Inflation leads to loss of gold reserves I am reading Murray's Rothbard What has government done to our money? and this is his reasoning for inflation leading to loss of gold reserves to other countries (assuming everyone is on gold standard)

Lets assume everyone is on gold standard. Then

Credit expansion in country A
Prices in A increase
Increase in imports from country B because foreign goods become cheaper
Country B redeems A's currency for gold. Hence gold outflow from A to B.

What I am confused about is how does inflation lead to increase in imports in 3. As monetary supply increases, A's currency would lose purchasing power and so imports would become equally expensive at that point. Why would that not be the case?

Thanks,

Inflation won't necessarily change the price of goods from country B in real terms, but it will change the relative costs of buying goods from country B now vs saving now and buying goods from country B later.

Under the gold standard, there are no central banks to force the interest rate up when inflation rises. If inflation goes up but interest rates don't go up, then consumers in country A will save less and spend more, leading to a temporary increase in imports from country B.


Competitive equilibrium with IRTS Suppose we have a static economy with one firm and one consumer. Consumer owns the firm and decides on how much to consume and to work: $$\max U(c,1-n_s)\ \text{s.t.} \ pc\leq wn_s+\pi$$
The firm is maximizing profit: $$py-wn_d\ \text{s.t.}  \ y\leq F(n_d)$$
We will assume that production function is characterized by increasing return to scale and $F(0)\geq 0.$. How can we show that there is no competitive equilibrium?
Since we have F is IRTS then $F(\lambda k,\lambda n)\geq\lambda F(k,n)$ and based on the theorems that CE is inconsistent with increasing returns to scale since a competitive firm would not have enough revenue to pay competitive prices for its inputs, there would not be a CE in the first place. To prove it do we need to follow dynamic programming or is there another way?

Here is an example where the two are actually compatible: The consumer's utility function $U:\mathbb{R}_+\to\mathbb{R}$ is given by $U(c,1-n_ns)=c-n_s$, the initial labor endowment is $1$ and $F:\mathbb{R}_+\to\mathbb{R}$ is given by $$F(n)=n(1-e^{-n}).$$
This function has IRTS, but still turns a unit of labor into less than one unit of consumption at any amount of input. If you let the price of consumption be $1$ and $w\geq 1$, you have a competitive equilibrium in which nothing is produced and the consumer simply consumes their endowment.
Side rant: The usual definition of IRTS is that when the inputs are multiplied by a number larger than $1$, the resulting output increases more than proportionally. Under this definition, no production function for which an input of $0$ is feasible has IRTS. Even if one restricts oneself to nonzero inputs, the definition does not work the way people seem to think. The standard example of a production function with IRTS is a Cobb-Douglas production function in which the sum of exponents is larger than $1$. The standard definition of IRTS applied to an input combination with some, but not all, entries $0$ would show that IRTS does not hold here. It does work when we restrict ourselves to input combinations that produce a positive output, and the function in the example is of this kind.
However, one can show that no competitive equilibrium exists if one makes the assumption that the consumer prefers to turn some labor into consumption and the production function produces zero output with zero input and is continuous and increasing, and the consumer's utility function is strictly increasing on the interior. For example, with Cobb-Douglas utility, every bundle in which the consumer enjoys both consumption and leisure is better for the consumer than a bundle in which they enjoy only one of these in a positive amount. Since every competitive equilibrium is Pareto efficient by the first welfare theorem (whose assumptions hold here), some amount of consumption must be produced here, and this is not compatible with profit maximization. Indeed, suppose there is an equilibrium with $p$ the price of the consumption good and $w$ the wage. Since the consumer's utility function is strictly increasing on the interior, an optimal consumption bundle can only exist if $p>0$ and $w>0$. Let $c_e$ and $n_e$ be the equilibrium consumption and labor supply. Efficiency requires $c_e>0$ and, therefore, also $n_e>0$. Since the firm can always have a profit of $0$ by using no input, profit maximization implies that
$$pF(n_e)-wn_e\geq 0.$$
But then, $$p F(2n_e)-w 2n_e>p 2F(n_e)- w 2n_e=2\big(p F(n_e)-wn_e\big)\geq p F(n_e)-wn_e.$$ Here, the strict inequality comes from IRTS and the weak inequality from $pF(n_e)-wn_e\geq 0.$ We see that the production plan that use an input of $2n_e$ produces a higher profit than the production plan that uses $n_e$, in contradiction to the firm maximizing profit with a production plan with input $n_e$.


What cognitive biases reduce savings? In Thinking Fast and Slow Kahneman explains that people can sometimes save less because they underestimate the future benefit to themselves because they view present and future self differently. I learned elsewhere that this cognitive bias is called hyperbolic discounting. If I understand correctly this will affect young more than old because old person's future self is much closer to present self.
My question:
Are there any other cognitive biases that might decrease saving?  Also, are there some cognitive biases that affect saving of young more than saving of old? I would like to know more about this topic so please provide references if possible.

A study of  Gopi Shah Goda, Matthew Levy, Colleen Flaherty Manchester, Aaron Sojourner, and Joshua Tasoff (2015) The Role of Time Preferences and Exponential-Growth Bias in Retirement Savings showed that in the US the most important cognitive bias is the exponential growth bias.
Exponential growth bias is bias that occurs because people intuitively do not understand exponential growth. So when people save they think about growth intuitively in linear way.
I don't know if there is a study that says it affects younger people more, but I think it would make sense since more time difference between present and future also means a larger difference between exponential and linear growth.


Have the stocks and flows of hunter-gatherer economies been formally analysed? A lot of work in economic anthropology seems to be about allocation mechanisms. This feeds into economic discourses about the institutions governing markets and non-market alternatives, e.g. Douglas North (1977):
Markets and Other Allocation Systems in History: The Challenge of Karl Polanyi

It is reasonable to assume that the forces that lead to the
substitution of firms for markets today may also help us to explain
the variety of forms of economic organisation in past societies.

I wonder if similar work has been done on stocks and flows, i.e. a formal economic analysis of stocks (e.g. rights to access common land, its fruits once harvested, services such as healthcare, tools, artefacts) and flows (e.g. reciprocity mechanisms, both within and between groups).
There is ample qualitative analysis, e.g. in this volume edited by John Gowdy (1997) which includes a contribution by Marshall Sahlins (Stone Age Economics, 1972):
Limited Wants, Unlimited Means: A Reader On Hunter-Gatherer Economics And The Environment
I wonder if there have been attempts to formalise the stocks and flows?

Anthropology is concerned with understanding a society in qualitative terms rather than quantitative terms. To try to understand it in these terms is to misconceive how those societies work and what anthropology is.


Walrasian demand with a twist of Leontief function A consumer has the utility function $u(x_1; x_2) = \min(x_1; x_2) + 5 \max(x_1; x_2)$.
Find its Walrasian demand $x^*(p; w)$.
I've tried searching it up when we have two Leontief functions summed together but to no luck. If this was a simple case we'd just have $x_1=x_2$ and substitute it to the budget constraint to find the demand for both. Should we take each function separately or as a whole together? Kinda lost here.

Why don't you just plug in some values for $x_1$ and $x_2$?
Start with something like
$x_1=1, x_2=1$ and find utility $u(1,1)=1+5*1$.
Then increase $x_1$ or $x_2$ and let
$x_1=2, x_2=1$ and find utility $u(2,1)=1+5*2=11$, and
$x_1=1, x_2=2$ and find utility $u(1,2)=1+5*2=11$.
The utilities of both bundles are identical, and the goods seem to be substitutable.
In fact for any $x_1<x_2$ you will find
$u(x_1,x_2) = x_1 + 5 x_2$, and, similarly,
for any $x_1>x_2$ you will find
$u(x_1,x_2) = x_2 + 5 x_1$.
Now, just for now, assume both goods have the same price $p_1=p_2=1$ and you have a budget of $w=3$ such that you can buy both bundles giving utility 11 up there.
You can see that it would be better to put all your money in one of the goods and get
$u(3,0)=u(0,3) = 0 + 5*3=15$. Now think about different prices and a general income $w$. Does it again make sense to buy only one of the goods? Is it the cheaper one?


Could a hike in interest rates cause a country to be unable to pay back it's debt burden? Sometimes I read in news articles, that a central bank can't hike the interest rates much higher, because then the government would be unable to pay the interest rate burden of it's government debt.
Is this really true? In my understanding this should only be true for government debt that will be issued after the interest rates are already high.

I mean, the biggest part of government debt that has been already issued is only traded at the secondary markt at a fixed nominal interest rate.
(except of an usually much smaller part of floating rate notes)

The short answer is no, rate hikes have no effect whatsoever on whether a government can service its debt and repay maturing issues.  Here's why---

A government that issues debt in its own currency can always print currency to make its debt payments.  This is an extremely important point, despite that certain political actors would like you to forget it.
Central banks set rates at the short end of the Treasury curve.  They do not have an effect on the long end of the curve, which is set by market participants' expectations of long term inflation and real growth.  What's more, central banks today are data dependent---they state explicitly that they will react to data that the market already has priced.  For example, this month the U.S. Fed's FOMC will likely increase rates due to stronger economic data (GDP revisions upward, better than expected inflation, decline in unemployment and jobless claims). However the Treasury curve has already steepened massively over the last month in response to these data releases.
Many governments issue debt in foreign currencies like USD and EUR (e.g., Brazil, Mexico, Ukraine, and almost every other emerging market).  Because of uncovered interest rate parity, rate rises push up the value of the domestic currency relative to the currency in which external debt must be paid.  This actually decreases the cost of servicing the external debt.


What do interest rates tell us about the state of an economy? I seem to have a misconception about what interest rates mean. On one hand, they signal how high a government's demand for money is, because if a government is ever in any serious need of money, they can sell bonds with a high enough coupon rate to ensure that investors will quickly buy them, which will have the knock on effect of raising interest rates. On the other hand, I hear that government will frequently increase/decrease interest rates in order to discourage/encourage consumer spending (although, frankly, I've got no idea how the governments go about changing these rates).

