texts:
I have data on disposable income, where some households have negative income. Albeit I can immediately compute the Gini with these dataset (e.g. with ineqdec0, inequal7 or fastgini in Stata), it is well known that Gini with some negative values could be higher than 1. An example from such reference:

Is there an "optimal" method to deal with such observations?

I can think of some approaches like:

truncating: eliminating all observations with negative income
censoring: assign zero income to all negative income
translation: add to every observation the largest negative income, so that the poorest observation has zero income
some type of normalisation, like the one the reference above gives:

In all these cases, the Gini will now be between 0 and 1. Is there a "preferred" or an "usual" method? (perhaps by multilateral organisations like IMF, OECD, etc)

As a secondary question, is there an inequality index that is better poised to deal with negative income?


texts: Vector Autoregression - Resource request

texts: I am looking for resources that give a self-contained introduction to vector autoregression. To be a bit more specific, I am interested in VAR models and their application to isolating and investigating monetary policy shocks.


texts: What are the differences between hedging with swaps, options or futures?

texts:
For instance if a bank wants to hedge against interest rate risk, it could use interest rate swaps, or options or futures contract. Or in any other example, when a manager is hedging against risks.

Can somebody show it how these differ from each other in an example?


texts:
Can you explain why the current account of a country is a relevant indicator for the stability of its economic development? I read about this but do not exactly see the link that qualifies it as a indicator.

Afteredit:

Wikipedia says this:

A current account surplus indicates that the value of a country's net foreign assets (i.e. assets less liabilities) grew over the period in question, and a current account deficit indicates that it shrank.

I do not understand why these points say us something about the stability of the development. (Sorry, that I didn't manage to express clearly from the beginning but I'm no native speaker.)

Is my problem now more evident?

Greetings Rico


texts:
I would like to better understand what is the wealth of a company and what is made of.

Is the wealth of a company similar to GDP of country, like a "gross company product" ?

As example: can we say GDP as total market value of good a services produced by a country in a certain amount of time, and wealth of a company is the market value of assets and services produced in a certain amount of time?

Could the two measures be compared ?
Or is the market value of a company conceptually a different thing than a "gross company product" ?


texts:
I know that printing money causes inflation, but what if we print it to pay back our debts?

For example, we have N dollars of debt to China.  We can just print the N dollars and give it to China.

This way, we would not have more money in our country which would cause inflation, and we would not be giving from our own money, which would cause deflation.  Also, China gets back the money U.S. owed it.

My guess is that it would cause some kind of weakening of the Chinese money against the USD, but could anyone verify that?


texts: The fundamental national income accounting identity is: $Y = C + I + G + X - M$. The multiplier effect tells us that an autonomous injection into the economy will result in a multiplied increase in the real national income due to rounds of induced consumption. My question is, if that is indeed the case, then wouldn't the national income identity need to be modified to include the multiplier? That is to say, wouldn't it become: $Y = k_c C + k_i I + k_g G + k_x X - k_m M$?


texts: In log-linearized New Keynesian model, what do $Y$, $Y_t$, $y_t$ actually mean?

texts:
This may be a weird question, but I am unfortunately confused by terms. Let us suppose log-linearized New Keynesian model as suggested by Gali here: http://crei.cat/people/gali/pdf_files/monograph/slides-ch3.pdf

My first question is, apparently steady value $Y$ is assumed to do log-linearization of $Y_t$, output, but is this $Y$ a constant value, or the whole steady output path? Equivalently, is $Y$ about how output will evolve if $Y_t$ evolves without stochastic factors and errors according to long-run natural rate?

My second question, related to the first question, is whether $Y_t$ refers to total output or normalized output. That is, if economy has positive output growth rate, will $Y_t$ grow? Or is it normalized output that does not change without stochastic elements?

My third question is, what $y_t$ actually mean. As I understand it, it is just $\log Y_t$. Is this correct?

The fact that consumption euler equation exists seems to support the intuition that $Y$ is steady output path, not constant steady value, as real interest rate is often positive for economy. My confusion all rises from here, and I am not sure if this is correct understanding.


texts: Is it valid to assume that the international price of consumer durables is constant?

texts:
While studying tariffs in International Trade, we often come across a Demand Supply diagram along with a world supply curve that is perfectly elastic. Here we assume that the international or the world price of that good is constant and based on this assumption we carry on with our analysis.

Considering commodities or goods such as wheat, it is safe to assume that the world price will remain the same as it is produced in huge quantities all over the world and no one country/producer can cause a shift in the supply curve.

However, consumer durable such as LCD or Plasma televisions are not produced in such abundance and are often produced by certain countries, say for instance Japan or China.

This reasoning has led me to question the assumption made while drawing the world supply curve in the tariff diagram. I would like to know whether this reasoning is valid or not and if not, then why?


texts: Normality of residual is violated, How to fix it properly?

texts:
One of the key assumption of the OLS is that the normality of the residual.

If this assumption is violated, how can we fix it generally?

Especially, I want to make predictions


texts: utility from providing public good as explained in Hindriks textbook

texts:
I think I understood the highlighted part: basically, by increasing $g^1$ my utility increases because more public good is being provided but at the same time it decreases because I have less money to buy private good $x^1$ - so the effect of increasing $g^1$ is ambiguous.

My question about highlighted part is whether I can somehow see that on a graph below? As it would seem like when I set $g^2$ to be constant and then increase in $g^1$ would only cause my utility to decrease. Is there a way to represent the "initial increase in utility"?


texts:
What is the difference between hidden information and moral hazard?

I cannot understand these two terms mainly. Please explain. Thank you.


texts: Help finding historical data for velocity of money (M1 or M2) for any country except USA

texts: Can anyone point me to a data set of money velocity for at least 20 years back for any other country than the US?


texts: How did Cowen and Tabarrok calculate the probability of Hewlett-Packard sales?

texts:
The discussion on prediction markets in the chapter on the price system in Tyler Cowen and Alex Tabarrok's Modern Principles of Economics, Second Edition (pp. 123-124) contains the following paragraphs:

Members of HP’s sales team bought and sold shares that paidoff when sales fell within a certain range. A typical security would pay out $\\\$1$,
if and only if future sales were, say, between $10,000$ and $15,000$ units. Another
might pay off if sales were between $15,000$ and $20,000$ units. The market con-
tained $10$ types of securities—a range broad enough to include all the relevant
possible sales outcomes.
By examining the prices of all $10$ shares, HP could assign a probability to any
combination of outcomes. For example, if the price of the $5,000–10,000$ unit
sales security was $10$ cents and the price of the $10,000–15,000$ unit sales security was $20$ cents, this suggests that the probability of selling $5,000 –15,000$ units
was $30\%$.

How did the authors arrive at this figure of $30\%$?


texts: Counter example for strong and weak Pareto optimality

texts:
We know that strong Pareto efficient is equivalent to weak Pareto efficient if we have continuous and strongly monotone preferences.
Please give me an example which we don’t have continuous and monotone preferences, so this statement doesn’t hold.
I think that the statement holds for quasi linear utility function.
But I cannot find the counter example.


texts: Economic interpretation of a CES production function

texts:
I am following a paper where a production function of this type is used.

$$Y=\left [\beta K^{- \rho}+\alpha \eta \left (\frac{K}{L} \right )^{-c(1+\rho)}L^{- \rho}   \right ]^{-1/\rho}$$

It is a modified version of a CES where in addition there is the term $\alpha \eta \left (\frac{K}{L} \right )^{-c(1+\rho)}$ which multiply the $L$ factor.

I was therefore wondering. What may be the economic justification interpretation for adding this factor?


texts: Are Microeconomics limited to one country?

texts:
For my IB Econ internal assessment I want to comment on the falling oil prices across the globe.

Would this be covered under Micro because it's 1 specific market? or is it international because it comes after OPEC lost it's influence on the market?


texts: On the uniqueness of utility functions for both risk and time

texts:
I have a question regarding the uniqueness of preference functionals under risky and dynamic settings. Two well known models to represent preferences for both settings are the Expected Utility Model and the Discounted Time-Separable Utility respectively. Formally

Risk:

$$V(f)=\sum_{\forall s \in S} p(s) u(f(s))$$

Where $S$ is the set of states and $p(s)$ is the probability of state $s$, and $u(\cdot)$ a cardinal utility function.

Dynamics:

$$W(c)=\sum_{t=0}^{T} \mathcal{D}(t) v(c_t)$$
Where $\mathcal{D}(t)$ is a discount factor and $v(\cdot)$ is a cardinal utility function.

We know that both $u(\cdot)$ and $v(\cdot)$ are cardinal utility functions, and I understand why. But while every representation theorem of this sort of preferences mention the uniqueness of the functions $u(\cdot)$ and $v(\cdot)$(i.e unique up to positive affine transformations), they are silent about the uniqueness of $V(\cdot)$ and $W(\cdot)$. My question is: are the functions $V(\cdot)$ and $W(\cdot)$ ordinal or cardinal? .

My intuition tells me that they should be ordinal, as they only rank objects of choice and the attitudes towards risk and time are captured respectively by the function $u(\cdot)$ in the case of risk, and the preference for consumption smoothing is given by the function $v(\cdot)$.

For example if $V(f)>V(g)$ then, it should also be that for every increasing function $H(\cdot)$, $H(V(f))>H(V(g))$.

Nevertheless by the linearity of the Expected Utility Functional, i.e,

$$h\Bigg(\sum_{\forall s \in S} p(s) u(f(s)\Bigg)=\sum_{\forall s \in S} p(s) h\big( u(f(s)\big)$$

[So if this is correct, $h(\cdot)$ should be affine, making $V(f)$ cardinal. ]

I suspect that my intuition might be wrong (same applies to the dynamic setting), so I was wondering if you guys could help me clarify this question.

Thank you very much!


texts: Where do remittances come into play in the formula for GDP?

texts: In the classic formula for GDP, i.e., GDP=C+I+G+X-M, where are remittances accounted for? With remittances as high as third of GDP for developing countries, I wonder how they are not explicit in this equation.


texts: reference request: models of how racism or sexism affects decision making

texts:
My background is more in statistics and applied math, so I am not familiar with the breadth of decision making models from economics. However, I am working on a project that involves decision making models, especially with reference to racism and/or sexism in hiring or labor market decisions. I was just wondering if there were any existing economics papers that model decision making where some decision-makers in the decision making process subscribe to differing levels of prejudiced beliefs.

Of course I did search google scholar and looked at the microeconomics section of the American Economic Journal. I found a bunch of statistical papers which demonstrate that there is bias in hiring. But I am really looking for something with a model of the decision making process that includes a racism or sexism component.

