicality, completeness, and existence of a best alternative; a social choice function takes more work to define, but in short, completeness is only required for at least one alternative which is socially ranked at least as high as all others.
Eliaz then proves that no non-dictatorial social aggregator can satisfy acyclicality, existence of a best alternative, weak Pareto efficiency, and "preference reversal", which is basically an independence requirement by which a reversal of the social relation must follow the same reversal in the preferences of an individual. He then shows that from the conditions above follow all the conditions in Arrow and Gibbard-Satterthwaite, which are thus just special cases of the general meta-theorem.
I have two key questions:

To be a social welfare function à la Arrow, do we not require more than just acyclicality - in particular, transitivity? Is it correct that what Eliaz calls a social welfare function, is actually a social decision function?

If so, isn't Sen's (1969) Pareto-extension rule a counter-example to the meta-theorem? For strict individual orderings, the Pareto-extension rule works as follows: all conflicting profiles (i.e. all those profiles in which there are two $x,y \in X$ and two $i,j \in N$, $N$ being the set of individuals, such that $xP_i y$ and $yP_j x$), then $xRy$ and $yRx$, $R$ being the social relation. In other words, the Pareto-extension rule resolves all conflicts by ties. This rule should satisfy all condition imposed by Eliaz: acyclicality (it is actually quasi-transitive, a stronger condition), existence of a best alternative, non-dictatorship, independence (subsumed by preference reversal), and clearly, weak Pareto efficiency.


texts: Why does quadratic utility function imply $\mu-\sigma$ preference?

texts: Why does investors having quadratic utility function mean that their optimal portfolios can be chosen by only considering mean and variance of returns i.e. imply $\mu-\sigma$ preference?


texts:
Let's say the Federal Reserve purchases a \$100 one-year Treasury bill from the market, and puts ~\$100 of cash into the economy. A year later, this T-bill comes due, and the Treasury pays the Fed $100. What happens with this cash?

I can imagine a few possibilities:

The money is immediately reinvested in new securities. Since no new money is created, the monetary base stays constant.
The money is destroyed, shrinking the monetary base.
The money is transferred to the Treasury as Fed revenue. Since this money (a Fed liability) is no longer backed by a security, the Fed's balance sheet goes into the red.

This question is motivated by this quote from the Wikipedia page on Debt Monetization:

  The central bank may purchase government bonds by conducting an open market purchase, i.e. by increasing the monetary base through the money creation process. If government bonds that have come due are held by the central bank, the central bank will return any funds paid to it back to the treasury. Thus, the treasury may "borrow" money without needing to repay it. This process of financing government spending is called "monetizing the debt".

This seems to imply the third of my listed possibilities, but as mentioned this seems to break the promise that all Fed-issued money is backed by assets.


texts: Difference between pigovian tax and sin tax?

texts: Could they be interchangeably used? Or, is one subset of the other?


texts:
It has been shown, for example in the papers

Deng, Du, The Computation of Approximate Competitive Equilibrium is PPAD-hard
Hirsch, Papadimitriou, Vavasis, Exponential Lower Bounds for Finding Brouwer Fixed Points

that finding competitive equilibria is in a certain sense computationally intractable.
So how does economic theory expect a market to reach a competitive equilibrium if each agent is presumably representable by an efficient computational process?
In fact, parallel computation doesn't really help because a polynomial number of processors can be simulated in polynomial time.


texts: How can the Fed enforce exit criteria if they begin yield curve control?

texts:
Over the past year, the notion yield curve control has resurfaced and appeared on FOMC minutes, decades after its last implementation.
According to the Fed's introduction page:

As the U.S. continued to incur debt, the Fed was obligated to keep
buying securities to maintain the targeted rates—forfeiting some
control of its balance sheet and the money stock. The public generally
preferred to hold higher-yielding, longer-term bonds. Consequently,
the Fed purchased a large amount of short-term bills, which also
increased the money supply, to maintain the low interest rate peg.
After the war ended, FOMC members grew more concerned with addressing
the rapid inflation that materialized. However, President Harry S.
Truman and his treasury secretary still favored a policy that
maintained YCC (which also protected the value of wartime bonds by
implying a price floor). By 1947, inflation was over 17%, as measured
by the year-over-year percent change in the consumer price index
(CPI), so the Fed ended the peg on short-term rates in an attempt to
combat developing inflationary pressures.)

