Why is this a zero sum game? The game is described as follows :

In a simplified version of the game Morra each of the players shows one finger or two fingers, and simultaneously guesses how many fingerss the other player will show. If both players guess correctly, or both players guess incorrectly , there is no payoff. If just one player, guesses correctly, that player wins a payoff equal to the total number of fingers shown by both players

I know that this game has to be zero sum but I want to understand well why it is the case, after all one player gains something which teoretically is not lost by the other in the sense that he had it before the game started. In this case, there is a situation in which the player who 'lost' the point could have win them but it is just the case because the game it's simmetric, it not always happens.
I thought about the following abstraction to explain what is happening, say the two players had before starting the game an amount of points so that to cover all the possible negative pay-off for them, and that who wins receives the number of points equal to the sum of the fingers from the other playes, now it seems to me that the game is zero-sum. Otherwise it seems to me that the pay-offs would be possible to be represented by
$$(\text{sum of fingers in the case of first wins something }, 0  )  \text{ or } $$
$$(0, \text{sum of fingers in the case of second wins something} )$$
which would make the game not zero-sum.
Should it be obvious? Am I totally wrong with my reasoning? Why?

A zero-sum game is one in which the players' payoffs sum to zero in every possible outcome of the game.
The given payoff description is incomplete. But if we assume that in the outcomes where only one player guesses correctly, the other player (who guesses wrong) would have to lose an amount equal to the total number of fingers shown (denoted $X$, say, to use @Bayesian's notation), then the game is indeed zero-sum:

In outcomes where both guess correctly or incorrectly, they each get $0$, which sum to zero.
In outcomes where only one guesses correctly, the correct guesser gets $X$ and the incorrect guesser gets $-X$, which also sum to zero.


Is debt servicing in the structural or cyclical budget balance? Are the interest payments on government debt to be considered in the structural or the cyclical budget balance?

I think, since it's independent on the state of the economy, then they should go to the structural budget balance, but I'm not sure.

The IMF methodology to determine the structural balance is given here: link to article.

I would summarise the methodology as: the sensitivity of budget components to the deviation of actual output from potential is estimated, as well as that deviation (the output gap). Taken together, that gives an estimate of the effect of the cycle on the budget balance.

It is unclear what estimates for their sensitivity of interest payments is, but since bond payments are contractually fixed, they are invariant to the state of the cycle. Only newly-issued debt costs are affected by current interest rates.

The only way that interest payments would be considered non-structural is that a steady-state interest rate is calculated, and this deviation from actual is used to determine the effect of the cycle. Based on the IMF document, this was not done in their methodology (on page 7, the author states that the only expenditure adjusted was  unemployment benefits). Realistically speaking, such an adjustment would be complex (how much are 10-year bond yields affected by current conditions?), and the effect is small in most countries (since the bulk of outstanding debt has long duration in most countries).


Following the prodtest manual they define omega as residuals from the model, that is
$$\omega_{it} = y_{it} − (\alpha + w_{it} \beta  + k_{it}\gamma)=y_{it}-\hat{y}_{it}$$
estprod does not have any comprehensible documentation but one way how we can get the above would be to extract the coefficients from the model and then calculate $y-\hat{y}$ manually.
We can do that with the broom package:
install.packages("broom")
require(broom)
coefs<-tidy(mod1)
# A tibble: 3 x 3
  statistic   bias std.error
      <dbl>  <dbl>     <dbl>
1     -3.71   4.77      2.35
2     10.5  -11.8       4.26
3      1.73  -2.14      1.64

the names are off but the first column gives the same coefficients as when I inspect the model with summary so they are correct.
Next we can just can just calculate $y-\hat{y}$ as
omega_1 = (data$Y - data$Labor*coefs$statistic[1] - data$Capital*coefs$statistic[2] - data$Materials*coefs$statistic[3])

the code is inelegant but it should do the job.
As a side note it might be worth while considering to estimate the TFP without these packages. Normally packages are the R's biggest strength but in this case estprod does not have any good accompanying documentation or manual and the prodest does not have the possibility to add the gross output yet as in the link the devs mentioned. In cases like this it might be better to just program your own function.


Alternative to Intermediate-macroeconomics book by Mankiw Please suggest a good alternative to intermediate macroeconomics by Mankiw. A book with better teaching and which develops better understanding but at a similar level in terms of difficulty. I personally do not like mankiw's book. I can understand concepts at superficial level but do not get in depth understanding.

I would highly recommend Blanchard's Macroeconomics, especially for the short and medium run.
Another book to look at, especially for the long run and growth is Burda and Wyplosz (2012)


Are any of these tax dodging schemes actually realistic or exclusive to billionaires? So there's been quite a bit of fuss over how the rich supposedly pay lower taxes (proportionally of course) than regular, hard-working Americans because of various tax schemes that "let the rich get richer"

This website - http://www.salon.com/2013/04/12/10_tax_dodges_that_help_the_rich_get_richer_partner/

probably makes the boldest claims - according to it, a billionaire could

avoid even capital gains taxes by borrowing money because the tax isn't due until the shares are sold (and they don't ever need to be sold) - but wouldn't the interest rate over 30 years wipe out the savings? Also, couldn't a regular person do that too?
It then (on #3.) it describes bartering - but I thought bartering was still taxable?
(on #4) it then describes fake charity scams - but wouldn't the IRS (not to mention some other federal agencies) audit multi-billion dollar charities for that?
(on #5) Couldn't a regular employee convince their boss to pay for their car "on paper" and split the tax savings?
(on #6) I always thought you'd go to jail for that stuff?
(on #7) Again, seems like just some more regular business expenses that incentivize R&D
(on #10) I don't understand how an IRA would benefit a billionaire more than a millionaire. Actually, 401(k) plans seem to be better than dividend stocks since they aren't taxed until it's converted to cash.

I understand the core point of your question as, "Do people with extremely high incomes pay proportionately less in taxes than average Americans?"

Yes, extremely-high-income individuals do pay a lower percentage of their income in taxes than do upper-middle-class and high-income households, and even more than many middle-income households, but they tend to pay more in taxes than low-income households.

This is due to a number of reasons, but it has less to do with elaborate tax strategies than it does the simple fact that people with very high incomes tend to derive a larger share of that income from dividends and capital gains than from normal cash compensation. Both of these have lower marginal tax rates than are paid to people who receive relatively high cash compensation— the top tax rate on dividend and long-term capital gains is 20%, which is roughly equal to the effective marginal income and payroll tax rate paid by the top 20% of income earners.

From the Brookings Institution/Urban Institute Tax Policy Center, we can see the total average effective tax rates for different groups (for 2011, the most recent year for which detailed data have been released, but things haven't changed much since then):

   Quintile  Avg Eff Tax Rate
      0-20%:  1.9%
     21-40%:  7.0%
     41-60%: 11.2%
     61-80%: 15.2%
     81-90%: 18.6%
     91-95%: 21.1%
     96-99%: 24.3%
     Top 1%: 29.0%
    Top 400:  <20%

The last line of the table is from the IRS Statistics of Income division, which publishes a distribution of the average effective tax rates for the 400 taxpayers with the highest adjusted gross incomes:

 Rate    Number
 0-10%    32
10-15%   147
15-20%   123
20-25%    40
25-30%    28
30-35%    30
  >35%     0

So you can see that the average effective tax rates rise sharply as you go from the poor to the middle class, then more slowly as you move from the upper middle class through to the top 1%, but once you get to the very top, the 0.1% and 0.01% of income earners, they do actually pay less proportionately in taxes than many middle-income families.

Finally, it's important to note that these statistics will tend to understate the degree to which people with extremely high incomes pay lower taxes than those with moderate incomes to the extent that those with high incomes make use of schemes (like the ones in the linked article) that lower their AGI.

To quickly answer your more specific questions:

No, regular people can't borrow against unrealized capital gains, because by definition, regular people don't own large amounts of capital.
Federal income taxes don't apply to a swap of similar assets (i.e., real estate for real estate). You're probably thinking about "barter clubs," which do trigger tax consequences, but those aren't like-kind exchanges, they're barter exchanges (they're not similar assets).
These aren't "fake" charities that are being described, they're real charities (if I recall correctly, they're required to spend 1% of their endowment annually on charitable purposes, which is more than offset by gains on capital income in most years). This is in fact a real and common tax-avoidance strategy that is entirely legal.
No, a regular person could not legally do this— there has to be a business justification for something to count as a business expense, and while a taxi home from work when working late counts as a business expense, personal autos don't meet the test.
If a tax strategy hasn't been determined to be illegal before it's tried, only civil penalties (i.e., no jail time) apply if it's ruled to be invalid.
The tax benefits they describe in #8 accrue to corporations, which are disproportionately owned by wealthy individuals. (See page 156 of this FRB chart deck on the results of the most recent Survey of Consumer Finances for a quick overview of who owns financial assets in the US.)
You're right that IRA plans benefit all very-high-income individuals equally, but they do provide greater benefits to high-income individuals than middle-income individuals (who are less likely to be able to contribute the maximum).


Monopoly's MC, AVC and TVC I do not quite understand the statement "total variable cost is the area under the marginal cost curve" Does it means MC inserts at the AVC at the lowest point (see picture)? But why AVC is drawn and not TVC?

Total variable cost would not fit on that graph: total cost has units of "dollars", while the axes of the graph are "items" and "dollars per item"

But you can multiply the two together, which implies that areas on the graph are measured in dollars.

For example, below the pale blue area is the total variable cost for the quantity shown, while the pink area is the total cost


Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/eigenvector I'm trying to understand the tools used/presented in Lars Hansen's Econometrica paper "Dynamic Valuation Decomposition within Stochastic Economies." In a part in the paper, Hansen introduces a long-term approximation. This approximation first requires us to solve for a principle eigenfunction of a kind of conditional expectation operator. As an exercise, I'm trying to solve the following example.
$\newcommand{\E}{\mathbb E}$
Suppose that
$$
X_{t+1} = A X_t + B W_{t+1}
$$
where A has stable eigenvalues and $\{W_{t+1} : t = 0,1,... \}$ is an iid sequence of multivariate standard normally distributed random vectors. Suppose that
$$
\log M_{t+1} - \log M_t = D \cdot X_t + F \cdot W_{t+1}.
$$
I want to show that there exists a solution to the equation
$$
\E \left [ \frac{M_{t+1}}{M_t} e(X_{t+1}) \mid X_t = x \right ] = \exp(\eta) e(x) \tag{1}
$$
for $\log e(x) = H \cdot x.$ I also want to compute that value of $\eta$.