Any suggestions would be appreciated.


texts:
How does one define a social welfare in terms of individuals’ preferences $\succeq_i$?
If we have utility functions $u_i$ then a social welfare maximizing outcome $x$ is simply one that maximizes $\sum_i u_i(x)$. How does one specify a social welfare maximizing outcome in terms of preferences?


texts: Can we have incomplete markets with a continuum of securities?

texts:
Imagine there is a continuum of firms in the economy. Each draws its productivity from the same stochastic process. The stochastic process has unbounded support.
The only securities in the economy are the firm's shares.

The claim is that markets are incomplete because the cardinality of the states of the world is $\aleph_2$ and the cardinality of the securities is $\aleph_1$.

However one could also argue that since there is a continuum of firms, the strong law of large numbers applies and one knows exactly the proportion of firms that will get each shock, hence there is no risk (and markets would be complete)

Which of the two statements is correct?


texts: Graphics card shortage - why don't they just raise prices?

texts:
See e.g.

Nvidia CEO: GeForce RTX 3080 and 3090 Shortages To Last Until 2021 (Tom's Hardware, 2020-10-05)
The great graphics card shortage of 2020 (and 2021) (BBC, 2021-01-24)

Why don't Nvidia and retailers just raise the prices of these graphics cards (as might be predicted by Econ 101 supply-and-demand theory)?


texts: Does Game theory consider opportunity cost?

texts:
Morton Davis in his book Game Theory: A non-Technical introduction brings the
following example of a non-zero sum game (pg.73) :

A Buisness Partnership
A builder and an architect are jointly offered a contract to design and construct a building. They are offered a single lump sum as a payment and are given a week to decide whether they accept. The approval of both is required, so they must decide how the lump sum will be divided. The architect writes to the builder suggesting that the profits be divided equally. The builder replies, committing himself to the contract in writing provided he receives 60 percent of the profits. He informs the architect moreover, that he is going on a two week vacation, that he cannot be reached, and it is up to the architect to accept the contract on these terms or reject it entirely.
The architect feels like he is being exploited. He feels that his services are valuable as the builder's and that each should receive half the profits. On the other hand, the probable profit is large, and under different circumstances, he would consider 40 percent of such a total an acceptable fee. Should he accept the builder's offer? Note that the builder has no more options; on the architect has the choice- to accept or reject the contact. This is reflected in the payoff matrix shown:
$$\left[\begin{matrix}(0.40,0.60)\\(0, 0)\end{matrix} \right]$$

My question :
The way the case seems to be presented is that the architect is forced to choose 40 percent in light of the alternative where there is no profits to be gained. What about the architect's opportunity cost? Isn't there what to be gained from the architect when refusing this split of profits in a 40-60 split as far as opportunity cost in concerned?


texts: How to get the percentage-change form of the quantity equation?

texts:
In my book, the quantity equation is presented as
$$M\bar{V}=PY$$
And on the next page, the author presents its percentage-change form:
$$\% \ \text{Change in}\ M + \% \ \text{Change in}\ V = \% \ \text{Change in}\ P + \% \ \text{Change in}\ Y$$
My question is: where exactly does the second equation come from? I've tried manipulating the original equation to see if I could get the percentage-change form, but I didn't get anywhere. Any help will be appreciated. Thanks.

@edit

I've actually found an explanation in a footnote in another chapter of the book (see below), but there's still one thing I don't understand: what are we differentiating with respect to? If it's $Y$, then $d(PY)=P$; if it's $P$, then $d(PY)=Y$; unless we're actually differentiating with respect to some third variable of which $P$ and $Y$ are both functions. In this case, what would that variable be? (I may be misunderstanding it too). Thanks.

Here's the explanation (Mankiw Macroeconomics 7th edition, page 26):

  The proof that this trick works begins with the product rule from
  calculus: $$d(PY)=Y \ dP+P \ dY$$ Now divide both sides of this
  equation by PY to obtain: $$d(PY)/PY)=dP/P+dY/Y$$ Notice that all
  three terms in this equation are percentage changes.


texts: Market efficiency in software, music, news, etc

texts:
I'm not an ecomonist, but have been tossing around some ideas in my head for a long time and thought I might ask here what resources or existing work might be out there.

There are a lot of market sectors where the cost of manufacturing one additional unit of a good is essentially zero. Almost all (or nearly all) of the cost is in development. It seems to me that the efficient market hypothesis must break down in this regime, since efficiency could always be increased by not redistributing goods but rather cloning them at no cost. I believe Pareto efficiency may not even apply in these markets. This is potentially a problem/opportunity for sectors such as software, music, news, website content in general, customer data, and more.

We see a variety of methods that have been adopted to help create more efficient markets. Subscription-based services, open-source software (the main currency there is not money), crowd-funding, snowdrift coop, and more. But I'm curious if there might exist a theoretical market economy that maintains some version of efficiency into this regime? Is there some modification to our current systems or some new form of currency that could be introduced that would self-regulate and optimize here? I'm not much concerned with practicality, just theory.

An alternative way of looking at this issue is that producing some types of goods necessarily benefits people who are not buyers or would not ordinarily be. From this perspective there might be other industries to consider such as public infrastructure, basic research, or military. Normally these are government-regulated, not market-regulated.

Anyway, that's the general scope of problems I've been thinking about. Is this even a real or recognized problem? Can it be measured? (I feel like the advertising industry may hold a key to measuring this, but I can't figure out how or even quite why.) How else is this effect characterized? What measures of efficiency have been proposed? Are there any solutions? I know I'm going to need additional education in this field, but I don't yet know which direction to head in. I feel like I might make some progress given some new definitions of efficiency and coding up simulations. (My background is in particle physics.) Existing terminology might help me search through literature.


texts: How was the Cobb Douglas function derived?

texts:
In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs (particularly physical capital and labor) and the amount of output that can be produced by those inputs. The Cobb–Douglas form was developed and tested against statistical evidence by Charles Cobb and Paul Douglas during 1927–1947.
How we get the formula $f(K,L)=AK^aL^{1-a}$? How we get that $K$ must be elevated to some factor "$a$" and this must be multiplied by $L$ elevated by some factor "$1-a$"? What is the proof of this formula? I can't find an answer to this questions i search it a lot.
Update.
I found an article that shows how to deduce it, but i don't understand some steps, could someone help me? Here goes the link:
https://www.studocu.com/en-gb/document/kings-college-london/mathemtics-for-economists/lecture-notes/cobb-douglas-revision/4229598/view
In these terms, the assumptions made by Cobb and Douglas can be stated as follows:

If either labor or capital vanishes, then so will production.
The marginal productivity of labor is proportional to the amount of production per unit of
labor.
The marginal productivity of capital is proportional to the amount of production per unit of
capital.

Solving.
Because the production per unit of labor is $\frac{P}L$
, assumption 2 says that:
$$\frac{∂P}{∂L} = α\frac{P}L $$
for some constant α. If we keep K constant($K = K_0$), then this partial differential equation
becomes an ordinary differential equation:
$$\frac{dP}{dL} = α\frac{P}L $$
This separable differential equation can be solved by re-arranging the terms and integrating both
sides:
$$\int \frac{1}P \, dP = α\int \frac{1}L \, dL$$
$$ln(P)=α*ln(cL)$$
For example here, from where it comes the constant "c"?, then following:
$$ln(P)=ln(cL^α)$$
$$P(L,K_0)=C_1(K_0)L^α$$
where $C_1(K_0)$ is the constant of integration and we write it as a function of $K_0$ since it could
depend on the value of $K_0$.


texts:
Newspapers like Forbes, CNet, WSJ and many other say that it is possible to have total profit of industry more than 100 %.

Examples:

  Apple and Samsung account for more than 100% of industry profits
  because other makers broke even or lost money

  Samsung and Apple combined to take 106% percent of the industry's
  profits. How do they take more than 100%? Well, it's a quirk of the
  fact that everyone else in the industry is losing money, or breaking
  even. Apple has 65% of the industry's profits, and Samsung has 41%.

Source: Business Insider: Apple And Samsung Have 106% Of The Smartphone Industry's Profits

I can't imagine that. Profit means positive value. Negative value is loss. Is it possible to count loss into total industry profit?

When I create an example like this:

  Company A - loss 100
  Company B - loss 100
  Company C - profit 10
  Company D - loss 10
  = total "profit" -200.

Company C would take -5 % of industry profits.
Company D would take 5 % ...

How it is possible that big newspapers use such irrational math?


texts: Could indexation of wages help Argentina?

texts:
In Argentina we experience one of the largest inflation rates of the world.(please click the top of the inflation rate column to order by inflation rate).

This is a large problem that causes stress and uncertainty to very big numbers of people. Periodically, indeed every year, there is a fight with the government called "paritarias" (spanish) in wich we agree, to put it more simply than it really is, by how much percentage the salaries will increase.

The government inflation rates are not credible. Big parts of the population, specially those opposed to the FPV, don't believe those are the inflation rates, they say they are higher in reality.

I was thinking to myself that maybe we could implement a system wich automatically raises wages according to inflation, at least for certain workers such as public teachers, that already have very established tasks and amount of hours of work per week assigned.

Then I read this article and though this is what i was looking for!

The article describes a process exactly to what I was thinking:

  Indexation is a technique to adjust income payments by means of a
  price index, in order to maintain the purchasing power of the public
  after inflation

But then I thought to myself: Actually our government, (I suspect since I'm ignorant about economics ), uses inflation, by creating money to pay it's debts (to the government officials it's salaries for example) so they are not going to want to raise the salaries at the same time as inflation, but try to wait as long as possible, because they save money. In the article says how the pain is passed from workers to the state:

  When a government decides to index wages of government employees to
  inflation it is to transfer the risk of inflation away from government
  workers onto the government.

What "helping Argentina" means: Increasing happiness of it's inhabitants in general. That's my way of viewing if a certain policy decision is ought to be taken. I focusing of making the public workers happier. In that sense, then yes, automation would be better for them.


texts: Why has China's integration into the global economy caused it to slow it's output?

texts:
In the following passage, what does it mean to be integrated into the economy and why does this mean that now China and India are integrated into the economy that their output has slowed down?

In the 1990s and early 200s, global commerce was growing at twice the
rate of output because big economies such as China, India and in
eastern Europe were being integrated into the global economy. Now they
have been more or less absorbed, it is only natural that things slow
down, but this does not mean we have reached the high-water mark, says
Okonjo-Iweala.

Ref: https://www.google.com/amp/s/amp.ft.com/content/87cb4674-6db7-41cf-a82e-44b83eaa436c


texts: Economies of scale in Robinson Crusoe economy?

texts:
I encountered the following question:

Which of the following will NOT exist in a one-man economy?
1. competition
2. private property rights
3. economies of scale

Turns out the answer was 1 and 2. I sort of understand why 1 and 2 won't exist but I don't really understand 3. How does economies of scale exist in a one-man economy?


texts: How will perpetual floating rate bonds respond to tighter capital requirements?

texts:
Floating-rate perpetual bonds will tend to rise or hold value with increasing market interest rates (in contrast to fixed rate bonds, which tend to exhibit and inverse relationship between price and rates).