This poses an interesting dilemma in configuring the bounds of the program. WW2 was a one-sided victory with rather clear end date. Yet the fact that YCC continued post-WW2 suggests that terminating the program was difficult. It's conceivable that marshaling the political will to end a program that the treasury likely derives massive utility for operating against a high fiscal-deficit backdrop was a major challenge. This phenomenon is sometimes termed "fiscal dominance."
A BIS paper goes into great length on the matter. Condensing one of the themes:

For many, a long period of large fiscal deficits and very high public
debt-to-GDP ratios raises the spectre of fiscal dominance. It will in
any case accentuate the links between fiscal policy, monetary policy
and government debt management.

Question
How can the Fed enforce exit criteria without a massive/dramatic macro impairment (such as double-digit inflation)?


texts: Contour set in Mas-Collel, Winston and Green

texts:
Mas-Colell, Winston and Green's Microeconomic Theory uses the notion of contour set, as shown hereunder:

In the context of Microeconomic Theory, what would be the definition of a contour set?


texts: Solving problem for optimal price (maximize profit) *attempt inside*

texts:
Let a demandfunction be defined as
$D(p)=B-bp$, where $b,B>0$. A firm has some production cost, $c$, and can set the price $p$ under the constrain given by the Demand.

What is the optimal price?
Is the priceelasticity higher or lower than $1$ (absolute value)
How does price depend on $b$?

How would one do such a maximization problem?
My attempt
The elasticity would be given by
$\frac{p}{q}\cdot(-b)$ since $D'(p)=-b$
Then the problem is
\begin{equation*}
    max_p(p-c)D'(p)
\end{equation*}
which then follows that
\begin{equation*}
    D(p)+(p-c)D'(p)=0 \Leftrightarrow
\end{equation*}
\begin{equation*}
    D(p)\left ( 1+(p-c)\frac{\epsilon}{p} \right )=0\Leftrightarrow
\end{equation*}
and then the optimal price $p^*$
\begin{equation*}
    p^*=\frac{\epsilon}{1+\epsilon}c=\frac{\left | \epsilon \right |}{\left | \epsilon \right |-1}c=\frac{\left | \frac{-bp}{q} \right |}{\left | \frac{-bp}{q} \right |-1}c=\frac{c\left | b \right |\left | p \right |}{\left |  b\right |\left |p  \right |-\left | q \right |}
\end{equation*}
and then we notice that
\begin{equation*}
    \left | \epsilon  \right |>1
\end{equation*}
...............................................................................................
I feel like this is not correct nor the right approach. Help appreciated.


texts: Are strict dominance solvable games weakly dominance solvable?

texts:
Okay consider a game $G$ if a strategy $s_i$ has the following property we call $s_i$ the strictly dominant strategy

$$u_i(s_i,s_{-i})>u_i(s_i',s_{-i}) \\ \forall s_{-i} \ \forall s_i' \epsilon S'_i$$

Where $s_{i}$ indicates the strategies of players other then $i$ in the game and $S'_i$ is the set for strategies of player $i$ except the specific strategy $s_i$

Now let's look at the definition of a weakly dominant strategy

if a strategy $s_i$ has the following property we call $s_i$ the weakly dominant strategy

$$u_i(s_i,s_{-i})≥u_i(s_i',s_{-i}) \\ \forall s_{-i} \ \forall s_i' \epsilon S'_i \ and \\ \exists s_i' \epsilon S'_i \ such \ that: \ u_i(s_i,s_{-i})>u_i(s_i',s_{-i})$$

Okay I believe from these two definitions we can derive that any strictly dominant strategy $s_i$ is also a weakly dominant strategy

Definition of strict dominance solvable is as follows :

A strict dominance solvable game is a game where the equilibrium outcome is strict dominance equilibrium.
A weakly dominance solvable games is a game where the equilibrium outcome is weakly dominance equilibrium.

So It seems like then a strictly dominance solvable game is always a weakly dominance solvable game. Am I wrong?


texts: Is it possible to have constant marginal cost and decreasing average cost simultaneously?

texts: I thought about possibility of occurring such event in the case of presence  of fixed costs, but I would like to know others opinions.


texts: Do stock markets price in existential risk (i.e. global nuclear war)?

texts:
Question Moved from Money StackExchange:
  https://money.stackexchange.com/questions/74002/do-stock-markets-price-in-existential-risk-i-e-global-nuclear-war

Q: Do stock markets price in existential risk?

