Effect of property tax on rent Suppose the government puts a tax on all apartment owners (e.g. a certain percentage of the apartment value), whether or not the apartment is rented. Will this tax cause an increase in rent?

From an economics point of view, it seems the answer should be no (at least in the short run): the tax has no effect on the supply or the demand so there is no reason that the rent should change. If landlords could take a higher rent, they would do so now. If they don't take a higher rent, it means that they cannot do so in the current market conditions, so they will not be able to raise the rent even when there is tax.

But from a psychological point of view, the answer may be yes. Why? Because landlords often don't raise the rent to the maximum possible level given the market conditions. Often, when a tenant rents an apartment for many years, the landlord prefers to keep the rent constant in order to keep good relations with the tenant. But, when there is tax, the landlords have an excuse to raise the rent. They can say "we are sorry, we would really like to keep the rent as it is, but we must raise it to cover the new tax".

Are these considerations correct?

What is more likely to happen in reality?

A property tax:

In the short run, a property tax will have no effect on rent, as the supply of homes is fixed (i.e., supply is totally inelastic in the short run), and demand is relatively inelastic but not completely so, so the incidence will fall on property owners. In the long run, a property tax will increase rental costs because supply of new units (i.e., construction) is highly elastic and long-run demand for housing looks just like short-run demand— relatively inelastic. As a result, the incidence of the tax will fall on occupants (both renters and owner-occupiers).

Intuitively, one could think of it this way: the cost of ownership will increase due to the tax, so for someone to see it as worthwhile to buy a newly-constructed home to rent out, the rental income would have to be relatively higher in the presence of a property tax than if one were not in place.

A tax on rental income:

The tax will increase rent; it will decrease the supply (and demand) of rental units (and increase the supply and demand of owner-occupied units). This will happen because the tax will reduce the return on apartments as revenue assets, causing some number of landlords to sell them to owner-occupiers, taking them out of the rental market. More importantly, though, there will be some renters who do not have the option of switching to owner-occupancy, and they'll bear the incidence of a tax on rental income.

I am assuming that there are three populations:

Landlords, who can choose to purchase homes for rent, but live elsewhere, so their choice to buy a unit to rent out can be analyzed separately from their own housing consumption
Renters, who must rent, due to some frictions (inability to afford a down payment, poor credit, unstable or difficult-to-document income history, etc.)
Potential owner-occupiers, who can choose between owning their own home and renting from a landlord, and who have some set of preferences between ownership and rental

Thus potential owner-occupiers and landlords compete for units for sale, while renters and potential owner-occupiers compete for rental units.

In this case, the choice of landlords to exit due to taxes will not pass through perfectly to the rental market due to the fact that while potential owner-occupiers who are currently renting can escape the tax by switching to ownership, there are some renters who are renting whose demand for renting is pretty inelastic— these people will bear the incidence of the tax.

Interestingly, in the US there is such a tax on rental income, though it's implicit. We have a bunch of incentives for home ownership, notably the exemption from capital gains for owner-occupied homes, but most importantly the fact that income on rental properties is taxed like any other business income, while owner-occupiers effectively rent their homes to themselves without paying tax on the implied rental income. (As an aside, people often point to the income tax deduction for mortgage interest payments, but this actually just creates tax equivalence between homeowners and landlords, who can deduct interest as a business expense.)


Why system of beliefs, $\mu(x)$, needed in dynamic incomplete information games We need to make statements about the sequential rationality of players who are in information sets that are not singletons. In these non-trivial information sets, we need to be able to say something like ...

  "In this information set, player 2 is not playing a best response, and therefore his behavior is not sequentially rational"

But how does this motivate us to develop the system of beliefs? I don't exactly see why making every player to have a well-defined belief over where she is in each of her information sets do in dynamic games of incomplete information.

In some ways, beliefs are a more natural way of interpreting solution concepts like Nash equilibrium and its refinements.

For example, consider a simple simultaneous-move coordination game as follows:
\begin{equation}
\begin{array}{c|cc}
&L&R\\\hline
T&1,1&0,0\\
D&0,0&2,2
\end{array}
\end{equation}
We say that $(D,R)$ is a Nash equilibrium because $D$ is a best response to $R$ and vice versa. But this is a simultaneous-move game; how does player 1 know that player 2 will choose $R$? Well, she doesn't need to know, she just need to believe that player 2 will choose $R$ (with sufficiently high probability), and such a belief alone can justify the play of $D$ as a best response.

Thus, we can think of a Nash equilibrium as one in which every player is best responding to their beliefs about what other players will do, and that their beliefs are correct, in the sense that other players choices confirm their beliefs.

To the extent that a simultaneous-move game can be modeled using a game tree with imperfect information, we can talk about beliefs at non-trivial information sets where a player is uncertain about which strategy the previous player has chosen. Furthermore, this framework can be generalized to include incomplete information games if we let this previous player be Nature/Chance.

By dividing Nash equilibrium into these two elements --- (i) best response to one's belief and (ii) beliefs are correct --- we obtain a more nuanced understanding of the concept, which in turn shed light on the ways we can refine this solution concept by placing restrictions on either or both elements.

Solution concepts like the (weak) perfect Bayesian equilibrium and sequential equilibrium require that beliefs off-equilibrium path cannot be arbitrary (they must follow Bayes' rule whenever possible).
Others such as quantal response equilibrium maintain the requirement that players have correct beliefs but relaxes the supposition that people always best respond to their (correct) beliefs.


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

It is true that we are usually interested in minimizing convex functions or maximizing concave functions, typically over convex sets. But I think you have two confusions:

The profit function is the result of a profit maximization problem. Not the objective function in the maximization problem. A profit function $\pi^*(p, w, r)$ identifies maximum profit given the price levels (p, w, r).
In the profit maximization problem, the objective function $\pi = pf(k, l) - wl - kr$ is concave in $k$ and $l$, the choice variables of the maximization problem.


Cournot model with piecewise inverse demand Do you know if there exist results for Cournot oligopoly (or duopoly) when the inverse demand is a piecewise continuous?
Something of this type

$P(Q) = \alpha-\beta Q$ (if $0\leq Q<Q'$)
$P(Q) = \gamma-\delta Q$ (if $Q' \leq Q \leq Q_{max}$)

In the book Sushko, I. (Ed.). (2002). Oligopoly dynamics: Models and tools. Springer.

there is a chapter,

Puu, T., Gardini, L., & Sushko, I. (2002). Cournot duopoly with kinked demand according to Palander and Wald. (pp. 111-146).

where the authors examine in detail a specific numerical example, among other variants.  They arrive at the best response functions and find that there exists two Cournot equilibria, for which, as they write

  "...both equilibria, the Cournot points, are locally stable. They hence coexist with each its proper basin of attraction in the space of
  initial conditions."

The authors are concerned with dynamics, hence the mention of "initial conditions". If one wanted to turn their conclusions into the static case with just one move to equilibrium, one should consider in which "basin of attraction" does the zero output vector belongs.


Where is GBP/EUR exchange rate going? Very recently, the GBP has been raising against the Euro. I understand this has to do with the EU injecting €1.1 trillion until Sep 2016 and the elections in Greece.

My question is: when is this going to stop? I am uncertain as I don't know if the result of the EUR being much lower than GBP is also the result of speculation and, for that reason, it might not go beyond that.

Just today, I was reading about a specialist saying now was the best time, but that specialist was also a seller pushing for a long-term contract to buy EUR (currency.co.uk) so I am uncertain about his opinion. He mentioned 1.32 was great, but later 1.3465 was achieved!

What to expect then?

What bdsl's comment means is this:

Suppose there was a way for "experts" (here or anywhere else) to predict when the pound would start depreciating against the euro, and that this method predicted that it would begin to do so tomorrow. What would the experts do with this information? They would start selling pounds today in order to get out of the market at the top. But this rush of selling activity would cause the value of the pound to fall (via the usual principle of supply and demand) today—a day earlier than forecast! This simple story illustrates the broader idea that a method for forecasting financial markets is self-defeating. As soon as anyone has information about the future direction of an asset price (be it currency exchange rates, stock prices, etc.), their buying or selling activity will, by itself, move the price in that direction. Thus, any information available to the public will be "built-in" to the market price you see quoted. Moreover, given the amounts of money at stake, large market actors have a huge incentive to act on new information very quickly so that information gets built into the price almost immediately.

This general principle—that it is impossible to use publicly available information to beat the market—is known as the efficient market hypothesis. So-called specialists who claim they can predict what the market will do usually fail to do better than a random guess. Such people usually earn their money from commissions or advisory fees rather than from profits on successful trades.


Pareto set and contract curve I am having some troubles in distinguishing, from a theoretical point of view, between contract curve and Pareto set.

I have looked around books and internet, and I have found that contract curve should be a subset of Pareto set, i.e. the locus of Pareto efficient allocations that can occur as a result of mutually beneficial trading between agents.

Am I right or there is something I did not understand properly? Someone can give me a formal definition of the two objects (if there is some differences)?

Let $N$ denote the set of consumers. Given a set of possible allocations $A$, an allocation $a$ is Pareto-optimal if no allocation $a'$ exists for which
$$
\forall i \in N: a \preceq_i a'
$$
and
$$
\exists j \in N: a \prec_j a'.
$$
So Pareto-optimality exists without any notion of property rights, you don't need to know the initial endowment is, who has what in the beginning. Given an initial endowment $\omega$ an allocation $a$ is individually rational for consumer $i$ if
$$
 \omega \preceq_i a.
$$
An allocation is in the contract curve if and only if it is individually rational for all consumers and is also Pareto-optimal. If the allocation $a$ is not individually rational for a given consumer $i$, he would not sign the contract which would take him there from $\omega$.

Thus the contract curve is indeed a subset of all Pareto-optimal allocations. Unless the initial endowments are given, it is not possible to determine the contract curve.


Bargaining Theory: reading list I looked around in the forum but I have not found this question yet. I would like to approach the topic of bargaining models in the spirit of Rubinstein, Ariel. "Perfect equilibrium in a bargaining model." Econometrica: Journal of the Econometric Society (1982): 97-109.
I have studied game theory but never actually worked with these kind of models (see for example: Chae, Suchan, and Paul Heidhues. "Buyers' alliances for bargaining power." Journal of Economics & Management Strategy 13.4 (2004): 731-754.)
I have done some timid google scholar searches, but I have found so much material that I cannot skim it on my own. Could you suggest a reading list of the main references that are a must read for these kind of models?
Thanks a lot.