So, put bluntly, what do interest rates actually mean? If we take for example the UK, I've never heard anyone claim that the interest rates are low because the government is in no real need of money, but I have frequently heard that the interest rates are low because the government wants to encourage consumer spending. What should be read in to that?

What do interest rates tell us about the state of an economy?

Very little. That is because interest rates are a mechanism aimed at influencing one of many variables of an economy, rather than to diagnose it/them. Interest rates are a one-dimensional dimensional parameter, whereas the state of an economy cannot be captured with just one number.

For instance, an economy might be analyzed from the standpoint of its GDP, its Gini coefficient, income per capita, inflation, an agent's (or sector's) purchase power parity, and other aspects which are not comparable to each other. A rate simply cannot describe all these aspects.

Your question itself reflects how interest rates are used for purposes which are not necessarily --or not always-- related: to aid governmental budget, and to influence consumption. In some situations, a cash-strapped government might wish for a reduced consumption (for instance, to be able to cope with public demand), whereas in other situations it might wish for greater consumption (to increase its tax revenues). The fact that two variables in an economy don't always go -or are not intended to go- in the same direction illustrates the ambiguity of how to interpret interest rates.

It should be added that interest rates are also a mechanism aimed at procuring currency stability. This goal can be at odds with patching a budget so that the government can fulfill its agenda. Hence the importance, at least among those of us with a neoliberal mindset, of keeping government and central bank separate; that is, to ensure that the latter is an autonomous entity.


What is a homothetic function? Suppose we have the following equations for the MRS of a utility function. $$U(x, y)$$
  Which of the following corresponds to a homothetic utility function?

  $$MRS (x, y) = \frac{x^2+y^2}{xy}$$
  $$ MRS(x, y) = 2(x + y)$$

The answer is 1. But why the second equation is not homothetic?

If a utility function is homothethic,
$-\frac {\frac {\partial u}{\partial x} (tx)} {\frac {\partial u} {\partial y} (ty)} = -\frac {\frac {\partial u}{\partial x} (x)} {\frac {\partial u} {\partial y} (y)} $

In other words, the MRS must be homogenous of degree zero.

Hence, for $MRS(tx,ty)=2(tx+ty)=2t(x,y)=t MRS(x,y)$ is homogenous of degree 1

While $MRS(tx,ty)=\frac{(tx)^{2}+(ty)^{2}}{(tx)(ty)}=\frac{t^{2}(x+y)}{t^{2}(xy)}=\frac{x^{2}+y^{2}}{xy}=MRS(x,y)$ is homogenous of degree 0.


What happened when the money from share issuance is spent? Let's assume that new bank is incorporated and it issued 100 000 shares with nominal value odf $100.
Let's also assume that all shares are sold for the same price, so bank now has 10 million dollars.
In equity section on balance sheet, there is now 10 million dollars of ordinary shares. Now let's assume further that 5 years has passed, the bank has spent all 10 million dollars for different purposes (R&D, expansion etc.) and now it doesn't have that money, but there are still 10 million dollar of ordinary share on its balance sheet.
If ordinary shares are vital part of bank's capital, how can they now respresent someting that can save the bank from bankruprtcy it problems occurs, when there is no money??? I'd understand if the bank wasn't allowed to spend that money, but it is used for various purposes.

You are concerned about...

someting that can save the bank from bankruprtcy it problems occurs,
when there is no money

This is an accounting question as much as an economics question. What you are asking about is "solvency".

assets minus liabilities equals equity

The bank or any company is solvent by definition if equity is positive and estimated values are realistic. Companies can even be solvent if equity is negative because estimated values are not realistic, for example, if assets are a "conservative" estimate which in this case means assets are underestimated.
You asked about the absence of money. All items in the assets are theoretically convertible to money. They are convertible regardless of the estimate of equity. In practice negative money balances are not necessarily a problem because if equity is large enough the company can obtain a loan. Typically a bank is holding cash because that is the nature of offering "demand" accounts which are the accounts where the depositor can withdraw cash almost immediately.


Banks are allowed to print money out of thin air. Black magic or what? Today it is wide spread notion that the commercial banks cat create a money out of thin air. Simply by typing numbers on computer. Every time a bank gives a load to a borrower, the loan money do not come from other people deposits (at least not entirely but fractionally) but they are simply created out of nothing. This form of banking is called Fractional reserve banking .

The problem I have with this concept is the following: A bank give a Merry loan of 100,000\$. Merry buys a house with this money. For a period of 1 year, Merry has paid back 10,000$ to the bank. Afterward Merry's finance condition worsen and she no longer can pay her debt. So in theory, if all the bank borrowers end up in the same situation as Merry did, the bank is going to bankrupt.

But if the bank never had the load money in the first place, every penny received from borrowers is a pure profit. Even if Merry returned only 10% of her loan, the Bank still profits 10,000$ because the given 100,000\$ to Merry were not bank's money in the first place.

This leads me to the question: Why do banks put interest on top of this fraud? And what prevents banks from putting huge amount of money to some people's account (for example to the Bank's CEO )? This black magic is not quite clear to me.

Very good question.

Let's break it down:

  A bank give a Merry loan of 100,000$

Concretely, the bank records an asset of 100,000 (the loan) and a liability of 100,000$ (the amount recorded in Merry's deposit account).

Note that at this point, the liability is what appears on your internet banking statements as 'money' and those liabilities to you from banks are today what is traded in exchange for goods and services. In this sense the liability is 'money',  and it is why people consider this money to have been synthesized commercially ex nihilo. This is essentially correct. Banks are licensed to create this money from nothing.

  Merry buys a house with this money.

Analyse it in detail: Merry finds a supplier, who implicitly trusts the bank, who probably has an account at another bank (though not necessarily), and agrees to accept payment in the form of a bank liability. Merry initiates a bank transfer from MerryBank to SupplierBank. MerryBank decreases its liability to Merry by 100,000, keeping only the asset, but adds a new liability to SupplierBank. SupplierBank records an asset of 100,000 (MerryBank's liability to SupplierBank) and a liability to Supplier of $100,000.

  For a period of 1 year, Merry has paid back 10,000 to the bank.

Yes, in 99% of cases in the form of bank transfers from other newly created debt from other banks. These become assets in the books of MerryBank (liabilities from SomeOtherBank) and the loan asset is reduced. So while MerryBank gains a 10k asset from SomeOtherBank it actually cancels 10k of loan asset, so its position has not changed - only its risk position.

  Afterward Merry's finance condition worsen and she no longer can pay
  her debt. So in theory, if all the bank borrowers end up in the same
  situation as Merry did, the bank is going to bankrupt.

No. The bank still has an asset of 90,000$ and will use debt collectors to take Merry's property. The bank will then cancel the 90,000 loan asset and record a property asset at market value.

  But if the bank never had the loan money in the first place,

Yes. Fractional reserve requirements for loans was/is often 0%. Also, the asset (for example) at SupplierBank is then used as reserves to issue further debt. Two banks in a fractional reserve system act as feedback-loop amplifiers, so if the reserve requirement was 10%, that does not mean that the money multiplier would be 10 times, but depending on flow rates and dynamic systems calculations you can end up with hundreds of thousands times the base reserve. Incidentally, this was the keystone to the financial crisis.

  every penny received from borrowers is a pure profit. Even if Merry returned
  only 10% of her loan, the Bank still profits 10,000 because the given
  100,000$ to Merry were not bank's money in the first place.

No. See above. The asset position is unchanged.

  This leads me to the question: Why do banks put interest on top of
  this fraud? And what prevents banks from putting huge amount of money
  to some people's account (for example to the Bank's CEO )? This black
  magic is not quite clear to me.

Interest rate is primarily determined by interbank lending rates to cover reserve and capital requirements.

I don't know if it applies to the rest of the world, but the main source of income for banks where I live is actually transaction fees.

As for CEO payments, auditors. But in general CEOs reward themselves by issuing debt (bonds) to cover stock buybacks, to boost stock price, to which their bonuses are tied. Calling this kind of activity fraud is to some extent true, as outside the US a lot of this kind of thing is regulated.

Banks could be pure digital banks that have a employees in the hundreds. Typically they are dinosaur institutions that employ in the 10s or 100s of thousands of people. The banks use fees and interest to cover the cost of employees mainly. Incidentally, this is one reason why governments chose to assist banks in 2008. Directly and indirectly they employ a big chunk of the economy, a consequence of Western deindustrialization and financialization.


How does keeping the value of the dollar by foreign US bondholders makes their exports more affordable? How does this work?

  In February 2018, China owned \$1.18 trillion of U.S. debt. It's the
  largest foreign holder of U.S. Treasury securities. The second largest
  holder is Japan at \$1.06 trillion. Both Japan and China want to keep
  the value of the dollar higher than the value of their currencies.
  That helps keep their exports affordable for the United States, which
  helps their economies grow. That's why, despite China's occasional
  threats to sell its holdings, both countries are happy to be America's
  biggest foreign bankers. China replaced the United Kingdom as the
  second largest foreign holder on May 31, 2007. That's when it
  increased its holdings to \$699 billion, outpacing the United Kingdom's
  $640 billion.

Source:
Article - Who Owns US National Debt

Suppose a camera is made in Japan and sold in the US. If the maker of the camera wants 10k Yen for it, and the ultimate buyer is paying dollars, then somewhere along the line, dollars have to be exchanged for dollars. For instance, the company that imports the camera might go out and buy 10k Yen, then give the Yen to the company that made the camera. They then pass on the cost of buying the Yen to the camera store, who passes it on to the customer. The dollar being strong with respect to the Yen means that one dollar can buy a lot of Yen. So that means that it doesn't cost very much dollars to buy the 10k Yen, which means that the camera store in the US can sell the camera for fewer dollars, which means that people are more willing to buy the camera, which means that the camera manufacturer gets more business.

