Should housing be considered a form of capital for the purpose of capital gains taxation? Economists across the political spectrum almost unanimously oppose the home mortgage interest tax deduction. While I'm sure there are a few whom I've missed, I could only find a single professional economist who supports it. Greg Landsburg believes that capital income should be untaxed, based on the Chamley-Judd model and its subsequent refinements. He argues that the home mortgage interest tax deduction effectively cancels the distortionary tax on home mortgage interest capital income, and so represents a step in the right direction, although he would prefer a complete elimination of all capital income taxation.

But does housing really counts as "capital" in the Chamley-Judd sense? A textbook example of capital gains is a lender lending money to a borrower who uses it to buy sewing machines, tractors, etc. and start up a new company, which then turns a profit and allows the borrower to repay the loan with interest. In this example, everybody wins (the borrow, the lender, and the new company's customers), and the Chamley-Judd result that these kind of loans should not be taxed is very reasonable and intuitive.

But as Greg Mankiw's Intro to Economics textbook points out, housing is somewhat of an edge case between capital and consumption, and the fact that "capital" is traditionally defined to include housing is a bit of a historical accident. Morever, there is debate among economists about whether or not housing should be properly classified as capital. (Mankiw also wrote a New York Times column on this issue.)

I'm not familiar with the precise assumptions of the Chamley-Judd model, but does the main result that capital income should be untaxed include income from housing appreciation? People typically buy first homes (the only kind to which the mortgage interest deduction applies) for their own personal use, not primarily as investment opportunities. It's not obvious to me why housing purchases would lead to the creation of new economic wealth as more traditional capital investments do. In contrast to Landsburg, Uwe Reinhardt claims that

  If pressed, the proponents of the capital-gains preference might concede that a tax preference for gains on transactions in residential real estate is hard to defend.

Under the assumptions of the Chamley-Judd model (or looser, less formal economic reasoning), is housing naturally classified as capital whose appreciation should not be taxed?

I think there are a few different ways one can go about examining the topic and general question you bring up. For that reason, I'd like to highlight that this isn't my primary field, and so my answer might not align with a more expert view from that field. However, to get the ball rolling...

First, we should probably take a short digression and consider the intuition behind what their results suggest; why exactly is taxation on capital income so problematic? Generally, it's because it creates a comparatively large distortion in future consumption. As Banks and Diamond (2010) shows starting on page 31, capital taxation leads to increasingly large wedges in consumption as the number of periods increases. Unlike labor taxation, which creates large, but contemporary, distortions in consumption, capital taxation creates intertemporal distortions.

From that point, I think there's a growing literature questioning whether the traditional Chamley-Judd result is actually as substantial in application (as opposed to theory) as some consider it to be. For example, there are several, different papers which get non-zero optimal taxation rates on capital if there's endogeneity in wages, or if wages from different types of labor cannot be taxed at their individually optimal rates. In fact, one of these potentially problematic areas is entrepreneurship: as Reis' dissertation (2007) points out in the third chapter, "when entrepreneurial labor income cannot be observed separately from capital income, then it is optimal to have positive capital taxation in the long run." A pretty comprehensive analysis by Straub and Werning (2015) does a wonderful job of thoroughly analyzing both models presented by Chamley (1986) and Judd (1985) and highlighting which assumptions end up leading to their landmark result. Perhaps a useful workthrough of the math can be seen in Moll's lecture notes, where it's relatively straightforward to get a positive optimal taxation rate, depending on the intertempoiral elasticity of substitution considered in utility.

Second, I'd point out that there are reasons to be skeptical, even inside either Chamley or Judd's frameworks, that housing interest payments should be considered as capital. Most prominently, both models (I believe) assume no financial constraints (they only require no-Ponzi scheme conditions). Therefore, any agent would be able to purchase a house "out of pocket" (or through costless single-period bonds where the only interest payment is the one imposed by discounting). This in and of itself suggests that mortgages (as we observe them in real life) shouldn't ever be used, since you never ought to pay for liquidity beyond the natural rate of interest. Since mortgages are effectively assumed away in the model, I'd be cautious of applying the model to the optimal taxation of mortgage interest in the first place.

