Venezuelan black market exchange EDIT: for future reference, I found out that many businesses price accordingly to the black market rate.

Trading at the official Venezuelan exchange rate is, at time of writing,  about 1:10 USD:VEF.
From what I've understood  black market exchanges offer more than 1:1000 USD:VEF.
They are technically illegal, but its use is widespread to the point of routine.

Now take a look at these numbers from expatisan.com comparing "Monthly rent for 85 m2 (900 Sqft)
 furnished accommodation in NORMAL area" between Los Angeles and Caracas.

  Official exchange rate for VEF:
  LA is 52% cheaper
  Black market rate for VEF: Caracas is 5288% cheaper

I understand Venezuela is in turmoil with inflation after Chavez' version of socialism had its way. Does the rent for one 900Sqft apt. in LA really pay for 52 apartments in Caracas? Naturally, a Venezuelan's income comes in VEF and not in USD by cash,
 so they are not seeing the (assumed) benefit foreigners with USD have.

With that comes my main question, can a foreigner really enter the country with 10,000 USD and turn that into eg. 22 years of rent for the apt. in above example? (assuming steady rate of 37,000 VEF)

There must be something I'm missing here?
Sorry if this Q isn't relevant, but where else to ask than economics stack?

The official rate is about 10, but the black market rate is about 1000.  Also, yes, apparently the real exchange rate at the 1000 rate is pretty low, in the sense that one dollar buys a lot of local goods, (like boarding). Indeed, that's what it means, 10,000 dollars buys you 1,000,000 VB's, which pays for years and years of rent. The ratio in your numbers is that Venezuela is about 50 times cheaper. In this story, staying in a hotel costs $5, which is also about 50 times cheaper than staying in a hotel in L.A....

(It would be hard to change such a large amount of dollars without getting noticed though...)


Can government just print a little of money to purchase some foreign resources? We know that government shouldn't just print money, because it's gonna be bad. Bad what if to do it in a small scale, just a little, for example to hire some scientist (probably nothing gonna happen because of printed salary for just one or three men) or get one oil tanker (to get a little of oil)?
And it both those cases it looks like a good investment that will return money.

We know that government shouldn't just print money

I partly disagree. The government (or, well, the central bank) should print the amount of money that is needed to keep the inflation stable. Anything above that shouldn't be done.

Bad what if to do it in a small scale, just a little

What if you stole something small from a nearby shop, just a little?

What if you took advantage of insider information, just a little?

What if you committed a small accounting fraud, just a little?

Printing money increases the monetary supply. That leads to inflation, which leads to increased inflation expectations. The increased inflation expectations raise the nominal interest rates.

Those who have net debt will benefit (if it's fixed rate), those who have financed the debt of others by depositing money into bank will suffer (if they are fixed rate deposits). The suffering will be greater than the benefit, because of the unpredictability of inflation (if the government is free to print money, you never know how large the inflation is going to be).

Generally, governments are in debt (and they should be because it offers investors the ability to invest into government bonds, which are a core part of a stable investment portfolio) and the debt is fixed rate. Thus, the people having the government bonds will suffer. Essentially, printing money steals from the government bond holders.

Those who have real assets like real estate, forest or non-financial stocks will not see any effect (expect perhaps by taxation because capital gains are typically fully taxed even if they occur in times of increased inflation).

Note the government will eventually suffer as well. The unpredictable inflation means government bonds have a higher yield, meaning if the government is going to finance most of its operations by obtaining debt from the public (even though printing money for the rest of its operations), the interest rates will rise. So, printing money is a bad strategy, even in a small scale. Soon there will be no other way of funding the government operations apart from printing even more money, which leads to hyperinflation.


Would this alternative to fractional reserve banking work? While reading the answer to Implications of abolishing Fractional Reserve Banking on mortgages and interest rates, I started to wonder if there wasn't a simple solution to the problems that would arise with the introduction of a constant money supply.

Right now, banks create the illusion of more money existing by accepting deposits and holding onto only a fraction of them while lending out the rest.  Alternatively, could they not just package up loans into investments and essentially sell shares in the investments to average people.  This would essentially have the same effect, your cash would be tied up in the bank and you would receive some amount of interest on it.  The investments could even be structured and insured in a similar way to the current system in order to maintain some amount of liquidity.  The only big change is that people would be very much aware of where there money is when they put it in the bank, which to me would only increase the robustness of the system and reduce the possibility of bank runs, as there would be a general understanding that some of your money is loaned out at any given time.

Has this idea been studied, and are there any known or obvious flaws that I am not seeing?

How, in practise, would that be different from what is happening now? ..or what you, as an "investor" could already do?

No one is forcing you to deposit all your liquid assets into a bank account - most banks offer some sort of investment-opportunities, where you can buy into different funds with different risk-profiles.

Next thing; suppose banks take all deposits and lend out to different customers for various purposes and they receive interest on those lendings - some of those interest are transfered back to you for allowing the bank to use your money. This would actually be the same, as putting your money into a fund. The bank "invests" your money with other customers and recieve some sort of yield on that investment (interest). Difference will be the risk-profile. By "investing" in the bank you recieve an extremely diversified portfolio, funding everything from consumer goods, cars, houses to actually backing large corporations. Most of your investment is being placed high up in the hierarchy of priotization if the lenders go into default, which makes your investment "safer" than if you go and buy bonds in that same company (but obviously also recieves a lower yield).

Your proposal will put peoples money in a different place in the hierarchy of debt if customer/lenders go bankrupt, actually increasing the general risk-profile of the bank.

In all everything comes down to your risk profile - which exposure do you want your investment to have. The risk of a AAA rated sovereign bond yielding -0.5%, receive 0% on your deposits in a government backed bank, 5% on a BB- mutual fund or 25% on an emerging markets bonds?


Tools for Forcasting Unemployment Rate I've noticed that economists have been very accurate when it comes to predicting unemployment rates.

Most of their predictions usually fall within a 0.2% difference between their forecasts and the actual unemployment rate or are dead on what the employment rate is. I've looked at this site for information on the forecast vs the actual unemployment rate recently, which prompted me to ask this question.

http://www.tradingeconomics.com/canada/unemployment-rate
http://www.tradingeconomics.com/brazil/unemployment-rate
http://www.tradingeconomics.com/italy/unemployment-rate

Im aware of Okun's law and the cross country differences in terms of the measure of its coefficient. (see: http://unassumingeconomist.com/wp-content/uploads/2016/08/cross-country-evidence-on-okun-sep-2016-paris-workshop-draft-with-tables-and-charts.pdf)

But I am generally unaware of forecasting methods used by economists to predict unemployment rates.

What are some basic formulas or models used to forecast unemployment rates? Is there a pdf book anyone can recommend?

I think one might use either vector auto-regression or perhaps factor-augmented vector auto-regression to make such predictions. The later will allow an economist to condition on hundreds of time series to predict future unemployment values without encountering the degrees-of-freedom issues that plague VAR whenever VAR attempts to condition on larger information sets.

Here is a paper detailing Kalman filtering and VAR for predicting unemployment:
https://www.degruyter.com/downloadpdf/j/ngoe.2015.61.issue-3/ngoe-2015-0009/ngoe-2015-0009.pdf

TLDR: VAR does better than does KF. This is for Romania's economy, FYI.

Here is another paper detailing the use of VAR to forecast unemployment:
https://www.brookings.edu/wp-content/uploads/2012/09/2012b_barnichon.pdf

Here is the seminal paper that introduced FAVAR:
http://faculty.wcas.northwestern.edu/~lchrist/finc520/QJE.pdf

Wiki for VAR:
https://en.wikipedia.org/wiki/Vector_autoregression

within the wiki, you will find a link to the seminal paper by Sims that introduces the VAR methodology to economics. Fair warning: this paper is dense:
http://www.ekonometria.wne.uw.edu.pl/uploads/Main/macroeconomics_and_reality.pdf


Proof on weak axiom of revealed preferences I read the following statement.
“ A utility maximizer with strictly convex and strongly monotonic preferences
satisfies weak axiom of revealed preferences.”
How can I prove or show this? I cannot realize this statement on my mind. Please show me it’s proof in order to understand its statement.

As far as I can see this comes just from definitions:
As given in MWG definition 1.C.1:

The choice structure $(\mathscr{B},C(\cdot))$ satisfies the weak axiom of revealed preference if the following property holds:

If for some $B \in \mathscr{B}$ with $x,y \in B$ we have $x\in C(B)$, then for any $B'\in \mathscr{B}$ with $x,y\in B'$ and $y\in C(B')$, we must also have $x\in C(B')$.

This basically states that under the weak axiom of revealed preference (WARP) if there is any choice set which contains both $x$ and $y$ and $x$ is preferred then there can be no set containing both $x$ and $y$ where $y$ would be chosen over $x$. Or we can say that "if x is revealed at least as good as y, then y cannot be revealed preferred to x."
Next according to MWG definition 3.B.2:

The preference relation $\succeq$ on $X$ is monotone if $x\in X$ and $y >> x$ implies $y \succ x$. It is strongly monotone if $y \geq x$ and $y \neq x$ imply that $y\succ x$.

In addition, according to MWG definition 3.B.4:

The preference relation $\succeq $ on $X$ is convex if for every $x\in X$, the upper countour set $\{y \in X: y \succeq x\}$ is convex; that is, if $y \succeq x$ and $z \succeq x$, then $\alpha y + (1-\alpha) z \succeq x$ for any $\alpha \in [0,1]$.

Lastly, utility maximization is often used to imply rationality (Simon 2001) and preference relation can be rational only according to MWG definition 1.B.1:

The preference relation $\succeq$ is rational if it possesses the following two properties:
(i) Completeness: for all $x,y \in X$ we have that $x\succeq y$ or $y \succeq x$ or both.
(ii) Transitivity: For all $x,y,z \in X$ if $x \succeq y$ and $y \succeq z$ then $x \succeq z$.

Given the definitions above if they are satisfied then if $y$ is revealed to be at least as good as $x$, $x$ cannot later be revealed as better.  So it follows from the definitions of those properties. For example, WARP would be violated if the following choices are made $C(\{x,y\}) = y$ and in $C(\{x,y,z\}) = {x}$, by a person holding their preferences constant - such situation would clearly violate several of the above definitions.