However, is it also the case that these bonds will increase in value (or hold value) if mortgage rates increase due to tougher capital requirements imposed by financial regulators?

The particular bonds in question trade at some fixed premium above the bank bill swap rate and can only be redeemed by the issuer by trading on the open market.

I am trying to solve a very specific problem here so I might as well just outline my scenario if that helps:

I hold a mortgage at an interest rate that is currently lower than the post-tax interest rate on floating-rate perpetual (unsecured) notes on some of the major banks in my country (Australia).

In the event of rising interest rates, I would expect the value of those bonds to increase accordingly, affording me the option of selling the bonds at a higher value and paying off more of the mortgage than I otherwise would have. If interest rates remain constant, I will have increased my income as these bonds pay out more than the repayments on my mortgage.

I am therefore considering buying these bonds instead of making repayments on my mortgage. The risk of this trade are;

Interest rates dropping further and remaining low for the duration of the life of my loan, and
the default of the bank issuing the bonds.

Both are risks I am willing to take, and beyond the scope of this question anyway. I am not asking about personal financial advice.

My question is; are my assumptions correct?

If mortgage rates increase because, as has happened recently in Australia, the regulator imposes tighter capital requirements on banks, would one expect the value of unsecured bonds issued by that bank (which, critically, do not count towards said capital requirements) also appreciate in value?


texts: Why exactly does a perfectly competitive market depend on consumers having perfect information about a product?

texts: My book states that one factor defining a perfectly competitive market is its participants having full information about prices and product characteristics. I can understand how having perfect information about prices promotes price taking behaviour (you can't charge me a higher price for your product if I know I can buy it cheaper from other producers). However, why exactly is having full information about product characteristics important for characterizing perfect competition? Thanks in advance.


texts: Proof coefficient in log-log model is equal to coefficient of elasticity

texts:
I am trying to see how we treat $\varepsilon$ in the following proof:

Suppose we have a log-log single variable regression model

$$ \ln(y) = \alpha + \beta \ln(x) + \varepsilon $$

then take partial derivative with respect to $x$ on both sides

\begin{align}&\implies \frac{\partial}{\partial x} \ln(y) = \frac{\partial}{\partial x} (\alpha + \beta \ln(x) + \varepsilon)\\&\implies\frac{\partial \ln(y)}{\partial y} \frac{\partial y}{\partial x} = 0 + \beta \frac{1}{x} + \frac{\partial \varepsilon}{\partial x}\\&\implies\frac{1}{ y} \frac{\partial y}{\partial x} = \beta \frac{1}{x} + \frac{\partial \varepsilon}{\partial x}\end{align}

We want to show that $\beta$ is equal to the elasticity of $y$ with respect to $x$

$$ \beta = \frac{\partial y}{\partial x} \frac{x}{y} $$

But how do we know the $\dfrac{\partial \varepsilon}{\partial x} $ term is zero?


texts: How to distinguish if production costs changes the elasticity of the supply or shifts it?

texts: I have specific doubts about how a factor affects supply elasticity and how it shifts the supply curve. In many cases, the literature shows that some factors affect supply in both ways. For example, a change in production costs. If an increase in production represents a rapid increase in costs, then there will be limited incentives to produce more, making supply more inelastic. However, on the other hand, an increase in costs decreases producers' profits and the quantity offered. This represents a shift in the curve to the left. How can I distinguish, then, between a change in elasticity and a shift in the curve? I think I am missing something.


texts: Implementing Coasian bargaining to achieve social welfare

texts:
In this excellent answer, Ubiquitous elaborates on the Coasian solution as an alternative to Pigouvian subsidies. I wanted to explore and understand the solution a bit further.

Consider the setting in this question - a set of agents facing losses $l_i$ and making investments $c_i$. The loss $l_i$ is a function of others' investments as well, i.e., $l_i=f_i(c_i,i=1,2,\ldots,N)$. Let us also assume that a bargaining hierarchy exists - agent $i$ has greater bargaining power than agent $i-1$.

How does one achieve the socially optimal investment levels in this problem through Coasian bargaining?
How does the answer change when there are connections among agents, as in commodity flow networks? Are there papers that study such bargaining across different tiers in such networks?


texts: Conditional maximum likelihood of AR(1) UNIFORM PROCESS

texts:
Let $Z_t = \phi Z_{t-1} + u_t$ where $u_t \sim uniform[-1,1]$ and $|\phi|<1$ I
I am facing problems coming up with conditional maximum likelihood estimate of an AR(1) process with uniform errors. I want to compute the conditional maximum likelihood estimate of $\phi$. Specifically, I want to see how I can come up with:

the joint distribution of the uniform random variables conditional on $Z_1$ (e.g. if initial values for $Z$ where $Z_1 = 0.3$, $Z_2 = 0.8$ and $Z_3 = 1.2$, $Z_4 = 1.6$) how can I get the joint distribution

What will be the conditional maximum likelihood estimate of $\phi$

I have tried to approach the problem as follows but end up with no solution:
Conditional on $Z_1$, $Z_2$ is distributed as:

$Z_2 \sim uniform[-1 + 0.3 \phi, 1 + 0.3 \phi]$ marginal distribution $ 1/2$

$Z_3 \sim uniform[-1 + 0.8\phi, 1 + 0.8 \phi$ marginal distribution $ 1/2$

$Z_4 \sim uniform[-1 + 1.2\phi , 1 + 1.2\phi$ marginal distribution $ 1/2$

I got the marginal distribution to be (1/2) for all of them got confused on how I can maximize the likelihood if the marginal distribution of the variables is not dependent on $\phi$, I am sure I missed something, any suggestion:

Assuming the processes are independent, I took the joint distribution to be a multiple of the individual marginals (1/2), but I think this is somehow wrong and it should depend on the interval they can exist together.

$ f_{z_2,z_3,z_4} = \prod 1 I(x_1 < \phi < x_n)$ but I couldn't get how I should approach this indicator function and also identify what should be the common interval where the marginal distributions overlap.


texts: How to compute elasticity of substituion in general?

texts:
We know that the elasticity of substitution is defined as
$$
e=\frac{d \ln(x_2/x_1)}{d \ln(MRS_{12})}=\frac{\frac{d(x_2/x_1)}{x_2/x_1}}{\frac{d(MU_1/MU_2)}{MU_1/MU_2}}
$$
When we compute ES for CES functions, MRS is function of $x_2/x_1$, so we can let $z=x_2/x_1$ and do the math easily.
But for other utility/production functions, such as quasilinear $u(x_1,x_2)=2x_1^{0.5}+x_2$, what am I supposed to do?
I believe ES will be depending on $(x_1,x_2)$. So maybe the question can be asked as
"What is ES of $u(x_1,x_2)=2x_1^{0.5}+x_2$ at $(x_1,x_2)=(1,1)$?"


texts: Why is the social value curve NOT the supply curve shifted downwards?

texts:
Abbreviate 'Social Value' as SV. In some other resources such as this, the SV curve is known as the Social Marginal Benefit curve.

The following quotes explain [1.] why the SV curve is the demand curve shifted upwards, but they don't explain [2.] why the SV curve is NOT the supply curve shifted downwards.

Here's my rationale for [2.]: Assume $SV > 0$. Because SV benefits society, the suppliers of this SV can consider the SV supplied, as follows:
Suppliers' true cost  $=$ their original costs $-$ SV, $\qquad$ for all quantities supplied.
So the new supply curve must underlie, and be parallel to,   the old supply curve.

Source: pp 179-180, Modern Principles of Economics (2 ed, 2011) by Tyler Cowen, Alex Tabarrok

  [See Figure 10.3.]
  The social value curve counts all the benefits of vaccine
  use, the private value plus the external benefits, so the efficient quantity is
  found where the social value curve intersects the supply curve.

  A final way of illustrating the underuse of vaccines is to notice that if people
  who got a flu shot did receive all the benefits of vaccination, then their demand curve would shift upward by $20 and would be the same as the social
  value curve. ...

  The last way of thinking about the problem of external benefits also suggests
  one potential solution. If every time someone was vaccinated, they were given
  a subsidy of $\$20$, the monetary equivalent of the external benefit, they would
  demand the amount $Q_{Efficient}$. Recall from Chapter 6 that we can analyze a subsidy
  by shifting up the demand curve by the amount of the subsidy. Thus, in
  Figure 10.3, notice that a subsidy set equal to the level of the external benefit
  would shift the demand curve up and increase the market quantity from $Q_{Market}$
  to $Q_{Efficient}$.

Footnote: I was reading p 201, Principles of Microeconomics (7 Ed, 2014) by N G Mankiw, when I encountered this problem. I don't quote Mankiw's book because it's brusquer than Cowen's above.


texts: Nested/Recursive Dynastic Utility Functions

texts:
I want to find a way of representing a dynastic utility function in which not only the head of the dynasty's utility is dependent on its descendants' utility, but all members of the family tree gain utility from the utility of some of their offspring. In particular, I would like for the total utility of a person $U_{x_{i}}=u(x_i)+u(x_{i+1}) + u(x_{i+2})$ for all $i$ in the dynasty, where '$u(x_{i})$' denotes the utility of $x_i$ which is not dependant on the utility of children and grand-children ('non-parental utility'). So I want a model which allows us to say that the utility of the dynastic head is partly a function of the utility of his children and grandchildren's utility, but where his children's utility is again partly a function of his grandchildren's and great-grandchildren's utility, and so on.
In Becker and Barro's model, we have that \begin{equation}
    U_{x_0}=\sum_{i=0}^{n}N_i   \beta_i(u(x_i)).
\end{equation},
where $N$ is the number of descendants in a generation $i$ and $\beta$ is an intergenerational altruistic discount rate. The problem with this model is it lacks the 'nested' or 'recursive' feature explained above--it simply states that the dynastic head derives utility from his descendants' utility without taking into the consideration that his descendants utility might in turn depend on their descendants' utility.
Adding in the discounting element, let me give a concrete example: suppose I, as the dynastic head ($x_0$), directly receive 50% of the utility of all of my children (i=1) and 25% of the utility of my grandchildren (i=2). Let us say I do not directly receive any utility form the utility of my great-grandchildren. I will still indirectly receive utility from my great-grandchildren since my children receive 25% of their utility and my grandchildren receive 50% of their utility. If we assume for simplicity that my child had one child, which in turn had one child, which in turn had one child $u(x_3)=1$, then I indirectly gain $50\%*25\%*1 + 25\%*50\%*1$= 0.25 utils from my great-grandchild. How do I get a general expression for this phenomenon which holds for $n$ generations?
Any suggestions or pointers are hugely appreciated!


texts: Using Stata to perform power calculations

texts:
I want to use simulation in Stata to help me determine whether or not I will have sufficient statistical power to detect meaningful effects (should they exist) in a given data set using generalized DiD approach.