Osborne and Rubinstein has a book called "Bargaining and Markets" where they have a detailed exposition on bargaining models. I think its free to download from Ariel's website. Apart from that, Abhinay Muthoo has a very nice book on bargaining: "Bargaining Theory with Applications".
You can always look up chapters on bargaining in Tirole's Game Theory or Myerson's Game Theory books. They're short, but quite detailed to develop the basic toolkits.


Why investing in bonds imply a decrease in money demand? In the description of so-called money market, we have demand,Md, for liquid money from individuals (and firms) and supply,Ms, of liquid money, likely from central banks. Now it is assumed that if interest rate,r, would increase, the demand for money,Md, would decrease due to people's preference of bonds(or other high yield securities) over money at high interest rate.

This doesn't make sense; whereas it is true that "households" would buy bonds in exchange for money at higher r, bonds are simply transfers of money, from households to firms or governments. So the aggregate money in the economy remains constant, as firms/governments would utilize the bonds' money in the economy. Thus, if we consider the economy as a whole, the "demand" for money does not change with people opting for bonds.

If we only consider the households' demand for money, then the analysis in money theory and LM curve would be inaccurate; In the discussion of LM curve, we have MV=PY and M/P =Md(Y,r). M/P essentially denote the "real money" supply from central bank. In the first formula MV=PY derived from money theory, If M/P hold constant, Y, also known as the aggregate income, is also constant; This is consistent if we consider the economy as a whole. However, in the second formula, It is understood that the money demand Md(Y,r) account for only the "households". It is unreasonable to discuss the dynamic between money supply and money demand when we have the whole economy in consideration on one hand and have only a sector of the economy weighted on another hand.

To sum up, I can understand that higher interest rate could encourage people to save up, thus effectively reduced the amount of money in circulation so reducing the "demand" but I do not see how opting for bonds decrease the demand for money unless only a sector of the economy is taken into consideration. Can someone provide some insight into this?

One thing to consider is that, when the Federal Reserve in the United States tries to manipulate the money supply, it does so through either putting more of its money into the market through bond purchases (supplying banks with money to lend) or holding money from the market through bond sales (leaving the money essentially dormant). It is not so much that bond creators receive money when people turn to bonds with higher interest rates but rather that the bonds change hands to people (households, firms, banks) who would have actually circulated money in some way if they held it in liquid form. The missing link is the central bank's money holdings.


Russian ruble drop in value due to low oil prices http://www.americanactionforum.org/research/impact-falling-oil-prices-russian-financing/

Based on the above article, the author states that "For budgeting, this favors the oil exporter, because a drop in oil revenues weakens the exporter’s economy—and consequently their currency". It makes sense that if oil prices are lower and traded based on USD values, it will hurt top line revenues for Russia since they produce oil. However, why does the second part of that statement have to be true? Why does the ruble depreciate against the USD?
The article as states "Since Russia sets its budget in rubles, not dollars, financing sources from foreign currencies are exceptionally strong relative to ruble". What does this mean for budgets to be finance in one currency vs another? Arnt all countries budgets in their own native currency? Why does this matter? What are the implications?

The Rouble depreciates against the US dollar because of demand and supply.

Think of it as a story that goes as follows:

a) In the ruble/dollar market, the supply of dollars consists of foreigners that have dollars and want to buy goods(oil and other things) and assets from Russia, while the demand for dollars consists of Russians that want to buy goods and assets from foreigners and need dollars to do so.

b) When the price of oil collapses 50%, then the foreigners only need to supply 50% as many dollars to buy all the oil they used to buy from Russia. So supply of dollars to the ruble/dollar market shrinks. When supply shrinks, prices increase.  Imagine that as the Russians want to buy foreign goods, say medicine, and they will be willing to pay lots of Roubles to buy said medicine, so demand for dollars does not change as much as supply of dollars.


How did Pareto came up with Pareto Distribution of wealth law? I am not an economist but a mathematics student. I heard about the Pareto law - the mathematical modelling of the distribution of wealth, how did Pareto come up with this law? technically speaking from the data perspective?
Is it a consequence of pure chance? The De Matthew principal in economics?
Are there any strong criticism to the law?

The Pareto distribution was derived based on the observation of Vilfredo Pareto that in Italy $80\%$ share of land belonged to $20\%$ of the country’s population, and he showed this held for many other countries as well (see Pareto Manual of political economy - the book is still being reprinted).
Consequently, based on this empirical observation it was argued that number of people $N$ with incomes higher than $x$ can be modeled as:
$$N = A x^{-\alpha}$$
and the Pareto distribution is based on the above.
In fact Pareto distribution is just another case of more general power law like Zipf's law (see Newman 2005). Power laws are quite common in nature for various reasons (see this article) - for example even human language follows Zipf's law (vsauce has nice video about this).
It is definitely not just due to chance wealth distributions can be approximated by pareto distribution as it is unlikely that this would be observed again and again in various countries across time if this would be just due to random chance. There are also economic models that imply that wealth distribution should follow pareto distribution. For example,  Wold & Whittle (1957) show that if you try to  model  the ratio of growth rate of wealth and mortality rate (which is important as wealth is distributed through inheritances) as a system of differential equations you can show that wealth should follow the Pareto distribution. However, this being said Pareto distribution pops out in many economic relationships (it even matters for income distribution which is log-normal with pareto tail), and I don't know of any generally accepted explanation for why this is (aside for the potential solutions offered in the sources mentioned here which still claim that this is not fully resolved puzzle).
As to whether there is any criticism of Pareto distribution in economics I am not aware of any substantial criticism. Pareto distribution is an empirical distribution so even in theoretical modeling it is mainly applied in situations where we can actually empirically verify that such distribution is present.
For example, optimal income and wealth taxation theory would work with any income/wealth distribution you can imagine. Pareto distribution was used for wealth for some time but until recently when it comes to income people used mainly log-normal distribution (e.g. Mirrlees; 1971), but recently people realized based on empirical observations that we should actually use log-normal distribution with Pareto tail for the upper incomes (e.g. Atkinson, A. B., Piketty, T., & Saez, E. (2011)). Hence if anything when it comes to research on income inequality the criticism is that it was not used enough. This being said I suppose if you would dig deep enough in  literature you could probably find examples when it was assumed/used even if it should not be. However, this is not really criticism of the Pareto distribution itself but rather its (mis)application in some specific instances.


CDO and Nonpositive Equity Questions I have two questions about statements made in this video: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/bank-bailout/v/bailout-2-book-value

At 6:25, the video shows a Collateralized Debt Obligation divided into an AAA-rated tranche, an AA-rated tranche, and an equity tranche, in order of increasing risk but also increasing return, and the claim is made that no one wants to buy the equity tranche. In my mind, the return on the equity tranche should self-adjust to make the market indifferent between the riskier and less risky tranches. Why would it have been so difficult to sell equity tranches that banks had to give up on the idea and hold them instead?

At 10:30, the video claims that a stock price goes to \$0 when a company has \$0 equity. Does this actually happen in the real world?  The video seems to state that this doesn't imply you can pick up the stock for free, but that's what a \$0 stock price sounds like to me. Since the value of a stock is indeed its equity divided by the number of existing shares, how does this case play out in companies that have \$0 or negative equity?

The speaker is too imprecise. Nobody wants to buy the equity tranche at a price that corresponds to its model valuation. If the tranche cannot be sold at that price, the bank structuring the CDO would take a loss. So they kept the equity tranche for themselves. Ideally, they would sell the equity tranche at model valuation, and eliminate their exposure to the deal (and just pocket the structuring fees for no long-term exposure risks).
It would be extremely unusual for someone to sell an equity of non-bankrupt firm at \$0, as the only conceivable motivation is to crystallize a loss for tax purposes. However, the equity can be made worthless in a bankruptcy restructuring, as the shares can be a claim on nothing. As such, the speaker in the video is speaking loosely.

There is no necessary relationship between the book value of a share and its market value. It is entirely possible that a firm has a negative book value for equity, yet a positive market price for its shares.


What are the benefits to the overall economy and consumer of horizontal integration? I understand that limited vertical integration can lead to a lowering of prices for products and services, but it seems to me that even limited horizontal integration only leads to less competition.

Horizontal integration may lead to lower costs by profiting from economies of scale. If the market demand for a product is spread over many enterprises, the costs will be generally higher because there will be more fixed costs in total. Instead, if there was a single company, fixed costs would be comparatively smaller.

The effect on the overall economy would be good. Lower costs mean more money for the company and/or lower prices for consumers. The effect on the consumers is not clear.


Walk through for calculating impulse response function, given VAR equation & coefficients Can someone walk me through how to manually calculate the IRF values that Eviews outputs for the effect of a nonfactorized one unit innovation.

I have my VAR equation and coefficients:

VAR Model - Substituted Coefficients:
===============================
MARKET_A = 1.38531644845*MARKET_A(-1) - 0.456533910287*MARKET_A(-2) + 0.0908884378218*MARKET_B(-1) - 0.0116001711851*MARKET_B(-2) - 0.0458678142475

MARKET_B = 0.0934164283416*MARKET_A(-1) - 0.0678660464848*MARKET_A(-2) + 1.34042022538*MARKET_B(-1) - 0.372260999882*MARKET_B(-2) + 0.0341759469926

The Eviews output for the effect of a nonfactorized one unit innovation from MARKET_A.

 Period MARKET_B    MARKET_A

 1   0.000000    1.000000
 2   0.093416    1.385316
 3   0.186763    1.471058
 4   0.258970    1.421328
 5   0.310545    1.318772
 6   0.346591    1.203253
 7   0.371878    1.092721
 8   0.389868    0.994217
 9   0.402869    0.909562
 10  0.412376    0.838231

Nonfactorized One Unit

To calculate period 2, I have tried plugging in the values in the equation i.e

0 for MARKET_B(-1),
0 for MARKET_B(-2)
1 for MARKET_A(-1)
0 for MARKET_A(-2)

but the output is not the same for the first period.
Obviously, I'm missing something. Could someone point me in the right direction?

I ended up figuring it out. I was including the estimated constant in my IRF equation/calculation in Excel, which shouldn't have been there and was throwing my calculation off slightly. This obviously compounded with each subsequent period.