Progress:

The beginning of the problem is straightforward. Using the properties of log-normal random variables, we can calculate from (1)
\begin{align}
\exp\{ (D' + H'A) x + \frac 12 (F' + H' B)'(F' + H'B)\} &= \exp\{\eta + H' x\} \\
(D' + H'(A - I)) x + \frac 12 (F' + H'B)'(F' + H'B) &= \eta.
\end{align}
This is probably a simple question from here. It seems clear that a solution exists, and I have solved for $\eta.$ But from what I understand, solving this problem involves making a "guess" that $e$ was linear in $x$. I don't know what $H$ is. Thus, I need to solve for $H$ and $\eta$. How would I do this?

Note: This problem is related to this problem about the "Decomposition of an additive functional into a Martingale part and other."

The progress given so far appears to be correct. Finishing this problem just requires us to argue that $H$ must be chosen so that the equation
$$
(D' + H'(A - I)) x + (F + H'B)'(F + H'B) = \eta
$$
holds for all $x$. Thus, we must have $D' + H'(A - I) = 0$ and, consequently,
$H' = D'(I-A)^{-1}$. This implies that $\eta = (F' + H'B)'(F' + H'B)$.


Is the S&P 500 now in a boom-bust cycle? This question was originally posted at money.stackexchange but was moved here per a commentor's suggestion after the question was put on hold for being opinion-based.  The original question was:

  When I google "SP500" I get the following chart:

  Isn't this a boom-bust cycle, that's overdue for a "correction" that
  drops everything back down to below the 1,000 level like in 2002 and
  2009? What are the arguments against such a prediction?

The first comment someone posted argued against a drop but was confusing because it claims drops can happen from "causal forces" other than cycles.  That actually sounds like an additional reason for a drop (causal forces, not just cycles) although I wouldn't understand how a cycle would be established or maintained without causal forces in the first place.

It also claims "you would only expect it to come back down on schedule if you believe that it goes up and down on schedule".  That sounds like "if there's a cycle, it will go up and down", but doesn't make it clear how you determine if a cycle is happening.

The second comment says "markets always move in cycles" although the first half of the graph doesn't seem to back that up.

The third comment says "in the long term the markets have exponential growth" although it then cherrypicks the portions of the graph that reflect that (in effect replacing a "long term" argument with "short term" examples).  And exponential growth can't happen forever, right?

The final comment suggest a log graph, though none is offered.  My first search result for a log graph led to this page, which actually seems to make the case the market is always cyclic, although it throws so many numbers around in such a complicated fashion I'm not left with a sense of real understanding.  (I also find it odd to compute things like annualized growth rate over 140 years, when any individual's investing career probably rarely exceeds 60 years, and most investors probably average much less.)

Returning to the original question, is there any argument the market is not cyclic, and not overdue for a substantial drop?  Also, is there any measurement indicating whether investors believe that, and are exiting index funds?

Here's the Efficient Market Hypothesis (EMH) explanation for why one cannot say that a correction is overdue:

Suppose that it were widely known that, by looking at the above figure, one could ascertain that the market was "due for a drop" one week from now. Financial analysts and investors would look at the graph and come to this conclusion. How would people respond to this knowledge? They would go and sell their stocks before those stocks loose a substantial portion of their value. However, this flurry of selling activity would cause the price of the stocks (and hence the stock index) to fall today—one week earlier than forecast.

This example is obviously a highly simplified and stylised exposition of how markets function, but it should serve to make clear the basic point: any hypothesised means by which one can look at a chart like this and forecast the future movement of prices is automatically self-defeating and any information about the future of the market is instantly built in to the current price of securities. The drop you think might be due will come, says the EMH, if and only if new information about the economy becomes available that suggests the economic outlook is less promising that people had thought.


Why should the statistical value of life exist? In areas such as insurance pricing and government policy analysis, it is often necessary to assign human life a monetary amount in order to compare it with other monetary amounts.  So economists have a measure called the statistical value of life, which in some sense quantifies how much a person values his own life.  It's usually calculated to be about 10 million dollars for most people.  Now this isn't literally the dollar amount a person puts on his life, because that amount is usually infinity; it's possible that no amount of money would convince the average person to give up his own life, and the average person would be willing to spend any amount of money to save his own life.  So the technical definition is trickier: the statistical value of a person's life is the dollar amount $X$ such that for all probabilities $p$, or at least all values of $p$ relatively close to 0 the person would be indifferent between a situation where their chance of dying is $p$, and a situation where their chance of losing $X$ dollars is $p$.  (An equivalent definition can be given in terms of reducing your chance of death and gaining money.)

My question is not about why this concept is useful; I understand its utility.  (No pun intended.)  My question is, why should the statistical value of life exist at all?  That is to say, why should there exist a single value of $X$ that satisfies this definition for all values of $p$, or even all values of $p$ that are sufficiently close to $0$?

Let's discuss this more formally.  Let $A$ is the set of possible preferences, and let $G(A)$ be the set of "gambles" or "lotteries" over $A$.  Then the von Neumann-Morgenstern theorem states that if a person's preference ordering over $G(A)$ satisfies certain rationality axioms, then the person's preferences can be represented by a utility function $u: A → ℝ$. That means that the value that a person puts on any lottery $L$ is the expected value of$u$ under the probability distribution of $L$.

So I would not be surprised at all if a person was indifferent between a 1 percent chance of getting 10 dollars and a 1 percent chance of getting a chocolate sundae, and was also indifferent between a 2 percent chance of getting 10 dollars and a 2 percent chance of getting a chocolate sundae; that would just indicate to me that the person's preferences satisfy the von Neumann-Morgenstern rationality axioms.  But I don't understand why, if a person was indifferent between a 1 percent chance of losing 10 million dollars and a 1 percent chance of dying, they would necessarily also be indifferent between a 2% chance of losing 10 million dollars and a 2% chance of dying.  That's because living and dying do not comport with von Neumann Morgenstern axioms; the average places the utility of survival at infinity, and yet they assign finite values to small risks of dying.  So I see no reason why lotteries involving risks of living and dying should obey the von Neumann-Morgenstern axioms.

And yet empirically, it seems that studies have found that the statistical value of life is a well-defined and measurable quantity, at least for sufficiently small values of $p$.  So what is the reason for this?  What is the reason that lotteries involving small risks of dying obey the von Neumann-Morgenstern axioms, when living and dying themselves do not?

You asked:

  why should there exist a single value of $X$ that satisfies this definition for all values of $p$, or even all values of $p$ that are sufficiently close to $0$

There isn't such a value. I would hope that no one claims that there is.

The statistical value of life is a (somewhat lazy) calculation of convenience. Lots of business case protocols need a value for anything that's going into the business case. Changing the probabilities of survival is an outcome of many interventions for which the decision-makers have insisted on business cases, so some method is needed to value these probabilities.

One of the earliest ways to do this, back when relevant research was scarcer than it is today, and computational power was much more limited, was to assign a single value of life, which was calculated using methods that assumed a priori that there existed a single value of $X$ that was an adequate approximation for all values of $p$ that are sufficiently close to $0$.

That method is still used today largely due to institutional inertia.


Robust Standard Errors for Control Function Approach? I need to know how to find robust S.E. for the CF approach to endogeneity.

Consider the model:
$$y_i=X_i\beta_1 + W_i\beta_2+\epsilon_i$$

Assume:
$$E[X_i\epsilon_i]=0$$
$$E[W_i\epsilon_i] \neq 0$$

Thus, $W_i$ is endogenous.

Now, let:
$$E[Z_iW_i] \neq 0$$
$$E[Z_i\epsilon_i]=0$$

The control function approach:

$W_i = \gamma_1 X_i + \gamma_2 Z_i + \phi_i  $
$\epsilon_i = \alpha \phi_i + \chi$

now we replace $\epsilon_i$ in our original equation:

$$y_i=X_i\beta_1 + W_i\beta_2+ \phi_i \alpha + \chi$$

where now we have $E[W_i \chi]=0$

Intuition: I think I used the series of linear projections to 'control' for the endogenous portion of $W_i$.

EDIT: I originally typed this incorrectly. I have changed the relevant orthogonality condition. Here is the intuition behind the (correct) orthogonality condition $E[W_i \chi]=0$:

Since $W_i$ is a linear function of $X_i , Z_i$, and both are themselves orthogonal  to $\chi$, we obtain the given orthogonality condition.

Okay - the question. I think that $\hat \beta_{2.CF} \equiv \hat \beta_{2.OLS} \equiv \frac{cov(W_i,Y_i)}{Var(W_i)}$

If this is correct, do I just use the R.S.E. form that I use in OLS if I want heteroskedasticity robust S.E. when using the C.F. approach?

123, the CF method is a specific case of when we have generated regressors. Check the appendix to chapter 6, pages 157-160, for the asymptotic covariance matrix of $N^{1/2}(\hat\beta_{CF}-\beta)$. The expression is truly enormous. ;)

Instead I will just cite wooldridge on page 160, 2nd paragraph:

«If $\mathbf{G}\neq \mathbf{0}$, then (...). Neither the usual 2SLS variance matrix estimator nor the heteroskedasticity-robust form is valid in this case.»The $\mathbf{G}\neq \mathbf{0}$ is the case when we have generated regressors.

Good luck ;)


Inelastic offer, tax paid by seller, who supports the charges I have a small problem, I have a situation where we have a perfectly inelastic offer and a normal demand, then there is a tax that is paid by the supplier who supports the totality of the charges ? Is it not the buyer ? Since the supplier can just lower his production ? I need some explanation om this thanks and sorry for my bad english.

If "supply is perfectly inelastic" it cannot be the case that the supplier can "just lower his production". The point of "perfectly inelastic supply", is exactly to represent the case, where the supplier will offer a specific quantity at whatever price, even zero.  The classic case here is a good that is it deteriorates quickly in terms of quality or even consumption safety (say fresh foods).

The equilibrium price is then determined by demand. If the state appears and wants to take a chunk out of the price by imposing a tax, the tax will fully burden the supplier.

Of course this is the static approach. In a dynamic setting, such a situation may for example create incentives for an unofficial market, where the supplier tries to hide sales from the state in order to reduce the tax burden.


What would happen if the world switched to a single currency? What would happen if all countries suddenly stopped using local currencies and adopted a global currency (like the Euro, but for everyone)?

The Euro was always conceived by most Economists as a political goal, not an economic one.