The Cuban Missile Crisis in November 1962 is an example of coming to the brink of global nuclear war, and while the markets were down until its resolution, the index price did not seem to reflect anything resembling "imminent end of the world".

More recently, Putin's declaration to escalate nuclear weapon systems development, Trump's comments on expanding nuclear capabilities, and Noam Chomsky declaring the exchange "very frightening" suggests that we're in a period of elevated nuclear war risk.

However, the US stock markets are at their historical highs. How can this be resolved? I can think of two possibilities:

Markets accurately reflect the risk. Cuban crisis was a real, but small risk, thus the market dip. Today, the risk is nearly zero, thus the markets are not down.
Markets ignore existential risk. Rational investors expect a return on investment, but if the investors believe an event would kill them and their estate, the loss due to that event is irrelevant. Thus the risk of existential, planet destroying events, does not correlate with the stock market prices.

Is this true, can stock market price be trusted to reliably reflect existential risk?


texts: How to know if I've done the necessary corrections to my data so that the regression is valid?

texts:
Obviously the data can't be changed to fit a regression, it should be (kind of) the other way around.

But, sometimes the data has stuff going on that needs correction. For example, I got raw data from the Law Enforcement Management And Administrative Statistics 2007 survey. I did a linear multiple regression on it using Stata, and then analyzed the residuals and found heteroskedasticity. So I corrected for it by using the , robust option in my regression code.

Sometimes the data have other problems like data points that are very influential. And sometimes the data doesn't have a very linear relation, more of a curvy one. And I don't know a lot about regression, but I think there are other possible problems with data. Maybe partially filled surveys or falsified information.

Anyway, how do I know that the data itself was good, and that instead (if there were a problem) the problem was in the regression?

I was using this page to try to guide myself through the process http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter2/statareg2.htm
but I don't know if that's everything I have to check for.


texts: Is the average age of economists getting higher than it was many years ago?

texts: I read Hamermesh's 2012 paper, "Six Decades of Top Economics Publishing: Who and How?". He collected the data from QJE, AER and JPE. It seems that the average age of economists is now higher than it was 20 or even 10 years ago. However, I wonder if things might be different in second tier journals. Maybe now young economists tend to submit their paper to these journals?


texts: calculation of the real domestic return of a foreign stock

texts:
I would like to calculate the real domestic return of a foreign stock

What I know
Real price is $$P_{Real, t} = \frac{P_{Nominal, t}}{CPI_t}$$
where CPI is consumer price index.
And I know that the nominal domestic return of a foreign asset is calculated as follows:
$$R_{Nominal, Domestic, t} = \frac{(P_{Nominal, Domestic, t}) \times E_t}{(P_{Nominal, Domestic, t-1}) \times E_{t-1}}$$
Then, when I want to calculate the real domestic return of a foreign asset, would I do as follows?
$$R_{Nominal, Domestic, t} = \frac{((P_{Nominal, Domestic, t}) \times E_t )/ CPI_t}{((P_{Nominal, Domestic, t-1}) \times E_{t-1}) /CPI_{t-1}}$$
where E shows the exchange rate.
Is this way true? How can I calculate?
Please share your ideas with me. Thank you in advance.


texts: Why does marginal cost (derivative of total cost) differ from variable cost at each level?

texts:
Why does the marginal cost equation (as the derivative of total cost equation) make predictions of variable costs that are very different from costs calculated using the Total Cost equation?

Marginal cost is simply the change in cost divided by the change in quantity.

MC = ΔC / ΔQ

However, marginal cost also can be computed using the derivative of the Total Cost function.

Suppose you have a short-term Total Cost equation for a production case in which no capital is used; labor is the only input.

TC = w * L

The production function is

Q = L^(1/3)   ... therefore
L = Q^3

And given that the w = 1, then

TC = Q^3

Therefore the Marginal Cost equation, as the derivative of the Total Cost equation, would be...

MC = 3Q^2

Of course, when Q = 0 then the TC equation and MC equation = 0.
But raise Q to 1, and TC is now 1. Therefore, MC = ΔC / ΔQ = 1.

But the MC equation gives MC = 3.