I found this resource provided the eureka moment for me: https://www3.nd.edu/~esims1/arp_companion.pdf


What is the economic interpretation of this utility function? I have a utility function $U(c,l)={{C^\alpha-1}\over {\alpha}}+{{l^\alpha-1}\over {\alpha}}$ where C denotes consumption, l denotes leisure. What is the economic interpretation of the term $\alpha$ ($\alpha<1)$? Does changes in $\alpha$ affect the economic interpretation of the utility function as a whole?

The full problem is to derive the optimal labour supply. I get the answer $L={{1}\over {1+[w(1-t)^{{\alpha}\over {\alpha-1}}]}}$ where t represents  the tax rate. I am trying to understand the effect of $\alpha$ on the labour supply as I increase the tax rate $t$. How can I intuitively explain the role of $\alpha$ in this case?

This looks like constant relative risk aversion (CRRA) utility . Usually CRRA is written like $U = \frac{C^{1-\rho}-1}{1-\rho}  $ (I omitted second part for brevity) in your case $a=1-\rho$. $\rho$ is the relative risk aversion. By extension $a$ is the function of $\rho$ so as $a$ increases (due to smaller $\rho$) the person should become less risk averse.


ECB bond buying from national banks, what are the national banks expected to do? The European Central Bank announced plans to buy government bonds from national banks. Quantitative Easing, 60 billion euros a month. Although ultimately I am trying to make a decision on what this will likely do to the exchange rate, I am currently at the point where I don't know what the national banks will do with all of the financing.

What does the ECB expect will happen to national bank bond yields with their buying? How abnormal in amounts would their buying be than from investors buying the government bonds?

What does the ECB expect the national banks will do with all of the new "demand" for their bonds? Do more commercial lending to spur the economy? I also didn't get the impression that there is any actual new productivity taking place to really grow any of the individual country's economy no matter how much additional lending takes place. Opening up the potential to a wave of defaults, presupposing that more commercial lending would take place.

If anyone could shed some light on this, that would be great. Ideally not really opinion based, but more so in line with something official or some school of thoughts.

For analogies' sake, I really couldn't see the US Federal Reserve buying Montana bonds to spur commercial lending in Montana and thinking this would help the economy in Montana.

This question is now very relevant, with the ECB committing to buy over 1 trillion Euros of bonds in 2020. My understanding is that the ECB buys open market bonds, thus pushing their value up.
The goal, therefore, is to stimulate the bond market, and thus the economy.
In practice, I am still looking for information on what exactly the ECB buys with all that money.
Simple official explanation here


Currencies fixed to gold Based on the quoted section & example below:

Why would the Franc or USD fall in price vs the other if they are both fixed to gold; why would having less gold cause paper money to contract?
Why would economic growth cause upward pressure on the price of gold in terms of goods and services; yet, downward pressure on the dollar prices of goods and services.

  "When a country joined the gold standard its exchange rate against other member countries became fixed. If the exchange rate of, say, the US dollar against the French franc were to fall, then it would be cheaper for American importers of French goods to pay in gold than in depreciated dollars. Gold would flow to France. The US would have less gold to back its supply of paper dollars, which would then contract, pushing up the value of the dollar until it returned to its official price in terms of gold"

Thank you!

When it is said that currencies are 'fixed' against each other, they are maintained fixed. The exchange rate will still keep fluctuating, as there is obviously still a supply of and demand for the currency. The goal of the central bank is just to keep it within a certain range. In the case of a gold standard, the central bank basically guarantees gold as accepted currency. That makes that, if the U.S. dollar depreciates against the French dollar, U.S. producers will prefer to pay in gold, as your excerpt states. This basically reduces the supply of dollars, and the demand for French francs (how old is that textbook?!). So you can see that by guaranteeing the use of gold as a currency, the exchange rate automatically readjusts to a fixed level.
But the key is that is still fluctuates! This point is easier to appreciate in case a currency is pegged against another one. In that case, the central bank will actively intervene in the market for the foreign currency to keep the domestic currency within a certain band, by selling its foreign reserves. In the case of a gold standard, there is a sort of decentralized intervention: the central bank's guarantee incentivizes producers and consumers to use the form of currency (gold or cash) that is cheapest to them, and that way, both forms' prices continually readjust wrt each other.


what is the optimum level of production? The demand function of a monopolist is $q = 12 - p$ where $p$ is the price. Using the total cost and total revenue I was trying to calculate the optimal (short term) level of production.

I tried to solve it using the total revenue $r = p x$. Then I calculated the marginal revenue (the derivative of total revenue) and set it to $0$.
Then I got $p = 6$ and $x = 6$.

However, I never used the cost function, what did I do wrong?

Try to think about what the the optimal level of production is supposed to be. What should it maximize? The revenue?

What you have calculated is the revenue maximizing level of production but maybe you wanted to find a level of production that maximizes something different?


Universal Basic Income: Indexation and Inflation Let’s assume a monthly Universal Basic Income (UBI) payment of \$1,000 and an annual inflation rate of 2%. I would like to understand what would happen to the real value of this UBI (its purchasing power) in terms of year-zero prices each year for say 20 years. Namely, how much the original \$1,000 worth after 5,10, and 20 years?
This is the link to a google spreadsheet - I hope that I did the calculations right.

My questions are:
How to calculate the real value of the UBI in each year in terms of year-zero prices if there is NO INDEXATION? Obviously, the real value must decrease due to inflation, but I would like to see what is left from the original purchasing power of $1,000 in years-zero every year for 20 years.

This is what I have done in the Excel file attached:

The Column “Real Value” represents the purchasing power of the nominal (NOT indexed) UBI of 1,000 dollars. Is it correct?

The Column “Inflated Value” represents the INDEXED UBI, namely the UBI than would maintain the real purchasing power of the original $1,000 despite inflation. It is correct?

If the calculations are correct, why then the loss to inflation is lower (and decreasing) than the amount of yearly compensation by indexation which is also increasing? What is the logic and intuition behind this?

Thanks a lot!

Your real value column is wrong, but only slightly. You are decreasing it by 2% per year, but inflation of 2% doesn't cause real value to decrease by quite 2%. If there is 2% inflation, real value doesn't decrease by 2%; it decreases by 1 - 1/1.02 which is approximately 1.961% .

This is just the way percentages work. Since they are multiplicative, the inverse is different in magnitude:

If you lose 80% of an investment you have to gain 400% to break even.
If you lose 50% of an investment you have to gain 100% to break even.
If you lose 20% of an investment you have to gain 25% to break even.
If you lose about 1.961% of an investment you have to gain 2% to break even.

If you change your real value formula to =F6/(1+$F$4) you will get the correct values. You can also calculate the real value column by just calculating what portion of the buying power is left (1000/H26) and multiplying it by the nominal value: =1000*1000/H26. Both methods will give you the same result.


Relation between Inflation and Bank deposit interest rate? I have my own novice theory that bank pays you interest for your deposit so that the value of principal amount remains the same in the future (as due to inflation, the price of the commodity will rise and our principal amount will not be able to buy the same amount of things). Is this theory true.

Because if not, then I have to way to con the banks, this is how it will be done:

As we know that Rs 10 would have bought me more good (lets say that good is 1 kg of aluminium) in the year 2010 than in 2020 (which only gets us 800 gram of aluminium for the same amount). Now instead of depositing Rs 10 cash to banks (lets say interest is 10% per decade) I will deposit an equivalent amount of aluminium. So in 2020 I will have more aluminium at a premium price (i.e. 1.1 Kg aluminium at Rs 13.75 and compare it with the usual Rs 11 for cash deposit ). I will take advantage of both interest and inflation.

The US doesn't have a long time series of deposit interest rates available for free. However, they do have one month CD data from 1966 to 2013. This is a short term loan to a bank, that pays a slightly higher interest rate than a savings account. It is widely available across banks and FDIC insured for smaller balances. The following figure compares those one month CD interest rates with the rate of inflation:

The correlation coefficient between these two series is 0.72. So they do move together (which is not surprising). However, you can see that there are long periods where there are large differences between the two series. Sometimes these differences are positive and other times they are negative.


Is there any variable commonly used as a proxy for the inflation target set by the Central Bank? I have been asiggned to estimate a monetary policiy rule à la Taylor for my macroeconometrics class. There are no explicit inflation targets stated by the Central Bank (of the country I am the estimating the model for (Costa Rica)) for a part of the period whose data I must use. I would like to know if there is some variable commmonly used as an aproximation of proxy of the inflation target chosen by the Central Bank. Any help, commentary or reference to any bibliography is deeply aprecciated. Thank you.

Actually Costa Rica publishes inflation target. See the graph below provided by IMF where the inflation target is given by orange band (it is completely normal to target range rather than precise number):

There are no proxies that can be just lifted from statistics that I know of but there are ways how to discover how central banks set monetary policy even if it is not public.

For example, you can start with specifying some possible rules that central bank could be following (e.g. Taylor rule etc.) and afterwards you can conduct an econometric analysis that can show you how much the central bank behavior matches the 'guessed' monetary policy rule. Or alternatively you can deduce it from case studies of central bank's decisions. There are actually many ways how to do this and it is beyond the scope of stack exchange to provide extensive overview of them all.
Commonly used variables to do this are the interest rates that central bank sets, wider interest rates, inflation itself, inflation expectations, money supply aggregates and many more. Have a look at the literature below. However, there is no simple proxy as far as I know.
Examples of such empirical papers include Castroa, (2011); Bec, Salem, & Collard, (2002); Bernanke, and  Mishkin (1992); McGouldrick, (1984). Of course, the list is not exhaustive I tried to include diverse range of papers on this topic. You should have look at the sources cited therein and do additional search based on the keywords you find.


Current knowledge about the empirics of consumer theory I would like to get up to speed on the current state of empirical work done to test the assumptions and predictions of consumer theory (think Chapters 1, 2, 3, and 6 of Mas-Colell et al.).

Can anyone recommend a good survey or provide a brief summary of what we currently know about how much empirical support there is for our primary means of modelling individual behavior?

The primary literature concerned with this type of question (at least where classical results break down) is behavioral economics. There's a great general compilation of papers put together by the Russell Sage Foundation called the "Behavioral Economics Reading List" that includes, among other things, a General Introduction section with overview papers by some of the big movers and shakers (Camerer, Kahneman, Laibson, etc.).