This, I hope, is a bit instructive for the third point- I agree with your skepticism that housing should be viewed as a capital good in this context. Not only because it isn't clear in the general debate of whether housing is capital or not, but also because it doesn't seem to create the same distortionary effects that lead to the zero-capital taxation result even if we accept the Chamley-Judd result. Given that the interest payments aren't an infinite horizon stream of payments (you'd hope), the wedge wouldn't necessarily lead to the same "intertemporal snowballing" that we observe in both models (and that serves as the basis of their zero-capital tax rate finding to begin with).

If I think of any more, I'll be sure to come back and update this answer. And I hope that this just gets the ball rolling for others (which more specialized knowledge in either public economics or optimal taxation theory) to provide more insightful comments. And let me know if this answer was just totally non-responsive to the question you were really interested in to begin with- it's pretty early in the morning here, so I can't guarantee my mind is working at capacity yet!


static/dynamic optimization The interesting paper Calvo and Obstfeld (1988) uses two-stage optimization on an OLG model which then reduces to a standard representative agent framework.

First stage optimization consists on a static optimization which makes the optimal allocation between different cohorts vertically(c.f equation (9) in the paper.) Authors solve this first stage problem as:

$$\mathcal{L}=u\left[c\left(t-n,t\right)\right]\Delta\left(n\right)P\left(n\right)e^{\rho n}+\lambda\left[C\left(t\right)-\int_{0}^{\infty}c\left(t-n,t\right)P\left(n\right)d\left(n\right)\right]$$

where $C\left(t\right)=\int_{0}^{\infty}c\left(t-n,t\right)P\left(n\right)dn$.

$n, P(n), \Delta\left(n\right)$ are given in the paper and not relevant for my question at this moment.

Normally, in this paper, the dynamics of capital accumulation are given as follows:

$$\dot{K}\left(t\right)=Y\left[K\left(t\right)\right]-C\left(t\right)$$

In fact, my question is trivial but I could not be sure.

Is the part with bracket in Lagrangian comes from $\dot{K}=0$ which gives us the equality $Y\left[K\left(t\right)\right]=C\left(t\right)=\int_{0}^{\infty}c\left(t-n,t\right)P\left(n\right)dn$ ?

As the Lagrangian is for a "static" problem, I think it makes sense but I can not be sure if this is the case.

Any suggestion or hints are welcome.

That's a coincidence, because they assume nondepreciating capital. If $\delta>0$ was positive we'd have
\begin{align}
\dot K = Y - C - \delta K
\end{align}
which gives
\begin{align}
\dot K = 0  \quad \Rightarrow\quad C = Y - \delta K.
\end{align}

But the static optimization would still read
\begin{align}
&U(C(t)):=\max_{c(t-n,n)}\int^\infty_0 u(c(t-n,n))dn \\
&s.t.\quad \int^\infty_0 u(c(t-n,n))dn \leq C(t)
\end{align}
Actually they define an indirect utility function with subject to a resource constraint. In every period (thus static) the sum of individual consumption cannot exceed aggregate consumption.


Adjustment to equilibrium in Cournot model with 2 firms In pg. 509, of Hal Varian's Intermediate Microeconomics Ch. 27, writer discusses the Cournot equilibrium.

In the figure, the reaction curve of firm 1 f1(y2) was steeper than firm 2 f2(y1).

When we started from the point (y1t, y2t), we were able to reach the stable equilibrium. But what if f2(y1) was steeper than f1(y2)? I cannot find any adjustment process. Can such condition be viable? If not, then why?![Adjustment process when f1(y2) was steeper than f2(y1)]1

The trick is to draw the whole reaction function—including the part that coincides with the axis. Hopefully these figures make it clear:


Benchmarking an Energy Investment I am currently working on a calculation to see whether it is economically feasible for a household to invest in an energy retrofit. I obtain a total profit of around $13\%$ over the lifetime of the investement ($25$ years), which translates to an average annual rate of return of $0.52\%$. This investment is mostly risk-free, to the extent that heating fuel prices remain stable.