You're also asking how the strength of the dollar is affected. It's a matter of supply and demand: every time Americans buy stuff from other countries, they are supplying dollars, and every time they sell things to other countries, they are demanding dollars. The strength of the dollar depends heavily then on how much the US exports (which strengthens the dollar) versus imports (which weakens the dollar). Since transactions between the US and other countries involve trading goods and dollars, the effect on the dollar is opposite of how the goods are moving from the US perspective: when someone in the US sells a good, that can be viewed as "buying" dollars, and the US buying goods can be viewed as "selling" dollars. A strong (or "expensive") dollar means that US goods are also expensive, but foreign goods are cheap, and a weak dollar means that US goods are cheap, but foreign goods are expensive.

Companies that facilitate exports generally benefit from a weaker dollar (the goods are cheap, so it's easier to sell them). This includes export companies, and people who work in industries whose markets are largely overseas.  Companies that facilitate imports generally benefit from a stronger dollar. This includes import companies, and companies that that sell a lot of foreign-sourced goods, which in the camera example would include the camera store.

Bonds aren't generally included when calculating exports, but they do have largely the same effect: US treasury bonds are denominated in dollars, so if people in other countries want to buy them, they have to buy dollars, which drives up the value of the dollar.   You can think of it in terms of analogy with a household: exports are like people going out and working for a paycheck, while imports are like buying stuff. A bond is like getting a loan, such as a mortgage or a car loan. The more money someone makes at their job, and the more loans they get, the more the cash they have to spend. A dealership wants to help someone get a car loan, because that makes it easier to but a car. Similarly, China and Japan want the US to be able to sell their bonds, because that makes it easier to buy stuff from China and Japan. Whenever China or Japan buy a treasury bond, they give more money to the US, and the US then uses that money to buy stuff. If China were to sell off their bonds, that would make it harder for the US to sell new bonds, which would make it harder for Americans to buy stuff from China.


Definition of market to book value? What is the difference between (market value of equity/book value of equity) ratio and (market value of assets/book value of assets) ratio?

In my opinion both measure fairly the same? Is this correct? The first (MV/BV equity) is commonly used as Tobin's Q. Can I use (MV/BV assets) for the same?

Thanks for your help!

They are not the same.

Basic accounting equation:

Assets = Liability + Shareholder Equity

Assets refers to what the company actually owns: cash, property, inventory, etc.

Assets are paid for in two major ways: debt (liability) and stock (equity). Essentially, everything a company owns is paid for by a combination of (1) getting loans from other entities or issuing bonds and (2) having other entities own a part of the company.

Equity includes a number of things, but the most common form is stock, or ownership of a company.

An example of this: if you own a pen company, assets might include pens, and equity would be your ownership of the company.


Why are readily available productivity data relative, not absolute? I've been trying to do some cursory research on labor productivity. In the process, I've noticed that the readily available data in the US, as accessed through either BLS or FRED (yes, I know it's the same underlying data), is all in terms of year-to-year change, or level relative to a fixed year. Is there any theoretical or technical reason for this? It seems like an absolute level of labor productivity should be well defined: GDP divided by total hours worked. Am I neglecting something that would prevent reliable calculation of an actual dollars-per-hour number? If not, where can I find this figure?

The data you ask for is in the OECD stats website under

  Productivity > Productivity and ULC – Annual, Total Economy > Level of GDP per capita and productivity

This is the graph (in 2010 PPP US dollars):

Aternatively, you can compute it manually:

Select a series of constant GDP of your interest.
Divide it by number of hours for a group of interest.

You can find both series in the above website. GDP is under

  National Accounts > Annual National Accounts > Main Aggregates > Gross domestic product

Hours are under

  Labour > Labour Force Statistics > Hours worked


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

There are three ways to define GDP:

Expenditure approach: The sum of all expenditures on final products. The only final products in this economy are cars; steel, machines, and tires are intermediate products. By this definition, GDP is 5000. Of this amount, 1000 is exported (NX), so 4000 must be consumed domestically (C). There is no information about I and G, so we must assume they're zero.
Production approach (value added approach). The output of the steel, machine tool, and tire sectors is worth 6500 combined (4000 for steel, 2000 for machines, 500 for tires). All output of these three sectors is "consumed" by the auto sector, whose output is worth 5000. Total sales of all four sectors: 11,500. GDP is obtained by subtracting sales of intermediate products from total sales: 11500 - 6500 = 5000. The car sector appears to be making a net loss of 1500.
Income approach (GDI: gross domestic income, i.e., sum of wages and net profits). By definition, one entity's expenditures is another entity's income. We have no information about income shares (wages, profits, losses) of the various sectors, but in the aggregate GDI = GDP. Therefore, total GDI is also 5000. Total domestic consumption C on final products is 4000. Thus, aggregate saving S must be 1000 (since GDP = C+S). Of this aggregate, 2500 is net saving of the household, steel, machines, and tire sectors, and -1500 is the dissaving of the car sector. For the non-car sectors, the only additional piece of information we have is that whereas the machine sector "consumes" 1000 in steel, its output is 2000. Thus, the entire net saving in this economy is due to the machine sector.


What idea was proposed to remove global poverty? I am not an economics student, but I would like to know about this simply but in details. I would like to understand this Noble Prize winning thoery by Abhijit Banerjee , Esther Duflo and Michael Kremer

Unlike many Nobel prizewinners, this year's award was not really given for a central theoretical development. All three of the winners have made important theoretical contributions relevant to development economics and that inspired their future work (for example Banerjee on networks or Kremer on technological change and productivity). However, their major contribution, and what they received the award for, is their major methodological contributions.

In particular, the winners are responsible for designing and enacting a number of large-scale field experiments in development economics. These experiments use theory and domain knowledge to break poverty down into a series of more manageable problems, and then attempt to actually alleviate one of those problems with a policy intervention. These interventions are administered in randomized ways that allow us to see whether they actually work (like incentives to reduce teacher absenteeism, they found) or not (microfinance, they found).

Through these field experiments they have improved the lives of millions of people in at least some small way, and their work has led to huge changes in the way that development economics operates as a whole (for better or worse, I think better). The field today is much more focused on experimental and other causal work than it used to be, using data and empiricism to answer questions about development economics rather than using theory. In many cases this work focuses on finding actually-effective ways to improve policy and conditions in developing countries.

You can see a more thorough description here: https://marginalrevolution.com/marginalrevolution/2019/10/the-nobel-prize-in-economic-science-goes-to-banerjee-duflo-and-kremer.html


Is the basic RBC model a weak model? There are a plethora of examples of weaknesses in my textbook, such as:

The Walrasian assumption
Not including nominal shocks
Not including indivisible labour
Not including distortionary taxes
Not including multiple sectors and sector specific shocks

In my opinion the greatest weakness is the Walrasian assumption, as I think this is not too realistic in the real world.

I think we want to measure degree of weakness by how closely we see the results posited by the model exhibited in the real world.

So if you have read some articles that improve on the basic RBC model, what are the common extensions (1-5, or other) that you see that address these weaknesses?

When is a model really weak?

A model is an abstraction of reality, to explain a part of it. A model is weak when it cannot explain what it's supposed to be explaining. Just adding features to a model has no intrinsic good. It's much different from a fruit salad, where usually, an increased variety in fruits will lead to a better taste. Here, adding more features makes it hard to understand which feature of the model was necessary to generate the result observed.

For example, When your focus is on variation of labor-supply within different income and skill groups, yes, lack of distortionary taxes could be a problem. If the model is not aimed at doing that, and it does fulfill its purpose without requiring those taxes, the lack therein is not a problem.

The most basic RBC model

There is no single RBC model. It's most simple (but not representative!) version is the seminal Kydland and Prescott (1982) paper. It lacks all those features that you mention, but it is aimed at explaining variations and correlations in output, investment, capital and labor. If it does that job well (I'm not going into that discussion here), it is a good model, and the lack of those characteristics is not a weakness.

The class of RBC models

The general RBC class of models are those, where variation along the balanced growth path is caused by (random) shocks to productivity. Of course, no economist really believes that a random number generator is attached to each firm and causes fluctuations in output. It's a simplification.

Hence, if you are after a weakness behind the RBC model in general, it ought to be that you believe that this simplification is false. That, whatever the reason for business cycle fluctuations we observe is not caused at the productivity wedge.

For example, some neokeynesian economists believe that it could be mood shocks. People sometimes are more or less lazy, and that recessions go really bad when you people really don't want to work (again, this is a simplification, but the point is that the relevant wedge is not at the output margin, but at the labor-supply and consumption wedge). A critique of these shocks to the household's objective function can be found in Chari, Kehoe, McGratten (2009).

These productivity shocks are, in the simple one-sector model that is mostly used isomorphic to shocks to technology. However, this doesn't mean that they necessarily are caused by them (hint at @Mustang). For example, Acemoglu and coauthors (2012) show how mathematically small shocks within firms and sectors (such as variations in the cost function, e.g. unexpected oil price changes), usually cancel each other out, but sometimes aggregate up to great shocks over the whole economy.


What are the effects of liquidity crisis? What are the actual effects of the lack of liquidity?
Economists always say, we need to increase liquidity at a time of recession, but why is liquidity is important for us? Could anyone explain it in an example?

Lack of liquidity depresses the output and can lead to recessions because it forces otherwise healthy firms to go bankrupt and it also undermines the financial infrastructure of an economy.

I think good way of understanding the problem is to explore the difference between illiquidity and insolvency. When firms go bust it is often mainly due to one of the two following reasons:

Firm is insolvent - when firm is insolvent it means that it is economically not viable. The insolvency means that the firm simply does not generate enough revenue and consequently also profit to meet its obligations.
Firm is illiquid  - when firm is illiquid it generates enough profit to meet its obligations but not enough cash. This is because the customers of the firm might not pay for the products on time (which during the crisis often happens - for example in the current corona virus crisis some people might pay their rents late - some countries even consider canceling them/postponing them). But this the hurts the ability of that firm to pay its employees suppliers and creditors in general. Consequently even though firms business might be economically healthy there might not be able to generate enough cash in short term to pay its own creditors.