Prologue: There is the theory of Optimum Currency Areas (OCA) which characterizes properties that a larger area would need to have if it were to operate on a single unit of currency. Since the announcement of the Euro around 1990, there were many papers that looked into whether the European Area actually satisfied the broader range of these criteria, and they mostly agreed that it did not.

Ex-post, we can now see this playing out as the ECB has a hard time setting up an inflation rate that is improving conditions of countries that are hit very badly by the crisis such as Greece and Spain, and countries which are not, such as France and Germany.

Intuition behind OCA

Basically, a country gives up the tool of monetary policy when it subordinates into such a currency union. In order to properly use monetary policy for a set of different economies (countries), you need these to be very similar in nature: If all countries react similarly to a housing bubble / oil shock / etc, you can easily improve outcomes for all countries with the same monetary tool. If the countries respond differently, it is much harder to do so.

Single currency for non-OCA

To the extent that all countries in the world are very different in nature, your experiment is similar to the gold standard (see Bretton Woods system). We think about that system mostly as a failure. While there is no hard data on the causal relationship, countries that abandoned the gold standard earlier tended to do better. We observed similar trends for countries that abandoned the dollar standard earlier. As a short intuition, among other explanations, when you abandon monetary policy and fix your exchange rate, you make yourself more vulnerable to inflation/deflation of other regions.


Since it doesn't change the money supply, how can an "expansionary" fiscal policy alone spur economic growth? I understand how monetary policy can be used to heat up an economy by increasing the money supply, but how can a fiscal policy do so? When the government borrows money to increase spending, it is not as if that money would have just been sitting under somebody's mattress; it would have been loaned to some other entity, whose spending of that money (as far as I know) would cause just as much economic activity as if the government spent it. In addition, the government's demand for money would should raise interest rates and/or strengthen the dollar, which is the opposite of what I generally think of when it comes to an "expansionary" policy. Also, while money could be lent by entities in other countries, that money would just have to flow back out in the form of more imports, so domestic AD shouldn't be affected, no?

The only thing I can think of is that the government can spend 100% of the money that it borrows, whereas if that money went into a bank account, a small portion would not be lent out due to reserve requirements; does that make all the difference?

It's been years since I took an econ class, and I know this is 101 stuff, but I can't figure out what I'm missing...

In an open economy, Government might be borrowing money from abroad and so the logic of how that capital might have anyway been employed to a  productive end doesn't work out. (Also sale of forex reserves or taking up loans would depreciate domestic currency leading to increased exports and higher AD).

Also, money supply itself doesn't determine the pace or level of economic growth. It is the consumption and Saving patterns that spur demand, leading to the virtuous cycle of increased incomes and investment.

Provided that the C and S patterns are themselves a function of trust and market expectations (especially during times of economic crisis such as recession or slowdown), government through it's expansionary fiscal policy and the popular credence attached to it, incentivise increased activity and growth.


Are monopolies always price makers? I have the following True/False question:

  A single price-taking firm on the market is called a monopoly.

As far as I know, a monopoly is a price maker not a price taker. That being said if it is a single firm how in the world can it not be a monopoly?

In my opinion, the answer to this question is False.

Could anyone possibly explain to me if my way of thinking is correct? and if a monopolistic firm can be a price taker?

Thank you very much

You are correct. A monopoly is a price maker. Not a taker.

A monopoly has the power to influence the price it charges as the good it produces does not have perfect substitutes. A price maker within monopolistic competition produces goods that are differentiated in some way from its competitors' products.

I suppose a monopolistic firm could be a price taker via matching random re-sellers prices on singular items, however that would be operating at a loss a majority of the time. The idea with that though is to retain the customer business for the future, not to make a single small profit on one item, one time.


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

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

Isn't the mixed extension of matching pennies a good example of this? The strategies $p,q$ are both elements of $[0,1]$, and
$$
\begin{align*}
U_1(p,q) & = pq + (1-p)(1-q) \\
\\
U_2(p,q) & = p(1-q) + (1-p)q.
\end{align*}
$$
There is a unique Nash-equilibrium at $p = q = 1/2$ but all $p$ and all $q$ are rationalizable, because in the equilibrium all strategies are best responses.

Even if you were to edit your definition of symmetry to include symmetric utility functions, a game with
$$
U(p,q) = -(1/2 - p)^2 \cdot (1/2 - q)^2
$$
yields the same result.

If you insist on some shrinkage one could easily edit the utility function to
$$
U(p,q) = - 1 \text{ if } p+q \leq 6/10.
$$
Then some strategies - the ones under $1/10$ - would not be rationalizable.


What is a good handbook for behavioral economics? I recently got interested in behavioral economics because it seems to have a lot of interesting applications in other fields such as macroeconomics. I managed to find a lot of interesting sources on development of behavioral models but I would like to get my hands on some handbook that is a behavioral economics' equivalent of lets say Varian Microeconomic Analysis or something like MWG microeconomic theory. Are there some comparable behavioral handbooks?

Sanjit Dhami's The Foundations of Behavioral Economic Analysis is arguably the most comprehensive review of the work in behavioral economics to date.


A graphic calculator for simple microeconomics problems I can do simple calculations in micro-economics, such as: given the utility function of a consumer, calculate his demand curves; given utility functions of two consumers and initial endowment, calculate the competitive equilibrium; etc. However, the calculations become tedious and I am looking for a software that can do them automatically. For example, I am looking for a software where I can:

Define utility functions, e.g. $u_1(x,y) = x^2 y$, $u_2(x,y) = x y^2$;
Define initial endowments $(x_1,y_1)$ and $(x_2,y_2)$;
Find and plot all the Pareto-efficient allocations;
Find and plot all the envy-free allocations;
Find a competitive equilibrium.

Is there a software that can do this? Or maybe a package for a general symbolic math software?

I wrote some silly program where you just fix endowment $e=(e_1,e_2)$ and utility functions $u=(u_1(x_1,y_1),u_2(x_2,y_2))$. The example provides an illustration for your utility functions and $x_1+x_2=1$ and $y_1+y_2=1$. I've drawn 100 indifference curves on an equally spaced grid of given utility levels $\bar u_1\in[u_1(0,0),u_1(1,1)]$ (blue) and $\bar u_2\in[u_2(0,0),u_2(1,1)]$ (red). The black line is the contract curve.

I added a second figure with some initial endowment $e_1 = (0.25, 0.75)$, $e_2 = (0.75, 0.25)$ and core.

e1 = [0.25 0.75];
e2 = [0.75 0.25];

X = 0.0:0.01:(e1(1)+e2(1));
Y = 0.0:0.01:(e1(2)+e2(2));

syms x1 y1 x2 y2 u1_bar u2_bar

u1 = x1.^2*y1;
u2 = x2*y2.^2;

I1_fun = matlabFunction(solve(u1_bar == u1, y1, 'PrincipalValue', true));
I2_fun = matlabFunction(solve(u2_bar == u2, y2, 'PrincipalValue', true));

u1_x = diff(u1, x1);
u1_y = diff(u1, y1);

u2_x = diff(u2, x2);
u2_y = diff(u2, y2);

u2_x = subs(u2_x, [x2,y2], [X(end) - x1, Y(end) - y1]);
u2_y = subs(u2_y, [x2,y2], [X(end) - x1, Y(end) - y1]);

contract_curve = matlabFunction(solve(u1_y/u1_x == u2_y/u2_x, y1));

u1_min = double(subs(u1, [x1,y1], [X(1), Y(1)]));
u1_max = double(subs(u1, [x1,y1], [X(end), Y(end)]));
u1_Array = linspace(u1_min, u1_max, 100);
I1_Array = zeros(length(X), length(u1_Array));

for i = 1:length(u1_Array)
I1_Array(:,i) = I1_fun(u1_Array(i), X);
end

u2_min = double(subs(u2, [x2,y2], [X(1), Y(1)]));
u2_max = double(subs(u2, [x2,y2], [X(end), Y(end)]));
u2_Array = linspace(u2_min, u2_max, 100);
I2_Array = zeros(length(X), length(u2_Array));
for i = 1:length(u2_Array)
I2_Array(:,i) = I2_fun(u2_Array(i), X);
end

hold on
[AX, H1, H2] = plotyy(X, I1_Array, 1-X, I2_Array)
set(AX(:),'YLim',[0 1]);
set(AX(:),'YTick',[0:0.1:1])
set(H1(1:length(u1_Array)), 'Color', 'b');
set(H2(1:length(u2_Array)), 'Color', 'r');
set(AX(2),'YDir','reverse')
axis(AX,'square')
%str1 = '\bullet e=(e_1,e_2)';
%text(e1(1),e1(2),str1)
plot(X, contract_curve(X), 'k', 'linewidth', 2)
hold off


Log linearising (Gali textbook) In Gali (2015)'s textbook Monetary Policy, Inflation, and the Business Cycle, variables in levels are denoted with capital letters, logged variables with lowercase letters.

However, when a log-linearisation is performed, say of the household optimality condition, why is the result in logs and not in percentage deviations, (lower case letters with a hat, for instance)?

Is there an intermediate step/reason for why we can go from percentage deviations to logs? Thanks!

$$\frac{x_{t+1}}{x_t} \equiv \frac{x_{t}+Δx_{t+1}}{x_t} = 1+\frac{Δx_{t+1}}{x_t}$$

Further,

$$\ln (1+a) \approx a,$$

an acceptable approximation for $|a| <0.1$ and certainly for $|a| <0.05$.


Saving increasing in interest rate Romer equation 2.55 on the Diamond model, says:

  Let $s(r)$ being the fraction of income saved, $r$ the interest rate,$\rho$ the discount rate, and $\theta$ the household's willingness to shift consumption between periods, with

  $$ s(r) = \frac{(1+r)^{(1-\theta)/\theta}}{ (1+\rho)^{1/\theta} + (1+r)^{(1-\theta)/\theta} } $$
  implies that saving is increasing in $r \iff (1+r)^{(1 - \theta)/\theta)}$ is increasing in r; equivalently $ds / dr > 0$ if $\theta < 1$

Is the first statement related to monoticity?  Also, how to show this graphically, that is to show, $s(r)$ a function of $\theta$?  Considering this, plotting $(\theta, s(\theta, r=.1))$ I do not see a change at $\theta=1$, but when I graphed $(r, s(r))$ with values $\theta=0.5,$ and $\theta=1.5$ I saw the desired change in orientation.  Which way is right?

$$y = \frac {a(x)}{b+a(x)} \implies \frac{\partial y}{\partial x} = \frac{\partial y}{\partial a}\cdot \frac{\partial a}{\partial x}$$

Since

$$\frac{\partial y}{\partial a} = \frac {b+a -a}{(b+a)^2} = \frac {b}{(b+a)^2} >0$$

because in your case "$b$"$>0$,

the sign of $\frac{\partial y}{\partial x}$ will be the same as the sign of $\frac{\partial a}{\partial x}$, which is what Romer is asserting.