What are example of benchmarks that I could use to evaluate this return rate? That is, to make a case for/against the household investing in the energy retrofit?

At its simplest, you just look at the cost of capital: if the household would have to borrow to pay the debt, then what's the borrowing rate? If they are currently saving, what interest rate would they forego by spending on the retrofit instead of saving?

The benefits of retrofit usually extend beyond the simple savings on energy bills, though. When it's done well, it also makes the home more comfortable and more healthy; and sometimes reduce noise from outside too. These things have value, but that value can be harder to quantify. Nevertheless, the value is certainly greater than zero, so just assuming zero because it's difficult to get a decent number, leads to the business case for retrofit being systematically under-valued.


Why should prices come down (in theory) in an educated society with a well-run government? In Chapter 1 of Robert Kiyosaki's "Rich Dad, Poor Dad", the rich dad says: "In an educated society with a well-run government, prices should actually come down".
Is there any economic theory that would support that claim?
Would that require a government/society of a particular ideology?
Sorry for the lack of research, but I was never big on studying economics. I'm mostly a software guy and an insect geek. I'm mostly looking for pointers - e.g. which economist I should read in order to understand where that quote is coming from.

Is there any economic theory that would support that claim?

As far as I'm aware - no.
In science of economics it's considered that predictable mild inflation is better than deflation (i.e. prices going down), as deflation causes higher unemployment and risks to spiral into self-systaining cycle which can be problematic to break. Also, inflation allows employers to decrease real wages of workers over years by just not raising wages (or raising not high enough). And unlike deflation, inflation stimulates people to invest money, rather than sit on them doing nothing, knowing that they will be able to buy more with them if they will just wait.
There is possibility that the rich dad supported the gold standard, for which it's indeed normal to experience deflation when economy grows (so well-run government would really just mean one that supports gold standard). But gold standard opens its own can of worms and very controversial choice at the best. For an example, there was established link between countries recovering from the Great Depression and their abandonment of gold standards, earlier abandonment of gold standard led to faster recovery


How does market work when there are few buyers and few sellers at the same market? If I understand it right, correct term for such situation is bilateral oligopoly.

Hendricks and McAfee (2007) offer a theory of bilateral oligopoly. They consider the example of the wholesale gasoline market on the west coast of the United States, which is composed of a small number of large sellers and large buyers who compete against each other in the downstream retail market. They are specifically interested in the effect of a merger of vertically integrated firms on the whole sale and retail markets. They discuss price and cost formation. They also offer a review of the literature.

The extreme case is bilateral monopoly with one buyer and one seller. Tirole's Industrial Organization  textbook (pp. 21-25) offers a nice discussion of how this market works and in particular price behavior under bargaining and contracting.


Difference between "Debt Held by the Public" and "Total Public Debt Outstanding"? On https://www.treasurydirect.gov/NP/debt/rss, we have three numbers:

Debt Held by the Public: $14,387,199,090,397.24
Intragovernmental Holdings: $5,552,709,700,473.24
Total Public Debt Outstanding: $19,939,908,790,870.48

It seems the latter number is often considered the U.S. national debt. What is the difference between the Debt Held by the Public and the Total Public Debt Outstanding?

The difference are the intragovernmental holdings, which consist of  treasuries that are owned by government agencies and are thus not counted as government debt - it's a debt that the government owes to itself.

From Wikipedia (https://en.wikipedia.org/wiki/Intragovernmental_holdings):

  In the United States, intragovernmental holdings are primarily
  composed of the Medicare Trust Fund, the Social Security Trust Fund,
  and Federal Financing Bank securities. A small amount of marketable
  securities are held by government accounts.


What is the difference between currency manipulation, and a fixed exchange rate regime? China is labelled by some to be a 'currency manipulator', that is supposedly pegged to the US Dollar. What is the difference between currency manipulation and a fixed regime?