(Note: I am using the words insolvent and illiquid in broad economic sense - in finance and accounting those words have little bit more narrow definitions)

You want to let insolvent firms to fail and be replaced with more efficient firms - its the part of Schumpeterian creative destruction. However, firms with liquidity problems are fundamentally healthy- especially when the iliquidity is caused by shock and is not chronic. Hence when illiquid firms fail it is more or less pointless loss. Unfortunately, in practice it is hard to distinguish which firm is actually insolvent and which illiquid and hence it is not possible to just have some regulation that would effectively shield illiquid firms from the bankruptcy (such regulations exists but unfortunately they often turn determining whether firm is insolvent or illiquid into legal battle that has less to do with economics). As a result most economists stress preventing liquidity crises in the first place.

Furthermore, in the above I was talking just about firms in general but liquidity is actually extremely important to the financial sector. Banks assets are essentially illiquid because they offer loans, and they cant just ask the people they lent money to repay it back before maturity. However, banks liabilities are liquid because they consist mostly of deposit accounts from which people can withdraw cash any time they want. Now most countries have deposit insurance - a regulation that helps prevent people frantically withdrawing cash due to fear of bank going bust (i.e. bank runs). However, this does not extent to other financial institutions and shadow banks which can experience runs by creditors who worry that they wont get their money back, and since financial sector is all interconnected falling of these institutions can spread to all other financial institutions.

Any problem affecting financial institutions will eventually hurt the real economy because financial intermediaries have first order impact on the economy, because many businesses relay on them for financing - especially startups, but they are important overall (see Levine, 2005 for discussion of that).

So to sum up a liquidity crisis often leads to recession and has negative impacts on economy because it damages the financial infrastructure and forces otherwise healthy businesses to go bankrupt.


The current economic understanding of the effect of labour unions on employment and wages What are the currently largely accepted views on the effect of labour unions on employment and wages? Where can I read more about the currently established theoretical models that model labour unions?

I'd recommend checking out Labour Economics by Borjas.
It is such a broad topic that really quite a detailed evaluation would have to be conducted.
In particular, the effect of a labour union on levels are unemployment are likely to be affected by the assumptions in your theoretical model.

Assumptions of perfect and imperfect competition (of some type) are likely to have different signs and magnitudes.

It follows that it is perhaps useful to look for empirical evaluations on the matter. Personally, it's not my field - but it is possible that someone like Borjas has done research, or potentially Kreuger.


What was the reason behind destorying or re-minting counterfeit gold coins of the same karats as the real ones? I remember reading about an interesting event which happened in the early 19th century, in the Habsburg Empire.

A criminal organization, mainly composed of workers and corrupt administrators at a gold mine, minted prefect-quality gold coins illegally. Normally, the extracted gold had to be handed in, in exchange for a very low commission, so they handed in only part of the mined gold, minting the rest into coins illegally. However, instead of producing counterfeit coins with a lower than official gold content, they minted coins which had the same gold content as the real ones.

When the operation was busted, the confiscated coins were marked (by hammering a nail through them, if I remember correctly) and transported away to be destroyed, probably to be cast into bullion or to be minted.

This is what I don't understand, why was it necessary if the coins had the required gold content?

The criminal operation was definitely a loss for the government, but from the point of view of macroeconomics it shouldn't have influenced the supply of money. If the criminals wouldn't have minted it, I guess that probably the government would have. So, why were those "perfect" coins needed to be destroyed, if they were to be later re-minted anyway?

I don't know about the story you refer to, but I'd say this was likely due to the intrinsic fungibility of gold as a commodity, before it serves as money.

Besides its natural scarcity and the significant amount of energy it requires to extract and mint, other important properties of gold (to serve as real money later on, anyway) include:

being stable (phys. / chem. speaking), portable, divisible, and fungible.

Fungibility: both as a store of value and as a medium of trade, any one ounce of gold is (relatively) easy to recognize and test for authenticity, and thus easily interchangeable with any other ounce of gold, of same purity -- if one excludes other considerations such as numismatic value or tastes in shape, etc.

Because the operation in the story you recall was fraudulent to begin with (extra-minting undeclared on the books) it was then important to find a way to differentiate unambiguously those ounces from the rest that were duly kept on the books -- i.e., to temporarily "deny" that gold its fungibility, so to speak, and at the physical level (by mangling it) -- if only temporarily.

Of course the rationale was to prevent a priori those coins from going into circulation on the market, after the bust -- and whether or not the decision would be made later on to reintroduce them (but this time in a controlled way).

Just my understanding anyway.

'Hope this helps.


Short Run Total Cost function Question I am confused about the Short Run Total Cost function of this problem.

If the firm's production function is $F(K,L) = K+\ln(L)$ derive the short run total cost function.

I was able to solve the Short run total cost function, but my TA had 2 cases for her function whereas I only had 1 part of her function.

I got $TC= W*e^{q-K} + r\bar{K}$ for all $q$ but my TA had 2 cases for $q$. Specifically, when $q<\bar{K}$ and $q>\bar{K}$

Thank you.

I'm just gonna try doing it. The problem is:

$$\text{min } C = rK + wL \\
\text{s.t. } q = K + \ln(L) $$

The implied constraint, of course, is $L \in [1, \infty)$ (non-negativity constraint, as $q > 0$, and $K = 0$ is, of course, possible).

We can try solving this using Lagrange multipliers. Define the Lagrangian:

$$\mathcal{L} = (rK + wL) + \lambda(q - K - \ln(L))$$

The first order conditions are:

$$\mathcal{L}_{K} = r - \lambda = 0$$
$$\mathcal{L}_{L} = w - \lambda(\frac{1}{L}) = 0$$
$$\mathcal{L}_{\lambda} = q - K - \ln(L) = 0$$

Using some algebra, we get $r = wL$ and $L = e^{q-K}$. Substituting into the original cost equation:

$$C = K(we^{q-K}) + we^{q-K} = we^{q-K}(K + 1) $$

I don’t think this can be simplified much further.

That seems to be the same answer that you got (I just expressed it in terms of wages and capital). So not sure – maybe I’m making a mistake.


Are risk-costs a form of external costs? An example to make to question more clear: With the use of nuclear power plants come several risk-costs (the risk of a nuclear disaster). These costs aren't included in the energy price and there is nobody who pays for it. So are they considered as external costs?

In the particular case of nuclear power plants, yes, the risk cost can be considered as a negative externality.

That's because nuclear power plant operators are explicitly limited by law in their liability for third-party costs in the event of damages to those third parties. The third-party risk they present could run into trillions (\$/€): at Fukushima, the current cost is estimated at \$200bn and rising. But operators' liability is capped at a much much smaller amount: this differs by country, but typically of the order of a few hundred million to a few billion (\$/€). This means that operators do not have to spend as much money as they otherwise would, on reducing those third-party risks.

If nuclear plant operators had to buy insurance to cover that entire risk, then it's they would be even more uneconomical than they already are. That is, their cost base would be much higher. The direct third-party damages are not paid by the operator, nor by the consumer; but instead are paid by the taxpayers, in the countries that have to clean up after accidents. So, the Japanese taxpayer has borne a large share of the costs, because Fukushima; previously, the USSR did, because Chernobyl - but in that case, some costs were spread all over the Northern hemisphere, due to widespread distribution of the radioactive material; for example, there were restrictions on farming in polluted areas, vast distances from the plant, for decades afterwards.

So, the consequences of the risk are borne as public subsidy. The risk premium itself is not a cost borne directly by anyone: it's an uninsured risk. So, it could be viewed as a negative externality that, if priced in, would move the supply curve.

Note that if you were to refer to these risks, and their consequences, explicitly as subsidies and negative externalities, then you're probably going to have to provide an accompanying explanation (as I've attempted to do above - hopefully you can be more succinct!), as for much of your audience, it won't be immediately obvious as to why you're using those labels.


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

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

There is generally no effect of employers not formally tracking their employees' subsidies on the labor market. Generally speaking government subsidy is already reflected in the labor market whether employers know about it or not.
A trivial example would be policy that gives unemployed people benefits as long as they are unemployed (let's say ${\\\$}100$). Employees only accept job if the benefits of having job outweigh the costs of having it. Simplifying by assuming that only benefit of job is the money and nothing else (unrealistic but does not affect underlaying mechanism) in the above scenario employee won't accept any job offer that does not pay at least ${\\\$}100$.
So in this case whether employer knows about the subsidy or not job will be created only if employer is prepared to bid for the job more than ${\\\$}100$ and only jobs that pay more then ${\\\$}100$ will be created in the economy. Really the only difference between scenario where employer knows about subsidy or don't is that those employers who don't know will wonder about employees rationale for asking ${\\\$}100$ but that has no additional effect on labor market. Employer has no reason to care about whether the ${\\\$}100$ is being asked because that is the employee's value of free time so employee won't accept less or whether this is because of another competing job offer or government subsidy. This the beauty of price system - you don't need to understand people's motivations or preferences or situation - they will already be reflected in prices they are willing to pay or they ask for (in symmetrical fashion some businesses also get subsidies from government that can be conditional on their size/profitability (e.g. some credit for small businesses) -these could affect labor market but are not dependent on employees actually knowing about these subsidies).
The above generalizes to the situations when subsidies depend on the wage as in your description above. Again such subsidies would have effect on employment/wage or other factors, but generally the employer knowledge of those subsidies would not.


Calculating Service Contributions to GDP Trying to get some clarification on how GDP is calculated for service industries.

Are input resources netted out (e.g. fuel for an airline), the same way wheat would be for a loaf of bread?

What about investment assets (e.g. airplanes for an airline) -- these get fully counted toward GDP the year they're purchased?