Many of the papers you will find through the Russell Sage paper list will be on alternative methods to classical consumer theory. If you want just the tests of assumptions/predictions, I would recommend looking through the abstracts of John Lists's papers on Testing Economic Theory. List is one of the most prolific experimentalist authors on the subject and has weighed in on most questions that other people work on in this field as well. Just reading his abstracts on that page should give you a pretty good idea of the state of the literature up through 2011 (the website isn't updated). His CV is updated, but doesn't give you the abstracts without looking up the papers individually.


Uniqueness of utilities in competitive equilibrium Suppose several traders are given some initial endowment of goods. Then, a free market opens and they trade until the market is at a competitive equilibrium. Each trader now has a final utility which is at least as high as his initial utility.

MY QUESTION: Is the vector of final utilities unique? I.e, is this possible that, with the same initial endowments and the same utility functions, there will be two different equilibria in which the final utilities are different?

EXAMPLE: Suppose there are two goods and two traders, Alice and Bob, with the same utility function: $u(x,y)=x+y$. The initial endowment is $(10,0)$ for Alice and $(0,10)$ for Bob. In competitive equilibrium, the price vector has $p_x=p_y$. There are many different equilibrium allocations, for example: $(10,0),(0,10)$, $(9,1),(1,9)$ and $(5,5),(5,5)$ are all equilibrium allocations. But, in all these allocations, the utilities of both traders are the same: $(10,10)$. I would like to know in what cases this uniqueness happens.

If you look at this manuscript by Jonathan Levin (2006), pages 25-26 provide an example where there is multiple equilibria, and calculating payoffs in this case (if I am not making any calculation mistakes) gives different levels of utilities in these different equilibria.


What's the difference between a "consequential" and a "direct" externality? I'm reading Png & Hui on the economics of privacy. (http://128.118.178.162/eps/io/papers/0505/0505007.pdf great review article). Can someone explain the difference between direct and consequential externalities to me? as in:

  "Generally, in competitive settings, an improvement in the accuracy of
  productive personal  information may lead the less informed party
  (seller or employer) to include more or  exclude some marginal persons
  (consumers or workers).  This is a consequential externality on some
  members of the better-informed side of the market.  The consequential
  externality might be positive or negative. "

According to the examples given in the paper, direct externality results from, among other things, unsolicited promotions, while the sources of indirect / consequential externality are price discrimination, etc.

In this sense, the externality on the individuals (whose information is collected and used) is deemed direct if the information about them is used directly back at them (in the form of targeted advertising, for example). In contrast, indirect externality only occurs if the individuals choose to engage in transactions with the firm which has (collected or purchased) their information, and that these transactions make them vulnerable to price discrimination, etc. In other words, externality of this second kind occurs consequently.


If central banks become shareholders, where can investors go? The ECB is buying corporate bonds. It could eventually also buy shares. What would be left for investors to invest in? Letting bank shareholders pay for bailouts resulted in crashes of their shares. It was interesting to see how fast they went down. It seems like bank shares are relatively volatile. Letting lenders take hair-cuts is very impopular (maybe this is a separate question) but, would the ECB becoming a shareholder / bondholder amount to the same thing? Could it soften or break the opposition against taking hair cuts? (Who would be paying ultimately?)

What would be left for investors to invest in?

Stocks and bonds, as always. Just imagine the CB as another institutional investor. Institutions invest in the capital markets all day every day. Another large player will put upward pressure on prices due to increased demand. Upward price pressure can either be good or bad depending on what side of the trade you sit. From the POV of other investors entering the market it could be bad. But for investors seeking to exit and the corporate management and employees who either own company stock or their compensation is impacted by their company's stock price, it could be good.

  ...would the ECB becoming a shareholder / bondholder amount to the same thing?

It depends. The scenario you describe simply amounts to a shift in the risk pool. The bond risk pool is shifted from sovereign debt to corporate debt. Which is inherently riskier but, again, it depends on which corporations. Risk quantification would require a thorough analysis in order to be useful.

  Could it soften or break the opposition against taking hair cuts?

Whose to say? Anything is possible. Further comment would be speculative.

  Who would be paying ultimately?

As with any bank or corporation, all profit and loss of the ECB is borne by its shareholders. In this case, these are the central banks of the EU's member states. Primarily, Germany, France and (soon-to-be formerly, post-Brexit) UK. Closely followed by Italy and Spain. See this page for more details.


Does concavity of the utility function has any bite? A utility function in general has only ordinal meaning, any monotone transformation preserves the order isomorphism of the underlying preference ordering. However, there are several econometrics papers, that estimate demand with concavity shape restrictions on the utility.
Is this justified?
My first thought is that yes, that the key idea is that there exists a concave utility representation, and this generates the dataset, however it worries me the identification issue since there is infinitely many of these utilities not all of them concave.
In short, does it make sense to require concavity restrictions on the utility function in econometric work?

This post shows clearly why in the world of "standard" ordinal utility, concavity of a utility function cannot obtain an economically meaningful interpretation, although it may be useful as a mathematical property.

But "standard" ordinal utility is not compatible with Econometrics, because Econometrics deal inherently with situations where there exists uncertainty, and in a framework with uncertainty we move from "fully ordinal utility" to Expected Utility theory, where properties like concavity have economically meaningful content -they express attitude towards risk (as well as "preference intensity", as this laborious post shows).

The concavity assumption/restriction is made because there is universal consensus that the vast majority of people exhibit risk aversion in their economic behavior.


Difference between NPV and PDV What is the difference between Net Present value and present discounted value when periods are given in infinity $\infty$ . Both are then equal to $\frac M r$?

NPV and PDV are two different names for the same concept. If you were to receive M every year and the discount factor is $\delta$ then NPV = PDV = $\sum_{i=0}^{\infty}\delta^i M= \frac{M}{1-\delta}$.


Is the CES a special case of the translog production function? I was discussing today with a classmate about the relationship between prodution functions, and we tried to prove that the CES is a special case of the translog production function, but we failed. We have related the CES, the cobb-douglas and the leontief already, but we are missing the link with the translog. Is it possible to show the assumption in terms of CES parameters that yield a CES? Any help is more than welcome.

Thanks! Jonas.

the translog is an approximation of the CES function. Let consider a 2 factors production function $A(\alpha K^\gamma+(1-\alpha)L^\gamma)^{1/\gamma}$.
First, take the log of this production function, and then approximate this to the first-order using the McLaurin series for $\gamma$.

Using Mathematica (laziness, sorry):

Series[Log[A(\[Alpha] K^\[Gamma]+(1-\[Alpha])L^\[Gamma])^(1/\[Gamma])], {\[Gamma], 0, 1}] // FullSimplify

You reach
$%\log \left(A K^{\alpha } L^{1-\alpha }\right)+\frac{1}{2} \gamma(1-\alpha) \alpha  \left((\log (K)-\log (L))^2\right)+O\left(\gamma ^2\right)$

$\ln Y=\ln(A)+\alpha\ln K+(1-\alpha)\ln L+\gamma \alpha(1-\alpha)\left(\ln K+\ln L -\ln K\ln L \right)+O\left(\gamma ^2\right)$

This corresponds to the usual translog functional form used in econometric estimation.


Lifetime Budget Constraint An agent lives for 2 periods, consumes $c$ and saves $s$ at interest rate $r$ in the first period of life from income $y$. In the second period the agent consumes for any savings. We introduce a percentage tax $T^c$ on consumption in both periods where $0 < T^c < 1$. Assuming initially that $T^c_1 = T^c_2$. What is the consumer's lifetime budget constraint?

Answer: $$c_t (1+T^c_1)+ c_{t+1} \frac{1+T^c_2}{1+r} =y_t$$

I don't understand how we can calculate the budget constraint, can anyone help?

This is more easily seen by writing out the budget constraints for periods 1 and 2 separately, and then eliminate the saving $s$.

In period 1, the agent spends $\left(1+T_1^c \right)\cdot c_1$ on consumption, and saves the rest, so
$$(1) \qquad \qquad s=y - \left(1+T_1^c \right)\cdot c_1.$$

In period 2, the agents lives on savings (together with interest income), i.e., consumes all the savings, so
$$(2) \qquad \qquad \left(1+T_2^c \right)\cdot c_2 = (1+r)s,$$ where we multiplied $s$ with $1+r$ because of the interest from period 1 to period 2.

Now putting the two equations together, we have
$$
\left(1+T_2^c \right)\cdot c_2 = (1+r)s= (1+r)( y - \left(1+T_1^c \right)\cdot c_1).
$$
Divide both sides by $(1+r)$ and rearranging the terms, you get the desired result.


How to calculate constant GDP in international $ from nominal GDP in local currency units I want to calculate a constant GDP serie from 1995 till 2014 based on nominal GDP expressed in Yuan (Chinese currency).

I already get stuck on how to first make a constant GDP serie based on Yuan, let alone on international dollars.

Would it be enough to use the GDP deflator with base year 2014 to get constant GDP series in Yuan in 2014 prices?

You need to use PPP rates. These convert basket of goods in one country (in LCU) to that of (normally) the US, in US dollars. You can find these rates here or here. With these rates you can transform nominal GDP in Yuan into nominal GDP in USD. Then, you can use a US CPI or GDP deflator index to transform these nominal international dollars into constant international dollars. The base year is given by the price index you use.

You can rear more about PPP and how to use it here.

Finally, in case you do not want to bother to calculate this yourself, or that you want to confirm your calculations, here is the actual series of China's GDP in 2011 international dollars.


Specification of the parameters of this utility function [Behavioral Economics] This is from page 274 of "Advances in Behavioural Economics" by Camerer, Rabin, Loewenstein.
This chapter of the book is entitled "A theory about fairness, competition, and cooperation".

I have difficulty understanding parts of this equation. (see attachment).
I would need an explanation of the equation in detail (I assume this book is designed for graduate students, as I am currently an undergrad).
What do alpha and beta represent? What does monetary payoff mean exactly? Is it similar to game theory? Why is there a 0 in [xj-xi, 0]? And why is it 1/(n-1) and not n-1? This is very confusing for me, who has little mathematical background.