Different motives?
I figure that it may be that a textbook fixed regime is undertaken to prevent instability, and is minor (just to correct volatility), whereas manipulation is done with the aim of gaining an unfair advantage.

Different means?
I have also read that it could be due to the fact that a manipulator creates domestic base money with which it can buy currency, without sterilisation.

Legality? BVJ below makes an interesting comment about the legality of the two... is there a legal framework in which some forms of fixed currency maintenance are allowed and some not?

Could anyone please clarify? Thanks.

Correct, both a fixed exchange rate and a manipulated exchange rate involve the government setting this price. In BOTH cases it is usually implemented by promising to standing ready to buy or sell any amount at the fixed price. Of course, countries don't always have enough foreign cash to sell it at the promised price, nor do they always want to buy as much as the markets sell to them

The difference is, as you suggest, whether the trading partners (the US is usually the one that labels others manipulators) conclude that the exchange rate is fixed at a too depreciated level. This level keeps foreign goods cheap in the US and US goods expensive in the foreign country.

Also, a fixed exchange rate is often set at a lvel that seems "too high", the only question being whether the government will manage to keep it so high, since it creates an incentive for its citizens to buy foreign goods. Instead a manipulated currency is deemed to be "too low".


What justifies the authority of a bank to create money when they make loans? This is somewhat of a political or philosophical question.

As explained by the Bank of England and elsewhere, the majority of broad money is created by credit to banks' accounts when they make loans. "Loans create deposits, not the other way around."

What is it that gives the banks the power to do this? In other words, why can't I do the same thing? With what I currently know, it seems unjustified.
In attempting to justify it, I'm wondering if maybe there is there some kind of cost to creating or debt created by these deposits and this somehow justifies their ability to create them. Do they owe something to a central bank or the state upon doing it?

This is due to Fractional Reserve System. In fractional reserve system when you make a deposit at a bank bank is required to keep a bit of it as a deposit and it is allowed to lend out the rest.

So for example if Central Bank makes an initial money injection into economy. Let’s say 100€ (and it does not really matter whether it’s by helicopter drop or directly putting them in banks) the money will eventually be put into deposit account sooner or later. Once money is deposited with fractional reserve being let’s say 10% the bank keeps 10€ and lends the rest 90€. The 90€ again sooner or later gets deposited once the lender spends it so it will end up at some bank which will keep 9€ as reserves and lends rest 81€. In the end using this system private banks create from original 100€ a 1000€ worth of money supply (the final effect can be calculated using the multiplier ($1/ra)$ where $ra$ is the reserve ratio so with 10% reserves original 100€ creates 10 times as much money. Although as pointed out in the article its not inevitable the money supply will increase to its maximum possible value given multiplier as its not guarantee that households will put later money into deposit accounts or bank could just decide too keep full amount as reserve because it does not find profitable to lend money or there can be lending restriction imposed by regulation so the 1000 should be viewed as an upper limit on the maximum new money that can be created.

You could also do this. For example, if you convince your friends to give you deposits and then you keep only a fraction of those deposits and lend the money out to some other friends you will create new money (although if you are hell bent on doing this first check local laws in some countries maybe you can’t just do this without license). But in principle anyone could do this. In past, like during the Renaissance or even in more ancient times even many private money lenders did this.


Finding Mixed-Strategy Subgame-Perfect Equilibrium I'm trying to find the Mixed-Strategy Subgame-Perfect Equilibrium of the sequential-move Battle of the Sexes game.

I know how to find the mixed strategy Nash equilibrium of the battle of the sexes:

Let player 1 play $O$ with probability $p$ and $F$ with $1-p$. (and symmetric for player $2$).

So, finding the best response correspondences for each player:

$\partial\pi_1/\partial p=\partial(2pq+(1-p)(1-q))/\partial p=3q-1$

Symmetrical for player 2 is $3p-1$.

So I graph the best response correcspondence and find the Nash Equilibrium:

So, now that I found the mixed strategy Nash Equilibrium is $(p,q)=(2/3,1/3)$, what do I do next? What is the Subgame-Perfect Equilibrium?