Here is a walk through from Stata of how to do this in a different setting.

I am not very familiar with Stata and so I am having trouble making this work for my setting. Maybe someone here can help me understand how to modify this code for my purposes?

A quick explanation:

I want to test whether or not a policy change at an institution has an impact on outcomes for people in that institution. Let us assume there are N similar institutions in our universe. Some portion of those N institutions, say $\alpha N$, $\alpha \in (0,1)$ implement this policy change of interest. Assume these institutions implement this policy change at staggered intervals (and implementation is i.i.d between institutions).

How could I simulate data to determine whether or not this policy change impacts the people working in these $\alpha N$ institutions using a generalized DiD approach?


texts: Is the contract curve orthogonal to the priceline?

texts:
Consider an exchange economy with two consumers A and B, two goods x, y. Consumers have identical preferences $U=xy$. Total available endowment are $E_x$ and $E_y$.

This is the background of a homework question which does not ask but I got this question when I try to draw the Edgeworth Box.

I find the contract curve to be the diagonal of the Edgeworth Box, with slope $\dfrac{E_y}{E_x}$. I also find the price in this economy to be $\dfrac{p_x}{p_y}=\dfrac{E_y}{E_x}$.

Then I got confused that if we start from an endowment point (for example, at the bottom right corner) and trade to the contract curve to get an equilibrium, then the line we trade along is called the priceline right? And its slope should be $-\dfrac{p_x}{p_y}$ right? If I did all these correct, I find my priceline is not orthogonal to the contract curve.

It is more likely I made something conceptually wrong? Is the contract curve in this economy the diagonal?


texts: Does the marginal product need to be diminishing to have a diminishing average product?

texts:
We have the rule 'If the marginal is less than the average, then the average declines'.

So if our production function for an input x and output y is concave, does that mean that MP must be diminishing given AP is diminishing?


texts: Von Neumann–Morgenstern implications for repeated strategic games

texts:
I am currently studying game theory and have just begun looking at repeated strategic games.
In my lecture notes, it states that "preferences are unique up to an affine transformation", which I understand. However, it then proceeds to talk about the implications of that statement for repeated games, namely,  "different payoffs for the same strategic game may generate different preferences for the repeated game". Am I correct in surmising that this is to do with the fact that different payoffs imply a non-affine transformation and hence the preferences change?


texts:
Suppose I attend college with 10k tuition fee per year meanwhile I have a part time job for 5k annually. After 3 years, I get a job for 45 years and earn 40k each year. What is my net present value in term of interate rate x?

I did try to form a formula like this, is it correct?


texts: GDP to employed people ration - solow swan model

texts:
Two countries A and B have identical production function $Y=AK^{1/3}N^{2/3}$, they are identical when it comes to all other factors with the exception that savings rate is $s_A>s_B$.
a) What is the GDP to number of people employed ratio in those countries?

Question is about Solow  - swan model. How to apply this model in this particular case, because i am completely lost.


texts: Is there a serious forum/chat (not Q&A like StackExchange) on Economics?

texts:
I am looking for a:

Serious forum/chat (like so many math and physics forums I know in the net)
Where I may able to chat about economics foundations & hypotheses, theory and empiria, and so on, with people who have some knowledge about it.
Which is NOT a Q&A forum.

Thank you very much!


texts: Greece national-accounts : deficit and debt doesn't seem coherent

texts:
I wanted to have a look at Greek's data to have an idea of the debt crisis' impact on various indicators.

Two of those indicators are national debt levels (in GDP% or in absolute value) and government deficit.
I've verified data on this site, they are coherent with other sources like OECD.

So those sources says that debt is growing on the last few years :

Date    Debt    Debt (%GDP) Debt Per Capita
2018    334,721 181.20%     31,217€
2017    317,484 176.20%     29,558€
2016    315,009 178.50%     29,254€

So far so good, but on the deficit side, the data says that they are generating a surplus since 2016 :

Date    Deficit (M.€)   Deficit (%GDP)
2018    1,826           1.00%
2017    1,299           0.70%
2016    858             0.50%
2015    -9,953          -5.60%

So my question is the following, how can the government debt rise (especially in 2018) while the government is generating surplus instead of deficits?

I suspect some variations in the accounting definition of the national debt, but I don't find any publication supporting this (so if that's the case, I'd be happy to have them and to know where to find them).


texts: What does n stand for in the taylor rule?

texts:
I was asked what the relationship of $\bar m$ and $\bar n$ are with the taylor rule.

Using $\bar m$'s definition which is the sensitivity of real interest rate to inflation in a market's monetary policy rule. I said $\bar n$ is the sensitivity of the interest rate to changes in short run output in a monetary policy rule.

To answer the question, i said the parameters  $\bar m$ and $\bar n$ indicate the sensitivity of the taylor rule towards changes inflation and short-run output.

The taylor rule being
$$R_t-\bar r  = \bar m (\pi_t -\bar \pi)+ \bar{n}\bar{Y}   \quad \bar m>0, \, \bar n>0$$

And the resulting new AD curve being
 $$Y^t_t = \bar a - \bar{b} \bar m (\pi_t -\bar \pi)-\bar{b} \bar{n}\bar{Y}$$

$$ Y^t_t = \frac{\bar a}{(1+\bar{b}\bar{n})} - \frac{\bar{b}\bar m}{(1+\bar{b}\bar{n})} (\pi_t -\bar \pi) $$

As in the addition $\bar{n}\bar{Y}$


texts: Intepretation of $dC_1=-\theta(dT_1+\frac{dT_2}{1+r})=0\Longleftrightarrow dT_1=-\frac{dT_2}{1+r}$?

texts:
We are studying the Ricardian equivalence in a macro course and we are asked to show that a tax cut today will be matched by a tax hike tomorrow. I believe the above is supposed to be the solution, however I do not quite understand the total differential and even less so the notation. I have three questions:

How exactly do I take the total derivative of $C_1=\theta(V_1+Y^L_1-T_1+\frac{Y^L_2-T_2}{1+r})$ with respect to $T_1$ and $T_2$?
How would I then get to $dC_1=-\theta(dT_1+\frac{dT_2}{1+r})$?
What is the interpretation of $dT_1$ and $dT_2$? Specifically, what is the interpretation of $dT_1=-\frac{dT_2}{1+r}$?


texts: Regression - Testing for autocorrelation in the presence of heteroscedasticity

texts:
I have constructed a linear time series regression model and estimated the parameters by applying OLS. I now want to test wether the assumptions for proper large sample inference (asymptotic Gauß Markov assumptions) are fulfilled.

Now, I am not sure how to test wether the residuals are autocorrelated or not. Since my model contains lagged dependent variables I can not use the Durbin-Watson test (since my independent variables are not strictly exogenous). Following Wooldridge I decided to apply the Breusch-Godfrey test. But the residuals are heteroscedastic, which I tested for via applying the Bresuch-Pagan test.

Wooldridge says that in the case of heteroscedasticity, one can not apply the usual Breusch-Godfrey test. How can I test for autocorrelation in the presence of heteroscedasticity? Is there any robust method? If that is of any interest - I am using R, so it would be helpful if there would be an implementation of the method (if there is one) in R.

EDIT: I have found a quite interesting paper that proposes a method of dealing with the topic: The modified Breusch-Godfrey test. Link: http://www.naun.org/main/NAUN/mcs/17-542.pdf.

Yet, I did not find any practical implementations of this test. As I am (just) an undergrad student, my possibilities regarding implementing such methods on my own are rather limited. So I am still looking for a general approach/test or method. (And I assume there has to to be a method, because the problem I am having strikes me as a rather common one.) Thank you!


texts:
While economy in india is experiencing a slowdown, the stock markets are having record highs.
can someone explain this dichotomy in simple language ?


texts: How do Sharks make money on Shark Tank through equity alone?

texts:
When the Sharks on Shark Tank buy equity in private companies, how do they eventually make money by purchasing only equity?

For example, if the company makes a lot of money for a few years but then goes out of business, does the Shark lose all of their money if they don't sell their equity share to another private investor before the company goes out of business even if the company was very profitable for a few years?


texts: Does ownership determine efficiency in an economic system?

texts:
what determines efficiency in an economic system?
a) ownership
b) competition
c)both
d) none

I am confused between option (C) and option (B) because I am not sure about whether ownership can be said to be determining efficiency although it is often argued that private ownership brings efficiency. so if you can lend me some clarity would be grateful.
competition is certainly a force that brings forth efficiency so no doubt about it.


texts: I'm writing a paper where I am using expected federal funds rates at different horizons and wanted to use the OIS as a proxy for what the market expects the FFR to be post FOMC-meetings. However, I can't seem to find the data anywhere. Does anyone know where I can get these and if not, what else I can use as proxies about market expectations about the FFR?


texts: Finding "own" price elasticity of demand

texts:
Only two groups buy the Dripfix, abbreviated as good $D$. Group 1's demand function for the Dripfix is $f_1 (p_D)=300-p_D$, where $p_D$ is the price of Dripfix. Group 2's demand function is $f_2(p_D)=120-p_D$.

What is each group's "own" price elasticity of demand?
What is the equation for the market demand?
At what price $p_D$ is the market elasticity $-1$?

Here is my work so far:

Group 1's price elasticity is $\epsilon_1=-\frac{p_D}{300-p_D}$. Group 2's is $\epsilon_2=-\frac{p_D}{120-p_D}$.
The market demand is $420-2p_D$ for $p_D \leq 120$ and $300-p_D$ for $p_D > 120$.

Are these two parts correct so far? If so, how do go about determining the market elasticity when the market demand is made up of two components?


texts: What's the speed of convergence to the potential GDP? (Empirical estimates)

texts:
Suppose a reform makes potential GDP higher, at what speed does actual GDP close the gap? I'm looking preferentially for empirical estimates, but anything that allows me to narrow it down will be helpful.

Dietz Vollrath says (https://growthecon.wordpress.com/2014/12/03/insert-policy-here-wont-boost-growth-rates/) that there's copious empirical evidence saying that the rate is about 2% (2% of the gap is closed each year); he doesn't provide sources and it seems awfully slow, but he is very confident on that. I've tried to find such an estimate, and failed.

Thanks!


texts: Question About Basic Supply/Demand Concepts

texts:
I am learning the basics of Supply/Demand, and I came across this question (it's not a part of my homework; I just want to know the answer/explanation because I'm doing some extra practice problems for a test).