As @Henry commented and according to https://meta.stackexchange.com/questions/117251/what-should-be-done-with-questions-that-have-been-self-resolved-as-a-comment-ins I made a community wiki with the answer:

  αi and βi are coefficients related to how much an individual i feels bad about being less wealthy or more wealthy than other people. max{xj−xi,0} is the difference between person j's wealth and person i's wealth if person j's wealth is higher than person i's wealth; otherwise it is 0. The division by n−1 to get an average is because there are n−1 individuals apart from person i for person i to compare to.


Difference between Maximum Output and Potential Output In macroeconomics, what is the difference between potential output and maximum output? Or they are simply equivalent concepts? If they are different, how can we graph it in comparison to LRAS on AD-AS model?

Potential output and maximum output are often interchangeable and be used in place with each other. Another term is Maximum Potential Output, but the most commonly used is Potential Output. This google search shows that all the results on the first page use the term Potential Output instead of Maximum Output.


Is increasing the money supply possible with a gold standard? How about controlling interest rates? I understand that under a fiat currency, the government can buy securities on the open market to increase the money supply, and decrease interest rates. This monetary policy is possible to help recover from recessions. could this be done with a gold standard? Could the government increase the supply / lower interest rates?

Yes,  in principle,  under a gold standard,  the central bank can buy more gold, or build a mine and mine it, which increases money supply. This lowers  the short run interest rates. But the issue is that it typically can't fight the market price of gold: when the price of gold increases beyond the parity, people rush to exchange their paper currency for gold at the bank. This happens until money becomes so scarce that ir regains its value relative to gold.

This is very different from what happens with fiat currency.  With fiat currency,  the central bank can buy bonds, or gold,  but it can even just print money and give it away. ( The act of giving it for free to individuals is called a "helicopter drop". Dropping it from a helicopter is one way to actually do it...)

Even though in a gold standard,  the central bank can increase money supply,  this is different than buying bonds. This is because since money is backed by gold,  it can't loose value relative to gold.  In this case,  it's really hard for the central bank to lower the value of money if it wants, for example, to stop a deflation. Instead, because bonds are also denominated in the country's currency, making money lose value also makes bonds lose value and vice versa.


Continuity of Prices for Constant Elasticity of Substitution Production Functions Imagine I have a CES production function

$$ Y_{\sigma}   = Z [ \sum_{i=1}^N  \alpha_{i} X_i^{\frac{\sigma}{1-\sigma}}]^{\frac{1-\sigma}{\sigma}}$$

I know that as $\sigma \to 1$, the corresponding production function becomes the Cobb-Douglas production function

$$Y_1  = Z  \prod_{i=1}^N X_{i}^{\alpha_i}$$

My question is, is the same true for the corresponding cost functions? That is, if I have the CES cost function

$$C_{\sigma} = \frac{1}{Z} [\sum_{i=1}^N \alpha_i^{\sigma} P_i^{1-\sigma}]^{\frac{1}{1-\sigma}}$$

Is it true that as $\sigma \to 1$, $C_{\sigma}$ converges to the following Cobb-Douglas cost function?

$$C_1 = \frac{1}{Z} \prod_{i=1}^N P_i^{\alpha_i}$$

I think so. I didn't work out the proof myself but found in Wikipedia another version of the CES production function that has the same shape as your cost production function by replacing $1-\sigma$ with $r$. Here is the link. The exponents in the parameters $\alpha_i$ should cause no further complication.


Supermarkets industry market structure If the industry is dominated by a few major large retailers like Walmart and target with thousands of many other small supermarkets around the country, what is the market structure of the industry? is it a perfect competition or an oligopoly?

Oligopoly is best understood as occuring when firms behave strategically: when firms decide how much to produce, under oligopoly they will take into account the optimal responses of other firms.

If you have a long tail of small firms, beyond a certain size these firms won't have much influence at all on prices and will act as 'price-takers'.

So either the firms are large enough to have an impact - in which case everyone is an oligopolist, or they are small enough not to matter much - in which case the market is still oligopolistic because only the larger firms matter. Note competition authorities regularly block mergers in markets with 2-3 large firms and a bunch of very small ones: E.g. the European Commission's DG Comp has just blocked Siemens/Alstom given the large market shares of these firms, despite the fact that they face competition from a few smaller suppliers.

Only if all firms were small / had to act as price takers would you have something (that might approximate) perfect competition


Adding scaled CRRA utility Suppose our utility function is the usual CRRA utility with $\gamma=2$ so that:
$$u(C) = \frac{C^{1-\gamma}}{1-\gamma} = -\frac{1}{C}$$
Now suppose there are 2 goods, A and B, available for consumption. The consumption of A and B are denoted $C_A, C_B$. How do I compute the final utility?
For example, if I just add the utility, then the summed utility will be less than consuming either one of the goods, because the utility function is negative.
$$u(C_A) + u(C_B) = -\frac{1}{C_A} -\frac{1}{C_B} < u(C_A), u(C_B)$$
Suppose also that we want to make good B "more valuable". ie. 1 unit of good B should be worth more than 1 unity of good C. How would I reflect this in the utility function? A simple scaling with a value greater than 1 won't work, again because of the negative utility:
$$u(C_A) + u(C_B) = -\frac{1}{C_A} -k \cdot\frac{1}{C_B}$$
where $k>1$
Thanks in advance.

You have to be careful when comparing different utility functions.
For example the function
$$
v(C_A) = - \frac{1}{C_A},
$$
and the function:
$$
u(C_A) + u(C_B) = - \frac{1}{C_A} - \frac{1}{C_B},
$$
cannot simply be compared. The first represents preferences over one good, while the second gives preferences over two goods.
So if you say:
$$
u(C_A) + u(C_B) < v(C_A),
$$
you are in fact comparing two different utility functions.
If you want to know what happens if you only consume one of the goods, you need to compare, for example $u(C_A) + u(C_B)$ with $u(C_A) + u(0)$.
Also if you increase $k$ in the function:
$$
-\frac{1}{C_A} - \frac{k}{C_B},
$$
you are in fact making $C_B$ more valuable. To see this let's compute the marginal utility of $C_B$ relative to the marginal utility of $C_A$:
$$
\frac{MU_B}{MU_A} = \frac{\dfrac{k}{C_B^2}}{\dfrac{1}{C_A^2}} = k \frac{C_A^2}{C_B^2},
$$
which does increase in $k$. So the higher $k$ the higher the value of an additional unit of $B$ compared to an additional unit of $A$.


Trying to track down the earliest usage of rivalry, tangibility, excludability, and durability in economics I'm interested in a history of these terms, and wondered if anyone knows where I might find such a thing.
The first mention I can find for excludability is a 1957 law journal paper referring to a court case (inaccessible to me).
The earliest citation I've been able to find for rival goods is Chapman (1909), but mostly I see economics papers cite more recent textbooks (1980-2000).
Tangible goods seems to be a legal term, for which I can find the first mention in an 1889 law journal (which I also can't acccess).
The earliest reference I can find for durable goods is John Law (1750).
A secondary goal might be finding an authoritative source where all of these terms are tied together for the first time.

You can try Google Books Ngram Viewer. On the bottom of the graph, there is a Search in Google Books giving access to the references.


Constant Elasticity of Substitution (non-special cases) I am trying to better understand the CES function:

$$Y_{t}=C\left[\pi\left(A_{t}^{K} K_{t}\right)^{\frac{\sigma-1}{\sigma}}+(1-\pi)\left(A_{t}^{L} L_{t}\right)^{\frac{\sigma-1}{\sigma}}\right]^{\frac{\sigma}{\sigma-1}}$$

I understand the special cases where $\sigma=1$, where $\sigma=0$ and where $\sigma\rightarrow0$.

I am, for some reason, having a really hard time developing intuition for other cases. Don't the exponents cancel for all other values of $\sigma$ and the expression reduces to:

$$Y_{t}=C(\pi(A_{t}^{K} K_{t}) +(1-\pi)(A_{t}^{L} L_{t}))$$

This, of course, can't be right as $Y_t$ should vary for different values of $\sigma$, no?

The exponents do not cancel each other out. E.g.,
$$
(a^2+b^2)^{1/2} \neq a + b
$$
because
$$
(a^2+b^2)^{1/2} \neq (a^2 + 2ab + b^2)^{1/2}.
$$


Interpretation of the World Bank's definition of Portfolio equity inflows The following is the definition from World Bank:

Does it imply that apart from FDI, portfolio equity includes net inflows from equity securities including shares, stocks, depository receipts and direct purchases in local stock markets by foreign investors?

Yes given that ownership of 10 percent or more of the ordinary shares of voting stock is the criterion for determining the existence of a direct investment relationship. This threshold of 10 percent establishes a controlling interest, per guidelines established by the Organisation of Economic Co-operation and Development (OECD).

According to the OECD Portfolio investment is the category of international investment that covers investment in equity and debt securities, excluding any such instruments that are classified as direct investment or reserve assets.


Foreign Currencies Exchange Data I need data for forex rates because I'm working on a project to predict the rise and fall of the rates. Where can I find such data?

This isn't really a proper question for this network, but try:

http://data.worldbank.org/indicator/PA.NUS.FCRF
https://www.imf.org/external/np/fin/data/param_rms_mth.aspx


The concept of information structure in incomplete information games I would like your help to understand the concept of information structure in the incomplete information game at p.6-7 of this paper.

Let me summarise the game as described in the paper.

There are $N\in \mathbb{N}$ players, with $i$ denoting a generic player.

There is a finite set of states $\Theta$, with $\theta$ denoting a generic state.

A basic game $G$ consists of

for each player $i$, a finite set of actions $A_i$, where we write $A\equiv A_1\times A_2\times ... \times A_N$, and a utility function $u_i: A\times \Theta \rightarrow \mathbb{R}$.
a full support prior $\psi\in \Delta(\Theta)$.

An information structure $S$ consists of

for each player $i$, a finite set of signals $T_i$, where we write $T\equiv T_1\times T_2\times ... \times T_N$.
a signal distribution $\pi: \Theta \rightarrow \Delta(T)$.

A decision rule of the incomplete information game $(G,S)$ is a mapping
$$
\sigma: T\times \Theta\rightarrow \Delta(A)
$$

My question:

I interpret $\pi(t|\theta)$ as a probability that, conditional on the realisation $\theta$ of the state, the players receive as signals $t_1,...,t_N$, respectively. According to the given information structure, signals are more or less informative.