Relationship between Interest Rates and Supply of a currency? I am aware of how the interest rates affect the demand for a currency, but am baffled by how it affects the supply for a currency. I've read conflicting theories. Is it true that an increase in the interest rate increases the supply of a currency?

Many thanks

Maybe it will be useful for you to start:  [http://www.wisegeek.com/what-is-the-relationship-between-money-supply-and-interest-rate.htm][1]"
 As asked I summarize the core ideas, written in the link.  So, higher interest rate decreases the supply of the money:

The central bank can set the reserve percentage, which tells how much percentage of the total money of each commercial bank must be hold back. The higher this rate, the less money the banks can give to the consumers as loans.
Central bank also can set the target percentage, which is the interest rate between commercial banks or between commercial banks and the central bank. The higher this rate, the more the banks must pay when making loans among them, so the less money remains to loan to the consumers.
Central bank can set the consumer interest rate, too. The higher rate the consumers have to pay after their loans, the less money remains at themselves. So the supply of the money decreased. (And as I think, but not in the link: if the interest rate after deposits are high, more people will think that it is better for them to save their money in the bank and not spend it for something else. If it is combined with point 1., it will also decrease the supply of money.)


Why does the Market Risk Premium increase in times of crisis? My question is a bit more specific as it is indeed well known that investors expect higher returns in times of higher risks/volatility.

However, isn't it counterintuitive to expect the market to achieve higher returns when the economy is slowing down ? For example, if we have a look at the current economic situation, how could someone expect the S&P500 index (let's assume we use it as a proxy for Market Return) to perform better than it did before the coronavirus crisis ?

So, in short, how can you realistically expect higher returns when the economy is in fact crashing down ?

Thanks in advance !

Risk premium is the excess expected return of the market over that of the risk-free asset. (There is no "(expected) risk premium".)

It is a property of the expected returns of two assets. It is an indication of investor's willingness to bear risk. High risk premium means less risk-bearing capacity in the market, where market participants are in risk-off mode.

Risk premium is not a forecast of future returns of the risky asset.
In contrast, something like a P/E ratio (or Shiller's cyclically adjusted CA P/E) is designed to reflect future returns. High P/E means asset is over-priced and lower future returns.

Risk premium can go up when price of risky asset decreases and/or risk-free rate decreases. Both tend to occur when market perceives uncertainty and shifts from a risk-on to risk-off regime. For example, S&P500 price and US Treasury yield (risk-free rate) could go down as capital shift from risky equity to safe US government debt.

This is not restricted to equity markets. Credit spread in the corporate bond market is also a kind of risk premium, for credit risk instead of market risk. The higher perceived default risk of the issuer, the higher is the yield demanded by investors. Corporates whose debt has high yield (junk) rating are perceived to have higher credit risk than those who are low yield (investment grade).
During market uncertainty, credit spread widens.


Volatility of investment: Joint-Volatility of mutually independent variables I´ve been trying to compute a volatility of invesment with currency hedging and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% volatility, we also know that the current volatility of a dollar toward our currency is 5%. We want to know the volatility of the whole invesment.

Can I compute as following? If so, what is the reason for adding the two deviations instead of mulitplying them considering the volalitity of an index and a currency are mutualy independent.

$$\sigma=\sqrt{(16^2)+(5^2)}$$

The variances of the sum of independent random variables are additive. Therefore, if X and Y are independent, Var(X+Y)= Var(X) + Var(Y). The standard deviation is defined as $\sigma_z = \sqrt{Var(z)}$. Therefore, if X and Y are independent, $\sigma_{X+Y} = \sqrt{Var(X+Y)} = \sqrt{Var(X) + Var(Y)}$. This gives the result above.


Why does the stock market tend to grow over time At its most basic, the value of a stock depends on how much people are willing to pay an entity that already owns the stock to transfer ownership. The question is, why does the amount people are willing to pay typically go up over time?

Obviously, a single rational investor may be willing to pay more for a stock if they expect that may other investors will also increase the amount they are willing to pay. But why would they expect other investors to come to the same conclusion? It would seem there needs to be a base reason that an “initial” investor would pay more for a stock than other investors.

I can think of two reasons that they may use:

Dividends: A stock not only has value from its potential for others to increase their valuation of it. But owners of some stocks may get direct payouts simply by being an owner.
Voting Rights: An owner of a stock has may have voting rights within a company. With enough stock, an investor may have sizable control over the actions of a company.

Are there many other reasons why investors may increase their valuation of a stock over time? Or is my (obviously very simplified) model just completely flawed?

Actually you are asking little bit different question in your title and then in your question. There is difference between asking why stock market always grows and why individual companies’ stock grow. In fact in case of individual companies you can see that many companies fail and their stock price gets wiped out despite the stock market always growing over time so those are fundamentally different questions but I will try to respond to both of them.

What determines individual stock price? There are multiple stock pricing models but they more or less boil down to estimating what will be the future discounted return on your investment in one way or another. An example of a stock pricing model would be the Gordon’s growth model, where the stock price is given by:

$$ P=\frac{D_0(1+g)}{r-g}$$

Where $P$ is the price $D_0$ is the current dividend, g is the dividend growth rate and r is the required rate of return.

So the individual stock price can increase either due to higher dividend payments, higher expected growth rate of these dividends or lower required rate of return.

However, as mentioned before there is no reason to think or even expect for any individual company’s stock price to always increase in a long term. In fact you have a lot of companies that simply fail and their stock price becomes zero.

Also note the explanation above is little bit oversimplification because there are firms that don’t pay out dividends but they are still being valued and their stock price can grow, but I on purpose did not wanted to make my answer overtly technical and include some more complex models that can handle that as well, and generally the explanation is still valid one.

How come that stock market tends to grow over time? This is because even though  individual companies can and often do fail they are usually replaced by new and more efficient companies. In general thanks to economic growth, which depends on technological growth, growth of population, or even due to endogenous factors like human capital accumulation, firms are constantly getting more efficient and more productive meaning they can generate larger profits with less inputs and consequently also payout more of this profit as dividends. Firms that can’t adjust to technological change and deliver better products more efficiently will fail and be replaced by those companies that can. Recent famous examples would be Kodak or Nokia.

This being said if the economic progresses of humanity would be halted for whatever reason the stock market could start failing over time. For example in case of some apocalyptic scenario such as nuclear war. It might also happen that eventually human race would end up in some stagnant state when there would be no more future growth because we would reach a point where we can’t get any new technological progress or accumulate more human capital - but that does not seem to be probable any time soon.


How to derive Hicksian demand? How can I derive Hicksian demand, when from the FOC I only get $\frac{p_x}{p_y} = \frac13$ without the usual x & y. So they cannot be derived directly from FOC, but if I plug the price relation into the budget constraint $I =p_x \cdot x + p_y \cdot y$ I get the income in the demand function, so this is Marshallian demand. Plugging the relation in expenditure function, obtained from the indirect utility function also doesn't lead to the Hicksian demand (that I obtained via Shephard's lemma and equals $h_x = U + x + 3y$).

The problem is to minimize

$$p_x \cdot x + p_y \cdot y \qquad\text{s.t.}\qquad x + 3y ≥ U$$

Expenditure minimization problem in the question is as follows :
\begin{eqnarray*} \min_{x\geq 0, y\geq 0} & \ \ p_Xx + p_Yy \\ \text{s.t.}& \ \ x + 3y \geq U \end{eqnarray*}
where $p_X > 0$, $p_Y > 0$ and $U \geq 0$ are given.
Since prices are positive, the cost minimizing choice will satisfy the condition that $x + 3y = U$. So, we can rewrite the above problem as :
\begin{eqnarray*} \min_{x\geq 0, y\geq 0} & \ \ p_Xx + p_Yy \\ \text{s.t.}& \ \ x + 3y = U \end{eqnarray*}
We can now substitute the value of $y = \frac{U-x}{3}$ in the objective and rewrite the problem as :
\begin{eqnarray*} \min_{0 \leq x \leq U} & \ \ p_Xx + p_Y\left(\dfrac{U-x}{3}\right)  \end{eqnarray*}

Since the objective ${\color{red} {p_Xx + p_Y\left(\frac{U-x}{3}\right) =\frac{p_YU}{3} + \left(p_X- \frac{p_Y}{3}\right)x }}$  is linear in $x$, solution is straight forward :
\begin{eqnarray*} x^h(p_X, p_Y, U)  \begin{cases} = U & \text{if } p_X < \frac{p_Y}{3} \\ \in [0, U] & \text{if } p_X = \frac{p_Y}{3} \\ = 0 & \text{if } p_X > \frac{p_Y}{3}\end{cases} \end{eqnarray*}


Measuring quantities for price indices? I'm confused about how one acquires the data necessary to compute price indices--specifically, how one acquires quantity data.

Suppose I wanted to compute the Laspeyres Index, defined as

$\sum\limits_{i=1}^{N} p_{i}(t_{f}) q_{i}(t_{0}) / \sum\limits_{i=1}^{N} p_{i}(t_{0}) q_{i}(t_{0})$

where $N$ is the number of different goods, each $p_{i}$ is a price, and each $q_{i}$ is a quantity. Each $p_i$ is measured in units of currency per units of a good, and each $q_{i}$ is measured in units of a good per unit of time.

But as far as I can tell, we can't measure $q_{i}(t_{o})$ or $q_{i}(t_{f})$. These represent the instantaneous rates that a certain good is sold at a particular time, whereas data-collectors are only able to ask how much firms have sold of a good over a period of time--in other words, we can measure

$\int\limits_{t_{0}}^{t_{f}} q_{i}(t)dt$

by summing the total sales of all firms that sell good $i$ during the period between $t_{0}$ and $t_{f}$, but not

$q_{i}(t)$

for any given $t$.

How do actual econometricians measure $q_{i}(t_{o})$ and $q_{i}(t_{f})$? Do they measure the number of goods sold $x$ days after $t_{0}$ or $t_{f}$, then divide by $x$ for a sort of local approximation? Or do they use some other method?