Question: "Starch from the stalks of potato plants is used to make packing peanuts, a complement in production. A decrease in potato demand that lowers potato prices will cause which of the following in the packing-peanut market?"

My thoughts:

So, we know potato prices decrease, and potatoes are a complement in production. From what I've learned, a decrease in the price of a complement in production leads to a decrease in supply of the original good (ie decrease in potato prices leads to decrease in supply of packing peanuts).

Now, what I don't understand is how demand plays a factor.  I know that when the price of a complementary good is decreased, demand for the original good increases.  But what's different in this case is that potatoes are a complement in production, NOT consumption.  From the examples given in the text, everytime they mention how changes in complement goods affect demand, they are referring to a complement in CONSUMPTION.

What I'm confused about is potatoes' relationship to packing peanuts.  Potatoes are a complement in production, so I'm thinking it shouldn't have any affect on demand for packing peanuts, since consumers are not concerned with processes of production, right? (So my answer would be that a decrease in potato prices leads to a DECREASE in supply of packing peanuts and NO CHANGE in demand of packing peanuts).


texts: In perfect competition, why is there economic loss if marginal cost > marginal revenue?

texts:
Here's a graph for reference:

In the left graph, I read from a book (CFA L1 notes) that

  At any output above the quantity where $MR = MC$, the firm will be generating losses on its marginal production and will maximize profits by reducing output to where $MR = MC$."

But now consider this:

$Q'$ is an output level above the one at which $MC=MR$. Shouldn't the yellow region represent a positive economic profit in this case? I can understand that at any output level above the one at which $ATC=MR$, the firm would start making losses. But isn't the quote above incorrect, or am I missing something? Sure, you might be making a suboptimal profit at output $= Q’$, but you’re certainly not making an outright loss.


texts: Does it make economic sense for only some universities in a certain area to pay their sports scholars?

texts:
Apparently

  ‘Athletic scholarships are common in the United States, but in many countries they are rare or non-existent.’

But are there countries where there are some universities that offer sports scholarships while other universities in the same country don't? We can shrink country to city, town, district, etc if you like (Note 2). I'll just say 'area'.

I have this relative: My relative and I are expats living in a certain area but permanent residents of the area. My relative recently got accepted into a first world university for an undergraduate degree in engineering and was accepted as a sports scholar...sort of.

None of the tuition is waived. The only thing my relative gets is a reduced fee to be on the team: Yeah, the university charges its students a fee to be on the team. My relative also gets lower grade requirements in admissions or retention, but my relative does not need that due to having outstanding grades in secondary. I figured this was a practice in this area where we both live and where we are both expats (see quote above).

However, I found out that several universities in this area apparently do offer sports scholarships ranging from 50-100% off tuition. One of the universities that offer is even of a lower QS ranking than the university that my relative is attending (Note 1). This to me seems like a big misunderstanding on my part, so I've emailed the university, although my relative has already asked, just to get first hand confirmation.

In the mean time: Why would anyone play sports for a university against other universities but not get paid or get tuition waived for the playing?

Some guesses:

Lower admission grade requirement
Lower retention grade requirement
Admission or retention for dormitory requirement
Possibility of future scholarships
Prospects of a sports-related careers after graduation that include but are not limited to professional sports

The thing is none of my guesses explain why those universities apparently have sports scholarships that waive tuition at least partly while this university doesn’t. Why wouldn’t sports scholars from a university that doesn't pay their sports scholars just transfer to another university in the next year thus causing the university to lose in inter-school competitions?

(Note 1): My relative applied to all universities in our area for sports scholarships and was rejected for all but this university. Also, our area has less than 10 universities, and they're all in the QS... Wait, lemme check...Yeah, ACTUALLY, my relative's university has the highest world QS ranking in our area. Meanwhile, the university with the lowest world QS ranking in our area has sports scholarships. Also, all universities in question are in the top 100 in our continent's world QS ranking, our continent is not Africa, and my relative's university is not the highest in our area for our continent's world QS ranking.

(Note 2): I'm thinking perhaps of a possibility where, say, in North America or Europe this might be the case but is not the case for a specific state or city or something like Massachusetts, Boston, UK or London. You can shrink as much as you want on the condition that universities in your shrunken area compete with each other in sports.


texts: determinacy vs. indeterminacy of equilibria in dynamic systems

texts:
As explained in Hommes (2018), equilibria in dynamic systems, like DSGE models, can either be determinate or indeterminate. A REE (rational expectations equilibrium) is determinate when there exists a unique solution, typically a saddle-path solution converging to the rational steady state. A REE is indeterminate when multiple solutions converging to the steady state exist.

question 1: so, there still is only one solution? But just multiple paths to get there? So, this equilibrium is still stable, once there?

Then Hommes (20180 goes on: A determinate solution can be computed, assuming that the equations of the economy are common knowledge.

A learning theory of coordination on a equilibrium, without the demanding assumption of perfect knowledge of the law of motion of the economy, is however lacking (Hommes, 2018). Without an adaptive learning process coordination on an equilibrium, even if it is unique, seems unlikely.

question 2: What would he mean here? There is no accepted general theory of how one converges to an equilibrium if RE are relaxed and replaced by adaptive learning? OK... @Without an adaptive learning process@ means what? RE?


texts: I have a set of data that I have gathered for an event-study. I computed the CARs, CAARs (cumulated average abnormal returns) and now I have to do a t-test to test if CAARs are significantly different from zero. I work with excel and I am not sure how to do that.


texts: Find Indifference curve/s and Marginal Rate/s of Substitution given only one point

texts:
Arka likes fries. She wants to consume as much as possible. She consumes either regular (1 oz) or large sizes (5 oz).

Draw her indifference curve through $(x_R, x_L) = (10,0)$ and her indifference curve through the bundle $(x_R, x_L) = (10,2)$.

Determine her $MRS_{R,L}$ at $(x_R, x_L) = (10,2)$

Give an example of a utility function that captures her preferences.

What I tried:

$(10,0)$: Corner solution?

$(10,2)$: I'm thinking some indifference curve that does not intersect the indifference curve passing through $(10,0)$. Is that unique?

How can I do this without prices, utility or marginal utility? The formula from Wiki:

$$MRS_{R,L}(10,2) = \frac{MU_R(10,2)}{MU_L(10,2)} = -\frac{p_R(10,2)}{p_L(10,2)}$$
or in some strange books
$$MRS_{R,L}(10,2) = \color{red}{-}\frac{MU_R(10,2)}{MU_L(10,2)} = \color{red}{+}\frac{p_R(10,2)}{p_L(10,2)}$$
Well if we are at a point of tangency then (following Wiki)
$$MRS_{R,L}(10,2) = \frac{MU_R(10,2)}{MU_L(10,2)} = -\frac{p_R(10,2)}{p_L(10,2)} = -\frac{dR(10,2)}{dL}$$
I got nothing.

Some $U(x_R, x_L)$

s.t.

Domain includes $(10,0)$ and $(10,2)$

$$U(10,0) < U(10,2)$$

$$x_R' + 5x_L' < x_R' + 5x_L'' \to U(x_R',x_L') < U(x_R',x_L'') \ \text{(thus making #2 redundant?)}$$

$$x_R' + 5x_L' < x_R'' + 5x_L' \to U(x_R',x_L') < U(x_R'',x_L')$$

Domain is all pairs of nonnegative numbers (thus making #1 redundant?)

Is that right?


texts: Investors in index funds pay lower taxes, but higher taxes on dividends?

texts:
Doesn't the second para. beneath contradict itself? Don't the boldened words contradict each other?

       So let’s pick up where we left off a few chapters ago.
Recall that the net annual return was 7.8 percent for the average equity fund over the past 25 years and 9.0 percent
for the S&P 500 index fund. With the high portfolio
turnover of actively managed funds, their taxable investors
were subject to an estimated effective annual federal
tax of 1.2 percentage points per year, or about 15 percent
of their total pre-tax return. (State and local taxes would
further balloon the figure.) Result: their after-tax annual
return was cut to 6.6 percent.
      Despite the higher returns that they earned, investors
in the index fund were actually subjected to lower taxes,
largely derived from their dividend income. The extremely
low costs of index funds consume less dividend income
relative to actively managed funds, resulting in higher dividend
yields and, therefore, higher taxes on dividends.

John Bogle's The Little Book of Common Sense Investing, 10th Anniversary Edn. Pages 87, 88.


texts: convexity of the profit function for profit maximization

texts: the profit function is convex in prices and wages (output and input prices respectively). How does this interact with profit maximization since convexity implies tangents always lie below the curve I would have thought convexity would be necessary for minimization rather than maximization.


texts: Where can I find a complete list of goods affected by NAFTA?

texts:
I am looking for the list of goods that NAFTA, preferably in the format of what is subject to tariff reduction.

I have found a few potential leads, but none seem to be exhaustive:
https://www.investopedia.com/terms/n/nafta.asp

https://fas.org/sgp/crs/row/R44875.pdf

https://aic.ucdavis.edu/pub/briefs/brief21.pdf

https://aic.ucdavis.edu/2003/02/01/role-of-nafta-in-california-agriculture-a-brief-review/

Here is the agreement in full (if someone is familiar, perhaps they could point me to a specific chapter?):

https://www.nafta-sec-alena.org/Home/Texts-of-the-Agreement/North-American-Free-Trade-Agreement?mvid=2


texts: I'd like to read a more detailed/mathematical analysis on the subject of Coase's theorem. Could you perhaps suggest any advanced textbook/paper on the matter?


texts: How to use the Girsanov theorem to prove $\hat{W_t}$ is a $\hat{\mathbb P}$-Brownian motion?

texts:
Let $T > 0$, and let $(\Omega, \mathscr F, \{\mathscr F_t\}_{t \in [0,T]}, \mathbb P)$ be a filtered probability space where $\mathbb P = \tilde{\mathbb P}$ (risk-neutral measure) and $\mathscr F_t = \mathscr F_t^{{W}} = \mathscr F_t^{\tilde{W}}$ where $W = \tilde{W} = (\tilde{W_t})_{t \in [0,T]} = ({W_t})_{t \in [0,T]}$ is standard $\mathbb P=\tilde{\mathbb P}$-Brownian motion.

Define forward measure $\hat{\mathbb P}$:

$$A_T := \frac{d \hat{\mathbb P}}{d \mathbb P} = \frac{\exp(-\int_0^T r_s ds)}{P(0,T)}$$

It can be shown that $\exp(-\int_0^t r_s ds)P(t,T)$ is a $(\mathscr F_t, \mathbb P)-$martingale where $r_t$ is short rate process and $P(t,T)$ is bond price.