$\theta >1$ would make $\frac{\partial a}{\partial x} <0$, so

$$\theta <1 \implies \frac{\partial a}{\partial x}>0\implies \frac{\partial y}{\partial x}>0$$


Solow Growth Model. Steady State. Can someone explain please? my lecturer is doing a rather poor job explaining what he's written down, so I'm wondering if someone would be able to explain the following graph for me?

This is a part of the Solow-Swann Growth Model lecture for Macroeconomics, and he's talking about the equilibrium that this model predicts, k stands for capital per worker, s is savings rate, z is technology, d is depreciation rate, n is population growth rate. My confusion is with the Y axis. How does an axis represent two equations..?

An axis is characterized not by the variable it measures, but by the unit of measurement. So an axis can measure any number of variables, as long as they are measured in the same measurement unit.

In your case, the unit of measurement is "units of output", and both $(n+\delta)k$ and $sf(k)$ are measured in it (capital is measured in units of output, in case you wonder).


What's a good alternative to Romer's Advanced Macroeconomics? I am not liking Romer's Advanced Macroeconomics. I feel like it demands a stronger intuitive knowledge of economics than I currently possess, and on the other hand, it is not as theoretically strong and deep.

While I am trying to increase my intuition ... is there an alternative that covers roughly the same as Romer's book, but actually goes in-depth with all of the issues at a deep theoretical level, rather than just treat it intuitvely?

I like Introducing Advanced Macroeconomics: Growth and Business Cycles by Sorensen and Whitta-Jacobsen. The text provides intuitive explanation and exposition of models. The book is neither too mathy nor descriptive, I would say, they offer somewhat balanced introduction.

A similar question was submitted before, have a look here.


What would be the impact on value of a country's assets and trade balance if its residents choose to increase their savings What would be the impact on value of a country's assets and trade balance if its residents choose to increase their savings by investing in overseas assets and why?
May please help with this question family.

An article on this topic:
https://www.investopedia.com/articles/personal-finance/022415/top-10-countries-save-most.asp
Generally economists would say that savings are bad for the growth because they decrease amount of money in the economy. Smaller group would say that savings are good because of higher stability, more thoughtful spending. There is no universal consensus on this question, but we can look at the data.
Countries where people save are usually less stable, get their money from resources. Probably this makes people realise that personal savings may improve stability. And low taxes make people save more too.
Data for europe and household savings:
https://howmuch.net/articles/saving-rates-around-the-world
It seems people save where they can. If they have growing income they save more. If they have large taxes or stagnation they save less. I dont know what will happen if people would change their saving behaivor contrary to the country's situation. If its too sharp change, economy would suffer, as with any change. If it is smooth, it could increase the growth, assuming international trade is significant enough to compensate reduced internal consumption.


Showing that the elasticity of arrival rate for workers wrt $\theta$ is between $0$ and $1$ Let $L=E+U$ where $L$ is labour force, $E$ is number of employed, and $U$ is unemployed people.

Let $u = \frac{U}{L}$ and $v = \frac{V}{L}$.

Given $m(u,v)$ as a matching function that determines the flow of matches between workers and firms, and assume $m$ has constant return to scale (CRS) in the two arguments $u$ and $v$.

The elasticity of the arrival rate for workers is given by $$\theta q(\theta),$$ where $\theta = \frac{v}{u}$ represents "tightness" in the labour market.

Elasticity ($\epsilon$) = $$\frac{\mathrm{d} f(x)}{\mathrm{d} x} \frac{x}{f(x)} = \frac{\partial m}{\partial \theta} \frac{\theta}{m(1,\theta)},$$

where $\theta q(\theta) = m(\theta^{-1},1) = m(1,\theta)$ (by using CRS property of $m$ in the two arguments $u$,$v$).

The rate at which unemployed workers find job: $$\theta q(\theta) = m(\theta^{-1},1)=m(1,\theta),$$ since the matching function, $m$, is constant returns to scale in the each argument.

Since $\theta q(\theta) = m(1,\theta)$, $$\frac{\partial m(1,\theta)}{\partial \theta} = q(\theta) + \theta q'(\theta).$$

So the elasticity of the arrival rate for workers, $$\epsilon = \frac{\partial m}{\partial \theta} \frac{\theta}{m} = \left [q(\theta) + \theta q'(\theta)  \right ] \frac{\theta}{\theta q(\theta)} = 1 + \frac{\theta q'(\theta)}{q(\theta)}$$.

Since $q'(\theta)<0$, $\epsilon<1$, but how can I formally show that it is between $0$ and $1$?

Let $m$ cobb-douglas. This means $m(u,v) = A u^\alpha v^{1-\alpha}$ for $\alpha < 1$ and $q(\theta) = A \theta^{-\alpha}$.

Then

$$\frac{\theta q'(\theta)}{q(\theta)} = -\alpha > -1$$

To what extent this holds for other functional forms I'm not sure, but I haven't seen anything but Cobb-Douglas being used as the matching function.


Relationship between government expenditure and exchange rate? I've read an increase in government expenditure can lead to increase the chances of currency crisis but shouldn't it lead to the opposite?
Fiscal deficit ----> Govt will undertake borrowings ---> crowding out -----> interest rates will rise ----> capital inflows -----> rise in forex/international reserves
what is wrong with my reasoning/logic?

The relationship between government expenditure and exchange rate is an important one. The key question in current policy and academic debates is What are the effects of fiscal policy on aggregate economic activity in a globalized world?
The central challenge in this debate is how to identify fiscal shocks in the data. Auerbach and Gorodnichenko (2015) address this challenge by using daily data on US government spending. Exploiting this high-frequency data, they find that unexpected government spending instantly affects exchange rates and the dollar appreciate, which if I understand correctly supports your intuition.
The direction of the response of the exchange rate is consistent with basic macroeconomic theory; in an economy with a flexible exchange rate, government spending shocks should lead to appreciation of the domestic currency.


Extraction and royalty time path for a non-renewable resource under a monopolist assumption I am trying to understand the time path of extraction and royalty (price) for a non-renewable resource under a monopolist framework.
The problem is that in the main books on environmental/resource economics and in the resources that I could find on internet the "results", either quantitative or qualitative, are given without proof, and the assumptions are not given ("most cases" :-( ).

Using optimal control, I have no problem to find that the Hotelling rule is here applied to the marginal profit over the extraction quantity, or that its discounted value remains constant and it is below the market price.
But what are the specific assumptions required to claim that (a) the initial price is higher than under perfect market competition/benevolent social planner; (b) that the depletion time is longer and finally (c) that the growth rate of price is lower than the (constant) growth rate of marginal profit ?

I would say that (a) follows from a downward sloping demand curve that causes marginal revenue to decline faster than price. As you write a monopolist accounts for that and to maximize profits thus extracts less to drive up the price. That also explains why generally exploitation would take longer.

That this is not always the case is shown by Stiglitz's (1974) Monopoly and the Rate of Extraction of Exhaustible Resources  where he shows that the extraction path for the monopolist and perfect competition are the same for a constant elasticity demand curve and zero extraction costs. That in turn, has been shown by Gaudet and Lasserre in "On comparing monopoly and competition in exhaustible resource exploitation" to depend on the fact that the resource stock is fixed and hence it is sometimes hard to restrict output to increase the price.

Lewis et al. provide examples where the monopolist may be more excessive than socially optimal


How do economists model VNM-rationality violation? This question concerns the need to generalise utility maximisation, the fact that it's a special case of a general problem familiar to physicists, and the question of whether economists have affected a similar generalisation or instead taken a different approach. A precise statement of my question is bold below, after some theoretical exposition.

A common model of preferences in economics is that agents choose to maximise the mean of some utility function. If the utility $U\left(x,\,\phi\right)$ depends on a random variable $x$ (possibly containing multiple parameters $x^\mu$) of pdf $f$ and a user-chosen $\phi$ (on which $f$ may or may not depend), we seek to minimise $S:=\int dx\mathcal{L},\,\mathcal{L}:=-Uf$. (I'm using a physicist's notation, but this sort of mathematical problem is common to both fields.) If only $x$ were known (viz. $f=\delta\left( x-x_0\right)$), $\phi$ could be chosen to maximise $U$; the $\phi$ which does this is in general a function of $x$. Generalising to random $x$, the solution is given by $0=\frac{\partial\mathcal{L}}{\partial\phi}$, an algebraic equation that can in principle be rearranged to express $\phi$ in terms of $x$.

Maximising mean utility is equivalent to having preferences satisfying the von Neumann-Morgenstern axioms, but some empirical results such as the Ellsberg urn violate these. One possible explanation is that Knightian uncertainty bothers people, i.e. people prefer investment opportunities with known $f$. (In particular, each of Ellsberg's observed preferences was for a known probability distribution over an unknown one, even though whatever the unknown distribution was at least one of the resulting preferences would produce lower mean utility than the alternative chosen over it.) Whatever the explanation, we apparently cannot assume agents minimise $S$ as defined above.

However, since new models should acknowledge the successes of old ones as much as their failures, a model in the above vein is warranted. When physicists work with such problems, typically $L$ also depends on $\partial_\mu\phi:=\frac{\partial\phi}{\partial x^\mu}$. The $S$-minimising result is then $0=\frac{\partial\mathcal{L}}{\partial\phi}-\partial_\mu\frac{\partial\mathcal{L}}{\partial_\mu\partial\phi}$ (the last term sums over $\mu$), which unlike the previous result is a differential equation. So my question is: Have economists taken this approach? If not, what have they done instead? In particular, I'm looking for a generalisation of $\int dx Uf$ maximisation.

Let me try to make this more concrete. Suppose I'm investing in crops. Then $\phi$ could denote my portfolio, $x$ could denote future weather, $f$ would characterise the long-term climate, and ongoing climate change may present such uncertainty as to result in something analogous to an Ellsberg paradox. In particular my $\mathcal{L}$ might also depend on $\partial_\mu\phi$, my chosen portfolio's sensitivity to a guess about future weather. For example, I might have $\mathcal{L}=-Uf+a\partial_\mu\phi\frac{\partial\left(Uf\right)}{\partial_\mu\phi}$ for a constant $a$. This is just a hypothetical example, since I've not found any economic literature on this.