If this interpretation is correct, then I'm confused about the first sentence at p.7 of the linked paper: "If there is complete information, i.e., if $\Theta$ is singleton, [...]".

My first guess was that complete information is characterised by specifying $S$ and not by restricting the support of the state. In other words, I thought that complete information corresponds to the information structure $\bar{S}\equiv (\bar{T},\bar{\pi})$ such that

for each player $i$, $\bar{T}_i=\Theta$.
$\bar{\pi}(\theta|\theta)=1$.

Where am I wrong? Why the author defines complete information as having $|\Theta|=1$?

What you are defining is the complete information structure $\bar{S}$ with $\bar{T}_{i}=\Theta$ for all $i$ and  $$ \bar{\pi}(t|\theta) = \begin{cases} \ 1, & \text{if} \;\; t_{i}= \theta \text{ for all} \; i \\ 0, & \text{otherwise}, \end{cases} $$ for all $\theta \in \Theta$.

Note that this is not the same as the case in which $\Theta$ is a singleton, but it is rather an extreme information structure. The same authors define this here (Bayes Correlated Equilibrium and the Comparison of Information Structures - Bergemann & Morris), it beats me why they didn't include this detail in the paper you are looking at.


Converting current to constant USD values for trade data (UN Comtrade) I am using WB (country GDP) data in combination with UN Comtrade (bilateral trade) data. I need to divide bilateral trade by GDP so as to find out which % of a country's GDP comes from bilateral trade.
The problem is WB has values in constant 2010 USD while UN Comtrade in current USD.

How can I transform the current USD values in constant 2010 USD values?

Use the World Bank data on US inflation to deflate the UN Comtrade dataset, so that it is also in constant prices.

Select Download, at the right side of the page, and you can get the dataset in csv or other formats.

To deflate the trade data, simply divide the values of bilateral trade by the value of each years CPI index, and then multiply them by the value of CPI in 2010 (the base year, which is 100 in this case). Alternatively, rebase the CPI index, by dividing all values by 100, so that CPI in 2010 is equal to 1. Then, divide the trade data by this new index. Both approaches are equivalent.


How does depreciation affect the cash flow in a tax-paying company? I came across a question in first year's finance book.The question is:

For a tax-paying firm, an increase in ______will cause the cash flow from assets to increase.

A. Change in net working capital
B. Production costs
C. Depreciation
D. Taxes
E. Net capital spending

C is the right answer, however I am not clear why depreciation increase the cash flow. Thanks for your help.

Depreciation is tax-deductible. The firm in question pays taxes. If depreciation increases, then taxes paid decrease. If taxes paid decrease, then cash flow increases. ceteris paribus


"Auction" versus "Bidding war" Real estate sales sometimes occur at an official auction.  But sometimes a seller who does not take their house to auction may find themselves entertaining multiple bids for the house.  In this case, the articles on real estate always seem to talk about managing a "bidding war".  What is the difference between a bidding war and an auction?  Are there regulatory issues that prevent a seller from converting their bidding war into a straight-up auction?

(For instance, a seller with multiple bids could simply notify all bidders of the current highest bid, set a minimum bidding increment, and see if anyone bids higher, and repeat until one bidder is left.)

From a practical standpoint, bidding wars are effectively informal auctions. What is usually done is that the buyers inform their agents of their maximum price, and the buyers' agents tell the seller's agent "This is my client's bid, but please let us know if we're outbid." Sometimes this is formalized through what is known as an escalation clause, which is essentially an offer to bid some increment more than any other highest bid, up to some reservation price.

Some sellers accept escalation clauses, some don't, and this decision appears to be influenced partially through strategy and partially through custom in the area. Not accepting an escalation clause can force buyers into what is effectively a first-price sealed-bid auction, while accepting them turns it into more of a traditional (English) auction.

As an additional note, the point that @desnep makes is true— while proof of other bids is required, it's not always possible to determine that those bids in fact represent genuine offers to buy. My understanding is that for this reason, when bids are expected to be few, buyers are encouraged to submit fixed bids and be prepared to walk away if they lose out, as there's a stronger incentive for sellers to fabricate bids (i.e., market manipulation is more effective in less-liquid markets).


How can perfectly competitive firms earn zero profits? Consider a firm that chooses the quantity of labour $L$ to hire which maximises its profits. As usual, we suppose that output $Y$ is increasing in $L$ but at a strictly decreasing rate; and for simplicity, we suppose that labour is the only input used in production. The firm takes wages $w$ and the price of its output $p$ as given (which is meant to capture the notion that the goods and labour market are 'perfectly competitive').

As everyone knows, the firm should hire labour until it has driven the marginal revenue product of labour down to the wage. That is, the optimal quantity of labour $L^*$ must satisfy

$ w=MPL(L^*)p$

Here is the puzzle. If the firm chooses this level of $L$, it will make no profit from the last worker. But since $MPL$ is strictly decreasing in $L$, that means it makes a positive profit on all of the previous workers. As a result, the firm must make a profit - something which is meant to be impossible in perfect competition, at least in the long run!

To see the point graphically, note that the firm's profits are given by the triangle below the 'VMPL curve' and above the market wage:

Clearly, the area of this triangle is positive!

Before opening this up to discussion, I'll review some possible solutions:

One might think that the solution relates to the distinction between 'economic profit' and 'accounting profit'. However, this is a mistake. Suppose that there are no costs associated with production other than the wage bill (e.g. decision making is 'free'). Then there is no distinction to be drawn (economic profit = accounting profit) and yet the puzzle persists.
One might think that, under perfect competition, prices (whether $w$ or $p$) somehow adjust to wipe out the profits. But, as can easily be seen (e.g. from the graph), profits will be strictly positive for any $w$ and $p$ that induces $L^* > 0$.
As you will have noticed, the firm won't make any profit if MPL is flat. Perhaps this needs to hold in the long run?
One final solution (my favourite) is that, in perfect competition, the only firms will exist are those which minimise their average costs. One might think that this then induces near zero $L^*$ and thus near zero profits. But here one hits a technical problem: there is no value of $L > 0$ which minimises average costs. For any $L^* > 0$ you choose, average costs will be lower if $L = L^* - \epsilon$ for some $\epsilon > 0$.

Thanks in advance for any thoughts on this!

First, let's deal with the semantics and terminology aspect: what the word "profit" means in Economics, and what the word means in the everyday/business/accounting use, are two different things.

In its everyday business use "profit" is the surplus above all expenses including depreciation. So what business call "profit" the Economics discipline calls "net return to invested capital".

In Economics on the other hand, "profit", although never really "officially" defined universally, it essentially means "excess returns to capital above the market level", where the "market level", sometimes means "average level" sometimes it means "perfect competition level", or some other notion of equilibrium returns in the absence of exploitation of market frictions, market power and the like.

Perfectly competitive firms earn zero profits because perfect competition drives prices down to average cost - but where in "cost" we include what business call profits, because for us, it is payment to capital used in production.

Now let's consider the specific example of the OP, where "for simplicity" we have a single production factor, and where, the production function is strictly concave:

$$Q= F(L), \;F'>0, \;F''<0$$

The profit maximization problem here is

$$\pi = pQ - wL,\;\; \text{f.o.c.}: \;pF' = w \implies L^* = (F')^{-1}(w/p)$$

$$\pi^* = pF - pF'L = p(F-F'L)$$

For zero profits we should have

$$\pi^*=0\implies F - F'L = 0 \implies \frac {F}{L} = F'$$

or that average product in real terms equals marginal product. As long as the functional form of the production function is such that there is a positive level of $L$ for which this equality can hold, the argument of the theory is that competition will push the price to a level where the level of labour chosen will be such that all revenues go to payments for labor.

And if the production function does not allow for such an equality, then it simply is not compatible with a perfectly competitive market structure.

The OP should figure out how and why the diagram used in their post is misleading.


Complementarity in CES Production Function I'm reading Fisher (1997, Journal of Monetary Economics). From the intermediate goods produced ($Y_t$), the final goods firm allocates into consumption ($C_t$), business capital investment ($I_{b,t}$), and household investment ($I_{h,t}$) s.t....

$C_t + (I_{b,t}^K + I_{h,t}^K)^{\frac{1}{K}} \le Y_t$

Fisher claims when $K>1$ there is complementarity in production, but my intuition is failing me. If $K>1$, $I_t = (I_{b,t}^K + I_{h,t}^K)^{\frac{1}{K}}$ is maximized when I invest all savings into either business or investment capital, while $I_t$ is minimized when I split my savings equally between the two. To me this sounds like anti-complementarity.

Can someone point one where my intuition is going awry? If it helps, on the utility side of things is log-utility w.r.t to $C_t$, $K_{h,t}$, and $L_t$ (leisure).

Total investment in terms of how much capital is augmented, is always $I = I_{b} + I_{h}$.

$(I_{b}^K + I_{h}^K)^{\frac{1}{K}}$ is equal to the amount of the intermediate good $Y$ that we need to allocate for investment. And given the formulation and when $K>1$ we see that we economize on the amount of the intermediate good $Y$,

$$Y_I = (I_{b}^K + I_{h}^K)^{\frac{1}{K}} < I_{b} + I_{h} = I$$

Further, if we split investments equally, we achieve the maximum possible economy (i.e. the minimum $Y$ required for given total $I$ to be achieved).

So inherently, the formulation "pushes us" to keep the two investment levels close, because the further apart they are (for given total $I$), the more $Y$ we will require, reducing consumption. This "closeness of levels" is what the author refers to as "complementarity" (perhaps confusingly, if one has the micro/demand-production theory meaning of the term in mind).

Fisher, J. D. (1997). Relative prices, complementarities and comovement among components of aggregate expenditures. Journal of Monetary Economics, 39(3), 449-474.


How can autonomous private spending change budget surplus? I was reading Keynesian economics in R.Dornbusch's book where he mentioned the defects of using budget surplus as a measure where he says it can be changed and effected by autonomous private spending which I couldn't logically get.Can someone explain?

In a very rudimentary sense, the question can be answered in the following way :
We see that
$BS = tY - G - TR $

As you put in the quote, Dornbusch is arguing that budget deficit/ surplus is not a good measure to gauge government policy.