We are given that

$$\frac{dP(t,T)}{P(t,T)} = r_t dt + \zeta_t dW_t$$

where $r_t$ and $\zeta_t$ are $\mathscr F_t$-adapted and $\zeta_t$ satisfies Novikov's condition. I don't think $\zeta_t$ is supposed to represent anything in particular.

Define the stochastic process $\hat{W} = (\hat{W_t})_{t\in[0,T]}$ s.t.

$$\hat{W_t} := W_t + \int_0^t -\zeta_s ds$$

Use Girsanov Theorem to prove $\hat{W_t}$ is standard $\hat{\mathbb P}$-Brownian motion.

What I tried:

Since $\zeta_t$ satisfies Novikov's condition, $\int_0^T -\zeta_t dt < \infty$ a.s. and

$$L_t := \exp(-\int_0^t (-\zeta_s dW_s) - \frac{1}{2} \int_0^t \zeta_s^2 ds)$$

is a $(\mathscr F_t, \mathbb P)-$martingale.

By Girsanov Theorem, $\hat{W_t}$ is standard $\mathbb P^{*}$-Brownian Motion where

$$\frac{d \mathbb P^{*}}{d \mathbb P} = L_T$$

I guess we have that $\hat{W_t}$ is standard $\hat{\mathbb P}$-Brownian Motion if we can show that

$$L_T = \frac{d \hat{\mathbb P}}{d \mathbb P}$$

I think I was able to show (lost my notes) that $dL_t = L_t \zeta_t dW_t$, $dA_t = A_t \zeta_t dW_t$ and then $d(\ln L_t) = d(\ln A_t)$

From $d(\ln L_t) = d(\ln A_t)$, I infer that $L_t = A_t$ and hence $L_T = A_T$ QED.

Is that right?


texts: Does the political claim "will create X jobs" have an economic definition?

texts:
I often see claims that new (generally government) projects will "create n jobs".

For example, this 2013 claim from the Economic Development Blog about the 2020 Olympic Games:

  The Olympic Games are expected to create 152,000 jobs nationwide across Japan. This includes 84,000 new jobs in Tokyo and 68,000 in the rest of the country.

I have always found such claims to be vapid, because it doesn't say how long the jobs last.

Sticking to the example: One of those new positions might be to be a security guard for a month during the games. One of those new positions might be to work on the planning for the event for seven years. One of those new positions might be to be a groundskeeper at a new Olympic facility for decades.

Lumping these together seems like it is a misleading metric. Perhaps saying "250,000 job-months" would be a better measure?

But I am economically naive. Perhaps economists have already considered this and have a standard definition I don't know about to allow them to properly compare.

Are these figures mostly meaningless, just being used to hype a project by its proponents? Are they accepted estimates of real economic boost a project might bring?


texts: What does efficient and inefficient innovators mean?

texts:
I have been reading through this article about Innovation Indexes.

In this, I have come across the terms: "Efficient Innovators" and "Inefficient Innovators" in this plot:

So, what do they mean? And how are they calculated/determined?


texts: Properties on conditional demand correspondence from the textbook of Mas-Colell et al

texts:
I have a question on the properties of conditional demand correspondence
Let $z(w,q)$ be the conditional factor demand correspondence, i.e. the solution of the cost minimization problem
\begin{align}
\min_z \quad& w\cdot z \\ \text{subject to}\quad & f(z)\geq q.
\end{align}
In the book of Mas-Colell, Whinston, Green, Proposition 5.C.2 (v) says that

if the set $\{z\ge 0 : f(z)\ge q\} $ is convex then $z(w,q) $ is a convex set.

Also, in the same property, it states that

if $f$ is quasiconcave then $z(w,q)$ is a convex set for every $w>>0$.

How can I prove these two statements? I would like to understand these two properties. Thanks a lot.


texts:
The excange of Chinese yuan is controled by Chinese government in part now.
What will  happen  if  Chinese yuan turn floating exchange rate system?


texts: Monetary Approach to a depreciating currency

texts:
I am currently doing some research on the monetary approach to the effects of currency fluctuations on trade balance. It's been a while since I took an int econ class back in the undergrad, so I hope I can glean some understanding from the gods of macroecon. I have a good understanding of the overall assertion being made by this approach (trade balance change dissapates in the LR), but am a bit confused by the details and how equilibria are reached. One of my old textbooks summarizes it as such: when the currency depreciates, money demand shifts up, and rates rise, trade balance improves. In the LR, investors will flock towards the higher rates, and the money supply shifts right, where equilibrium will return to the initial interest rate. This doesn't really make sense to me....

What is causing the currency to depreciate here? When I think of a devalued currency, I think of an expansionary policy/decrease in rates. But here, rates increase due to the depreciation
Where is the deviation from the net zero trade balance and where does it return in terms of the process of the money market changes?
How do foreign investors affect the supply of the currency? I thought that when higher rates existed, that the demand of the currency increased (which would explain why contractionary policy leads to currency appreciation)
More as a question about the theory in general, is there empirical evidence of this? The US has had a trade deficit for a very long time. Does this approach suggest that our net exports should be zero?

Thanks!


texts: Dynamic programming problem with dimension over 1000

texts: I am working on a project which need to solve a dynamic programming problem with dimension over 1000. In past literature, there exist several methods like Smolyak algorithm and Sparse grid method that can solve dynamic programming problem with dimension no more than 100. My question is that does there exist such a brute force method that can solve problem with high dimension efficiently. Or I need to apply some approximation or reduce dimension.


texts: What does the adjective "structural" mean in "structural reforms" or "structural effects"?

texts:
Economists frequently speak of structural reforms and structural effects.

For example, Manmohan Singh (1992):

  The economic crisis was used as an opportunity to implement basic structural reforms in the areas of industrial policy, trade policy, tax policy, public sector management and the financial system.

Donald Walker (1984):

  money plays a central role as a means of payment, and its presence in the economy has structural effects.

What purpose does the adjective structural serve in the above sentences? What difference would it have made if the word were deleted or replaced by non-structural?

Are there mere reforms and effects that differ from structural reforms and structural effects? Are there non-structural reforms and non-structural effects?

Is the word structural just a fairly vague term with a connotation similar to fundamental or important?


texts: Conditional probability in Kaplan, Menzio (2014)

texts:
This is question about Kaplan and Menzio's shopping time model.

Pages 7,8: Unemployed search once or twice (for a seller).

$\psi_u$:probability of searching twice, searching once with prob $1-\psi_u$
$\nu$ is the probability of finding a seller.
Searches are independent. An unemployed who searches twice, hence has the probability of finding two sellers of $\nu^2$.

Now here's the problem, on page 10, they look at it from a seller's point of view. Conditional of the seller of being matched with a buyer, what is the probability of the buyer being matched with another seller?

$$ Prob(\text{being matched second seller} | \text{being matched with first seller}) = \frac{Prob(\text{being matched with first and second seller})}{Prob(\text{being matched with first seller})} \\
= \frac{\text{search twice and find both times}}{\text{search once and find a seller or search twice and find one or two sellers }} \\
= \frac{\psi_u\nu^2}{((1-\psi_u) * \nu) + (\psi_u)*(\nu + \nu)}\\
= \frac{\psi_u\nu}{1+\psi_u}\\
$$

However, what they get is

$$ \frac{2\psi_u\nu}{1+\psi_u}$$

They compute some "intermediate probabilities" on page 8, but I don't see how they help get their result. How does one get their result?


texts: How to calculate price function from demand curve when marginal cost is given?

texts:
This example is in a oligopoly market with two firms. The demand curve is given and also two firms' MC is given. How would one calculate price function in this scenario?

I found the slope using the demand curve and then found the y intercept to the get the price function. However, I also know that MC is the derivative of the price function. If I take the derivative of the price function I got, it's not the same as the MC.. Any thoughts on this?


texts:
The Nash bargaining solution selects the unique solution to the maximization problem $\max_{s_1, s_2 } (s_1 - d_1) (s_2 - d_2)$ such that the solution satisfy the following axioms :

Invariance
Symmetry
Pareto efficiency
Independence of irrelevant alternatives

Does replacing the maximization problem by $\max_{s_1, s_2 } (s_1 - d_1)^{\alpha}  (s_2 - d_2)^{1-\alpha}$  (i.e. give different bargaining power to the players) change the list of axioms satisfied by the former maximization problem ? From my understanding symmetry will be no longer be satisfied, but does that affect other axioms as well?


texts:
Im working on college enrollment linear probability model where enrollment is regressed on income.

I have the following regressions

$$y=\beta_0+\beta_1x_1+u$$
$$y=\beta_0+\beta_1x_1^2+u$$
$$y=\beta_0+\beta_1x_1+\beta_2x_1^2+u$$

where $x_1$ is Income and $y$ is a binary variable which indicates

In cases (1) and (2) I have statistical significance at the 1% level ( *** ), but in regression (3)I have no significance at all in these variables.

How do I remedy/ interpret this?


texts: Question about the effect on economic productivity due to a hypothetical wealth distribution requirement

texts:
Assume a sovereign state that functions like a joint stock corporation does: it will be comprised of shareholders and its "stateshares" will have a market value since they are tradeable. Now assume that most wealth has to be held in these stateshares. This means if your private wealth goes up 10% in market value, then you will need to increase your stateshare wealth by 10% to make sure most of your wealth is always in stateshares. The point of this hypothetical regulation is to make sure the aggregate economic interest in increasing the stateshare market value is larger than all the other aggregate economic interests combined.

Now the question is about this hypothetical regulation's effect on economic productivity. The argument is that because a capitalist will have to either sell off or mortgage part of his quickly appreciating asset to afford to buy an asset appreciating at the average rate, then the incentive to create a quickly-appreciating asset disappears. Thus, economic productivity disappears.

This argument is not convincing to me though. I believe the incentive to grow my own personal enterprise is still strong even though I would have to mortgage part of my enterprise as it grows in value to buy more stateshares.

Are my doubts correct? If not, why does economic productivity suffer under this hypothetical mandatory wealth distribution?


texts: is it possible to find PPP monthly data?

texts:
For most of the databases, monthly PPP data is not provided. How it can be possible to find monthly PPP data?  i mean PPP(exchange rate) conversion factors.
Thanks


texts:
If I pick up a stone there and sell it to you for 1 million dollars, 1 million dollars added value is created and added to GDP. If you sell it to me for the same price, virtually nothing has happened but GDP increased by 1 million dollars.

We can increase GDP by any number we want.

Why do we care about GDP?


texts:
I have doubts about whether my solution is right.

Let $x>z>y>1$.
Given the extended game above, we have two subgames and will find the Nash equilibria of these.

Observe that player 2 will play $b$ in the right subgame.
In the left subgame player 2 will be indifferent between playing $a$ and $b$.
Let $0 \le r \le 1$ such that $(r,1-r)$ is a mixed strategy for player 2 and such that the player plays this strategy in the left subgame.