Services will be calculated at the final price they are given in market. That price includes all value added items in providing the service. So, to calculate contribution of airlines in GDP, you just need to sum up the total value of tickets that are sold. Other things will automatically be counted in that.


Hayek's defense of competition regulation This article claims Hayek endorsed competition regulation:

  As it evolved, neoliberalism became more strident. Hayek’s view that governments should regulate competition to prevent monopolies from forming gave way – among American apostles such as Milton Friedman – to the belief that monopoly power could be seen as a reward for efficiency.

In which work did Hayek advance such view?

This article states:

  In  both  of  his  seminal  works  in  political  theory,
  The  Constitution  of  Liberty  and Law, Legislation and Liberty, Hayek endorsed as a legitimate function of the state the  power  to  regulate  monopolies  and  curtail  industry  practices  in  restraint  of  trade.

For example, in the first book, in Chapter 15, Hayek declares the importance of the nature of government intervention:

Notice that Hayek considered trade unions as workers' monopolistic institutions that damaged free market. Hence, in his view, these are undesirable. In Chapter 18 of the above books it says:

More on monopoly is in Chapter 17:


Leontief's Paradox and the amount of capital Leontief (1953) showed that US exports in 1947 embodied considerably less capital and somewhat more labor than would be required for domestic production of competitive imports. \$2.55 million worth of capital was used to produce \$1 million (against $3.1 million for "imports"). What is being measured here is the total capital stock which I guess exceeds that part of the capital stock that was used to produce exports that year.

Would it be more appropriate to measure the capital used that year by the depreciation on the total stock? Is there any reference on this?

Leontief did not use total capital stock for his calculation of capital/labor requirements in the export/import sector. He measured 'requirements per million dollars of exports and imports replacements', and this for various industries (Leontief, 1953, section III, table 2). So he also did not use total capital stock, he used capital requirements AKA capital inputs.

He did provide summary statistics on the total capital and labor required per million dollars of total output for each industry. This might have confused you.

Note that he obtained these numbers only after computing them from available data, and he discusses their accuracy in the same section.


Why salaries counted under Government expenditure in GDP In the expenditure approach of GDP calculation, why are government employee's salary counted under Government approach while for private firms, we don't count salaries. I am unable to understand if there is asymmetry and if yes, then why?

The expenditure measure of GDP counts final expenditure, i.e. consumption by individuals and government and foreigners (exports) plus all capital formation (i.e. investment), and then subtracts imports since that part of final expenditure is not satisfied by domestic production.

The salaries of government employees count as government consumption in the same way as the government's purchase of services from private companies also count as government consumption.  So the effect of paying for this work is the same whether the individuals are employees or contractors.


preference relations Can anybody give an intuitively explanation for the following problem?

  Let $\succeq$  be a preference relation on a set X. Define I(x) to be
  the set of all y ∈ X for which y ∼ x. Show that the set (of sets!)
  {I(x)|x ∈ X} is a partition of X, i.e.,

  For all x and y, either I(x) = I(y) or I(x) ∩ I(y) = ∅.
  For every x ∈ X, there is y ∈ X such that x ∈ I(y).

Let $X$ be the set over which a preference $\succsim$ is defined. The question asks you to prove that $X$ can be divided up into numerous subsets defined by the indifference relation, i.e. all elements within an indifference set, denoted $I(x)$, have the same desirability according to the preference $\succsim$. The collection of these indifference sets is denoted $\{I(x)\vert x\in X\}$. The two bullet points tell you how to proceed with the proof.

First, you need to argue that the indifference sets defined by any two elements $x$ and $y$ are either identical or distinct.

Second, you need to argue that every element belongs to one of the indifference sets that divide up $X$.

Here is a simplified example to give you some intuition.

Suppose the set $X$ contains the following items: an apple ($a$), a banana ($b$), a cherry ($c$), a dragon fruit ($d$); that is, $X=\{a,b,c,d\}$. I like cherries best, bananas and apples the second (I'm also indifferent between the two), and dragon fruits the least. This is my preference over $X$. Define the indifference sets as follows:

$I(a)=\{a,b\}$ (i.e. the set that contains items indifferent to apple includes both apple and banana);
$I(b)=\{a,b\}$;
$I(c)=\{c\}$; and
$I(d)=\{d\}$.

As we can see, for any $x,y\in\{a,b,c,d\}$, $I(x)$ and $I(y)$ are either identical (as when $x=a$ and $y=b$, or vice versa) or distinct (as when at least one of $x$ and $y$ is $c$ or $d$). This satisfies the first requirement.

For the second requirement, it is clear that the four items ($a,b,c$ and $d$) belongs to one of the three indifference sets ($\{a,b\},\{c\},\{d\}$).

To properly prove the claim, you need to generalize the example above to cases where the set $X$ contains an arbitrary number of elements. Strictly speaking, you'd also need to consider arbitrary preferences. But since the preference relation $\succsim$ is complete and transitive, such consideration is less crucial.


ratio independent time-invariant variable I run the following function:
$$Y_{it} = a_0+a_1*X_{it}+K*a_3+\epsilon_{it}$$

where $X_{it}=M_{it}/N_{it}$ is a generated variable. I got data $Y_{it}$ for the period from 2010 to 2015. Due to data unavailable , I just got data $M_{it}$ and $N_{it}$(two resources) in 2010, $K$ is other control variables.

Actually, I run this
$$Y_{i2010-2015} = a_0+a_1* M_{i2010}/N_{i2010} +K*a_3+\epsilon_{it}$$

Is there any problem to run this model? Can I use coefficient $a_1$ to explain the allocation of resources?

Given that you have one value for this $M/N$ allocation variable per individual, it can be considered a time-invariant explanatory variable.  If you estimate this model without including individual fixed effects (which control for all unobserved time-invariant differences between individuals), you will be estimating a pooled cross-section regression, which will allow you to get an estimate of $a_{1}$ but which will ignore the panel dimension of your data.  As a result, the estimate of this coefficient and all other coefficients will be based on the assumption that the model applies in the same manner to every individual (individuals are not unique) and that there are no effects across time.  (You could include dummy variables for each year in the model and do a joint test on those dummies to see if the assumption about the effect of time is valid, though you would not be able to include any other variables that vary only over time.)

If you, however, wanted to estimate a fixed effects model because you thought that there are unique attributes of individuals that do not vary across time (in other words, you thought that outcomes of the same individual were correlated in different periods), you would not be able to use this kind of time-invariant explanatory variable in the model.  This is because in a fixed effects model, coefficients are identified using only variation over time within each individual.  So if a variable varies only across individuals, but not over time, then its effects cannot be identified at all in a fixed-effects model.


Why does a rise in the savings rate result in an increase in the capital stock intuitively? I understand mathematically how it works. But what is the actual process intuitively.
Thanks

The story in the other answer is not fundamentally wrong but incomplete and bit inaccurate.
Saving does actually affect capital stock through investment in Solow model (assuming based on the Solow tag that is the model you want intuition for), but there is more complexity to it.
What is saving
Investment is actually equal not just to private saving but both private and public saving since saving is actually defined as (following Blanchard et al Macroeconomics: a European Perspective pp 51):
$$S \equiv Y - T-C$$
Combining this definition with output identity for closed economy $Y\equiv C+I+G$ gives us:
$$S = I +T -G$$
However, it is often convenient in Solow model to just ignore government by assuming $G=T$, in which case $S+I$.
Why does saving rate increase capital stock:
Next the way how savings rate affects capital accumulation is depicted in the picture I took from Romer Advanced Macroeconomics 4th ed pp 19.

As you can see the intuition really works this way. Here $s$ is the savings rate and $f(k)=Y$. Higher $s$ means that savings increases, for example if $Y=100$ with $s=0.5$, $S=50$ and with $s=0.7$, $S=70$. Then if we assume away government indeed $S=I$ so $I=70$.
This is why the evolution of capital accumulation (per unit of effective worker) is given by:
$$\dot{k}(t) = sf (k(t)) − (n + g +\delta)k(t)$$
where actually $sf(k(t)) = sY = S =I$, so it is through increased investment. The $n$ and $g$ would be population and technological growth respectively and $\delta$ the rate of depreciation (although these are not important for intuition about raising level of capital).
Does this push capital beyond steady state?
Now this is surprisingly common misconception. Increase in savings rate can increase the level of capital stock - it just cannot increase the growth rate at which new capital per effective worker accumulates.
According to Romer Advanced Macroeconomics [emphasis mine]:

, a change in the saving rate has a level effect but not a growth
effect: it changes the economy’s balanced growth path, and thus the level of
output per worker at any point in time, but it does not affect the growth
rate of output per worker on the balanced growth path.

However, this is quite common misconception because of the confusing terminology. Increase in level in macroeconomic. Consider for example the visualization from Romer Advanced Macroeconomics pp 20:

The upper graph shows you the growth rate of capital per effective worker. Indeed here savings rate has only one-of impact that quickly dies out (in fact this is just level increase in disguise as growth).
However, on the bottom panel you can clearly see that the level of capital per effective worker is now higher thanks to higher savings rate.


Existence of Linear Representation Consider a preference relation $\succeq$ on $X=\mathbb{R^2_{+}}$. If $\succeq$ satisifies:
$$
\begin{align}
&1.\mbox{ }(a_1,a_2)\succeq (b_1,b_2)\implies(a_1+t,a_2+s)\succeq (b_1+t,b_2+s),\forall t,s\\
&2.\mbox{ }a_1\geq b_1 \mbox{ and } a_2\geq b_2 \implies (a_1,a_2)\succeq (b_1,b_2)\mbox{ (and the analogous for }\succ\mbox{)}\\
&3.\mbox{ Continuity }
\end{align}
$$
Then: exists a linear representation for $\succeq$.

Could anyone give me some hints on how to prove this?