The notation $q_{i}(t_{0})$ does not necessarily mean number of goods sold in instant $t_0$. It can also mean the number of goods sold in the period denoted by $t_0$. As you point out the first one would be somewhat difficult to measure.

In fact I have not yet seen the notation you use. The notation I am familiar with is usually something like $q_{i,t_0}$, which better indicates that time is treated as a discrete variable. The unit of time could be anything, but it is usually a year or quarter.


Wage Growth Rate in the R&D Model I am trying to understand the R&D model and how to calculate the growth rate of wage in this model.

There is no equation given, but it’s stated that : household income must equal total consumption. as income is total profit plus wage income, and the two are fixed in proportions, wages grow at the same rate as output $g_w=g_y$

I tried to write down the equation of this statement, however, I don‘t really think it’s right: $\pi+w= C_t$.

Can anyone help with the equation and it’s intuition?

Addition: the R&D model introduces final good producers that sell their good in a competitive market and intermediate goods producers that produce either a produced intermediate good or “ideas” that are sold to the final good producers and used to produce the final good. The intermediate good and “ideas” are substitutes.

income is total profit plus wage income, and the two are fixed in proportions

I.e. $y_t = w_t + \pi_t$ and  $w_t = \alpha y_t$ and  $\pi_t = (1-\alpha)y_t$, where $\alpha$ and $(1-\alpha)$ are the fixed proportions.

For $y_{t+1}$ we have $y_{t+1}=(1+g_y)y_t$ and $w_{t+1} = \alpha y_{t+1} = \alpha (1+g_y)y_t = (1+g_y)\alpha y_t = (1+g_y) w_t$ and $\pi_{t+1} = (1-\alpha) y_{t+1} = (1-\alpha)(1+g_y)y_t = (1+g_y)(1-\alpha) y_t = (1+g_y) \pi_t.$

I.e. $g_y = g_w = g_{\pi}$


Question on Pareto optimality problem In an economy with two agents whose utility functions are
$$
U_A(x_1,x_2) = \alpha \cdot x_1 + x_2 \hskip 20pt U_B(y_1,y_2) = y_1 \cdot y_2.
$$

The given allocations are bundle (4,0) for A and bundle (1,5) for B.

Consider the following question

Taking into consideration the respective utilities for the bundles, we have $U_A=4\alpha$ and $U_B=5$. For this allocation to be a No Envy allocation, it has to be $4\alpha \geq 5$, which means alpha has to be greater than or equal to $\frac{5}{4}$.

Is this the right approach to solve this problem? If its not, please find the solution and show me the steps.

As denesp mentioned, your solution is incorrect. To check whether there is envy, you have to compare the two bundles from the point of view of the same agent. So in our case we have:

For agent A: the utility of his own bundle is $4 \alpha$ and the utility of the other bundle is $\alpha+5$. So he feels no envy as long as $4\alpha \geq \alpha+5$, which is equivalent to: $\alpha \geq 5/3$.
For agent B: the utility of his own bundle is 5 and the utility of the other bundle is 0. So he never feels envy.

This means that the correct answer is (c).


How to make a timeline in given problem? How much money should be deposited each year
  for 12 years if you wish to withdraw $309 each year for
  five years, beginning at the end of the 14th year? Let
  i = 8% per year.

In the problem what does "end of 14th year" refer to? Will that amount remaining will compound interest when deposited at the "end of 14th year"?

End of the 14th year is essentially the same as the start of the 15th year. As in, you need to apply the interest for the 14th year before you withdraw the $309.

This problem has several steps and is most easily solved in reverse. First you need to figure out what principal A you need to withdraw $309 for 5 years. Second, you need to figure out what principal B you need with 8% interest over 2 years to reach principal A. Lastly, you need to find what annuity payment needs to be made each year for 12 years to reach principal B. That will be your answer.


What is the characteristics of economic downturn and which countries experience economic downturn from 2010 to 2018? I would like to know the characteristics of economic downturn. Is downturn the same as recession? and which countries experience economic downturn from 2010 to 2018?

A downturn is characterized by a time period of lower economic growth or economic contraction. The term economic downturn has no formal definition and can mean many things including a recession. An economic downturn might also be used to describe periods of lower economic growth. On the other hand a recession is a specific term that is often used to describe two consecutive quarters of economic contraction.
For example, Australia has experienced near continuous growth since the early 1990s. In that three decade span Australia has experienced individual quarters of contraction but never two consecutive quarters of contraction. So it can be said that Australia has experience brief economic downturns but no recessions in the past decades.
Not completely the same as a list of countries that have experience economic downturns, but Wikipedia has a list of economic crisis by decade. A few notable examples in the 2010 to 2018 time frame are Brazil, Greece, and Venezuela.
Here is a chart from a World Bank research paper that shows the number of countries in recession by year.

This definition comes from the site Market Business News and offers a more precise definition of economic downturn.

An economic downturn, or a downturn, occurs when the value of stocks, property, and commodities fall, productivity either grows more slowly or declines, and GDP (gross domestic product) shrinks, stands still or expands more slowly.


What is equilibrium dependent upon in Generalized Second-Price Auctions? Theory states that GSP auctions induce truthful bidding.  Is it the case that this is true ONLY IF

a) each of the bidders truthfully bids their value ($b_i = v_i$) (each bidder's optimal strategy) AND

b) each bidder assumes that all of the other bidders are also truthfully employing their own optimal strategy ?

My question arises out of the following possible example:

Two bidders bidding for a single item, Vickery sealed-bid second-price auction.

The bidders have equal values for the same item (say $v_1 = v_2 = 10$)

$b_1 = 7$

$b_2 = 9$

$b_2$ will win the auction and pay $7$; with a surplus payoff of $2= (9-7)$.  This outcome is equivalent to the example where:

$v_1 = b_1 = 7$

$v_2 = b_2 = 9$

$b_2$ wins in either example but neither bidder is using the optimal strategy in the first example.  What logic am I missing?

The surplus is the value of the object obtained minus the price paid. In your first example, the surplus would be $10-7 = 3$. The reason why you don't find examples where BOTH players are not using optimal strategies is because $b=v$ is weakly dominant. Unlike a lot of games where you need to consider best response functions, this one can be solved simply by removing dominated strategies.

Using your first example, there exists no bids that will give a higher payoff than $b_i=10$ regardless of what $b_{-i}$. Suppose we look at player 1, then consider all cases:

$b_2 < b_1 < v_1$: surplus is the same as $b_1=v_1$

$b_1 < b_2 < v_1$: surplus is 0, $b_1=v_1$ is profitable deviation

$b_1 < v_1 < b_2$: surplus is the same as $b_1=v_1$

$v_1 < b_1$ surplus is negative or 0 (depending on $b_2$), $b_1=v_1$ is profitable deviation

Also, auctions are usually used for a non dividable object, which means that examples with multiple players with the same value require a tie breaking rule. Whether or not this weak dominance survives depends on this tie breaking rule.


Abolishing all tariffs without reciprocity Is a policy of abolishing tariffs without expecting other countries do so a sustainable economic policy? What are the arguments for or against it?

Fear of imports is very common among people. Money going out and products coming in is not a loss of anything, since products and services are just as valuable as fiat money, or any medium of exchange.

In a country with trade deficit, I should expect depreciation of the domestic currency in short term. Devaluing currency is supposed to encourage exports, and exporters but things they need for cheaper too, so it should cause some growth in exports.

If abolishing tariffs is "such a good idea", why do politicians try to push for trade agreements instead of abolishing tariffs within their countries and benefit from the results?

You get cheaper access to inputs. For a large advanced economy that is relatively diversified, it is possible that unilateral tariff reductions across many or all sectors can be good for the economy by freeing up resources presently occupied in low-value activities with few prospects to contribute to technological progress. The additional ease of doing business in that country may also attract additional financial investments and human resources talent from abroad, which would tend to increase technological progress and productivity at the same time.

For a small economy that specializes in some specific sector (e.g., tourism, finance), a unilateral tariff reduction may improve the competitiveness of the sector they specialize in, and therefore be good for the economy and/or technological progress over both short and long time frames.

These are somewhat special conditions, and most often countries do not see benefit in unilateral tariff reductions.

As for what politicians do, this is a somewhat different question and should be considered separately from the economics argumentation about unilateral tariff reduction. It is very straightforward to argue that some concentrated interest(s) in just one or two industries could be major campaign contributors in a winning campaign, leading the politician to try to impose tariffs which benefit specific industries while causing overall negative impacts across the entire economy.

Theoretically, it would be possible to be in a situation where both a) unilateral tariff reductions could benefit the economy and b) at the same time concentrated interests could legally and/or illegally obtain political influence which resulted in an increase in their own profits at a cost to the overall economy.


Does Household final consumption Expenditure include Consumption expenditure of Imported Goods From World Bank, I got the Household final consumption Expenditure for many countries across time. I wonder if this consumption includes Consumption expenditure of Imported Goods / Import Volume?

If I want to compute the share of consumption of home goods in total consumption, should I use the following formula?

$\frac{Household final consumption Expenditure - Import Volume}{Household final consumption Expenditure}$

or should I use:

$\frac{Household final consumption Expenditure}{Household final consumption Expenditure + Import Volume}$

Many thanks for your help.

Yes.

Household final consumption expenditure consists of the expenditure, including expenditure whose value must be estimated indirectly, incurred by resident households on individual consumption goods and services, including those sold at prices that are not economically significant and including consumption goods and services acquired abroad.
(From System of National Accounts, 2008, p. 623, PDF).

To elaborate, in the familiar identity $$Y = C + I + G + (X - M),$$ the reason we subtract $M$ (imports) is that the terms $C$, $I$, and $G$ also include imported goods and services.
In particular and to your secondary question, let:

$C_d =$ Consumption of domestically-produced goods and services.
$C_m =$ Consumption of foreign-produced goods and services.

Then: $$C=C_d+C_m.$$
And what I believe you want is $\frac{C_d}{C}$ or equivalently $1-\frac{Cm}{C}$.