It appears you are looking for literature on Ambiguity Aversion and/or "Uncertainty Aversion".
You can start by looking up the work of L.G Epstein, I. Gilboa, and  D. Schmeidler.

It is an attempt to formalize the behavior of agents exhibiting behavior consistent with the Ellsberg paradox.


Does risk aversion cause diminishing marginal utility, or vice versa? Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. Then each person would have a preferred ordering of the states in $A$, as well as a preferred ordering of the lotteries in $G(A)$. The von Neumann-Morgenstern theorem states that, assuming your preference ordering over $G(A)$ obeys certain rationality axioms, your preferences can be represented by a utility function $u: A → ℝ$. (This function is unique up to multiplication of scalars and addition of constants.) That means that for any two lotteries $L_1$ and $L_2$ in $G(A)$, you prefer $L_1$ to $L_2$ if and only if the expected value of $u$ under $L_1$ is greater than the expected value of $u$ under $L_2$. In other words, you maximize the expected value of the utility function.

Now just because you maximize the expected value of your utility function does not mean that you maximize the expected value of actual things like money. After all, people are often risk averse; they say "a bird in the hand is worth two in the bush". Risk aversion means that you value a gamble less than expected value of the money you'll gain. If we express this notion in terms of the von Neumann-Morgenstern utility function, we get the following result through Jensen's inequality: a person is risk averse if and only if their utility function is a concave function of your money, i.e. the extent to which you're risk averse is the same as the extent to which you have a diminishing marginal utility of money. (See page 13 of this PDF.)

My question is, which direction does the causation run? Do the values of the von Neumann-Morgenstern utility function reflect the intensity of your preferences, and is risk aversion due to discounting the preferences of future selves who are well-off compared to the preferences of future versions of yourself who are poorer and thus value money more (as Brad Delong suggests here)? Or does the causation run the other way: does your tolerance for risk determine the shape of your utility function, so that the von Neumann-Morgenstern utility function tells you nothing about the relative intensity of your preferences?

I think I've found an answer to my question, in this excerpt from Nobel laureate John C. Harsanyi's 1994 paper "Normative validity and meaning of von neumann-morgenstern utilities", presented at the Ninth International Congress of Logic, Methodology and Philosophy of Science.  Harsanyi starts by proving the same lemma that Alecos proved in his answer, namely that if $u$ is a vNM utility function of an individual, then $u(10) - u(5) < u(5) - u(0)$ if and only if they would prefer a guaranteed 5 dollars compared to a 50% of 10 dollars and a 50% chance of 0 dollars.  In the comments section I said that was insufficient to demonstrate that the vNM utility function represented intensity of preferences, because what if the individual's actual pleasure and pain was accurately described by some other utility function $v$, which is a monotonic transformation but not an affine transformation of $u$?  In that case couldn't $v$ fail to satisfy the expected value property, and couldn't $v(10) - v(5) = v(5) - v(0)$?

Harsanyi has a clever argument dealing with this issue. Let $L_1$ be the lottery where you get 5 dollars guaranteed, let $L_2$ be the lottery where you have a 50% chance of 10 dollars and a 50% chance of 0 dollars, and let $L_3$ be the lottery where you have a 50% chance of 10 dollars and a 50% chance of 5 dollars.  Then obviously the person prefers $L_3$ to both $L_1$ and $L_2$.  And Harsanyi argues that $L_3$ is preferred to $L_1$ less strongly than $L_3$ is preferred to $L_2$ if and only if $v(10) - v(5) < v(5) - v(0)$.  That's because in the choice between, $L_3$ vs $L_1$, 50% of the time they get 5 dollars, and 50% of the time they have to make a choice between 10 and 5.  Similarly in the choice between $L_3$ and $L_2$, 50% of the time they get 10 dollars, and 50% of the time they have to make a choice between 5 and 0.

Now here comes the master stroke: $L_1$ is preferred to $L_2$ if and only if $L_3$ is preferred to $L_1$ less strongly than $L_3$ is preferred to $L_2$.  Therefore, $L_1$ is preferred to $L_2$ if and only if $v(10)-v(5) < v(5) -v(0)$.  And thus we reach the grand conclusion that $u(10) - u(5) < u(5) - u(0)$ if and only if $v(10)-v(5) < v(5) -v(0)$.

Thus Harasanyi reaches the conclusion that the vNM utility function represents preferences intensities.  So the answer to my question seems to be that diminishing marginal utility in the vNM utility function reflects genuine diminishing marginal utility when it comes to intensity of preferences, and thus (assuming the vNM axioms are true) diminishing marginal utility really is the cause of risk aversion.

By the way, on a side note I wonder whether we could identify the set of all functions $v$ that satisfy the constraint that $u(x) - u(y) < u(z) - u(w)$ if and only if $v(x)-v(y) < v(z) -v(w)$ (and similarly for greater than and equal to).  (EDIT: I asked about this on Mathematics.SE here.)


Why does $\frac{MP_L}{MP_K} = \frac{w}{r}$? I did a practice problem set. I was given a production function $F(K,L)$ and had to derive the firm's cost function. To do this, I used the following relationship:

\begin{equation}
\frac{MP_L}{MP_K}=\frac{w}{r}
\end{equation}

I found this formula in a set of lecture notes online. I have no idea where it comes from. I understand what $MP_K$, $MP_L$, $w$, and $r$ are but I don't know why these ratios are equal. I got the problem correct, but I want to understand this point better.

My Question:

Can someone explain why this ratio is true?

This is a result of firm maximization.  Consider a problem that a profit maximizing firm faces --it must rent capital, $k$, at rate $r$ and hires labor, $l$, at wage $w$ to produce goods ($F(k, l)$) for which we can sell at a normalized price of 1.

$$ \max_{k, l} F(k, l) - w l - r k $$

Then if we just think about the firm's maximization, we can take derivatives w.r.t $k$ and $l$ to get:

$$ F_k(k, l) - r = 0 $$
$$ F_k(k, l) = r $$

and

$$ F_l(k, l) - w = 0 $$
$$ F_l(k, l) = w $$

Notice that by definition $MPL_K = F_k(k, l)$ and $MP_L = F_l(k, l)$.  If we take the ratio of the two equations then we get what you initially introduced --that is:

$$ \frac{F_l(k, l)}{F_k(k, l)} = \frac{MP_L}{MP_K} = \frac{w}{r} $$

Edit: As mentioned in another answer, this is imposing some assumptions on the behavior of $F(k, l)$.  These assumptions are $\frac{\partial F}{\partial k} > 0$, $\frac{\partial F}{\partial l} > 0$ and $\frac{\partial^2 F}{\partial k^2} < 0$ $\frac{\partial^2 F}{\partial l^2} < 0$


Paying Filipino workers in USD. What should the inflation rate be? I'm not sure where to ask and, since this is not Personal Finance, I'm gonna ask it here.

Here's my situation: for the past 2 years, I hired and trained a team of Filipino workers. They are paid in USD and receive a 8% raise every year and x% for inflation. The workers then take their pay and exchange it for PHP.

When I came up with the analysis 2 years ago, I used the inflation data for Philippines to figure out the yearly inflation raise.

However, this year's inflation rate was 5.5%, which is ungodly high IMO; which got me thinking. Then, it occurred to me that I should have used the US Inflation rate the whole time!

My logic is that, if the price of goods increase in the Philippines, it wouldn't matter because the USD to PHP exchange rate would change so that US$1 would be worth more Pesos. If I recall correctly, Russian was experiencing a lot of inflation a few years ago. The price of the Ruble dropped; so, if Russian employees were paid USD, they were safe from the inflation, even if they exchanged their money every pay period.

Is this logic correct? Let me know. I gotta fix their pay.

Your employees are at risk of PHP inflation; you are not, so you should be paying in USD, and adjusting for USD inflation if you want to.

Yes your reasoning is correct. If you increase their pay by US inflation, in theory the exchange rate to PHP should increase MORE due to the higher PHP inflation (relative to USD). So when they convert their USD to PHP, their resulting PHP income would reflect PHP inflation.


Utility function in Ramsey-Cass-Koopmans model We are studying Ramsey-Cass-Koopmans model (RCK) in my macro course, I am already stuck in the starting section on assumptions of the model. In particular, I do not quite understand why the ulitity function in RCK is called CRRA, constant-relative-risk aversion function and why it is the case that the coefficient of relative risk aversion is theta θ = -Cu"(C)/u'(C) and is therefore independent of C.
Would appreciate if someone could clarify this.

Recall that in the RCK model households choose their consumption and savings so as to maximise current and future utility (i.e. future generations). Then the objective function is given by
$$ U = \int_{0}^{\infty} u[c(t)]e^{nt}e^{-\rho t}dt$$
The RCK model assumes the functional form of utility
$$ u[c(t)] = \frac{c(t)^{1-\theta}-1}{1 - \theta} $$
Note that this function is increasing and concave, and that assuming that $\rho > n$, it ensures that lifetime utility does not diverge. This is a very practical assumption as it ensures that households would not have infinite lifetime utility and therefore allows for a well defined solution.
This is is called constant intertemporal elasticity of substitution (CIES) or constant relative risk aversion (CRRA) utility function (note that this isoelastic utility function is the only class of utility functions with constant relative risk aversion).
You can check for this by computing the risk aversion coefficient, $\frac{1}{\sigma}$, where $\sigma$ is the intertemporal elasticity of substitution (measures the willingness on the part of the consumer to substitute future consumption for present consumption) and is defined as
$$ \sigma =  \frac{1}{u''(c)} \frac{u'(c)}{c}$$
From the functional form of utility you obtain
$$ \sigma = \frac{1}{\theta} $$
And therefore the risk aversion coefficient equals $\frac{1}{\sigma} = \theta$, which is constant and independent of consumption.
Note that the intertemporal elasticity of substitution is analytically derived as the inverse of risk aversion. This follows from considering fluctuation in the marginal utility of consumption over time as a form of risk. For example, a risk-averse individual would choose to smooth their consumption path to avoid such risk (fluctuations).


What does Adam Smith mean by equality of condition? According to Chomsky, Adam Smith distingushes between equality of opportunity and equality of condition and that he supported the latter over the former.

Although I have come across the former term and have some appreciation of what it means, I have not come across the latter term. What does Adam Smith mean by it?

The term "equality of condition" can also be thought of as "equality of outcome."

In this context, it refers to the idea that people in a society/state have approximately the same overall quality of life, regardless of opportunity, socioeconomic circumstances, prejudicial treatment, advantages/disadvantages, etc.