Thanks for helping! :D

How about this: For each vector $(x,y)$, there is a unique $z\in \mathbb R$ such that $(x,y) \sim (z,z)$. WLOG assume $x \geq y$. Then to see this claim, first notice by A2 that $(x,x) \succeq (x,y) \succeq (y,x)$. Then traveling along the $45^\circ$ from $(y,y)$ to $(x,x)$, A3 ensures the existence of our $z$. (Strict) Monotonicity assures uniqueness in the obvious way. Let $u: (x,y) \mapsto z$ where $z$ is defined in this way.

Now let $(x,y) \sim (z,z)$ and $(x',y') \sim (z',z')$. Then by A1 we have
\begin{align}
(x + x',y+y') &\sim (z + x',z + y') \\
(x' + z,y' +z) &\sim (z'+z,z'+z)
\end{align}
so by transitivity, $(x+x',y+y') \sim (z+z',z+z')$. Verifying that $u$ is continuous is trivial.

So $u$ is additive and continuous. As this Math SE post explains if $\mathbb R^2 \to \mathbb{R}$ is additive and continuous then it is linear.


How large is the Underground Economy in the U.S How large is the Underground Economy in the US, and is it growing or getting smaller as a percent of GDP?

There has been some research on this. For example, see the papers by Cagan (1958), Tanzi (1983) and Schneider (2007), Schneider et. al (2010).

If you would like a survey kind of thing, there is a staff paper from St. Louis Fed: Restrepo-Echavarria (2015). Link: https://www.stlouisfed.org/publications/regional-economist/january-2015/underground-economy
and also Schneider and Enste (2000).

Based on Table 3.3.3 (page 24) of Schneider et. al (2010) and the discussion (page 17-19 of same paper) which makes me believe that the numbers on the table are percentage of GDP, USA moved from 8.8% in 1999 to 8.4% in 2007 with a country average of 8.6% in this time period.

Note that (as these papers would mention) there is significant debate about defining and estimating "shadow economy".

References

Cagan, Phillip. "The Demand for Currency Relative to the Total Money Supply." Journal of Political Economy, August 1958, Vol. 66, No. 4, pp. 302-28.
Restrepo-Echavarria. "Measuring Underground Economy Can Be Done, but It Is Difficult"
Federal Reserve Bank of St. Louis The Regional Economist, First Quarter 2015, Vol. 23, No. 1
Schneider, Friedrich. "Shadow Economies and Corruption All Over the World: New Estimates for 145 Countries." Economics: The Open-Access, Open-Assessment E-Journal, July 2007, Vol. 1, No. 2007-9, pp. 1-66.
Schneider, Friedrich & Buehn, Andreas & Montenegro, Claudio E. "Shadow economies all over the world : new estimates for 162 countries from 1999 to 2007," , 2010, Policy Research Working Paper Series 5356, The World Bank.
Schneider, F. and Enste, D. Shadow Economies: Size, Causes, and Consequences. The Journal of Economic Literature, 2000 , 38(1): 77–114.
Tanzi, Vito. "The Underground Economy in the United States: Estimates and Implications." Staff Papers—International Monetary Fund, 1983, Vol. 30, No. 2, pp. 283-305.


Compensating variation versus change in value of goods consumed? I study an economy with two goods ($x$ and $y$) and two consumers ($A$ and $B$). First there is no trade between $A$ and $B$, so they consume their endowments $e^A_x$ and $e^B_x$ and reach utility levels $u^A_1$ and $u^B_1$. Thereafter, trade develops between $A$ and $B$ and they reach utility levels $u^A_2$ and $u^B_2$.

I now want to find how much better off each consumer has become due to trade. I understand that looking at the increase in utility does not give any meaning, since the utility function is an ordinal function. From what I can gather, the correct way of doing this is to calculate the compensating variation $CV$ - how much more of the nominal good they need in autarchy in order to reach $u^A_2$ and $u^B_2$, respectively.

However, whouldn't comparing the value of each consumer's endowments (i.e. their autarchy consumption) and the value of the goods they end up consuming after trade also tell us how much better off they are after trade?

It wouldn't.  The value of consumer's endowments and the value after they trade should be the same.  i.e. Neither consumer becomes richer in terms of money.  They just allocate their money towards buying goods they value more.

Additionally, prices are a function of both consumers' demands while CV only depends on the demands of one consumer.  Consider the following example

In autarky consumer 1 has endowment, $e_1=(1,1)$ and utility
$$u_1(x,y) = x + 2y $$
so $u_1(1,1)=3$
Now there is trade where consumer 2 has endowment, $e_2=(1,1)$ and utility
$$u_2(x,y) = 2x + y $$
When the consumers trade the equilibrium price is $p_x = p_y$  and equilibrium consumption bundles are that consumer 1 gets $(0,2)$ and consumer 2 gets $(2,0)$.  The value of both consumers' endowments and equilibrium allocations is $2p_x$.  But in terms of compensating variation (with $x$ as the nominal good) consumer 1 would require 2 units of $x$ to move from free trade to autarky while consumer 2 would require 1 unit of $x$.


Does mathematical education imply a better salary? In some sense this is a follow-up to

Correlation between salary level and housing prices in a town

There I was reminded to ask for causality, not correlation. I am interested in the causal effect of mathematical education on salaries even if I do not use those words below.

Now, my question is the following: does mathematical education result in a better salary? Here, by mathematical education, I do not mean mathematics as a major but rather a major with heavy mathematics in it. Probably a better formulation is this: is there any literature on whether studying applied mathematics pays off? Again not an Applied Mathematics as a curriculum per se, but a course with heavy applied math content.

Math is easier if you are smarter. As such, math education is a costly and therefore credible signal of general intelligence. Below are two experiments that try to get around this selection issue by looking at exogenous variation in worker mathematical ability on labor market outcomes. However, a word of caution. They do not present evidence that mathematical education makes you more productive. Even if all mathematical education is is a signal of intelligence, it can be valuable to individual workers to get more mathematical education, and they will on average benefit from interventions that lower the cost of getting a mathematical education

  We examine the link between math skills and labor-market outcomes
  using a resume-based field experiment. Specifically, we send
  fictitious resumes in response to online job postings, randomly
  assigning some resumes to indicate stronger math skills, and measure
  employer responses. The resumes that are randomly assigned to indicate
  stronger math skills receive more interest from employers than the
  comparison resumes. Our findings add to the body of evidence showing
  that stronger math skills positively affect labor-market outcomes.

Math skills and labor-market outcomes: Evidence from a resume-based field experiment by Koedel and Tyhurst (2012)

  Outsourcing  of  jobs  to  low-wage  countries  has  increased  the
  focus  on  the  accumulation  of skills – such as Math skills – in
  high-wage count ries. In this paper, we exploit a high school pilot
  scheme  to  identify  the  causal  effect  of  advanced  high  school
  Math  on  labor  market outcomes.  The  pilot  scheme  reduced  the
  costs  of  choosing  advanced  Math  because  it  allowed for at more
  flexible combination of Math with other courses. We find clear
  evidence of  a  causal  relationship  between  Math  and  earnings
  for  the  students  who  are  induced  to  choose  Math  after  being
  exposed  to  the  pilot  scheme.  The  effect  partly  stems  from
  the  fact  that these students end up with higher education.

Is there a causal effect of high school math on labor market outcomes? by
Joensen and Nielsen (2009)


Why did Greece not solve its debt problem by selling treasury bond to its own people? Since the Greek vehemently opposed the conditions imposed by the EU for the 3rd bailout, I don't understand why the Greek government did not raise the money needed to repay the previous loans by selling treasury bond or privatizing public assets before the full blown of this whole crisis.

there are a few reasons:

Directly selling bonds isn't a common method to get money from your people. Raising taxes works more effectively. A promise of future spending would be roughly equivalent to selling bonds.
why not sell bonds to everybody? not just the Greeks? To a large extent, this has already been done. You don't get to 158% Dept to GDP without a lot of borrowing. Borrowing to pay interest is common. It isn't a long term solution.

The Greeks have been negotiating the terms of the bailout for many months now. Liquidating assets would have been considered and I expect will happen as part of these new measures.


Why must the rate of GDP growth be positive? There are always expectations that GDP should be growing at a certain rate. This is what I see in the newspapers. I am not an economics major and this is a very basic student question. After adjusting for level of prices, meaning that forget about inflation and price related issues, it is expected to grow at say $2\%$. Why is this a case and what should it be driven by? Assume there is an economy that only produces apples, for simplicity. So, it is expected to make $2\%$ more apples every year? So the growth would be driven by the larger amount of goods produced? Why is this economy expected to make more apples every year?

You would expect the rate of growth to be generally positive because inventing things or inventing more efficient ways of doing things, is generally a one way process - things don't get un-invented. So we would expect things that are made by machines to be made ever more quickly as the machines evolve and improve. Periods of negative growth are likely to correspond to some financial cock-up (e.g. asset bubbles) or increasing scarcity of some natural resources for which a replacement can not be found.


An agent's expected utility depends only on mean and variance Consider an agent with the expected utility function $U(L) = \sum_{s=1}^{S}\pi_s U(Y_s)$ over the lottery $L = (Y_s, \pi_s)$ where $\pi_s$ is the probability of state $s$, $Y_s$ are state $s$ payoffs, and $U(y_s) = -\frac{1}{2}(\alpha - Y_s)^2$ for $Y_s < \alpha$ is the utility index
  over payoffs. Show that this agent's expected utility depends upon only
  the mean and variance of the state-contingent payoffs.

I do not really understand what the question is asking of me to show. Any suggestions or comments are greatly appreciated. Specifically, is the question asking me to find $$E[U(s_s)]$$ and $$Var[U(Y_s)]$$ if so how do we do that when we don't really have any defined distribution for $Y_s$? Also what does even mean that the mean the agent's expected utility depends upon only the mean and variance of the state-contingent payoffs. Does not make sense to me, I do not have much of an economics background as a graduate student in Applied Mathematics.