Financial Crisis text book recommendation I am looking for an academic textbook on the science of financial crises, such as bank runs, monetary crisis, bubbles, stock market crashes etc.
Ideally, the textbook would address what is currently known about why crises happen, explained in objective and scientific language, explaining the underlying mechanics and/or the known leading indicators.
Finally, the textbook does not need to focus on a particular crisis e.g. the 1929 or 2007 crisis, preferably it would be a general treatment of the subject.
Thank you!

One of my favorites in this dimension is "This Time Is Different" by Reinhart and Rogoff. Both are respected scholars. The title already suggests what they aim at.

Covering sixty-six countries across five continents, This Time Is Different presents a comprehensive look at the varieties of financial crises, and guides us through eight astonishing centuries of government defaults, banking panics, and inflationary spikes—from medieval currency debasements to today’s subprime catastrophe.


Monopoly and Taxes (Nicholson Exercise) Hello I'm working through Microeconomic Theory : Basic Principles and Extensions of Nicholson and Snyder 10e, for an exam and I fail to get how to answer this question (p.517) :

  A specific tax is a fixed amount per unit of output. If the tax rate
  is t per unit, total tax collections are tQ . Show that the imposition
  of a specific tax on a monopoly will reduce output more (and increase
  price more) than will the imposition of an ad valorem tax that
  collects the same tax revenue.

So I state that both tax collects the same (s for specific and a for ad valorem)
$$q_s^m \times \tau_s =A$$
$$q_a^m \times p^m_a \times \tau_a=A  $$

Then I have tried some identities of $q^m$ and $p^m$ but I can't get to the proof.

$$q_s^m=\dfrac{C'(q_s^m)+\tau_s-p^m_s}{P'_s} $$
$$q_a^m=\dfrac{C'(q_a^m)}{(1-\tau_a)P'_a}-\dfrac{p_a^m}{P'_a}$$

where $P'_i$ is the derivative of the inverse demand function at the equilibrium point of the monopolist under the tax type $i$

I tried replacing $\tau$ as $\tau_s=\dfrac{q_a^m \times p_a^m \times \tau_a }{q_s^m}$ and then replacing it in $q_s^m$ but I get a quadratic form of no use...

First let's look at the specific tax. The profit is
$$\pi_s=[P(q)-\tau_s]q-C(q).$$
Differentiating to establish the first-order condition:
$$P'(q)q+P(q)-\tau_s-C'(q)=0.$$
If we write $A=\tau_s q$ for the tax revenue then we can rewrite the FOC thus:
$$P'(q)q+P(q)-C'(q)=\frac{A}{q}.$$

Now for ad valorem:
$$\pi_a=(1-\tau_a)P(q)q-C(q)$$
First-order condition:
$$(1-\tau_a)[P'(q)q+P(q)]-C'(q)=0.$$
We have $A=\tau_a q P(q)$, which can can use as follows:
$$[P'(q)q+P(q)]-\tau_aP'(q)q-\tau_aP(q)-C'(q)=0.$$
$$[P'(q)q+P(q)]-\frac{A}{P(q)}P'(q)-\frac{A}{q}-C'(q)=0.$$
$$P'(q)q+P(q)-C'(q)=\frac{A}{q}+\frac{A}{P(q)}P'(q).$$

Note the the left-hand side of the last line in both sections is the same. Moreover, this expression ($P'(q)q+P(q)-C'(q)$) is the derivative of profits assuming zero tax. If profits are concave then this derivative is decreasing in $q$.

We can see that, for any value of $q$, the right-hand side is smaller for the ad valorem tax (because it has an extra term that is negative--remember that $P'(q)<0$). Thus, we have something that looks like this:


Does an increase in the money supply increase or decrease interest rates? What I understand is that an increase in the money supply brings about a fall in interest rate as there is more money available, the price of money will be cheaper. But some theory such as liquidity effect posits that increase in money supply will increase in interest rate. Is that they view the problem differently or the two situations are different?

  "Money growth also affects interest rates and prices and those in turn will
  influence stock prices. Assuming that money demand remains constant, increase in money supply raises interest rates thereby increasing the opportunity cost of holding cash as well as stocks. Lured by higher interest earnings, people are likely to convert their cash and stock holdings to interest-bearing deposits and securities with obvious implications for stock prices. Since the rate of inflation is positively related to money growth, an increase in money supply may lower the demand for stocks and assets (as real value of such assets decline due to inflation) resulting in higher discount rates (as banks become more cautious in its lending) and lower stock prices. The rising interest rates and inflation will also adversely affect corporate profits (earnings) leading to lower stock returns (both actual and expected) and thereby making stock possession (as well as new purchase) less attractive."

The above is quoted from an article. It mention that increase in money supply raises interest rates thereby increasing the opportunity cost of holding cash as well as stocks. I don't understand how increasing in money supply would increase interest rate. Could you explain?

I will frame this in the context of modern monetary policy and for the sake of clarity assume we are discussing the American economy.

1) Whenever the Fed wants to bring about some change in the economy, they do so by using one of three tools: open market operations, setting the discount rate, setting reserve requirements. I will only discuss open market operations. The Fed recently introduced two new tools: interest on excess reserves and forward guidance. I include these to be complete.

2) The Fed conducts open market operations through its NY branch's buy/sell desk. In simple terms, the Fed can buy/sell securities in the open market. This causes two things: a change in total bank reserves and security yields (by way of shift demand/supply curves, for example).

Your question is whether or not it makes sense to think about an increase in the money supply causing an increase in interest rates. Since we want to discuss increasing the money supply, let's assume the Fed is buying securities in the open market. Whenever the Fed buys securities, it buys securities from banks and 'pays' the banks by 'adding excess reserves' to the banks' balances at the Fed. Total reserves in the banking system rises. All else being equal, banks have more money to lend. This increases the available supply of loanable funds. Since we assume demand for loanable funds is unchanged, and since interest rates are the equilibrating force in this market, we should see that interest rates drop (because the supply curve shifts right/up).

You might also want to think in therms of what is happening to security yields. If banks start buying a large amount of securities in an effort increase the money supply, we should see a large increase in demand for securities. Assuming all else equal (in particular, assuming that there is no change in the supply of securities) we should see yields on securities fall (this is equivalent to the purchasing prices of securities rising).

And so we see that the logic, whenever we consider either adjustment mechanism, points toward a fall in interest rates whenever the Fed increases the money supply.

With this in mind, I think it is reasonable to conclude that the paper you've cited gets it wrong. And as a point of fact, we have witness recently (during QE) that money growth is not necessarily inflationary...as counterintuitive as that might be.


central banking using the term reserve The central bank of united states is called federal reserve and central bank of india is called Reserve bank of india.
What does the term reserve in central bank mean??

It refers to the reserves that banks have to hold in fractional reserve system. A fractional reserve system is a monetary arrangement where bank is allowed to use depositors money for loans as long as they keep a fraction of it as a reserve. For example, if reserve requirement is set to 10% if you deposit 100\$ in your bank they must keep 10\$ and they can lend the rest 90\$.

Portion of the reserve requirements in US is hold by the Federal Reserve (Fed). Also, as a central bank Fed can create new bank reserves (money) for the domestic banks in times of need. Hence this is where the name comes from - from the fact that central bank can hold reserves or create new ones.

However, I would not read too much into the names of banks, note virtually all banks around the world operate in similar fashion like Fed but they are not called reserve banks. For example, Bank of England, Bank of Japan, ECB they all have similar functions.


Supply Deman Equilibrium When in surplus or shortage, in order to achieve equilibrium price must change. I understand that. But what if when in surplus, suppliers choose to instead sell less, but for the same price? Vice versa for shortage.

In the standard competitive-market supply and demand model, the prediction is that, when an above-equilibrium price leads to surplus, prices will naturally fall. You're asking why suppliers don't just sell less at the same price instead, yes?

The basic reason why this doesn't happen is that doing this would require coordination on the part of the sellers, and there are too many of them to all work together.

Imagine, for example, that the equilibrium price is 10, but the current price is 15, leading to a surplus, with $Q_s=20$ and $Q_d=10$.

In your scenario, you end up with sellers agreeing to sell 10 units at a price of 15 each, and no more. However, at this high price, each seller will have an incentive to produce just a little more. One of the sellers, let's call her Jane, will sneak an 11th unit into the market, and either try to sell it as one of the ten units in the market at a price of 15, hoping that one of the other sellers will end up with an un-sellable unit, or Jane will try to take over the market by offering at a slightly lower price of 14 (which she can certainly afford to do - 14 is still much higher than her marginal cost).

For the plan to fall apart, there just has to be one person like Jane willing to work in their own interest against all the other sellers. And since there are by definition many many suppliers in the market, surely there's at least one Jane sitting around drooling at the thought of all those sales.

Most of the sellers would be better off overall if they were able to stick to an agreement to have a high-price and sell a low-quantity (after all, this is basically what monopolies and oligopolies do). But because there are so many competitors, each of whom has an individual incentive to break that agreement, the agreement is going to fall apart, leading prices to drop and quantity-traded to increase up to the equilibrium point.


How do you formulate a distance constraint and a budget constraint? Everybody knows about budget constraints and how they are represented:

but what if I want to represent a distance constrain from the shop you buy the goods?  How can I build that?

Because you are talking about constraints, it appears you do not consider the case of inserting such "access costs" (because this is what they are) in the utility function. It implies that they do not create disutility directly, only direct or indirect monetary costs.
Let $d$ be the distance in some units. Let $C_d = c_dd$ be a linear (for simplicity) distance cost function,  where $c_d$ is the average cost per unit of distance. This cost may include fuel consumed, or opportunity costs of spending the time to go to the shop. It is realistic to also postulate the existence of a strictly non-zero minimum distance, $d_{min}$, because the shops are not inside your house.
Your budget constraint now looks like (the undefined symbols have the usual meaning)
$$\sum p_ix_i + c_dd \leq I,$$
while you also have the additional constraint $ d \geq d_{min}$. So the Lagrangian is here
$$U(\mathbf x) + \lambda \left(I-\sum p_ix_i - c_dd\right) + \mu(d- d_{min}),$$
with $\lambda, \mu$ being the non-negative Karush-Kuhn-Tucker multipliers. Your optimization problem involves maximizing the Lagrangian with respect to the $x_i$s and with respect to $d$.
One could specify reasonably a convex non-linear distance cost function. Finally, one could include $d$ in the utility function as generating directly disutility.
I guess you can take it from here.
Just note that with the formulation as above, you should obtain that at the solution, $\mu^* >0$ meaning that the constraint will be binding and so you will always choose to go to the nearest shop... which aligns, at least in this case, with intuition (don't start thinking about shop/product differentiation, that would be a whole different situation).