Player 1 has expected payoffs
$$
E u(s) =
(rx+(1-r)y) \cdot 1_{s=A} + z \cdot 1_{s=B}
$$
Observe that player 1's best response is $A$ if $r \ge (z-1)/(x-y)$ and $B$ if $r \le (z-1)/(x-y)$, hence SPNE will be
$$
\{(A,(r,1-r))|r \ge (z-1)/(x-y) \} \cup \{(B,(r,1-r))|r \le (z-1)/(x-y)\}
$$
Is this correct?


texts: Cost function from CES production function

texts:
How can I find the cost function $c(w,p)$ given that the production is
$$ f(x)=(x_1^p + x_2^p)^{1/p} \ \ for\ \  0<p <1 $$
I tried to solve it and found that
$$TC(y) = \left\{
        \begin{array}{ll}
            w_1y & \quad w_1 < w_2 \\
            wy & \quad w_1=w_2 \\
            w_2y & \quad w_2 <w_1
        \end{array}
    \right.
$$
Can you say me if I'm on the right way?


texts: What is the prime sign that a country is transitioning from a developing to a developed economy?

texts:
Developed Economy = low human capital flight, good infrastructure, low corruption, high per-capita income, dominated by hi-tech industry, high expenditure in R&D, high-quality higher education, high-quality health care, and so on.

Developing Economy = high human capital flight, bad infrastructure, high corruption, mediocre per-capita income, dominated by agriculture or service sector, not enough expenditure in R&D, low quality higher education, low life expectancy, and so on.

What is the first sign that a country is transitioning from a developing to a developed economy?

If we want to point to 'only one sign', what would that be?

And, Why?


texts: Relation $\Delta Unemployment$ and $\Delta GDPgrowth$

texts:
I have studied the development of the difference in unemployment and the difference in the growth of real GDP in the Netherlands over the years 1963-2016.

From the picture it seems like a change in unemployment has a positive effect/predicts a change in GDP growth. How is this possible? Has this to do with the fact that unemployment is a lagging variable?


texts: How does a division of a company spinning off from it's 'parent' company change it from a cost center to a profit center?

texts:
Reading an article about how many IT divisions of big companies in Japan, became seperate companies. The motivation is apparently to turn them in profit centers. Can anyone explain how becoming a seperate company would be profitable for the original company?

Extract from article:

"Software development is a critically important part of the Japanese IT sector.  The software developers can be categorized into three groups – Maker, User, and Independent System Integrator (so-called SIer). The Maker group consists of computer manufacturers and their subsidiary companies which provide total system solutions including software development and support as well as hardware. Representative companies are Fujitsu, NEC, Hitachi and IBM.  Companies in the User group are former IT divisions which were spun off from parent “user” companies in order to transform themselves into profit centers from cost centers. Most of the large players in financial, manufacturing, and trading sectors keep vertical relationships with their IT subsidiary companies. "

Source: Evaluating The Strategic Implications
Of Japanese IT Offshore Outsourcing
In China And India


texts: Using dependent variable's and exogenous variables' lags as instruments in 2SLS

texts:
Suppose we have the following structural equations:
$$y=\beta_0+\beta_1x+\beta_2z_z+\beta_3z_3+\epsilon,$$
where $x$ is the endogenous variable and $z_1,z_2$ are exogenous variables. In the literature, as well as in software packages (ivreg in STATA), I find that it is quite common to add dependent variable's as well as lagged exogenous variables as intruments in the first stage of 2SLS (to capture exogenous variation of the endogenous variable). In our case, we can consider $y_{t-1}, x_{t-1}, x_{t-k}$ as instruments for $x$. Is this legit and what is the rational behind this? Also, please provide some resources to read more about this. Thanks!


texts:
Ramsey model with income tax

Question:

For this question you are required to setup a Ransey-Cass-Koopmans model economy with a Cobb-Douglas constant returns to scale production technology, with inputs of capital (K) and labour (L). Setup the model with a constant depreciation rate, constant rate of labour- augmenting technological progress and constant rate of population growth. Also incorporate a government that finances its spending each period via a proportional income tax system. Assume that both labour and capital income are taxed at the same rate – say τ. You can assume that government spending is completely wasteful; or you can make some other assumption about how the tax revenue is used, however do not allow government spending to generate endogenous growth.

I am asking only this past

    Use the model to explain the income gap that exists between wealthy and poor countries.

———

What I did:

I solved this model with hamiltonian. And I got the following results (I posted picture of my results, because this is only extra information that helps to solve question.)

And the phase diagram

And at steady state, saving rate is

$$s^*={(delta +n + x)(1-τ)a\over p+delta+θx}$$

x is growth rath of technology. (Productivity growth rate)

Delta depration rate. and production function $Y=K^a(AL)^{1-a}$

My interpretation:

Economic growth is measured only by x. So only x and A affect the income.

Assume that we have $k_i<k^*$ and every parameters are constant for two countries except for x . Poor country has lower x.

When x increases, saving decreases, MPK decreases, so capital rate of return decreases, capital stock increases. And eventually they have the same growth rate. (This is substitution effect)

But I could not know how to explain this question better. Any help is appreciated. Really I need a help too much!


texts: Queuing Discipline and Lipschitz Continuity

texts:
I was reading a paper by Platz and Østerdal (2014) titled "The curse of the first-in-first-out queue discipline". I was wondering about a particular section of it, particularly the part about last-in-first-out mechanisms. $R(t)$ is defined as the cumulative arrival distribution, and they try and show:

  Let $R(t)$ be a Nash Equilibrium for the FIFO (first-in-first-out) queue discipline. Then $R(t)$ is Lipschitz continuous.

This is the second Lemma on page 2.

I am not quite understanding why we are trying to show this property to lead into the third Lemma. What is the importance of Lipschitz continuity here? A basic intuitive answer should be okay, but some math would help me I think. Are they trying to ultimately show that $R(t)$ is a unique Nash equilibrium for FIFO?


texts: Help needed to understand proof in Myerson and Satterthwaite (1983)

texts:
The following image is an excerpt taken from Myerson and Satterthwaite's 1983 paper Efficient Mechanisms for Bilateral Trading:

I know what the theorem is all about, all I need is some help with the integrals
 (especially the one at the second equality sign).


texts: Is "management science" a subsection of economics?

texts:
Reading about the academic journal Management Science, one can read the following:

  Management Science is a scholarly journal that publishes scientific research on the practice of management. (...) Our articles are primarily based on the foundational disciplines of economics, mathematics, psychology, sociology, and statistics, and we encourage cross-functional, multidisciplinary research that reflects the diversity of the management science professions.

So is management science (the scientific research that is published in journals like this) a separate science, similar to the way economics uses Mathematics? What is the view of economists on this?


texts: What policies are in place to police financial speculation in the modern era?

texts:
Maynard Keynes in section VI in chapter 12 of his General Theory of Employment, Interest & Money writes:

If I may be allowed to appropriate the term speculation for the activity of forecasting the psychology of the market, and the term enterprise for the activity of forecasting the prospective yield of assets over their whole life, it is by no means always the case that speculation predominates over enterprise. As the organisation of investment market improves, the risk of the predominance of speculation does, however, increase.
In one of the greatest investment markets in the world, namely, New York, the influence of speculation (in the above sense) is enormous. Even outside the field of finance, Americans are apt to be unduly interested in discovering what average opinion believes average opinion to be; and this national weakness finds its nemesis in the stock market...
...Speculators may do no harm as bubbles on a steady stream of enterprise. But the position is serious when enterprise becomes a bubble on a whirlpool of speculation. When capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done.
The measure of success attained by Wall Street, regarded as an institution of which the proper social purpose is to direct new investment into the most profitable channels in terms of future yield, cannot be claimed as one of the outstanding triumphs of laissez-faire capitalism - which is not surprising, if I am right in thinking that the best brains of Wall Street have been in fact directed towards a different object.
These tendencies are a scarcely avoidable outcome of our having successfully organised 'liquid' investment markets. It is usually agreed that casinos, in the public interest, be inaccessible and expensive. And perhaps the same is true of stock exchanges...
The introduction  of a substantial Government transfer tax on all transactions might prove the most serviceable reform available, with a view of mitigating the predominance of speculation over enterprise in the United States.

One such transfer tax is the Tobin Tax but this seems very specific in that it is applied to 'spot conversions of one currency into another'; what other specific proposals in line with Keynes suggestion are there? And have any been implemented and if so what have been the results?


texts: When companies export do they receive the foreign currency or their domestic currency? (net capital outflows)

texts:
In Mankiw "Economics" (Fourth edition) it states when a company exports (UK BP Oil to Japan):

Two things have occured the UK has sold to a foreigner some of its output in the goods market
(the oil).....In addition the UK has acquired some foreign assets (the yen), and this increases net
capital outflow.

The book then goes on to say specifically "BP" (not the UK) will not hold onto the Yen.
My question is:
What happens if the Japanese customer pays in UK pounds (by exchanging at a Japanese bank from the Japanese £ reserves). That must mean that BP never receives the yen. Does this mean there has been no inflow of yen and infact an inflow of pounds. And going by the logic of the book, if an inflow of yen is "BP acquiring foreign assets (from foreign residents)". Then BP acquiring pounds = BP (domestic resident) acquiring domestic assets from foreign residents. Which doesn't fit into the schema of NCO.

Purchase of foreign assets by domestic residents - Purchase of domestic assets by foreigners.

I look forward to you enlightening comments here. They are very much appreciated.


texts: Heckscher-Ohlin with different technologies

texts:
Consider two countries: Home and Foreign that produce two goods, cars and wheat. The production technologies are such that:

$q_{c} = K_{c}^{0.5} L_{c}^{0.5}$ and $q_{w} = 0.5 K_{w}^{0.5}L_{w}^{0.5}$ for Home. And for Foreign:

$q_{c}^{*} = 0.5 K_{c}^{0.5*} L_{c}^{0.5*}$ and $q_{w} = K_{w}^{0.5*}L_{w}^{0.5*}$

$K_{c}$ denotes the amount of capital used in the production of cars.

The asterix denotes the Foreign country. The endowments are:

$K_{c} + K_{w} = K_{c}^{*} + K_{w}^* = 1$ and  $L_{c} + L_{w} = L_{c}^{*} + L_{w}^* = 1$

Preferences are homothetic and identical between the countries and given by $\frac{D_{c}}{D_{w}} = \frac{p_{w}}{p_{c}}$.

So both countries have the same endowments but their production technologies differ.