In order to understand this problem, I will work through the generic case. Say that a user had generalized quadratic (Bernoulli) utility, similar to your problem:

$$u(x) = \beta x^2 + \gamma x$$

and suppose that there is a distribution for the outcome of $x$, denoted $F(x)$. Thus, utility over this distribution is equal to

$$\begin{align}
\int u(x) \text{d}F(x) & = \int (\beta x^2 + \gamma x) \text{d}F(x) \\
& = \beta \int x^2 \text{d}F(x) + \gamma \int x \text{d}F(x) \\
& = \beta \int x^2 \text{d}F(x) + \left[ - \beta \left(\int x \text{d}F(x)\right)^2 + \beta \left(\int x \text{d}F(x)\right)^2 \right] + \gamma \int x \text{d}F(x) \\
& = \left[\beta \int x^2 \text{d}F(x) - \beta \left(\int x \text{d}F(x)\right)^2 \right] + \beta \left(\int x \text{d}F(x)\right)^2  + \gamma \int x \text{d}F(x) \\
& = \beta\cdot(\text{variance of F(x)}) + \beta\cdot(\text{mean of F(x)})^2 + \gamma \cdot (\text{mean of F(x)})
\end{align}$$

So utility is determined by the mean and variance of the payoff distribution. If you understand the above work, then it should be easy to do the specific case you have given us. Try it for yourself.

Considering your specific case:

$$U(Y_s) = -\frac{1}{2}(\alpha - Y_s)^2$$

implies

$$U(L) = \sum_{s=1}^{S}\pi_s (-\frac{1}{2}(\alpha - Y_s)^2)$$

You can technically work with either finding $\int U(L) \text{d}L$ or $\int U(Y_s) \text{d}L$. Best of luck with your work.

Edit: Working in the discrete case will mean using expected values may prove helpful.


Buying and selling in the stock market I am a total beginner to this, but from the few online videos about how (practical) trading works, I understand that when buyers dominate the market the prices go up and when sellers dominate the prices go down (of course this is an oversimplification). I am not sure I understand how can buyers or sellers dominate. I thought then whenever someone sells some shares someone else buys them. If that is not the case, then where are these shares going, and where are the money going to the seller come from? Going to the extreme case of assuming that everyone sells their stocks, and no one buys, who owns the share anymore and who is paying the people who sold the stocks (which for a reasonable company they are worth a few billions)? Thank you!

I understand that when buyers dominate the market the prices go up and when sellers dominate the prices go down (of course this is an oversimplification).

People want to treat trading as some mechanical force. People are buying and selling shares, and the prices reflect where they want to transact. As news comes in, people can change their minds about a company’s value without any transactions taking place.
For example, if a company announces accounting irregularities and an imminent bankruptcy, everybody is going to revise down what they think the shares are worth. Prices will be adjusted lower by everyone, and you could even have more people lining up to buy on the theory that the company might have more value than what is suggested by the price.

I thought then whenever someone sells some shares someone else buys them.

This is always the case, by definition. To deal with you other questions, in an ideal world, if we add up all investor’s shares, the net position is 100% of the amount outstanding.
(The real world is slightly messier. Stock trading does not settle instantaneously, settlement is later. This allows short sellers to “sell” shares that they do not currently own - they borrow them from somebody else before the settlement. This obviously complicates things, but it makes sense once we realise these are credit transactions. A seller is not immediately selling, instead they have entered into a contractual obligation to deliver shares at a future date.)


Money invested vs increased valuation I am looking for a name and historical data for a concept. I think it is easiest to explain by example. Consider stock in XYZ Inc worth \$10 per share and there are 10 shares, so the market cap is \$100. I really want to buy a share, but the current owners are happy with it so I have to pay \$11. So I have added a new dollar to the stock ecosystem, but now the market cap is \$110. That means there are \$9 of new value that have appeared out of thin air.
Is there a name for my $1 that I added and the \$9 of new created value? Is there a name for the ratio of the two?
I am curious about these values because I suspect the ratio has been abnormally high for the stock market at large since the Great Recession. In other words, the value of the total stock market has outpaced the amount of new money invested in the stock market.
Is this suspicion accurate? Does anyone track this data?

I don't know the name of the term you are looking for but the ratio you are looking for can be calculated as the volume of trade data is usually available for each stock. A similar metric that you may like is Volume-Weighted Average Price which takes into account the volume of trade.

Is this suspicion accurate?

It's very subjective but your suspicion seems to be based on your hypothetical construct which needs further discussion. You say 'I really want to buy a share..'. Now why would that be? For a rational investor, it will be when she sees it's value to be \$11 rather than market value of \$10.
When enough investors are there in the market that think that the value of the share should be high then the price of the stock goes up (and there's nothing wrong with it), which reflects, in a way, the collective sentiment about the stock.
In the above reasoning, we consider the market as a non-cooperative non-atomic game, in which single player's decision has no influence on market outcome. Therefore, an individual is not pushing the price of the stock but rather the general consensus that the stock is going to giver higher returns.
So your suspicion is correct when these at least one of the following assumptions are not be valid: (a) investors are not rational (domain of behavioral finance); (b) game cannot be considered non-atomic (there are big players that can alone move the market - almost always true); and (c) there is collusion among investors to bid the price of a stock up.
So yes, for some stocks, to some extent it is perfectly possible that some investors bid the price up to the level that it doesn't reflect the real valuation. This is more common with penny stocks which is why there are more restrictions/regulations around them.


Why is macroeconomics about general equilibrium? In a fairly popular paper published a couple of years ago ("On the future of macroeconomic models"), Blanchard (2018) makes the following statement, among other "widely believed propositions":

  (i) Macroeconomics is about general equilibrium.

Unfortunately, no note or reference is given for this statement.

Is this statement true? How can it be formally proven? What is the intuition behind it?

Not sure what you mean by formally proven in this case, but it’s just true by definition.

Macroeconomics is by definition branch of economics that studies the behavior of economy as a whole as opposed to individual markets or actors separately which is studied by Microeconomics.

General equilibrium is by definition an equilibrium of whole economy or several markets.

Hence it just follows from definition of both general equilibrium and macroeconomics. Most of the economics is devoted to study of equilibria for better or worse so if you study macroeconomics you almost always study general equilibrium in one way or another. It’s equivalent to say that microbiology is about small organisms. It’s true just by definition.


Solving a problem using CAPM and capital structure theory I am given the following problem:

A firm currently owns assets worth $4$ milllion dollars that have a beta of 1. The risk-free interest rate is 10% and the market risk premium is 8%. Suppose the firm has the opportunity to invest in a project that will earn a 13% rate of return for certain into the indefinite future. The cost of the project is $1$ million dollars. Should the firm make the investment?

How do I solve it using CAPM or capital structure theory?

Is it correct to say that the firm should not invest because, using CAPM, the required rate of return should be:

$r_i = r_f + \beta_ * (E[R_{Mkt}] - r_f) = 18\%$

@chsk gives the correct answer if the firm has to raise funds using the equity market and the cost of those funds is the same as that for the firm. However, I would recommend that this firm do the project.

As indicated in the project, the risk free rate of return is 10%, and this project "...will earn a 13% rate of return for certain into the indefinite future." So this is a risk-less project with a return above that of the risk free rate. So, if you can borrow at the risk free rate, such a project will be profitable. That should be clear by introspection, but here are some numbers, even assuming that there are no cash flows during construction:
$$\mathrm{PV} = \$-1,000,000 + \sum_{t\ge 1} \frac{ \$130,000 }{ 1.1^t } \approx \$295,000$$
and if cash flows appear during the initial period the value is about \$425,000.

In general, the internal cost of capital should be tied to project risk and not overall firm cost of capital. Consider that we could start a new firm that does only the new project. What is the appropriate cost of capital to lend to this new firm? Well, by assumption, the new project has no risk. Therefore, the appropriate cost of funds should be the risk free rate (10% in this problem).

In the real world this might be tricky. You might have synergies which complicate considering the project as a stand alone firm. You might not actually be able to find a investor that will provide funds to you based on project risk. You might have other frictions which put you in a pecking order project financing setting. But, safely in the confines of a study problem, these frictions are not of first order importance.

The way that I would answer this problem is as follows:

  The appropriate cost of funds for this project should be the risk free
  rate because there is not uncertainty to the project's returns.
  Therefore, the NPV of this project should be positive (show math to
  that effect). However, there are a number of reasons (sketch some of
  these out) why it might be difficult to raise funds for a risk-less
  project at the risk free rate. It is likely that an upper bound on
  market financing on this project would be the firm's average cost of
  capital, which is 18%. At an 18% discount rate this is not an
  economical project (show math to that effect). This firm should
  review its financing choices to determine their marginal cost of
  capital for this project. The internal rate of return on this project
  is 13% (show math to that effect), so as long as the firm's cost of
  funds is $<13$% then they should fund this project.


Why is not tram popular in most countries? This list suggests that tram systems are massively unpopular in most of the countries outside the Western sphere.

Why is not tram popular in most countries?

My guess: high investment costs, low gains relative to alternatives such as buses. You need rails and electric lines, which are expensive. In the western hemisphere trams already existed before alternatives such as large buses came about, so the costs consist mainly of maintenance. In other parts of the world the infrastructure is not in place, and getting it is expensive. For buses the infrastructure is already there as all you need is a decent road.


Foundational equations or concepts of Finance For the other sciences it´s easy to point to the most important equations, inequalities, propositions or concepts that ground the discipline. If I want to explain Finance to a physicist say, what are considered to be the most fundamental, foundational or important equations, inequalities, principles, propositions (theorems, lemmas, etc) or concepts that underly the subject which I should introduce and attempt to explain?

Above paraphrased from: Fundamental equations in economics

My guess would be the fundamental theorem of asset pricing or some Pricing Principle, but that's coming from a mathematical finance background. Would people coming from a corporate or personal finance (or whatever else finance is out there) background say something similar?

Considering this is an Economics Stack Exchange site, I’m going to answer in the spectre of Financial Economics. These are the most foundational equations and ideas of Financial Economics to understand more complex applied or academic research.