EXPLANATION:
For example, a deficit doesn't always mean that $G$ is large or that the government is spending to increase income. An increase in budget deficit can occur if there is a reduction in private spending (which is $I$) - since that leads to a reduction in $Y$, which reduces $tY$ (tax collections) that increasing deficits.
When he says that private spending can affect budget surplus, he means that private spending $I$ can affect the level of income $Y$ which can affect $tY$ (tax collections) which can impact Budget Deficit/Surplus.
Hope this helps!


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

Think of your function as

$$Y=[A_1Q^\sigma+ A_2X^\sigma]^{1/\sigma}$$

where $Q=L^\alpha K^\beta$ (I removed unnecessary bits like $\gamma$ and exponent of $A_i$). This is a standard CES, where the optimal use of $Q$ and $X$ depend on $\frac{A_1}{A_2}$ and $\sigma$.

For a relatively low substitution ($\sigma<0$), an increase in $A_1$ (holding factor prices fixed) means firms make use of that extra increase in productivity of factor $Q$ by using less of it and more of $X$. Since $A_1$ corresponds to a Hick neutral change regarding $Q$, you will use the bundle $Q$ with the same initial $K/L$ ratio than before the change in $A_1$. Therefore, you will reduce both $K$ and $L$. In consequence, an increase in $A_1$ could be thought as labour-saving technical change with respect to $X$, and in absolute value (although notice that $K/L$ remains unchanged).

The reverse is true if $0<\sigma \leq 1$, namely an increase in $A_1$ leads to more use of $Q$ relative to $X$, thereby expanding the use of $L$ and $K$.

Meanwhile, in the inbetween case ($\sigma=0$), the function collapses to a Codd-Douglas:

$$ Y = \left(L^\alpha K^\beta\right)^{\phi} X^{1-\phi} $$

where $\phi = \frac{A_1}{A_1 + A_2}$. Here a change in $A_1$ does not affect the K/L ratio, albeit it does affect the optimal ratio with respect to $X$. But commonly technical change is though as a change in some $A$ rather than in the elasticities of factors, so this case does not nest well with the above. I think this might be because the original function is not properly normalised. This is, the terms $A_1$ and $A_2$ do not add up to one, which is necessary given your original assumption of constant returns to scale.


IV - Is this procedure valid? I have three variables: $y$, $x_1$ and $z$.

I'm interested in finding the effect of $x_1$ on $y$.
Unfortunately $x_1$ is endogenous so I use an instrument z.

I know that $z$ is correlated with $x_1$. The problem is, $z$ is correlated with another variable ($x_2$) that arguably has an effect on $y$. $z$ is unlikely to have a causal effect on $x_2$, but $x_2$ may still be endogenous for other reasons (e.g. reverse causality, etc.).

Will the following procedure give me a consistent estimate of $\beta_1$:

two stage least squares with $y$ regressed on $x_1$ and $x_2$, with $z$ as an instrument for $x_1$?

Actual availability of regressors may be an issue here, but if all four mentioned variables are available, the situation is as @Michael mentioned in a comment:

Since $X_2$ is correlated with $Y$, it should be included in the regression specification as a "control".

$$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + u$$

This is intuitive, but it also takes care of the technical aspect.
Then since $X_2$ is endogenous, i.e we have ${\rm Cov}(X_2,u) \neq 0$, but we have an instrument that is not correlated with the error term $u$ since $X_2$ has been included in the specification, we end up with

$$Y=\beta_0 + \beta_1Z + \beta_2X_2 + u$$

for which the OLS estimator will be asymptotically consistent, since (writing $\mathbf W = [1:Z:X_2]$)

$$ \hat \beta = \beta + \left (\mathbf W'\mathbf W\right)^{-1}\mathbf W' \mathbf u$$

and its consistency will depend on the following probability limit being zero

$${\rm plim}\mathbf W' \mathbf u ={\rm plim} \left[\begin{matrix}
\frac 1n\sum u_i\\
\frac 1n\sum Z_iu_i\\
\frac 1n\sum X_{2i}u_i\\
\end{matrix}\right] \rightarrow  {\rm plim} \left[\begin{matrix}
\frac 1n\sum E(u_i)\\
\frac 1n\sum E(Z_iu_i)\\
\frac 1n\sum E(X_{2i}u_i)\\
\end{matrix}\right]= \left[\begin{matrix}
0\\
0\\
0\\
\end{matrix}\right]$$

holds because both $Z$ and $X_2$ are orthogonal/uncorrelated to the error term $u$.

In other words, the fact that the regressors $X_2$ and $Z$ are correlated with each other does not create any problem (as long as of course the co-linearity between them is not near-perfect), on the contrary it more generally justifies including both in the regression specification, making it "multiple regression" -it exists exactly for such cases.


Is there a definitive way to tell if an action causes a movement or shift in a supply-demand graph? I am taking AP Macroeconomics, and am about 2/3 of the way through the curriculum. We have learned about various supply-demand graphs, and right now we are working on the market for money. I have noticed that with every model we learn about, there are a set of rules to remember which tell whether something will be a shift in the supply-demand graph. However, it is not ideal to have to remember these rules for every model we have looked at.

Is there any general rule for what events will definitely cause a movement, and what events will definitely cause a shift?

Thanks!

The supply and demand curves are plotted as functions of price. Hence:

Changes in price will result in movements.
Changes in anything else will result in shifts.


What are the alternatives to currency devaluation? What are (or are there) alternatives to currency devaluation? Phrased differently, what are the mechanisms that a country could use to make its products more competitive and to boost exports, when:

it is under a currency board?
it has an external1 central bank ?

1. When the local central bank is not allowed to print its own money. For example in the Eurozone , the capital stock of the European Central Bank is owned by the local central banks of all 28 EU member states, however the ECB alone administers monetary policy.

The only alternative is what is often called "internal devaluation". This basically means reducing the actual (domestic) prices of goods in a country.

This is what is often called as increased "competitiveness". It is most often achieved through cutting wages or slowing down wage growth. This is because wages are most often a huge cost factor and the price of capital (which is often bought internationally) is harder to reduce just like that. However there is also the phenomenon known as "downward nominal rigidity", which means people don't accept lower nominal wages, so it's very difficult to lower wages. Much harder than increasing them. In fact, in practice, it's easier to increase inflation to reduce real wages than actually reducing the number printed on your check at the end of the month. However in this case, we want deflation (reduction in prices) to boost exports, so the whole matter gets more complicated.

Technically a devaluation only makes all your domestic goods cheaper abroad. This can also be achieved by just reducing your prices of course. However, as we saw, this is difficult. Also there is a coordination problem, as each industry would have to adjust (thousands of prices must adjust) for the same effect as the exchange rate adjusting (one price adjusts).

Milton Friedman used to compare this to daylight savings. We could all just agree to push all our appointments and activities by an hour for some time, which is hard (this would be internal devaluation). Or just change the time for the same effect (exchange rate devaluation).

A surge in quality is technically also an alternative, but not possible always and especially not short-term.


Inc Linear Transformation of Bernoulli Utility According to MWG Proposition 6.B.2, it illustrates that the expected utility form is preserved only by increasing linear transformation.

What is the significance of this proposition?

The part I find challenging in connecting the dots is when right after the proof of this proposition, the authors claim that this proposition allows us to interpret meaning in differences of utilities. How are these two exactly connected?

This is a subtle topic. Any strictly increasing transformation will preserve the ordering of lotteries. This is the standard result saying that utility is just an ordinal thing, we really don't care about the level of it.

In the other hand, there are representations os someone's preferences that are easier to work with, from the calculations point of view, or improve our understanding of the underlying economics of the problem. One example is when we have quasilinear preferences on good 1 (check MWG, chapter 3 for this example). When this is the case, we have that $U(x_{1},...,x_{I}) = x_{1} + \phi(x_{2},...,x_{I})$. Of course, if we take, say, the exponential of $U$, we will preserve ordering, but not this very useful representation.

When it comes to chapter 6 and lotteries come on the stage, the same happens. One's utility over a lottery (think about it as a distribution of consumption over different scenarios) might be a very complicated function. Maybe, the utility you get by holding an umbrella if it starts to rain also depends on the utility you get when your football team wins and you are not at home watching the game. The V.N.M. utility representation is useful exactly because it separates utilities of different scenarios.

So, when you start comparing lotteries, the effect of an increase in the probability of holding an umbrella when it rains in a given lottery is completely isolated from the effect of a higher probability of another scenario. If we keep consumption fixed over scenarios and let only the distribution of probabilities describing what can happen vary, the V.N.M utility form will let us isolate effects of different probabilities over scenarios and express difference of total utility by difference in probabilities over scenarios between two in-comparison lotteries.

The reason behind only linear transformations conserve this format is that the V.N.M utility form is linear, by definition, and non-linear transformations of linear functions are not linear. This is somewhat related to Jensen's inequality, from my perspective (that's at least how I intuitively interpret that).

I hope this helps!


Question on overlapping generations My question is from over lapping generations
Question is as follows

I found that
$$k(t+1)= \frac{\beta(1-\alpha)}{(1+\beta)(1+n)}A(t)k(t)^{\alpha}$$
How can I deal with A(t) to find the steady state $k^*$?
By the way, at steady state,$ k(t+1)=k(t)=k^*$

Is that derivation for $k(t+1)$ correct? Technically, you never reach the steady state, but only asimptotically as $t\rightarrow\infty$, but at infinity the $A(t)$ will also be infinite because it grows exponentially with time. I suspect that $k(t+1)$ should depend on $(1+g)$ instead of $A(t)$.
Usually these models are expressed in units of effective labor, that is, dividing the capital stock $K(t)$ and the labor $L(t)$ (and hence, the production and consumption) by $N(t)$ and $A(t)$.


How to estimate loss of customers due to customer support inefficiency? I have a data about customers and their activity on a website for a two-year period. Also, I have a customer support work evaluation data for a shorter period of that two-year period. The question is:

How to find out if inefficient customer support affected loyalty of customers and, in particular, how many customers were lost due to this factor?

So far, I just made a simple comparison on how many customers kept using the website after leaving the negative (unsatisfactory) or positive (satisfactory) evaluation of the customer support work. The comparison shows that the customer retention rate for customers who left negative feedback is lower than for those who provided positive (satisfactory) feedback.

I'm not an economist, but I'm sure there's a more scientific way to estimate the influence of one factor on another using statistical analysis.