This is an oversimplification but, to put it another way, you could think of equality of opportunity (in regards to material wealth, access to luxuries, health and quality of life, etc.) as "equalizing how people start" and equality of condition as "equalizing how people finish."


Greek default versus Euro exit Talk about Greece leaving the Euro has been reignited by the recent election of Syrzia, with some again talking about how it is practically inevitable.

Why are these people viewing a Greek default as likely triggering an exit from the Euro? Couldn't Greece simply default on its debt and continue to use the Euro? Would this trigger the ECB to freeze the accounts of Greek banks (and if so, why?).

I understand why moving to a local currency, which can be devalued, might make sense for a country that needs economic stimulation. But I don't understand the direct cause-and-effect from a sovereign default to an exit from the Euro.

As far as I recall, you're dead on: they don't have to. The contracts don't allow for "some countries kicking others out of the Euro Zone", they never envisioned this scenario when writing them.

On the other side, Greece can, and should, leave on its own. Sharing the currency is hurting them economically, the only reason they're not is that the continuous inflow of loans is preferred over leaving the zone. But if Greece really defaults, I don't think there will be any more lending in the short run. And then really there is no reason for Greece to stay.


Averaging data over 5 years with Stata or Excel I need Stata commands or Excel function to calculate the average over 5 years groups of the values in a panel dataset. In particular, this procedure as to take into account the presence of possible missing values (empty cells in Excel) and thus adjust the computation accordingly to the actual number of non-missing in the period.

Is this what you want (in Stata)?

 clear all
 * Generate Data (n=5, T=20)
 set obs 100
 gen id = floor((_n-1)/20)+1
 by id, sort: gen year = 1990+_n
 gen x = rnormal()
 xtset id year
 * Convert
 gen t5 = floor((year-1991)/5)+1
 gen idt5 = id*10+t5 /* 10 can be 100, 1000, etc., depending on T */
 by idt5, sort: egen xbar5 = mean(x)
 *drop t5 idt5  /* drop if you want; you can also use tempvar */

If not, please clarify your question using an example.


Mathematical framework for modelling the relationship between price and sales of a product In my job as a data scientist, I am required to model the relationship between the price of a product and the sales or number of unit sold. I am trying to build a simplistic model, the assumptions of which are given below. I am not sure if all the assumptions will hold true simultaneously, or if there is a missing assumption or if some assumptions are wrong. Can any expert have a look and comment/give suggestions?

Assumptions:

Different customers have different income so the product priced at $P$ may be affordable to some and not affordable to others. But from a practical business point of view, we cannot build a model of each individual. So we assume that average income of the customers remains fairly constant in the short term and so we assume that we are trying to model the behavior of a single customer whose income is constant and equal the average income of all the customers.

All other conditions external conditions such as macro economics, competitive products, government policies and business rules remain constant
The product has demand, it is mature and stable and so at present the no. of units of the product sold depends only on its price.
As the price changes, the probability that th customer will purchase the product changes. Let $a_1$ be the probability that the customer purchases the product at price $P_1$ and $a_2$ be the probability that the customer curchases the product at price $a_2$. Then $a_2$ depends only on the initial price, initial probability and the new price i.e. $a_2 = f(a_1,P_1,P_2)$ where $f$ is some probability function whose behavior we are trying to find out assuming that such a function exists in the first place.
If price remains constant, then the purchase probability remains unchanged i.e. $f(a_1,P_1,P_1) = a_1.$
Hypothetically, if the product is critical for survival (e.g. purchasing your daily oxygen in a Mars colony) the customer will buy it no matter what the price is i.e. $f(1,P_1,x) = 1$ for all $x$.
If the product is not critical for survival then it will be out of demand at infinite price i.e. $ Lim_{x \to \infty} f(a_1,P_1,x) = 0.$
If the product is important and very cheap then everybody will but it i.e. $ Lim_{x \to 0} f(a_1,P_1x) = 1$.
As price increases, sales decreases i.e. if $P_1 < P_2 < P_ 3$ then $0 \le f(a_1,P_1,P_3) < f(a_1,P_1,P_2) \le  1.$
Since $f$ is a probability density function, its value must be between 0 and 1 i.e. $0 \le f(a,x,y) \le 1$ for all $x$ and $y$.
Mathematically, since $f$ is a probability density function, and price cannot be negative the total area under the probability density curve must be 1 i.e.
$$\int_{-\infty}^{\infty} f(a_1,P_1, x) dx = \int_{0}^{\infty} f(a_1,P_1,x) dx = 1.$$

Now there will be infinitely many functions $f$ satisfying all the above conditions. For example

$$
a_1^{P_2/P_1}, \frac{a_1\log(1+P_2/P_1)}{\log 2}
$$

We eleminate the ones that do not fit the observed data. But even then we can still be left with multiple functions that satisfies all the assumptions of the framework as well as fits the data within an acceptable error range as defined by the business.

Question 1: What other criteria/conditions/assumptions can we use to choose one mathematical model over another?

One way is to use Occam's Razor and go with the simplest model defined as the one which uses the least number of parameters in which case
$$
f(a_1,P_1,P_2) = a_1^{P_2/P_1}
$$

Question 2: Lets ignore my entire framework. What are the other models in economics that can be used to estimate the purchase probability given $a_1, P_1$ and $P_2$.

Question 3: Which assumption is simple impossible and should be removed? What additional assumptions are required if any?

The main problem of your framework is that you talk about sales but model only demand. Assuming that the supplier is not a monopolist you should take competing suppliers into account, when estimating sales. To do that any real world examples will have to define the extent of the market. Having said that your framework is a pretty good job as a first try!

@3, 4. Classic micro relies on the irrelevance of independent alternatives. Translating this to your framework $a_2 = f(P_2)$, unless $P_1$ directly affects the consumer's budget in $t_2$. For example - if oxygen was more expencive than your income yesterday, you had to borrow to buy it and today will have to repay your debt. As far as such intertemporal concerns may be important, you need to specify the consumer's planning horizon, which will generally depend on the type of good. For example - if durable goods are involved - cars, fridges etc., and I buy today I won't return as a consumer to this market for the next five years no matter what. However if I know (or expect) that the price of cars will come down next month I will wait until it does and buy than. I.e. it can be that $a_1 = f(P_1, P_2)$. I cannot see why $a_1$ should affect $a_2$ or vice versa through a channel different than the price vector unless there are some asymmetric capacity issues in some periods and demand in excess of capacity thus moves back and forth between periods. I am not exactly sure about search frictions but I think that their effect is quite similar with regard to your question. As long as you have simple consumer goods that you buy every month $a_t = f(P_t)$ is okay.

@5 If the oxygen is so expencive that the purchase violates your consumer's life-time budget constraint I am sorry but he is going to have to die. In this case it is obvious that $a_2 = f(P_2)$ only.

@8 There are goods for which the quantity demanded increases when their price goes up. They are called Giffen goods. Apart of that if your consumer from @5. can afford oxygen he will buy. I.e. it can be that $P_1 > P_2$ and $f(P_1) = f(P_2) = 1$.

Demand is usually modeled as a $Q_t = f(P_t$, control variables) + $\epsilon_t$,

where $f$ is deterministic and all randomness comes from the error term, which should be familiar to you from your daily work.


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

A thought experiment
Let us for a moment suppose that all of the tractors, trucks, fertilizer plants, irrigation systems, shovels and other production equipment (capital goods) used in the US agriculture instantly disappeared and that no food could be imported from abroad. Under these hypothetical circumstances, do you think that all of the expert ballet dancers, sushi chefs, pole vaulters, computer scientists and basket weavers would continue to practice their niche talent? A more likely outcome is that they will revert to subsistence farming like everyone else. Now suppose that all tractors, trucks, fertilizer plants, etc. became twice as efficient, allowing food to be produced at even lower costs. Do you think this will result in an increase or decrease in the number of people who can make a living pursuing their niche talent?
The point is that a country with a large amount of capital goods has an easier time satisfying the basic needs of more people. This allows these people to engage in other activities. We can therefore rephrase your question in the following way:
"Is there any logic to the market economy that makes the accumulation of capital goods likely, or even inevitable?"
As an illustrative example, suppose that you and a couple of friends are stranded on a deserted island and are forced to survive by catching fish with your bare hands. If one day you happen to catch so many fish that you have enough for a week, you may decide to eat them while you construct a fishing rod. This "investment" will allow you to improve your "fish productivity". If you catch so many fish that you have more than you can eat yourself, you might trade some of them to a friend if he promises to build a hut for you. Maybe you loan out 10 fish to another friends so he can build a fishing rod of his own. In return he promises to give you 15 fish at some later date. If the project is a success you might sell off your old rod and fashion a musical instrument out of some coconuts. You can entertain your friends in exchange for fish.
Saving and investing resources in capital goods and voluntarily exchanging goods and services allows you to solve your most urgent problems and to raise your standard of living. You can get away with living from playing coconut music because valuable consumer goods are made readily available by this process.
Now suppose that I declare myself Chief of the island and mandate that fishing rods can only be owned if form 1304-b is filled out and delivered to my hut atop the volcano before summer solstice. Also, they may only be constructed by and bought from my best friend who holds an exclusive patent. Furthermore, anyone catching more than 20 fish per day is required to hand 35% of the excess over to me for my personal use. The rest will be handed to those who did not catch as many that day (no matter how hard they tried). Moreover, to protect hut-builders from exploitation, it is forbidden to pay them less than 100 fish per day to construct housing. Charging "interest" for loaning out fish is also exploitative and forbidden. To enforce these rules, some islanders who could have been engaged in production are recruited to my court and paid with part of the fish-tax I collect. Anyone caught engaging in illegal "black market activities" are put in prison for at least one month.
The example is admittedly cartoonish, but hopefully illustrates why Adam Smith might believe that an unhampered market has an easier time facilitating the build-up of capital goods than one subject to intervention.


How does the core relate to strong equilibrium? An allocation is in the core if there's no coalition that blocks it.

A strong equilibrium (Aumann, 1959) is a Nash equilibrium in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all members of the coalition.

How are these distinct? I usually don't think of the core as a solution concept, but I'm struggling to disentangle it from strong equilibrium.

Strong Nash equilibrium is different from core mainly because of communication. In a Strong Nash, unlimited private communication is allowed. The core is a concept that is linked to Coalition-proof Nash equilibrium rather than Strong Nash. People can freely communicate but cannot make binding commitment before deciding.