The difference grows as Q increases more. When Q = 2, the TC equation returns 8, a cost change of 7, while the MC equation returns 12.

I understand mathematically why these are different, but I don't understand why both are supposedly correct and useful in economics.

Marginal analysis says to only produce a quantity if the marginal cost is less than or equal to the price at that quantity. But in this example, if the price were \$2, someone using the TC equation would produce the first unit for a profit of \$1 while someone using the MC equation would not produce the first unit because the MC equation predicts a \$1 loss. It seems like at least one of these methods lacks practical value. So, could someone explain the difference?


texts: Having trouble solving system of equations through matrix approach

texts:
So I have this system of reaction functions:

$$s_1 = 2 + \frac{1}{3} s_2$$
$$s_2 = 7 + \frac{1}{8} s_1$$

I have to solve this through inverse matrix and confirm the result through Cramer's rule. The result is I'm getting awkward values:

$$ \begin{bmatrix} s1 \\ s_2 \end{bmatrix} = \begin{bmatrix} 52.6 & 2.6 \\ 54.6 & 15.6 \end{bmatrix}$$

I don't think so this is the correct result since Cramer's rule cannot really be applied to this system. Any suggestions?


texts: What is the impact of a technology to produce gold at low cost?

texts:
Let's say in a few decades we can find a new technology to produce gold at low cost which will cause the price of gold to be as low as other metals.

My question is that how would this have an impact on the economy of countries which hold significant amount of golds? And how would this impact on the economy of other countries?


texts: In a trading economy with many agents, can two agents with the same income envy eachother?

texts:
In a economy with an arbitrary number of agents whose preferences all satisfy the usual equilibrium conditions and with each starting with a random starting endownment, are there any two agents with the same income at equilibrium who might envy eachother?

Please notice that not all agents have the same income.


texts: What are the most popular technical models used for forecasting exchange rates in international economics?

texts:
Are there any de facto standards when publishing, or is there substantial latitude in deriving one's own methodology?

I understand in practice, even the St. Louis Fed is gently skeptical of the validity of most technical methods, but I was wondering how academia viewed them.

While Dooley and Shafer (1976, 1984) were largely dismissed, Neely and Weller (1999) seemed to fare fairly well using genetic algorithms, and Markov and ARIMA methods are reviewed more or less favorably in terms of predictive value.

Is accuracy of prediction (and consequently profitability) even necessarily a factor in modelling for academia, or is the simplicity and explanatory value more heavily favored?$^1$
$^1$*Note: Not sure if this merits a separate question, or can be answered as an elaboration of the primary*


texts: Price elasticity of demand in the point of economic equilibrium

texts:
The function of demand is:\begin{align*} D(p) = 66-3p-p^2 \\\end{align*}
The function of supply is: \begin{align*}S(p) = 4p^2+8p-114\\
\end{align*}
The task is to find price elasticity of demand in the point of economic equilibrium.

I have found out that the equilibrium price is 5 and equilibrium demand is 26.

I also have a formula that states that $E = k * P/Q$
, where $P$ - equilibrium price, $Q$ - equilibrium demand and $k$ - coefficient  of $S(p)$ slope

How to find $k$ or are there another methods to solve this task?


texts:
I'm revisiting some old topics from introductory economics and I am not quite sure I have convinced myself of the theory behind marginal utility. I have a few simple questions if anyone could please help me with.
On a demand curve, if we move from point 1 to point 2:
the increase in demand is due to two classes of buyers:

Buyers who would've bought at a higher price but are now buying even more at a lower price (marginal utility of second quantity now greater than new price at P2)

Buyers who were not buying at all at the previous price and are now buying (marginal utility of first quantity now greater than new price at P2)

In general, is the increase in demand attributed more to buyers of class 1 or class 2? Intuitively, I always thought it would be class 2. In my personal experience, decisions for buying or not buying tend to be more binary in an all or nothing fashion so the marginal utility theory applied to class 1 has not held as strongly as it has in class 2.
If theres no simple answer, is there a topic I should look into to get a better understanding?


texts:
I'm a little confused about the terminology used in economics literature while describing iterative and continuous auctions. Have I understood the difference correctly?

Iterative Auction: The auctioneer repeats the auction and the traders submit bids/asks until a purpose (welfare maximization etc.) is reached.

Continous Auction: The auction does not happen only once and there are different rounds of auction happening continuously.