The best way would be to use a regression analysis, What i would do as an economic major would be use two independent variables such as in your case level of customer support, customer feedback to see if the dependent variable "customer retention rate". also you need to use parameters for customer support evaluation, customer feed back and customer retention rate for the years. Then run a regression analysis to find if the independent variable are co-related to your dependent variable, thus you can arrive at a statistical justification for your problem.


What are good dataset alternatives to estimate value functions? Suppose we want to estimate for many goods in the economy (or classifications thereof) the preferences of each household for these goods. We may want to restrict the analysis to specific utility classes, e.g. translog or CES utility. Naturally, we can not obtain the utility function but only the value function.

To my knowledge the Nielsen Datasets from U Chicago seem to provide such a possibility, but have highly restrictive access. What are good alternatives?

As I understand it, you're trying to estimate a demand system for different goods.

Have a look at Aguiar and Bils (forthcoming AER), who use the consumption expenditure survey to do exactly that. The previous link also contains their data and code.

From their abstract:

  We do so by constructing an alternative measure of consumption expenditure, using data from the Consumer Expenditure Survey (CE), that employs a demand system to correct for systematic measurement error. Specifically, we consider trends in the relative expenditure of high-income and low-income households for different goods with different expenditure elasticities.


Does Direct Benefit Transfers make an economy poorer? Printing money and giving to the poor causes inflation.
Increases demand and hikes prices. This is basically certain.

But on the contrary, a paper titled Debunking the Stereotype of the Lazy Welfare Recipient:
Evidence from Cash Transfer Programs1 by Nobel Laureate Abhijit Banerjee ,MIT stresses that directly giving out monetary benefit does not make workers lazy and increases productivity with experimental proof from 7 programs.

Is this not in direct conflict with this concept that handling out money to poor,when goods and services are limited would cause inflation.
It turns out this is even being implemented in my home state post a cyclone amidst the pandemic, so I'm confused as to which outcome is possible given they are in direct conflict with each other ?

You seem to be having some misconception how these transfers work

  Printing money and giving to the poor causes inflation. Increases demand and hikes prices. This is basically certain.

This is not generally how government transfers are done. In fact it is very rare to see in practice transfers that are payed by directly printing money. However, if it would be done it would ceteris paribus increase price level and hence cause inflation. It might happen indirectly by central bank buying up government bonds, but governments issue debt for plethora of reasons so its not straightforward to attribute it to any particular transfer. Moreover, if the policy is just paid out of the budget without accompanying monetary expansion then in principle it should not lead to inflation per se. Even if it did, inflation in principle does not necessary decreases the economy's output making it poorer (especially if the inflation is very low, as its rate increases it can also negatively affect output but that usually requires high rates of inflation).

Next the article from Banerjee does not even discuses whether transfers make economy richer or poorer.  The article only shows that the labor supply responses of the recipients of cash transfers are not as bad as is often thought and that they are relatively efficient way of combating inequality and poverty compared to other transfers. Moreover, they also show they do not provide incentives for  some bad behaviors as much as was thought. This is not the same as saying transfers make society richer.

Now to your main question whether direct cash transfer makes economy poorer or richer depends on what is their effect on output. Unfortunately there is no straightforward answer as it depends. Transfers create efficiency loss because they distort incentives of people to produce goods and services in several ways. First, the transfers must come out of somewhere - so usually countries have to raise taxes. These in turn lead to dead-weight loss as these taxes distort peoples optimal choices when it comes to their consumption/labor supply and their economic activity in general (for example income tax creates substitution effect from working to leisure). At the same time they also distort the behavior of recipients, as people have less incentive to work when they receive transfers (this is not an exhaustive list of all effects just examples).

However, transfers also create several benefits for society. For example during economic crises some transfers (such as unemployment benefits) serve as automatic macroeconomic stabilizers and can help recessions to be milder. There is some tentative evidence that economic inequality is actually bad for economic growth although jury is still out on that (see Barro, R. J. (2000). Inequality and Growth in a Panel of Countries. Journal of economic growth, 5(1), 5-32. -  the research shows some evidence for inequality retarding growth in poor contries and boosting it in richer countries - but see also sources cited therein some authors claim that inequality retards growth even in rich countries). There might be other efficiency reasons why transfers, including cash transfers, might help to raise output.

Whether the benefits of transfer to the economy are larger than cost is complex question that is frankly poorly understood and not yet intensively studied as it depends on what are the effect on inequality on growth and productivity and the relationship between them is anything but straightforward. The answer will for sure depend on what is exactly the size of these transfers and also how exactly they are paid for. However, to the extent that our society wants to have transfers the research of Banerjee shows having direct cash transfers might be one of the more efficient ways how to do that, and thus even in case that the transfer would make economy poorer in general a direct cash transfer might have less negative effect than other type of transfers.


Currency triplets - arbitrage opportunity? I have three currency pairs - USDEUR - 0.88, USDINR - 67.13 and EURINR - 75.88 , so simple math tells me that EURINR should be USDINR/USDEUR = 76.28 ...this is a fairly significant deviation from an exact conversion and i am sure i am forgetting something basic here.

Take the yen now and when i do a similar calculation USDJPY - 100.21 and USDINR - 67.13 and JPYINR - 0.67 ..result of USDINR/USDJPY gives me 0.6698 which is extremely close to the exchange rate.

Questions

a) what explains the difference in the first case? Is it because the factors impacting exchange rate between the pairs of countries are different ? (for e.g. US invests a lot more in India than Europe as a whole hence INR should be very reactive to changes in USD but not so for EUR ? )

b) How come there's a difference in the two cases shown? JPY seems to fit the equation rather nicely.

Apologies if this sounds confusing, I regret not paying attention to these classes in B school :(

Think currency rate as simply the price, on the currencies market, of one currency in terms of another. But this is not a perfect market, so to answer your question with some concrete cases:

even if you want to purchase at time T(price) a certain amount of currency at price P, it's not guaranteed that at the time T(transaction) the price is still P; market is open 24/7 with several transactions every minute that modify the price with rapid changes in supply/demand;
currency market is not like a grocery store where there are two actors, a price, a transaction, and calculations can be done on the back of the envelope. To sell / buy currencies you need to involve external agents like banks and third-party agencies, all contributing to the final real price;
risk is not 0: as per first bullet, events can cause currencies fall several points, and the losses should be considered in the real-rates model.


Formula for the unconditional variance of the sum of observations from an autoregressive time series I have notes that say that we can make the following calculations. I'm a little confused about some of the calculations that are being made. What assumptions would I need to get the following results? Or are there errors? Specifically, I am confused by equation (1) below. In particular, this is strange to me because if I let $\rho = -1$, then equation (1) sometimes gives negative variance. (Perhaps the calculation is undefined when $\rho = -1$?)

Let $r_{t,t+n} = \sum_{i=1}^n r_{t+i}$. Suppose that $r_t$ is an AR(1) process (say with errors given by a mean zero Normal distribution with variance $\sigma^2$) where
$$
\text{Cov}(r_t,r_{t+j}) = \rho^j \sigma^2
$$
and thus
$$
\text{Corr}(r_t, r_{t+j}) = \rho^j.
$$

The notes that I have say that $\text{Var}(r_{t,t+2}) = 2(1 + \rho) \sigma^2$ and that
$$
\text{Var}(r_{t,t+n}) = \left( n + 2 \sum_{i=1}^{n-1} \rho^i (n-i) \right) \sigma^2. \tag{1}
$$

(FWIW, this question deals with cumulative (log) returns.)

For an AR(1) process (I omit any drift), the coefficient on the lag is the 1st-order correlation coefficient,

$$r_{t+1} = \rho r_t + u_{t+1}$$

So

$$r_{t,t+2} = \sum_{i=1}^2 r_{t+i} = r_{t+1} + r_{t+2} = \rho r_t + u_{t+1} + \rho r_{t+1} + u_{t+2}  $$

$$=\rho r_t + u_{t+1} + \rho \big(\rho r_t + u_{t+1}\big) + u_{t+2} = \rho(1+\rho)r_t+(1+\rho)u_{t+1} + u_{t+2}$$

and now the three components are independent. So

$${\rm Var}(r_{t,t+2}) = \rho^2(1+\rho)^2\frac {\sigma^2}{1-\rho^2}+ (1+\rho)^2\sigma^2 +\sigma^2$$

$$=\left( (1+\rho)^2\frac {\rho^2+1-\rho^2}{1-\rho^2}+1\right)\cdot \sigma^2$$

$$=\left( \frac {1+\rho}{1-\rho}+1\right)\cdot \sigma^2 = \frac {2}{1-\rho}\sigma^2$$

So we arrive at a different formula for ${\rm Var}(r_{t,t+2})$, compared to the one provided in these notes, and we will arrive also at a different expression for general $n$.

Note that my result is valid for $\rho =-1$, giving ${\rm Var}(r_{t,t+2}) = \sigma^2$ in this case since here

$$r_{t+1} = - r_t + u_{t+1}$$

and so

$$r_{t+1} + r_{t+2} = - r_t + u_{t+1}- r_{t+1} + u_{t+2} = - r_t + u_{t+1} - \big(- r_t + u_{t+1}\big) + u_{t+2} = u_{t+2}$$


What happend to the dollar value in the time of the housing crisis I am wondering what happens to the value of the coin in a country with an housing crisis. Take the USA as an example: They had a housing crisis and I wonder how it effected the value of the dollar and why?
In addition to this particular example, are there any general effects on a currency that are observed in countries in which a real estate bubble burst?

It is not immediately obvious precisely when the recent US housing crisis took place: prices started declining in 2006 (https://fred.stlouisfed.org/graph/?g=cvjE) causing disruption in the financial markets in 2007. The peak of the crisis was possibly in September 2008 when Lehman Brothers failed and the mortgage securitizing enterprises Fannie Mae and Freddie Mac were taken over by the federal government.

US consumer prices fell slightly in the second half of 2008  (https://fred.stlouisfed.org/graph/?g=cvjm) while it was rising both before and after that period, so you might say money became slightly more valuable in terms of goods and services

In the same period, the value of the US dollar rose against other currencies (https://fred.stlouisfed.org/series/TWEXB), typically described as a flight to safety by worried investors during the worldwide financial crisis

There is no particular reason to believe exactly the same things would happen in other housing crises or in other countries, but it is reasonable to expect a housing crisis to reduce consumption (the construction sector shrinks while others feel poorer) possibly leading to a recession and perhaps lower inflation.