Difference between representation of LM function in different textbooks In Blanchard, the LM curve equation is represented in the following manner:

$$ \frac{M}{P} = L(y,r) $$
Whereas in Branson it is given as

$$ \frac{M}{P} = L(r) + k(y) $$

L(r) is speculative demand for money and k(y) is transactions demand.

How are both the representations appropriate? Can we do this for any two(or more) variable functions?

The function $L(y,r)$ is a placeholder for any rule that says

  "give me a $y$ and and an $r$, and I will spit-out a value for $L$."

For example, we could have

$L(y,r)\equiv y+r$;
$L(y,r)\equiv y + \cos(y)+\sin(r)$;
$L(y,r)\equiv y \ln (r)$;
$L(y,r)\equiv yr$;
etc.

$L(r)+k(y)$ imposes an additional restriction. We con no longer pick any rule. Now we are only allowed to use rules where any terms involving $r$ are separated from those involving $y$ by a $+$. we call such function "additively separable".

Thus, in the Branson formulation encompasses rules such as 1 and 2 above, but not 3 and 4 (because the latter two are not additively separable).

This additional restriction means the Blanchard function is a more general formulation than that in Branson.

If we have a result that we know to be true for any function $f(x_1,\ldots,x_n)$ then we automatically know it must be true for additively separable functions of the form $f_1(x_1)+\ldots+f_n(x_n)$ (because the additively separable form is just a less general subcase of the more general form $f(\cdot)$).

But the same is not true in reverse. A result that we know holds for additively separable functions $f_1(x_1)+\ldots+f_n(x_n)$ need not hold for more general functions $f(x_1,\ldots,x_n)$.


Data: Attitude towards global warming I'm interested in data that reveals public opinion towards global warming in the US.

It'd be best to have a time dimension to it, but I'm interested in data from around the year 2000. Since it is quite a hot topic, I expect there to be much around this, but I couldn't find anything with scientific standards - say, anything beyond political institution X / news channel Y  asked 1000 and we are not even sure what the phrasing of the question was.

I am especially interested in data that includes an indicator for income/wealth.

There's this from Polling report showing raw survey data (question, sample data, and responses) back to 2012.

Additionally this paper by Lorenzoni and Pidgeon and this paper by Leiserowitz (both 2005) discussing said data in a more academic context. You would need to do some substantial extrapolation to get time-series out of these though.


Difference between pigovian tax and sin tax? Could they be interchangeably used? Or, is one subset of the other?

A pigouvian tax is on goods or services that are known to have negative externalities, and for which some estimation of the economic value of those negative externalities can be made, and is there to correct the market failure. Its goal is to improve economic efficiency.

A sin tax is on goods or services judged to be morally negative. Its goal is to reduce consumption and/or appease the moralists and/or raise revenue in a way that is less likely to be successfully opposed.


How much would the EU budget reduce by after Brexit? Would it reduce the budget of some €133bn by the gross amount after the rebate but before any spending from the EU into the UK (€17bn, about 12.5% according to Table 6, Page 11 of the 2017 draft budget) or by the net amount, which is some lower figure, (perhaps 6% ?) of the budget?

Assuming no changes due to other countries contributing more, etc. as a result of the UK leaving. It's purely about discerning what proportion of the budget is contributed by the UK's contribution, not what the actual change to the budget will be.

Part A: how much does the UK contributes to the EU Budget

This depends on whether you use fiscal year or calendar year estimates. The figures for the 2015/2016 fiscal year are here. The key is the following graph:

The calendar year estimates are here. The following Table summarizes the data:

Naturally, the net contribution is what matters for analysis the case of "EU budget without UK". However, as both report point out, the UK receives other contribution, which come from an "allocation of funds via competition". Think of the EU having a fund for, say, improvement in infrastructure. Countries apply to this fund, and some countries get it. Well, as the first report says, the UK got £1bn extra through that mechanism in the 2015/16 year. Should this be counted as part of the exercise? Probably not, because those extra funds would have been allocated to another country anyway.

So, given that the total budget of the EU in 2015 was €141,280 million, and taking an average EUR/GBP of 0.73, the percentage of contribution of UK to EU budget in 2015 was:

$$ \frac{8,473}{141,280 \times 0.73} = 8.2\% $$

Regarding 2017, table in page 11 shows only the gross payments, including the rebate, but not the public rector receipts. As such, the effective contribution of the UK is not going to be 12.5% as the document notes, but lower. Given historical levels of receipts, you could estimate that the contribution of the UK to the EU budget would be perhaps around 9%. In any case, as far as I know, this cannot be known ex-ante, reason why it is not included in the official budget document.

Part B: how would the EU budget change after Brexit

Since this relates to a future event, it is impossible to tell. This is for several reasons:

Budget are negotiated annually among all members, and contributions vary accordingly. As such, if countries expect less revenues, they might either lower expenditures, or increase demand for contributions to other countries. For instance, immediately after the Brexit vote, speculation arose that Germany would cover any hole left by the UK.
An important component of budget (31% in 2014) does not come from individual countries contributions. As such, how these evolve affects particularly how much countries contribute.
Brexit might induce an adjustment on the so-called correction mechanisms.
Countries contribution vary over time depending on many national circumstances, including the size of their economy, which then depends on economic growth, uneven across the EU.
The UK is expected to pay the EU before it leaves, known as a "divorce" or "exit" bill, which depends on the outcome of negotiations.
It depends on what deal the UK and EU have after Brexit. A Norway style of deal means the UK would have to pay to the EU.

In conclusion, it is simply impossible to tell. The calculations you make are a simple ceteris paribus exercise of removing the UK from the _current EU budget. That might be illustrative, but given the huge uncertainty on the issue, it's probably a rather brute calculation.


Differences between best response, dominant strategy and Nash equilibrium I can't seem to get the differences of these terms.
I watched this video that has the differences of best response and Nash equilibrium:

But then I heard about dominant strategies from another video and searched for differences to land at this quiz question:

Is a player's best response in a game the same as his dominant strategy?
Not necessarily. If a player has a dominant strategy, then it is his best response; however, every best response is not always a dominant strategy.

Is there a table form that shows the differences of these 3 based on a specific player and what other players would do?

Consider the following game between P1 (row player) and P2 (column player):
\begin{array}{|c|c|c|}\hline
& L & R \\\hline
T& 1,1 & 2,0 \\\hline
B& 0,0 & 1,1 \\\hline
\end{array}

$T$ is P1's dominant strategy
$T$ is P1's best response to both of P2's strategies $L$ and $R$
$L$ is P2's best response to P1's strategy $T$
$R$ is P2's best response to P1's strategy $B$
$(T,L)$ is the only Nash equilibrium

Generalizing from the above observations:

A strategy is dominant if and only if it is a best response to each of the other player's strategies, e.g. P1's $T$.
A strategy that is a best response to some but not all of the other player's strategies cannot be a dominant strategy, e.g. P2's $L$ and $R$.
A Nash equilibrium is a pair of mutually best responding strategies, e.g. $(T,L)$.


If an item is rarer than others, is it that much more valuable? Say I am selling a pack of trading cards, and there are 5 cards inside. Four of these cards are basic cards, but the last card has a 1:10 chance of being a special insert card.

Does the fact that the special insert has a 1:10 chance of appearing mean that it is ten times as valuable as a base card?

I understand that value is almost entirely subjective, so I suppose this is a philosophical question more than anything else, but I'm also not really an economist so I don't know if there are any axioms around this.

(1) What value an item has to you depends on your preferences, not scarcity.

(2) The market clearing price of an item will depend on the preferences of market participants and the supply schedule ("scarcity") of the item.

The way you seem to be thinking about value is very "non-economic", if that's a word.


Heckscher-Ohlin with different technologies 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?

As the companies doing the production will minimize costs in equilibrium
$$
\begin{align*}
|MRTS_c(K_c,L_c)| & = r/w \\
\\
|MRTS_w(K_w,L_w)| & = r/w
\end{align*}
$$
will hold. (Or you can also use the general form of your equations (1),(2),(5) and (6) to get this.) Given your particular production functions the marginal rates of technical substitution are
$$
\begin{align*}
|MRTS_c(K_c,L_c)| & = \frac{L_c}{K_c} \\
\\
|MRTS_w(K_w,L_w)| & = \frac{L_w}{K_w}.
\end{align*}
$$
Taken together, this means
$$
\frac{L_c}{K_c} = r/w = \frac{L_w}{K_w}.
$$
It follows that
$$
L_c + L_w = (K_c + K_w) \cdot r/w.
$$
The total amount of Labor and Capital are given in your exercise, and these will determine the factor price ratios as well as the $L_c/K_c = L_w/K_w$ ratio. Once you plug those in, your equation system will become linear.

Notice that this is true both in autarky and in free trade equilibrium, we have not used demand functions so far at all. Setting the appropriate demand equal to the appropriate production will give you the remaining equations you need to determine the equilibrium price ratio.