1. Gross yield

The gross yield is the yield on an investment before the deduction of taxes and expenses.
$$1+R_{t+1}=\frac{P_{t+1}+D_{t+1}}{P_t}$$
$R_{t+1}$: net yield
$P_{t+1}$: price of the financial asset
$D_{t+1}$: dividend

2. Present Value

Present value ($PV$) is the current worth of a future sum of money or stream of cash flows given a specified rate of return.
$$PV=\frac{FV_n}{(1+R)^n}$$
$FV$: future value $R$: interest rate

3. Gordon’s growth model

The Gordon growth model is used to determine the intrinsic value ($V_0$) of a stock based on a future series of dividends ($D_0$) that grow at a constant rate ($g$).
$$V_0=D_0 \frac{1+g}{R-g}$$
$R$: interest rate

4. Bond pricing
The price of a bond is the sum of the present values of all expected coupon payments plus the present value of the par value at maturity.

$$P_{bond}= \sum_{t=1}^T \frac{\text{Interest}}{(1+r_{it})^2}+\frac{\text{Par Value}}{(1+r_{iT})^2}$$

5. Duration

A measure of the sensitivity of the price (the value of principal) of a fixed-income investment to a change in interest rates. Given the relation between present value, future cash-flow and yield to maturity:$$PV=\frac{\sum CF_t}{(1+YTM)^t}$$
The second order Taylor polynomial is the following:
$$dPV=\underbrace{
                \left(
                      \frac{dPV}{dYTM}
                \right)dYTM}_{\textbf{Duration}}+
\underbrace{\left(
                      \frac{1}{2}
                \right)
                \left(
                      \frac{d^2 PV}{dYTM^2}
                \right)dYTM^2}_{\text{Convexity}}$$

$YTM$: yield to maturity

6. Convexity

For any given bond, a graph of the relationship between price and yield is convex. This means that the graph forms a curve rather than a straight-line (linear). The degree to which the graph is curved shows how much a bond's yield changes in response to a change in price.

$$dPV=\underbrace{
                \left(
                      \frac{dPV}{dYTM}
                \right)dYTM}_{\text{Duration}}+
\underbrace{\left(
                      \frac{1}{2}
                \right)
                \left(
                      \frac{d^2 PV}{dYTM^2}
                \right)dYTM^2}_{\textbf{Convexity}}$$

7. Liquidity premium

A premium that investors will demand when any given security cannot be easily converted into cash, and converted at the fair market value.

8. CAPM (Capital Asset Pricing Model)

A model that describes the relationship between risk and expected return and that is used in the pricing of risky securities. It can be estimated by simple OLS:
$$ER_i=R_f + \beta_i(ER_m-R_f)$$

$ER_i$: expected return of portfolio $i$, $ER_m$: expected return of the market portfolio, $R_f$: risk-free portfolio,  $\beta_i$:CAPM-beta of portfolio $i$


How is hyperinflation categorized, and how is it fixed? I have a few questions about hyperinflation that I’m really curious about:

I learned there are two types of inflation - demand pull and cost push. I was wondering if hyperinflation fits into the former category since printing too much money leads to increase in the money supply, lowering interest rates and increasing Investment and Consumption, moving the AD curve. So hyperinflation should be demand-pull right?
My textbook states that only with a strong credible fiscal policy can hyperinflation be fixed, but I don’t understand what it means. Does it mean that monetary policy is useless when it comes to hyperinflation? And does it mean that the solution to hyperinflation is “contractionary fiscal policy” or “expansionary fiscal policy?”

So hyperinflation should be demand-pull right?

The Weimar Republic in the 1920s is the classic example of hyperinflation. An oversimplified summary is that the Weimar Republic had to pay reparations that was way beyond what its economy could support: to put it differently, forced exports led to a heavily increased AD. And so this is a case of primarily demand-pull. In general, many hyperinflations start because of expenditure increases due to war, reparations, or poor government spending. I couldn't find a clear cut primarily cost-push hyperinflation trigger but it is theoretically possible to construct such an situation: stop all production of goods and services by raising the minimum wage to infinity and taxing inputs to infinity. Of course, probably a black market will just result. Once hyperinflation sets in, supply can often collapse as people stop investing in productive assets, so both demand-pull and cost-push apply.

  strong credible fiscal policy can hyperinflation be fixed, but I don’t understand what it means. Does it mean that monetary policy is useless when it comes to hyperinflation? And does it mean that the solution to hyperinflation is “contractionary fiscal policy” or “expansionary fiscal policy?”

You could trivially create hyperinflation by just unnecessarily printing increasing quantities of money. In this case, trivially adjusting your monetary policy to simply stop printing money is the solution. But it is important to remember that states almost never just print money for the sake of printing money: it is often a last choice that are forced to do to make some kind of payment (reparations, war, etc). And so the ideal solution is to stop the cause behind those payments, which is usually impossible. This would indeed be technically under the definition of contractionary fiscal policy. But to use the phrasing "contractionary fiscal policy is the solution" probably doesn't convey the severity of the situation: for example, case by case descriptions such as diplomacy (begging reparations to be reduced as in the case of the Weimar Republic) or ending the Second Congo War and self-dealing (in the case of Zimbabwe) will probably be more appropriate.


Does the value of a pure strategy Nash equilibrium(if exists) equal the value of the mix strategy Nash equilibrium in two-person zero-sum game? Given a two-person zero-sum game, a mixed strategy Nash equilibrium always exists and all such equilibria have the same value. A pure strategy Nash equilibrium, however, may not exist.

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

Pure strategy Nash equilibria are a subset of mixed strategy Nash equilibria, so as long as your statement

  a mixed strategy Nash equilibrium always exists and all such equilibria have the same value

is true, all pure strategy Nash equilibria will have the same value as well.


Random Choice interpretation Due to McFadden Economists usually interpret Random Choice, in the population sense, as each DM being drawn from the probabilistic choice rule independently and identically. However, Psychologist have maintained that individual DM are actually stochastic, in the sense that when presented with the same menu several times they would choose different alternatives. I am not fully convinced by either way of understanding probability in Decision Making, is there any work on understanding this, neuroeconomics, epistemological or anything related.
In short, what is the interpretation of random choice for an individual DM?

I don't feel these two interpretations are mutually exclusive, they belong to different sides of the same problem - one is empirical the other is theoretical. The conflict you seem to see between these two methods is that the "population" interpretation is individual specific. But the population component is a statistical convenience. It is "everything else" that the researcher has no time to model, and it is variation on the level of the population of observations not people - so it is not an individual specific error.

In fact, one acceptable interpretation of this convenience is that conditional on non-random components individuals are the same, and the errors are such that if presented with the same decision again the individual would make a different choice. This is precisely equivalent to your neurological interpretation. Extra structure on the random component may change the degree to which this justification applies - if errors for an individual are assumed to be correlated over time it decreases the relative impact of a neuroeconomic explanation and starts to be about unobservable heterogeneity on the level of the individual. But random utility can still easily encompass both explanations as answers to different sets of questions. The residual error will include both neuroeconomic reasoning and any variables that have been omitted.

To the extent that the randomness is specifically designed to capture "everything else" talking about what causes it is something most empiricists don't want to focus on. This being said, Michael Woodford has written something recently about neuroeconomics and random choice. And the "stocastic neural functions imply stochastic choice" is apparently a fairly common assertion in neuroeconomics: (see here, here, and here though some of these references point out that neuroeconomics places constraints on the form of random choice). But given the variables omitted in an average econometric study, I would hazard a guess that the random term captures relatively more of this omission and less of neurological processes.


Rationale behind teaching History in University I wrote an answer to this question regarding how economists evaluate a specific subject in a given curriculum.

Subjects which develop skills that have labour market significance are valuable to a curriculum from an economic perspective. However as an armchair economist I find it difficult to argue a for a reason why to teach a country's history or any world history at all if it has no labour market implications.

However we find that many high schools and universities require students to take electives in history. Why is this the case?

Please provide sources for your reasoning.

To understand why some countries are rich and others are not, we need to understand what happened to each of them in the past. How and why they developed depends to a large extent on events that took place decades or even centuries ago. This is what economists broadly refer to as path dependence. Brian Arthur was probably one of the first economists to point that out in the late 1980's.

Recently this type of arguing was appreciated again by mainstream economics. There is a growing number of scholarly articles that show how and why some countries developed the way they did. With huge implication for future economic development. Two good summaries are Nunn - The Importance of Economic History for Economic Development and Nunn - Historical Development. So the conclusion would somewhat be like that one can't ignore history if she wants to understand why some countries are poor. And more generally why some things are the way they are (one prominent example was the somewhat random event of why we have a QWERTY keyboard system that is a lot slower than other potential alignments of letters on a keyboard. It was determined once by "luck" let's say, and we never switched back...)

So all in all I would argue that knowing (and potentially understanding) some history is essential to understanding how our world works. It's certainly nothing that you can sell as a key feature in your CV (like a specific programming skill), but knowing sufficient history would certainly alter anyone's view of the world. And in order to not repeat huge mistakes that were made in the past (as a "society"), we actually need to know what they were and how and why they came about.


Is a small business owner without employees a capitalist? If a man has a small business where he is the only employee or if he is self employed, that makes him a capitalist?

For example a freelance writer. Or a subsistence farmer that only produces enough to feed himself and his family. Or a subsistence farmer that makes a little income on top of feeding himself and his family. Is there an income threshold that makes them capitalist?

(Bowing to peer pressure) According to original Marxist theory, no, he is not. Here, the defining characteristic of a capitalist is that he appropriates (as "profits") the surplus value that is created during the production process by other people's labor (capital does not produce surplus value).

Your freelancer or small business owner without employees appropriates only their own surplus value, created by their own labor. And it doesn't matter how large is their income, as long as they make it without employing other people as their employees.

According to some other theory? Well, somebody name the theory, and then we can clarify who is a capitalist and who is not, according to that other theory. Otherwise, it will be too much "personal opinion-based".