In some games, both happen to be the same, but in generality, the core is a concept derived from Coalition-proof Nash equilibrium rather than from Strong Nash Equilibrium.


History of Macroeconomic Measurements before GDP What is the earliest mention of any type of macroeconomic measure?

I know proto-economist William Petty coined the Term GDP but was there any other measurement used before then to determine the welfare of an economy?

Maybe the earliest economic quantities to be measured are the number of people in a tribe or nation as a measure of economic and military potential. Roman (Roman king Servius Tullius) and ancient Israeli censuses (Prophet Moses duing the Egyptian Exodus) were said to have been conducted in the 6th and 13th centuries before the common era (Wikipedia -- Census).

William Petty's (mercantilist, 1623-1687) political arithmetic is often considered the first work related to economic measurement and econometrics and crudely and innovatively estimated the population, national income and national
wealth for Ireland and England. François Quesnay (physiocract) is often regarded as his fellow pioneer and his Tableau Economique (1759), is often considered a forerunner of the modern national income and product accounts (Hillinger (2007)).

For more precise economic estimates, measures of national production of pig iron goes back in the USA and the UK at least as far as 1870.

  Productivity Change in British Pig Iron, 1870-1939 Donald N.
  McCloskey The Quarterly Journal of Economics Vol. 82, No. 2 (May,
  1968), pp. 281-296


Aren't all cost functions step functions? Long Question:

Overview:

While I understand that over certain intervals (i.e. less than the width of the step), they may appear not to be because the step is outside of consideration, and over other intervals (much, much larger) the step seems continuous as opposed to discrete, but at the end of the day aren't these merely artifacts of the analysis, as opposed to properties of the underlying function?

Admittedly, I was never much good with the calculus of discrete functions, but I remember there being some substantial differences between their derivatives (e.g. the need to invoke the finite difference method as opposed to a limit).

Further, given the potential steepness of the step, and its unknown location, isn't predicting difficult?

A Picture:

For example, the graph below shows a cost function for $n$ units with and without a step.

The red line is:

$$C(n)=5n$$

and the blue line is
$$C(n) = n+(n-\mod (n,5))$$

Analyzed over $(0,5)$ these would coincide, and an analyst might not have any expectation that increasing by a small factor would dramatically increase cost, and while the (simple) derivative at any point on the line is the same for either line (inside the step interval), this is very misleading.

Further, I chose $5$ at random, a more generalized idea might be something along the lines of:

$$C(n) = n+\frac{S(n-\mod(n,w))}{w}$$

where $S$ is the step cost, and $w$ is the width.

Summary:

Given these concepts, why are step cost functions generally treated as less preferential in discussing models? Or is that just my experience, and not indicative of the way the field treats cost functions as a whole?

I ask this, because whenever I see a discussion of a cost function, it seems to be continuous, and whenever I see mention of a step function it seems to be an afterthought.

Analyzed over (0,5) these would coincide, and an analyst might not
  have any expectation that increasing by a small factor would
  dramatically increase cost, and while the (simple) derivative at any
  point on the line is the same for either line (inside the step
  interval), this is very misleading.

Good question, but mainly of theoretical validity. The "analyst" in question would most probably have some indications of the cost for most if not all production scales of interest. There are few cases when a production plan is about producing on a scale no-one has seen before (not only the specific company, but any company). So data to compare and get an idea will be around, and also, as a last resort, "engineering" data can, and do, assist also (and engineering is much more of an exact science than Economics is).

Firms' practitioners have a rather clear view of "Fixed Costs" that are not really Fixed but step cost functions, trust my corporate experience on this one. They "sense" when the step is about to be taken -and they sit down and calculate it. The whole Cost-Accounting business is essentially about learning how to detect, separate and handle Fixed and Variable Costs, as well as Variable and Marginal Costs (in the real world, the distinction between Variable and Marginal Cost is very existing, and very important).

In the case of aggregate/average cost functions, the individuality of each firm alongside the common structural base that exists in all production activities, helps in smoothing the relationship.


What is the concept of ordinal utility? I have read in many books that since utility cannot be measured - so ordinal concept or comparison concept is used.
If that is so, how can one define a mathematical function for utility which gives a cardinal value for inputs.
The two things mentioned above are inconsistent with each other.

Can somebody explain what I am missing here.

Suppose Alex, Bryan, and Chris run in a race. Alex is the fastest and Chris is the slowest. So far I have only given you ordinal information about where they finished.

I guess you'd be okay with me taking that ordinal information and saying "Alex finished first, Bryan finished second, and Chris finished third". But then I just defined a function that assigns a number to each of the ordinal places:
$$f(x)=\begin{cases}1\text{ if }x=\text{Alex}\\2\text{ if }x=\text{Bryan}\\3\text{ if }x=\text{Chris}.\end{cases}$$
Note that the numbers 1, 2, 3 don't tell us how much faster Alex was than Bryan, only that he was somewhat faster.

Utility functions are just like this: they give bigger numbers to the best alternatives. But the size of those numbers don't tell us how much better the best alternative is, only that it is better. That is the sense in which the function is ordinal.


Stagflation and the Labor Force Which of the following best explains how an economy can experience stagflation.

Women and teenagers stayed out of the labor force.
Negative supply shock cause the factor prices to increase.

Official answer : 2.

My thoughts: While 2 is correct, I think 1 is also correct. the fact the  women and teens stay out of the labor force will increase the wage and thus cause the supply curve to shift to the left and thus cause stagflation. Am I wrong?

Definition In economics, stagflation, a portmanteau of stagnation and inflation, is a situation where the inflation rate is high, the economic growth rate slows down, and unemployment remains steadily high.

Stagflation hence requires a high unemployment rate. The unemployment rate can be defined as

$$ u = \frac{U}{POP}\\
u =\frac{U}{LF}
$$

Direct increase of unemployment?

that is, either the number of unemployed over population (more common) or over the labor force. Removing women and teens from the labor force does not affect anything in the first definition, and decreases the unemployment rate by the second definition.

Indirect increase of unemployment?

As stagflation requires a high unemployment rate, reducing the labor force size cannot directly create stagflation. Your only argument could then be that a reduced labor force somehow leads to a higher unemployment rate. Most likely, this is orthogonal. Equilibrium unemployment is a composite of frictional unemployment and voluntary unemployment. I cannot think of a reasonable argument why a reduction of the labor force should increase the relative share of either of these (unless of course, voluntary unemployment is higher among men than women, which is false).

Level effects and growth rate effects

Even more importantly, there is an important distinction between shocks to the level versus shocks to the growth rate. To the extent that - after women and teens have left - the growth rate of the labor force is the same as before, long term effects are negligible.

In a world with exponential growth, a shock to the level is - in the long run - negligible, as we will catch up quite quickly. A shock to the growth rate however, is permanent. Of course, "in the long run" is relative, but there is some idea of persistence behind stagflation. An exit of women from the labor force would, in my opinion, cause a sudden drop in output, but would not affect growth rates.


What are the costs of requiring banks to have more equity? In The Bankers' New Clothes: What's Wrong with Banking and What to Do about It (2013), Admati & Hellwig recommend much higher equity requirements:

Requiring that banks’ equity be at least on the order of 20–30 percent of their total assets would make the financial system substantially safer and healthier.

In contrast, under Basel III:

Banks’ equity can still be as low as 3 percent of their total assets.

Admati & Hellwig make some persuasive arguments. However, I am wondering:
What are the costs or trade-offs of requiring banks to have higher equity?
Admati & Hellwig repeatedly claim that there are no costs or trade-offs whatsoever (see quotes below). But if so, why wouldn't they recommend even higher equity ratios like 50% or even 100%? Why stop at 20–30%?
This leads me to think that there must be costs or trade-offs which they haven't mentioned. However, I am not sure what these are and hence my question.

if banks have much more equity, the financial system will be safer, healthier, and less distorted. From society’s perspective, the benefits are large and the costs are hard to find; there are virtually no trade-offs. ...
the view that there are significant trade-offs is flawed ...
long-term benefits of much higher equity requirements are large, and the costs are hard to find. ...
Best of all, these many critical benefits of significantly higher equity requirements could be obtained at virtually no cost to society. Taxpayers would save on subsidies, and the public would benefit from a more stable and healthier financial system. There are therefore no trade-offs associated with this approach. Society would obtain large benefits for free. [Emphasis added.]

If banks are forced to hold 20-30% of their assets as common equity, their cost of capital is much higher. This is because the expected return on equity needs to be close to other industries, and that generally is much higher than interest rates. Typical targets for return on equity are around 20%, even in the modern low interest rate environment.

The result is that banks are much less competitive versus non-bank finance, and so would lose market share. Since non-bank financial entities are less well regulated, the risk to the system would rise if they take over lending.

So the immediate question is: how exactly can regulators stop all risk migrating to non-bank finance? Considering the flexibility of contract law, that is not easy, since financing arrangements can be embedded into almost any commercial contract (e.g., accounts receivable). You cannot just look at existing non-bank financial practices, you need to deal with any new structures that pop up to take advantage of the situation.

Once that question is answered, we would then need to figure out how to get borrowing rates to be a relatively reasonable spread over government bonds, since the lending spreads have to cover the return on equity for 20-30% of the balance sheet.


Social planner's first order condition (current-value Lagrangian) Here is (one of the ways to state) social planner's problem:

Eric Sims' notes then immediately gives the solution:

I am trying to connect these two lines. This is what I get after taking a derivative with respect to consumption.

Question is: how did he get rid of expectation and discount factor?

At $t=0$, consumption in future periods is indeed uncertain because output is uncertain since $A_t$ is stochastic. But the maximization we are doing here is taking place in each period $t$. In each period $t$, the realization of $c_t$ is observed; that is, $E_t[c_t] = c_t$. By the same logic, $E_t[\lambda_t] = \lambda_t$. Since we are maximizing in each period $t$, the first-order condition of $\mathcal{L}$ with respect to $c_t$ is not a summation. Instead, $\frac{\partial \mathcal{L}}{\partial c_t} = 0$ implies

$$
\begin{align}
\beta^t E_t[c_t^{-\sigma}] - \beta^tE_t[\lambda_t] &= 0 \\
\beta^t c_t^{-\sigma} - \beta^t \lambda_t = 0.
\end{align}
$$

Note that if the coefficient of relative risk aversion were not assumed to be constant across time; that is, if $\sigma_t \neq \sigma$, then the result we wish to show does not follow. Just some subtleties about expectations to keep in mind.