Price distribution: Negative values? In their equation (5), Kaplan and Menzio claim that the price distribution in their Burdett-Judd market is given by

$$ F(p, u) = \{u \cdot A_1 \left[1 - \left(1 - B_1(u)\right)\frac{(r-c)p}{(p-c)r}y_u\right] \\
+ (1-u) \cdot A_2 \left[1 - (1 - B_2(u))\frac{(r-c)p}{(p-c)r}*w(u)\right]
 \}/C$$

For positive $A_i$, $B_i$, $C$, where $u$ denotes the unemployment rate and $p$ denotes the price. They continue claiming that

$F$ is continuous
has connected support

$c$ is the households outside option, $r$ is the reservation price, hence the distribution should only give positive mass to prices between $[c, r]$.

$$ B_1(u) = 2\nu(u)\frac{\psi_u}{1+\psi_u}$$

where $\nu(\sigma(u)) = \frac{s}{b} = \frac{1-u}{1+u(\psi_u - \psi_e)}$. In their calibration: $\psi_e = 0.02$, $\psi_u = 0.27$. Hence

$$ B_1(u) = 2\frac{1-u}{1+0.25u}\frac{0.27}{1+0.27}$$

The Issue

For example, at an unemployment rate of $0.05$, we have $B_1(0.05) = .38$. However, for $p = c + \epsilon$ (for small $\epsilon$), the denominator $p-c$ becomes very small small.

This means that the product of $1-B_1(0.05)\cdot (r-c)\cdots$ becomes very  large. One minus that is an very large negative number. The denominator $C$ is positive. A similar phenomenon happens with $B_2(0.05)$.

They call $F(p, u)$ the distribution. I assume this means the pdf. Can a pdf have negative values? Or what am I missing here?

In Lemma 1 they say that the support $\left[\underline{p}_t, \bar{p}_t \right]$ is such that $ c < \underline{p}_t $.
So even though the support is connected, it does not extend to $c$, hence the $p \to c$ problem never arises.


Data on inflation target on different countries around the world Does someone know if there's a page, like a "global bank" online page, where one could see the inflation target for different countries?
For example, in x country, for x' year, the inflation target is $x''\%\pm 1$.
I know that this information can be found on the different central bank's online pages for each country, and if one would like to know about them, then one would need to check each page of them, one at a time.
Thank you in advance.


How would profit from labor exploitation be possible in a relatively competitive market? Marxists often state that capitalists exploit workers by paying them less than than their labor is worth. The extraction of this surplus value results in profit.
I'm wondering why this would be possible assuming most markets are fairly competitive.
It seems like if labor is really producing so much value that profit is possible, other companies would come along and snap up those workers with higher wages and eventually profits would minimize.
But this doesn't seem to happen. Most industries are quite profitable.
And the general trend of wealth accumulating in the upper class suggests that a balance has not been reached.
I have seen it suggested that we shouldn't need minimum wage because it forces companies to pay people more than their labor is worth, but if that were true, it seems like profits should already be small.
I understand that the situation differs considerably between industries, but the overall trend seems to be that most industries are able to be fairly profitable.
Would it be fair to say that while wage labor isn't inherently exploitative, most industries have some sort of market failure (externalities that result in only a few large companies, etc...) so in practice most wage labor IS exploitative (i.e. workers are paid less than the value of their labor)?

In competitive industry it is not possible as wages will be paid their marginal product of labor, and 'accounting' profit will arise either from marginal product of capital or entrepreneurial labor.
In economics, it is important to distinguish between economic and accounting profit, the economic profit in perfectly competitive market is zero, but you cannot observe that just by looking at the accounting profit firms report as that does not take into account various costs such as opportunity costs (generally accounting serves practical purposes not to scientifically describe true underlaying economic reality - for example in many countries sole traders/self employed people will be by accounting systems allowed to write of let's say $30\%$ of revenue as a cost - this may make sense from accounting perspective but economically it is completely absurd to state that all self-employed people have such costs).
In addition, just because there are imperfections on goods market (allowing firm to earn economic profit) that does not mean there will be imperfections on labor market (meaning employees will still get their marginal product).
Lastly, even when labor market is imperfect, and these imperfections result in labor getting less then its marginal product (there could also be imperfections that would result in more) there is no exploitation going on in the Marxian sense of exploitation.
The Marx's theory of labor exploitation can be summed as (see Stanford Encyclopedia of Philosophy):

To understand Marx’s charge of exploitation, it is first necessary to understand Marx’s analysis of market prices, which he largely inherited from earlier classical economists such as Adam Smith and David Ricardo. Under capitalism, Marx argued, workers’ labor power is treated as a commodity. And because Marx subscribed to a labor theory of value, this means that just like any other commodity such as butter or corn, the price (or wage) of labor power is determined by its cost of production—specifically, by the quantity of socially necessary labor required to produce it. The cost of producing labor power is the value or labor-cost required for the conservation and reproduction of a worker’s labor power. In other words, Marx thought that workers under capitalism will therefore be paid just enough to cover the bare necessities of living. ...

But while labor power is just like any other commodity in terms of how its price is determined, it is unique in one very importance respect. Labor, and labor alone, according to Marx, has the capacity to produce value beyond that which is necessary for its own reproduction. In other words, the value that goes into the commodities that sustain a worker for a twelve-hour work day is less than the value of the commodities that worker can produce during those twelve hours. ...

According to Marx, then, it is as though the worker’s day is split into two parts. During the first part, the laborer works for himself, producing commodities the value of which is equal to the value of the wages he receives. During the second part, the laborer works for the capitalist, producing surplus value for the capitalist for which he receives no equivalent wages. ...

Capitalist exploitation thus consists in the forced appropriation by capitalists of the surplus value produced by workers.

As you can plainly see above the idea of exploitation rests on the idea of labor theory of value (LTV). Labor theory of value is no longer accepted theory since it leads to empirical inconsistencies and it is generally considered incorrect (the current accepted theory of value is subjective theory of value). Under subjective theory of value anything can create value, including capital and indeed as we are seeing more and more automation that eliminates the need for labor this is becoming more painfully clear than ever.
In addition, the Marx's analysis implies that industries which are more labor intensive should have higher rates of profit (since according to Marx profit is earned through exploitation) and this empirically does not hold (Böhm-Bawerk 1898).
Next, the whole theory on which Marx build contained analytical mistakes that were not resolved by Marx (see Grant & Brue The History of Economic Thought 7th ed).
Lastly, the Marx's theory of exploitation also relied on an argument that workers are forced to work for capitalist as they don't have access to capital. That could seem reasonable in context of early 19th century England, when capital was very expensive and incomes low so for most part only richer people could afford to invest in it, and thus they were 'forced' by circumstance to work for capitalist.  However, this is not applicable when workers have access to out option (welfare benefit) as they often do in modern countries. In addition,  with modern financial systems the access to capital if you have good idea is arguably better than in 19th century where capital markets were still developing.
Hence as pointed by KennyLJ in the comments the Marx theory of exploitation is discredited in the profession. There were some scholars who tried to 'resurrect' the Marx idea of exploitation by dropping the labor theory of value and arguing only some of the 'worker surplus' is being exploited, and also trying to argue it applies to situations where workers are not forced to work  (see Kymlicka 2002, Contemporary Political Philosophy: An Introduction), these ideas are not generally accepted in economics and rather live on in some corners of philosophy/sociology.


Current accounts as savings? The book I'm reading shows that
$$ S= I +CA$$
where $S$ is savings, $I$ is investment, and $CA$ is the current accounts surplus.

The book then states "any domestic savings not absorbed by domestic investment must be shipped outside the country in the form of goods and services." I can understand how this works from an accounting equation point of view, but intuitively it doesn't seem to make sense. It seems odd that saved money would end up in the form of exports.

This is accountancy and double-entry bookkeeping, but intuitively there are two ideas underlying this:

The net difference between domestic investments and domestic savings has to be financed from abroad (or leads to financing foreigners if domestic savings exceed domestic investments) and this is reflected in the financial or capital accounts of the balance of payments.  Put more simply, if you want to build new buildings or buy new machinery or just put stuff into warehouses to sell next year, and your domestic economy is not saving enough to pay for this, then you need to get the extra stuff (probably represented in money terms, but really it is goods and services) from foreigners, creating new liabilities to them.
The financial or capital accounts should be balanced by the current account of the balance of payments (note the accounting use of the word balance). The net stuff you need for the excess investment over savings needs to bought from abroad (or if savings exceed investment then this needs to represent net stuff sold abroad).

There is a subtle difference between the balance of trade and the current account balance, with the difference representing income flows on existing international investments, but this is often relatively small and in accountancy terms is taken into account in the calculation of domestic savings.


What is the term for 'forgone cost' as 'opportunity cost' is for 'forgone profit'? For example, suppose I made \$100 from an investment. If I'd had deposit the same amount of money in the bank I would have get \$60 of interest. Then the 'forgone profit' or 'opportunity cost' in this example is \$60, and the economic profit is \$40.

Now let me use another example. Suppose I would need to spend 1 hour to make a spreadsheet for my homework assignment, but I instead spent 1.5 hours to write some VBA code and the code generates the spreadsheet programatically. Then the 'forgone cost' or '_____' in this example is 1 hour, and the economic cost is 0.5 hour.

What is the right term that can fit in the _____ in the 2nd example above ?

The short answer: we don't need a separate term for "foregone cost", because opportunity cost of doing something = highest (forgone benefit - foregone cost).

I'd like to stress two points about opportunity cost.

First, it doesn't make much sense to say "the opportunity cost in this example"; you need to specify the opportunity cost of doing what? We always explicitly state the opportunity cost of doing something, or opportunity cost of choosing something. In your investment vs bank savings example, the opportunity cost of using the money to invest is \$40, and the opportunity cost of depositing the money in the bank is \$60 (assuming investing and saving are the top 2 most productive use of your money, and assuming no ex-ante risk in investing). In your spreadsheet example, suppose you only have two options to spend 1.5 hours: A - you can spend 1 hour to make the spreadsheet, and use the rest 0.5 hour to do whatever is most productive, or B - you can spend 1.5 hours to program in VBA. The opportunity cost of choosing A is the net benefit of doing B, and the opportunity cost of choosing B is the net benefit of doing A.