The first question is to find the autarky quantities and relative prices. This I have managed to do by setting up the profit maximisation problem in each sector, then finding the wage-rental ratio. And seeing as the Cobb-Douglas exponents are the same, I know that equal amounts of labor and capital will be used in the production of each good. I won't include the algebra but here are my wages and rental rates in each sector. For cars:

$w = 0.5 p_{c} (\frac{K_{c}}{L_{c}})^{0.5}$ $\quad$ (1)

$r = 0.5 p_{c} (\frac{L_{c}}{K_{c}})^{0.5}$  $\quad$ (2)

$w^* = 0.25 p_{c}^{*} (\frac{K_{c}^*}{L_{c}^*})^{0.5}$ $\quad$(3)

$r^* = 0.25 p_{c} (\frac{L_{c}^*}{K_{c}^*})^{0.5}$ $\quad$ (4)

And for the wheat sector:

$w = 0.25 p_{w} (\frac{K_{w}}{L_{w}})^{0.5}$ $\quad$ (5)

$r = 0.25 p_{w} (\frac{L_{w}}{K_{w}})^{0.5}$  $\quad$ (6)

$w^* = 0.5 p_{w}^{*} (\frac{K_{w}^*}{L_{w}^*})^{0.5}$ $\quad$(7)

$r^* = 0.5 p_{w} (\frac{L_{w}^*}{K_{w}^*})^{0.5}$ $\quad$ (8)

For the autarky case, dividing (1) by (3) and setting $K_{c} = L_{c}$ shows that for Home, the relative price, $\frac{p_{c}}{p_{w}} = 0.5$. Similarly for Foreign, $\frac{p_{c}^*}{p_{w}^*} = 2$. And using the preference function I can find the quantities of each good produced.

It is finding the free-trade relative price and quantities that is causing me some trouble. I know that in free-trade factor and output prices equalise and that world demand equals world production. I also know that Home has a comparative advantage in cars and Foreign in wheat (given the autarky relative prices). But I have tried for hours now to manipulate (1)-(8) but without much progress.  Any suggestions as to how I can proceed?


texts: In a social accounting matrix, what does Capital refer to?

texts:
In the process of building a social accounting matrix for Panama, I am trying to understand what capital refers to. The Panamanian National Accounts have tables on capital, but they describe gross capital formation. In a social accounting matrix, gross capital formation represents investment and not capital. So what does capital mean?

I was also wondering if capital was included as part of Gross Value Added (GVA) and, if so, could it be calculated using GVA data?

Thank you!


texts: Dornbusch Sticky Price (Overshooting) model

texts: Stupid question: What do the phi and lambda from the equations above represent?


texts: Why is there a deadweight loss in this lemons market?

texts:
Is there a deadweight loss in this used car market and why?

On the plums side we can make a pareto improvement by exchanging information and matching 200 buyers and sellers who will gain from trade.

On the lemons side, we can't say for certain that it is inefficient. Lemons are being exchanged at the expected value of a car (50% of cars are plums and 50% are lemons) which is 12k. This becomes the maximum WTP of an ignorant buyer, so the exchange is not inefficient, there are equity issues but not efficiency issues. A Pareto improvement is not possible because any gain that buyers make when given information (they will keep their money in their pockets) is a loss to sellers. (Is this correct? the sale of 600 lemons is Pareto efficient but why can you not return to this point once you're off equilibrium without making sellers worse off?)

So is the deadweight loss the 400k on each side, or just the 400k in the plums market, or is it something else - 2 million on the right hand side for example because the true WTP is 16k? What do you think?


texts: Geometric intuition behind the point where the indifference curve meets the budget line

texts: So, this isn't to solve any kind of problem, but rather about the intuition behind the concept. I was wondering if at the optimal point where the indifference curve is tangent to the budget line and utility is maximized, at say, some point A. If you were to draw a vertical line from A down to the horizontal axis, and then draw a horizontal line from A to the vertical axis, would the resulting rectangle have a larger area than any other rectangle created by the other points on the curve? Kind of like the intuition behind least squares regression, but trying to maximize area? Thanks in advance for any help.


texts: Why should government bonds have been a part of FSB rules on repo markets?

texts: Since the financial crash, reforms have been made by the FSB, I would like to know why there is the opinion that government bonds should have been part of FSB rules on repo markets


texts: Is unemployment benefit part of national income measurement?

texts: Since unemployment benefit is a form of government spending, which is a component of aggregate expenditure, then shouldn't unemployment benefits be part of national income measurement?


texts: Has contest theory ever been used to design real-world contests?

texts: Contest theory, very much like auction theory, studies how people act in a contest and the properties of such a competition. There is a large literature that investigates different aspects of the contest, including efficiency, participation, total effort. However, while I am aware of many examples in which auction theory has been then applied to design real-world auctions, I have found no examples of contest theory being applied to design real-world contests.


texts: person owns object, loses it and refuses to buy it the second time. Is it really an example of sunk cost fallacy?

texts:
I was traversing the web with examples about the sunk cost fallacy, and bumped into some example that a bit confuses me. The example is taken From here (https://market.subwiki.org/wiki/Sunk_cost_fallacy) and I repeat it below in short. My question is whether it is a fair example of sunk cost fallacy?

Consider person owns an object A, and then the person loses it. Then (quote from that link):
“Assuming rational behavior, whether a person chooses to buy or not buy should be independent of whether the person loses the money or the object. However, what the sunk cost fallacy predicts that losing the object ￼ makes the person less likely to buy another copy of ￼, because the person does not want to admit that the initial purchase of ￼ was wasteful”

I’m confused and not sure because this example is so much different from traditional examples when you keep spending money/effort/time because you already did it in the past. Could anyone clarify?


texts: A world only with two contries (net exporter)

texts:
We assume that we have two and only two contries: Albania and Bulgaria. There is complete free trade between the two countries.
The aggregate investments in Albania are given by:
$$I^A=A-ar$$
where $A, a >0$ and r real interest rates.
The aggregate investments in Bulgaria are given by:
$$I^B=B-br$$
where $B, b >0$ and r real interest rates.
They have total savings $S^A$ and $S^B$ who are independent of the interest rate.
Now I have to derive the condition that Albania is a net exporter.
My though so far is that I have to use that BNP(Y): $$Y=C+I+G+NX$$ and $$S_A=publicsavings+privatesavnings=(T-G)+(Y-T-C)=Y-C-G$$ and that $NX>0$. But when I use these can only find an expression of the form $S_A>f(A,a,r)$. But I think I have to find an expression of the form $S_A>f(A,a,B,b,r)$. Can someone help me?


texts: What is preventing the United States from printing USD to buy up prized assets from foreign countries given that USD is the world's reserve currency?

texts: USD is accepted all over the world. U.S can easily print USD to buy up the most valuable assets from all over the world. Ethics aside. What is preventing the U.S from doing so? What did I miss out?


texts: Elasticity, link between demand and supply

texts:
I have a exercise with the corresponding answer, but i don't get it:

  Suppose there's a better wheather this year and the size of the harvest of soy increased a 60%. The demand curve for soy did not change. The price of the soy dropped a 20%. We can conclude that the elasticity of demand is -3.

Is this true? Under what circumstances? Why? Thank's a lot!


texts: Economic implications of allowing competition with essential services i.e police, fire department, etc

texts:
I'm wondering what are the implications of allowing competition between firms that deal with essential services in public welfare. I.e assuming there is no government regulation of such services, what would happen if there was competition between firms in the policing industry or if there was competition allowed among different fire departments?

What would the industry look like and what kind of methods would we use to analyse such a situation?


texts: Count panel models for endogenous regressors

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I have a count variable as the dependent variable and several continuous regressors on the RHS. The dependent variable and some regressors are supposed to be endogenous to unobserved factors. I have a set of IVs for the endogenous regressors.

I have two questions:

Is there any model for count panel data (especially for fixed effect) that addresses endogenous regressors?

I have been looking into the literature and have not found anything. It is either count models for panel data, or count models for endogenous regressors, not both.

Some books mention that it is difficult to address endogeneity in count panel data, but they do not really explain why. Anyone knows why?

Thanks!


texts: Compute evolution of a distribution over time

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We have a population of people with different age $a$, time is indexed with $t$. There is a rate at which people die, $d(a, t)$. For simplicity, ignore births. I want to compute the evolution of the distribution of ages over time.

Denote the mass of people at or below age $a$ by $F(a,t)$

$$ F(a,t) = \int_0^{a} m(\tilde a,t) d\tilde a $$

Ultimately, I am after some Kolmogorov forward equation, that is, the solution for

$$ \partial_t F(a,t)$$

My approach Let $f(a, t)$ denote the density of people at age $a$ and point in time $t$. I will start with a discrete time approximation and let $\Delta$ go to zero. At each discrete point in time,

$$ f(a+\Delta, t+\Delta) = (1-P(a, t))f(a, t)$$

where $P(a, t)$ is the discrete time analogue of $d(a,t)$. As I'm going to let $\Delta\to 0$, I can approximate $1-P$ with $1-\Delta d)$:

$$ f(a+\Delta, t+\Delta) = (1- \Delta d(a,t))f(a, t)\\
\frac{f(a+\Delta, t+\Delta) -f(a,t)}{\Delta} = -d(a,t))f(a, t)\\
(\partial_t + \partial_a)f(a,t) = \lim_{\Delta\to 0}\frac{f(a+\Delta, t+\Delta) -f(a,t)}{\Delta} = -d(a,t))f(a, t)\\
$$

I can integrate both sides w.r.t. a and get

$$ \partial_t F(t, a) = - f(t, a) - \int q(t, a) f(t, a) da \\
\partial_t F(t, a) = - \partial_a F(t, a) - \int q(t, a) \partial_a F(t, a) da $$

I know that $\partial_a q(t, a) = q(t, a) (1-q(t, a))$. However, that doesn't really help me with solving the integral. Is there perhaps another angle to attack this problem? Or did I miss something?


texts: Does returns to scale always lead to economies of scale?

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I can tell the difference between returns to scale and economies of scale, but then I still don't know if returns to scale ALWAYS leads to economies of scale?
Please could you help me?


texts: What are some examples of modern economic research that integrate economics and computer science?

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I am entering my first year of graduate studies in Economics this fall and I'm curious about which areas of economic research utilize various fields of computer science (e.g. Machine Learning, Graph Theory, etc.) to study economics. More specifically, how are recent advancements in the field of computer science being used to answer economic questions that were previously difficult or impossible to answer?
Thank you in advance for any responses.


texts: Will the services rendered by a worker from an unorganized sector be counted in GDP?

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My guess is it won't be because the unorganized sector isn't captured in GDP? but I read somewhere it will be. not sure if I am wrong or it was an error in the answer key.

please help


texts: Expected inflation in the real interest rate equation

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Real interest rate = Nominal rate - Expected inflation

In the above equation, in a quarterly data-set, which expected inflation shall be used? next quarter (q+1) or the same quarter of next year (q+4)? and why?