But since indeed $\sigma_t = \sigma$, it then follows that

$$c_t^{-\sigma} = \lambda_t.$$


The link between US debt of $250 Trillion dollars and "Promise to pay" on US Dollar currency Giving background to my question: a prominent economist was discussing the problems of the US currency and predicting it's collapse, said the following:

"...a currency is a store of value, it's a promise of a government to repay"

He continued as follows:

"People are eventually going to realise, with the US issuing even more debt, historic amounts of debt, the dollar has to go down, because we can never repay the debt...we have 250-260 trillion dollars in debt when you include all the obligations that we have in terms of social welfare entitlement programs, medicare, medicaid and it just keeps going up and up and up, and eventually the dollar is going to go down and down and down...because people are going to realise they are worthless...".

So, my question is in 2 parts as follows: As the US uses fiat currency with no physical commodity attached to it (since 1971)...

(i) How does the economist link the total national US debt of 250 trillion dollars with the US governments promise to repay when defining currency?  In other words, what has 'a promise to repay' definition part of the currency got to do with the huge US debt?

(ii) The explanation of what the economist means when he defined the US currency as a "promise of a government to repay"?  I mean, what is there to repay when a currency has no physical commodity attached to it other than swapping it for another dollar?

Thanks.

Note: The link to that programme on youtube (please fast forward to position 15:33) is here.

I looked at that video only briefly. Trying to interpret what that interviewee said would be an opinion-based answer, which this site wants to avoid. I will instead try to answer the question without referring to his comments. In my opinion, I have serious doubts that the economist in the video could offer a convincing explanation of what he said.

Note: it is incorrect to refer to future entitlement spending as a “debt”. At most, it is a “contingent liability.” A debt is a financial claim, held by an owner. An inability to distinguish between debts and contingent liabilities is a signal that he is an ideologue, and not a reliable source. This also means that the 200+ trillion debt is a worthless figure, as it would need to be held in context against future tax revenues as a capitalised asset - which will also run into the hundreds of trillions of dollars.

(1) The linkage between “the promise to pay” on currencies large existing debts and contingent liabilities is presumably the threat of inflation or hyperinflation. In the case of a hyperinflation, a currency is often withdrawn from circulation, and so it cannot be used to pay for things. However, I cannot name a serious body of economists that treats hyperinflation in the US as a possibility under current policy settings.

(2) A promise to repay on currency is just a promise that it will be redeemed at par value by the US government. This means that banks can convert currency to deposits at the Fed (“reserves”) at par. Although this is just converting one US government liability for another, it does distinguish currency from other tokens that might circulate (foreign currency, gift cards, etc.). For an individual, since they do not bank at the Federal Reserve, it gives them a right to exchange currency at par for a bank deposit - or to settle tax payments.

From the perspective of Chartalism (or neo-Chartalism), the “promise to repay” derives its importance from the fact that currency will be accepted at par to settle future taxes. The prospect of the need to settle taxes is what gives currency its value.

Although settlement at par seems natural, it was not always the case. Pre-Federal Reserve, cheques (check in American spelling) drawn on other banks with weaker reputations would not settle at par. That is, you might need to write a cheque of \$110 to settle a debt of \$100 at another bank. The “promise to repay” (and payment system regulations) mean that these “internal exchange rates” disappear.


General Equilibrium - Mas Colell Problem 17.D.2 Taken from Chapter 17 of Mas Colell "Microeconomic Theory"

  Consider an exchange economy with two commodities and two consumers. Both consumers have homothetic preferences of the constant elasticity variety. Morover, the elasticity of substitution is the same for both consumers and is small (i.e. goods are close to perfect complements). Specifically

  $u_1(x_{11},x_{21})=(2x_{11}^{\rho}+x_{21}^{\rho})^{1/\rho}$ and $u_1(x_{12},x_{22})=(x_{12}^{\rho}+2x_{22}^{\rho})^{1/\rho}$

  And $\rho=-4$, The endowments are $w_1=(1,0)$ and $w_2=(0,1)$.
  Compute the excess demand function of the economy and verify that there are multiple equilibria.

My attempt

After applying fist-condition and normalizing prices as $\frac{P_1}{P2}=p$, I have that the demand functions are:

For the first consumer: $x_1=\frac{p}{p+(p/2)^{\frac{1}{1-\rho}}}$ and $x_2=\frac{p(p/2)^{\frac{1}{1-\rho}}}{p+(p/2)^{\frac{1}{1-\rho}}}$

For the second consumer: $x_1=\frac{1}{p+(2p)^{\frac{1}{1-\rho}}}$ and $x_2=\frac{(2p)^{\frac{1}{1-\rho}}}{p+(2p)^{\frac{1}{1-\rho}}}$

So the excess demand function would be:

$\begin{pmatrix}
z_1\\z_2
\end{pmatrix}=\begin{pmatrix}
\frac{p}{p+(p/2)^{\frac{1}{1-\rho}}}+\frac{1}{p+(2p)^{\frac{1}{1-\rho}}}-1
\\ \frac{p(p/2)^{\frac{1}{1-\rho}}}{p+(p/2)^{\frac{1}{1-\rho}}}+\frac{(2p)^{\frac{1}{1-\rho}}}{p+(2p)^{\frac{1}{1-\rho}}}-1
\end{pmatrix}$

The thing is that this is not the answer stated in Mas Colell's Solutions. Here it is:

I guess the elasticity of substitution has something to do here? But I don't get it anyway because if we had some corner solution, the answers would be $(x_1,x_2)=(1,0)$ for this consumer and $(x_1,x_2)=(0,1)$ for second consumer.

Any idea?

Your answer is essentially the same as Mas-Colell's.

$z_{11}$ is excess demand for good $1$ by consumer $1$. $z_{12}$ is excess demand for good $1$ by consumer $2$. They sum up to zero at the price vector $(1,1)$, which means that the market for good $1$ clears. By Walras' law, that implies that the market for good $2$ clears as well, hence $(1,1)$ is an equilibrium price vector.


Consumer Utility Maximization equivalent of economies of scope Economies of scope captures the idea of having efficiency in variety. I've come across this idea only in producer theory to capture the idea that companies may benefit from their ability to reduce cost of production through horizontal or vertical integration.

Quoting Micheal Carter from his book Foundations of Mathematical Economics,

  The production technology displays economies of joint production or economies of scope at y  y1; y2; . . . ; ym
  if the total cost of producing all the outputs separately is greater than the cost of producing the outputs jointly

Is there a consumer theory equivalent of the idea of economies of scope?

Nothing explicit, but I think that there is no real need for a special consumer theory...

If we see diversity as similar yet not identical products, for example red and yellow shirts, then for the theory to hold, you should have specific demands for yellow shirts and red shirts

We touch marketing basics, but this is the core element of differentiation:
Markets split into sub-markets until an imperfectly imitable product is being made, then a premium can be collected on
A premium labeled red shirt for example


Why does capital flight cause inflation? Context: I was watching a video about Venezuela, and, it all started with capital flight due to poor confidence in the government. The government tried to stop it, and in the process it created a bubble in the exchange market, causing smuggling and exportation into neighboring countries highly profitable in order to buy the dollar outside Venezuela and to sell at high prices in the bubble inside Venezuela. I can see how that causes inflation (same money supply chasing less domestic goods).

But then, the video said: if the foreign exchange market is open in order to end the bubble once and for all, allowing the currency to depreciate to its normal levels, thus allowing capital flight to happen in the first place, it would trigger more and more inflation (in hyper levels). And that's when I bugged me. I started searching in other sources, for instance this one, and several of them said that capital flight can indeed trigger inflation. But why?

Let's focus on capital flight: It is my understanding, that capital flight shifts the supply curve of a given currency in the exchange market, causing its depreciation with respect to, say, the dollar. But then.....:

(1) Shouldn't it cause a deflation? Currency is less and less available (due to flight) for the purchase of domestic goods, thus.. deflation. That is, a smaller amount of currency chasing the same goods.

(2) But also, capital flight is done with saved money, instead of money reserved for purchases, and that means aggregate demand is not affected much, meaning, purchases are done as normal, and normal life follows. Surely, that doesn't mean a deflation, but it doesn't mean an inflation either.

(3) Consider this: Assume for whatever reason, interest rates has fallen. This means, borrowing money is cheaper, and that is likely to cause a shift in aggregate demand and domestic consumption, possibly boosting the economy, and causing some inflation in the process. However, with capital flight, there's less and less investment done inside the nation, so, the supply of investment shifts, causing an increase of interest rates -- which again, should tend to cause a deflation due to a decrease in the money supply (basically, the reverse reasoning of lower interest rates).

My question: Why does capital flight can trigger inflation? What is wrong with my reasoning in these three situations?

I am not an economist.. so... forgive me if this is such a simple question.

(1) Shouldn't it cause a deflation? Currency is less and less
  available (due to flight) for the purchase of domestic goods, thus..
  deflation. That is, a smaller amount of currency chasing the same
  goods.

The dollar is less available, whereas the purchase power of the bolivar (Venezuela's domestic currency, apropos of your example) becomes negligible: To buy the same goods, today Venezuelans need more bolivars than in the past. Inflation comprises two factors: economic activity and purchase power. In cases like this, inflation is driven up by the bolivar's drastic loss of purchase power.

  (2) But also, capital flight is done with saved money, instead of
  money reserved for purchases, and that means aggregate demand is not
  affected much, meaning, purchases are done as normal, and normal life
  follows. Surely, that doesn't mean a deflation, but it doesn't mean an
  inflation either.

Capital flight results in a reduction of supply. If demand remains unchanged, then the intersection of supply and demand curves occurs at a higher equilibrium price. That means that the bolivar has lost purchase power.

  (3) Consider this: Assume for whatever reason, interest rates has
  fallen. This means, borrowing money is cheaper, and that is likely to
  cause a shift in aggregate demand and domestic consumption, possibly
  boosting the economy, and causing some inflation in the process.
  However, with capital flight, there's less and less investment done
  inside the nation, so, the supply of investment shifts, causing an
  increase of interest rates -- which again, should tend to cause a
  deflation due to a decrease in the money supply (basically, the
  reverse reasoning of lower interest rates).

It is difficult to make conjectures where a situation gets out of control. In broad terms, the relation between interest rates and money supply can certainly break down when chaos strikes the markets. But even in a less-than-extreme scenario, that relation may hold and yet the net effect can still be a higher level of prices.

Also keep in mind that printing extra money to honor the government's bonds contributes to depreciation of the domestic currency, and interest rates might not be high enough to attract lenders.