Second, I highlighted the net benefit at the end of the previous paragraph. Opportunity cost of doing something is the highest foregone net benefit of the alternatives. Here the foregone net benefit is defined as the (foregone benefit - foregone cost). Let me go back to your spreadsheet example. Suppose finishing the spreadsheet gives you \$50 equivalent of utility, regardless of how you make the spreadsheet. However, let's say, manually making the spreadsheet bores you, incurring \$30 equivalent disutility, and making the spreadsheet via VBA bores your less, incurring \$20 disutility. I also assume the most productive use of your time in that 1.5 hours is taking some rest, which gives you \$40 per hour utility. Now here is the net benefit of option A: \$50 (benefit for finishing the spreadsheet) - \$30 (cost for making the spreadsheet manually) + \$20 (benefit for 0.5 hour rest) = \$40. And the net benefit of option B: \$50 (benefit for finishing the spreadsheet) - \$20 (cost for making the spreadsheet via VBA) = \$30. Therefore the opportunity cost of choosing A is \$30, and the opportunity cost of choosing B is \$40. We don't need a term for "foregone cost".


Can Okun's Law be used for forecasting? Can one forecast $\Delta Unemployment$ and $\Delta Inflation$ using a VAR model based on Okun's law?

Well you can essentially forecast anything using a VAR/VECM framework.

If you're wondering if such estimates will be accurate the answer really depends on the region, as the Okun Coefficent differs depending on where you are. (much like the law of gravity on earth).

a working paper released by the IMF titled Do Forecasters Beleive in Okun's Law? its conclusions were rather in favor for the use of Okun's law in forcasting.

  Our results show that professional forecasters believe in Okun’s Law to a degree merited by how
  well it holds in the data. For all nine countries we study, the relationship between forecasts of
  changes in unemployment and changes in real GDP growth is negative, which is consistent with
  Okun’s Law....

Its generally more accurate for short run forecasts then it is for long run. However the same counter-cyclical relationship is maintained between Real GDP growth rate and Unemployment Rate.

  the correlation between output and unemployment forecast revisions is stronger in year-ahead
  forecasts than in current-year forecasts; this finding leads us to conjecture that forecasters’
  reliance on Okun’s Law is stronger in the early stages of the forecast horizon, when information
  about the likely departures from Okun’s Law is scarce.


If 1% of the solar energy of the Sahara can power the entire world, why isn't it happening? There is an article on Forbes where Mehran Moalem, UC Berkeley professor, argues:

  1.2% of the Sahara desert is sufficient to cover all of the energy needs of the world in solar energy. [...] The cost of the project will be about five trillion dollars, one time cost at today's prices without any economy of scale savings.

I know 5 trillion dollars is a lot, but it's definitely worth it. Are there economical reasons against such project, or is it a political issue?

It's lots of things, which added together means it's not going to happen.

Firstly, the initial calculation of area required was just to illustrate how small the world's energy use is, compared to the amount of energy we receive in sunlight, even after compensating for the 20% efficiency of PV modules. So it wasn't actually intended as an engineering solution.

Secondly, there is little political interest globally in becoming completely dependent on a handful of North African countries for electricity supply: most countries made that mistake with oil and OPEC, creating decades of geopolitical mess.

Thirdly, it's not a great renewables scenario, because the amounts of energy generated in any two spots of that 1.2% of the Sahara are very closely correlated over all timescales from hours to decades, which means the whole output of the theoretical farm would not show a lot of smoothness. It doesn't span that many timezones, so there'd be several hours every day with no output, for the entire world. Now, that can be addressed with back-up power - just use excess PV to generate hydrogen which is stored, then burnt when its dark to generate electricity then - but that's when it starts getting expensive.

It's cheaper to diversify both the types of energy harvested (wind, tidal, geothermal, hydro, biomass), and the geographic area over which it's harvested (both latitude and longtitude), which significantly reduces the storage requirements needed, and reduces the risks associated with intra-annual and inter-annual variability of supply. This also hugely reduces the geo-political implications, and means that all countries get a decent chunk of internal investment from the project.


Information sets game theory I'm studying game thoery and i'm on extensive form games. One thing I don't understand in my textbook is the following:

I would like to clarify exactly what does an information set mean by the example I drew in the first picture.

So, by what I understand, red player (second player), has 3 information sets. So, on each information set, he has 2 actions. So in total, he has 6 strategies (not $2\times 2 \times 2 =8$). Would this be right? Did I understand the definition of information set right?

Also, if there was no dotted line, i.e the red player knows what the blue player did, would there be a difference in what is the information set? As in the red player would have 1 information set instead of 3? So this would mean he has 2 strategies.

If someone could clarify these concepts for me that would be great as I have trouble understanding these

As a first point, in general, the dotted line indicates that the nodes are in the same information set. So in your example, there is a single information set for the Red player and as such she has 2 actions---since she cannot tell which of the 3 nodes she is in, she cannot condition her action on this information, and therefore must take the same action (either left ($l$) or right ($r$)) irrespective of her position.

If, instead, there was no dotted line, then the Red player would know which action the Blue player had taken: lets call them $L$, $M$, or $R$. Contrary to your understanding, in this situation, the Red player does indeed have 8 strategies. Specifically, she can choose to play $l$ or $r$ conditional on each of the three actions she might observes Blue play: letting $(x,y,z) \in \{l,r\}^{3}$ denote the strategy where Red plays $x \in \{l,r\}$ conditional on $L$, $y \in \{l,r\}$ conditional on $M$, and $z \in \{l,r\}$ conditional on $R$, the 8 strategies are

$$(l,l,l),(l,l,r),(l,r,r),(l,r,l),(r,l,l),(r,l,r),(r,r,r),(r,r,l)$$

To understand more generally what is going on, it might help to think less formally and more philosophically about what an information set is. An information set is a collection of game positions (nodes) that a player cannot distinguish between (you can think of the dotted line as representing this entanglement). Then, if a player cannot distinguish between positions, she certainly cannot choose different actions at different positions, for how would she practically make this happen. So the player makes one choice per info set. If, on the other hand, the player can tell the difference between positions, she has many info sets and thus must make correspondingly many more choices.

The combinatorial explosion in the strategy space comes from the fact that each of these choices can be made independently.1 So changing what the Red player will do after the choice of $L$ by the Blue player yields two strategies for
every fixed choice out of the other information sets. When there are more periods of play, this growth becomes very very fast (I remember in grad school calculating the number of strategies in tic-tac-toe to be much larger than the atoms in the observable universe). On the other hand, having many strategies does not make the game necessarily more complicated, as many of the strategies may be identified via symmetry or other heuristics.

1 There is a subtly here that some actions might preclude reaching other information sets: nonetheless, in general a strategy is taken as a choice of action at every information set---including the ones precluded by earlier actions in the same strategy


Two firms competing ala Cournot So I´m a bit stuck on this one. There are two firms in the country that sell cars. Both sell Toyotas and they buy their cars directly from the manufacturer, which is Toyota. We can assume that quantity is the strategic variable, and that the two car dealers have no other marginal costs than the wholesale price "r".

The inverse total demand:
P = 1500 - 5(q1 + q2)

MC = 30

And I got:

q1 + q2 = Q

Q = 2(1500-r)/(2+1)5 = (3000-2r)/15

Which wholesale price, r, will the Toyota set? What is the equilibrium retail price, p, and the number of units sold?

When I solve for "r" I get:

r = 1500 - 7.5Q

But after this I am stuck and I can´t figure out what to do next. Anyone with any suggestions on how I should proceed or point me in the right direction?

In dealing with problems like this, it's helpful to do it in stages. You know that the two dealers take the wholesale price $r$ as a given (they can't change that), and car dealer $i$ choose retail price $q_i$ to try to maximize their profits $q_i \cdot (P - r)$.

You also know that these car dealers are exactly the same... they have the same cost, set some price, face the same demand (we say the two firms are "symmetric"). So in the end you know that whatever is the best quantity $q_i$ for the first car dealer would be the best choice for the second dealer as well, so we know $q_1 = q_2 = Q/2$.

With this, the dealers are choosing $Q$ to maximize $\pi(Q, r) = \frac Q 2 \cdot (P - r)$, with $P$ given by the demand function (solve the inverse total demand for $P$). Let's call this profit-maximizing quantity $Q^* = 2q_1^* = 2q_2^*$ and the resulting price $P^*$.

Now that we're done with the car dealer, let's step in Toyota's shoes. You want to make as much money as you could, so the higher $r$ is the better off you are. But you also know that if you set the retail price too high, the dealers will lose money with each car they sell and will likely stop ordering from you (maybe switch to selling Hondas instead). What's the maximum you could charge while still keep the dealers not losing money?


Financial Economics and International Economics What is the difference of Financial Economics and International Economics? Why, How? What are the implications of these differences?

Will a model of international economics suddenly become a model of financial economics if I simply change the names?

Apples, Bananas, Carrots, Drupes are named Financial Products A, B, C and D.

England and France are named investor E and investor F.

I saw myself repeating the same exact basic math and coming to the same conclusions, different names notwithstanding.

Both are Arrow-Debreu general equilibria. I can't understand the differences besides there necessarilly being money in financial economics.

The difference between them is as follows:

International Economics: Following the definition from the famous textbook by Krugman et al. (2017) the international economics is defined as a branch of economics that focuses on the special problems of economic interaction between sovereign states.

Financial Economics: According to W. Sharpe financial economics is a sub-field of economics that "concentrates on exchanges in which money of one type or another is likely to appear on both sides of a trade."

Why? The purpose of science is not just to come up with new ideas but to also organize them and categorize them. Thats the reason why we dont have just Physics but also astrophysics, geophysics, theoretical physics etc, why we dont have just biology but zoology, botany etc, why we dont have just psychology but clinical psychology, forensic psychology etc.

How? At some point the knowledge in any branch of science will become so wast that some scientists decide to focus only on special subset of the science and hence create sub-branch. For example, all physical sciences started as natural philosophy and all social sciences as moral philosophy but as  science grew in complexity they started to diverge into different fields like physics, biology, economics or psychology, and as science grew ever more complex these fields further subdivided into their respective subfields.

  Will a model of international economics suddenly become a model of financial economics if I simply change the names?

Its not about changing names. A model becomes an international economics model if it is applied to economic situation involving two or more sovereign states. A financial economics model will be a model thats applied to a situation where transactions involve money on both sides of a trade.

However, note the same models might be useful in different sub-fields. For example, laws of thermodynamics are widely used directly or indirectly in many branch of physics. A model that includes laws of thermodynamics but is a model pertaining to stellar phenomena will become an astrophysical model. A model based on laws of thermodynamics applied to some geothermal spot on earth will become geophysics model.

  I saw myself repeating the same exact basic math and coming to the same conclusions, different names notwithstanding.

Yes, if a two subfields look at similar interactions its highly likely that they will use similar models and will result in similar conclusions. If anything I would be very worried if a scientific model/theory would work only in one narrow application and was unusable anywhere else. A hallmark of successful scientific theory is if it can explain a large number of phenomena with the least amount of effort. For example, marginal utility can explain a large number of phenomena whether you apply it labor economics, industrial organization, financial economics etc. Its a good sign when a scientific theory can be applied to multiple situations and yields similar conclusions (of course conditional on also testing those conclusions and making sure they are accurate).

References:

Krugman, P. R., Melitz, M. J., & Obstfeld, M. (2017). International trade: theory and policy.


Solving a Cournot oligopoly game with N firms This is the full question: Find all pure strategy Nash equilibria of the Cournot oligopoly game with $N$ firms facing linear demand $P = a − Q$ when the total cost for each firm is $c_i(q_i) = q_i^2$.

My understanding is that:

$$\pi_i = q_i(a − Q) - q_i^2$$

$$\max_{q_i} \quad q_i(a − Q) - q_i^2$$

Therefore, the FOC:

$a - Q - 2q_i = 0$

This FOC can be derived for each firm.

This is the part that I get stuck at. How do you add all the FOCs of $N$ firms together? Thank you!

Your FOC is wrong.

So $$\max_{q_i} \quad q_i(a − \sum_{j=1}^nq_j) - q_i^2$$

$$\implies \max_{q_i} \quad aq_i − q_i\sum_{j=1}^nq_j - q_i^2$$

The real FOC is

$$a - \sum_{j\neq i}q_j - 2q_i - 2q_i = 0.$$


Empirical tests for symmetry of cross-price elasticities It is a well known fact in consumer theory that for a Hicksian demand curve the cross-price elasticity of good $i$ with respect to the price of good $j$ equals the cross-price elasticity of good $j$ with respect to the price of good $i$. This result (iirc) depends only on the utility function being continuous and so has great generality.

Of course, no consumer is actually Hicksian (though firms of course are) but the vast majority of goods take up only a small portion of a person's expenditure and so we expect the income effect to be small, and so the consumer de-facto Hicksian. What is the empirical status of this prediction? Do economists agree with my claim that most consumers are de-facto Hicksians? If the answer to the second question is no, have similar empirical tests been done for firms?

Even if it is a very general result, its implications are not immediately intuitive and actually often quite difficult to accept. Why should the impact of an increase in the price for fresh strawberries on the demand for gasoline, be the same as the impact of a price increase for gasoline on the demand for fresh strawberries (while keeping $u$ constant) ?
One of the more convincing empirical investigation of Slutsky symmetry is experimental and provided in this paper which is also very closely related to the questions your ask:
Sippel, Reinhard, 1997, "An Experiment on the Pure Theory of Consumer's Behaviour," The Economic Journal, 107, 1431-1444.


Term for partial resource use economics In economics, economies of scale are "the cost advantages that enterprises obtain due to their scale of operation" (Wikipedia/User:Loraof).
There is a common type of scaling, mostly in services, where the cost input is negligible, but users are in turn expected to use a small amount of the resource compared to the potential maximum they are provided. Good example includes Internet service providers or cloud storage providers, or banking if we go with traditional services. This allows a service provider to manage a small amount of resources which, if everyone utilized the maximum they could at a given time, would make the service or provider collapse.
What is the term, if it exists, for this type of scaling/economics?

I think what you are looking for is known as overselling.


Why is the martingale factor a martingale in Hansen's 2012 Dynamic Valuation Decomposition? In this question, I'm continuing to explore the tools used/presented in Lars Hansen's Econometrica paper "Dynamic Valuation Decomposition within Stochastic Economies" (2012).

This might be an easy question, but I can't quite see it. In the paper linked above, the factorization is presented in which one component is a martingale.
See p. 937. On this page it presents this formula and says

  Given a solution to (21), I construct a martingale via
  $$
\widetilde M_t = \exp(-\rho t) M_t \left [ \frac{e(X_t)}{e(X_0)} \right ]
$$
  which is itself a multiplicative functional.

Maybe it's easy, but I just don't see right away how to show that $\widetilde M_t$
is a martingale. How can I show this?

NOTE: This question is related to the following two questions:

Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/eigenvector
Example of the change of measure proposed in Hansen (2012)

The idea is that after the Perron-Frobenius problem is solved, you have $e$ such that
\begin{align}
E \left[\frac{M_{t+1}}{M_t} e(X_{t+1}) \middle | X_t = x \right]
 &= e(x) \exp(\eta) \\
E \left[\frac{M_{t+1}}{M_t} \frac{e(X_{t+1})}{e(X_t)} \exp(-\eta) \middle | X_t = x \right]
 &= 1 \\
E \left[\frac{\widetilde M_{t+1}}{\widetilde M_t} \middle | \mathcal F_t \right]
 &= 1 \\
E \left[\widetilde M_{t+1} \middle | \mathcal F_t \right]
 &= \widetilde M_t.
\end{align}

Thus we see that $\widetilde M_t$ is a martingale.


Bothersome Mean/Variance Analysis I'm currently writing my thesis in which I compare a series of ESG General Equilibrium models. I fell over this proof in Pastor, Stambaugh, Taylor Sustainable Investing in Equilibrium (2019) page 42. Here, they prove going from a given utility function to the models portfolio weights. These are the calculations of which I simply don't understand how they start on the second line and arrive at the third:
\begin{align}
\mathbb{E}( V(\tilde{W}_{1i},X_i)) &=\mathbb{E}(-e^{-A_i(W_{0i}(1+r_f+X'_i \tilde{r})-b'_iX_i)}
\\&= -e^{a_i(1+r_f)} \mathbb{E}( e^{-a_i X_i'(\tilde{r}+\frac{1}{a_i} b_i)})\\
&= -e^{a_i(1+r_f)} ( e^{-a_i X_i'(\mathbb{E}(\tilde{r})+\frac{1}{a_i} b_i)+\frac{1}{2}a^2_i X'_i\Sigma X_i})
\end{align}
We've previously defined $\tilde{r}\sim(\mu,\Sigma) $.
I've been staring at this for hours. I hope somebody can help me out with a hint on what is happening between these two steps.

The equality in question follows from the expression for expectation of a log-normal distribution.
For example, if $X \stackrel{d}{\sim} N(\mu, \sigma^2)$, then
$$
E[e^{a X}] = e^{a \mu + \frac12 a^2 \sigma^2}.
$$
This is the reason that CARA/normal or CRRA/log-normal (agent utility/asset return distribution pair) set-ups reduce to the mean-variance case, up to certainty equivalence.


Confusion about the EMP approach to perfect complements. Solved UMP but struggling with EMP I have successfully done the UMP for perfect complements. I got

$$x^* = y^* = \frac{m}{p_x +p_y}$$
This makes intuitive sense  because for whichever good I have the least of, I don't want to buy more units of the other. So the total amount I should spend should be the optimum quantity times $p_x + p_y$.

However, I am completely lost about how to do the EMP version of this. I keep going in circles.

I have done the Lagrangian and gotten for $x > y$,  $e = p_y \bar{U}$ and for $x <y$ that $e = p_x \bar{U}$.

Here is my work:

https://math.stackexchange.com/questions/1252173/can-one-optimize-a-function-with-minx-y-as-a-constraint/1252341#1252341

But this doesn't make sense to me.  don't see how this relates to the solution I got for the UMP which did make sense.

What I am misunderstanding about the EMP that is leading to these nonsensical results that don't match what I did for the UMP?

You already got your answer in the math forum, from the economics point of view maybe it could help that you can use the relation between the expenditure function and the indirect utility to get your solution.
Your indirect utility of the UMP is $v(p,w)=\frac{m}{p_x+p_y}$, this provides the expenditure function for the EMP $e(p,\overline{u})=\overline{u}\ (p_x+p_y)$. Now the hicksian demand is $h(p,u)=(u,u)$. This is the case of course of the utility $u(x,y)=min(x,y)$.


Rationality and Common Belief in Rationality in Brandenburger & Dekel (1987) One of the fundamental results in epistemic game theory is that the solution concept of correlated rationalizability gives exactly those action profiles that are compatible with rationality and common belief in rationality. A precise statement and formulation of this result is given in

  Tan, Tommy Chin-Chiu, and Sérgio Ribeiro da Costa Werlang. "The
  Bayesian foundations of solution concepts of games." Journal of
  Economic Theory 45.2 (1988): 370-391.

as Theorem 5.2 and Theorem 5.3. An alternative reference often cited for this result (at least in the context of finite games, Tan & Werlang allow for compact metric action spaces) is

  Brandenburger, Adam, and Eddie Dekel. "Rationalizability and
  correlated equilibria." Econometrica: Journal of the Econometric
  Society (1987): 1391-1402.

For example, the survey on epitemic game theory in the fourth volume of the handbook of game theory credits Brandenburger & Dekel for this result (online version, see Theorem 1 there). I have actually seen many such references but was not able to locate the result in their paper. That paper contains 4 propositions and none of them corresponds to this result. The authors actually credit Tan & Werlang and write "Tan and Werlang (1984) and Bernheim (1985) provide formal proofs of the equivalence between rationalizability and common knowledge of rationality." (Tan & Werlang 1984 is the working paper version).

What am I missing that everyone else gets?

The concept that Brandenburger and Dekel (1987) call an "a posteriori equilibrium" is roughly the same as what Dekel and Siniscalchi call an "epistemic type structure for a complete information game" in which all types are rational and there is common belief in rationality. Therefore, Brandenburger and Dekel's Proposition 2.1, together with the remark that immediately follows the proof of Propoistion 2.1, is roughly the same as Theorem 1 in Dekel and Siniscalchi.