Consider the subgame following 1's choice of $Y$. This is simply a simultaneous move Battle of Sexes game. To compute the SPNE, you first need to find the Nash equilibrium of this subgame.

It has 3 Nash equilibria: 2 pure and 1 mixed. The mixed strategy gives a value of $\frac{2}{3}$ to player 1 in this subgame. Now move up to the root node and compare whether player 1 should choose $Y$ or $N$.
This would complete the computation of SPNE.


Why is the percentage of Australian businesses that don't have any employees so high? I'm trying to understand this Australian Bureau of Statistics release, which says:

  In June 2014, 61% of actively trading businesses in Australia had no
  employees, 27% had 1-4, 10% had 5-19, 2% had 20-199, and less than 1%
  had 200 or more.

I didn't realise so many businesses didn't have employees. Why is this percentage so high?

Employment excludes non-salaried directors, volunteers, persons paid by commission only, and self employed persons such as consultants and contractors.

The actively trading businesses with zero employees are therefore those businesses where the staff members are drawn exclusively from that group. That may cover most one-person outfits, perhaps some family firms, groups of self-employed people, and so on. These businesses are typically formed in that way as a response to particular regulations, usually tax rules.

The answer is in the explanatory notes attached to that dataset, section 56, from where the above quote is taken.  The explanatory notes are attached to that dataset to answer questions such as this. When you have questions about a particular dataset, the explanatory notes (which might also be called metadata, data descriptors, or similar), will usually have the answer, as they do in this case, and should be any enquirer's first place to look.


Nash equilibrium of sequence of games My setting is the following.

I have a sequence of  games $\lbrace G_n \rbrace$ in which the strategy space is $S=[0,1]^2$, there are two players $(I=\lbrace 1,2 \rbrace)$, and payoff functions are given by the continuous (no other restrictions so far) functions $U_i^n(x_1,x_2)$ for each player $i=1,2$. That is, each game is  defined by $G_n = (U^n, S,I)$.

Now, I know that the payoff functions $U_i^n$ converge pointwise to a (discontinuous) limit $U_i$. I therefore write down the 'limit game' $G = (U,S,I). $ We can write down a correspondence that maps a game to its nash equilibria. Call that correspondence $EQ$, and we define, for a particular game $G_n$, that $EQ(G_n) = \lbrace (s_{n1}^*, s_{n2}^*), (s_{n1}^{**},s_{n2}^{**}) \dots\rbrace $ where the right hand side is the set of (potentially infiite) nash equilibria for the game $G_n$ and, generically, we allow each equilibrium strategy $s_{ni}$ to be a mixed strategy. That is, a probability measure over $[0,1].$

I then analysed the limit game, and have found a unique mixed strategy nash equilibria in that game. That is, $EQ(G) = \lbrace (s_1^*, s_2^*) \rbrace$.

I do not have closed form solutions for the equilibria, $\lbrace (s_{n1}^*, s_{n2}^*), (s_{n1}^{**},s_{n2}^{**}) \dots\rbrace $, of the games in the sequence $\lbrace G_n \rbrace$. Naturally, though, I would like to say something about how the equilibria converge to the equilibrium of the limit game.

My questions are (to start) as follows.

Given the pointwise convergence of payoff functions $U^n \rightarrow U$, in what sense can I say the games $\lbrace G_n \rbrace $ converge to the limit game $G$?
What conditions do I need on the equilibrium correspondence $EQ$ so that I can say something about the convergence of the equilibrium strategies? That is, am I able, with some argument, to establish that there exists a sequence of equilibria that converges to the equilibrium of the limit game in some sense. That is, $\lbrace (s_{n1}^*, s_{n2}^*)\rbrace_{n=1}^\infty \rightarrow \lbrace (s_{1}^*, s_{2}^*)\rbrace$, perhaps in the weak sense, perhaps in the strong sense, or perhaps in some other sense.

Any help or references are greatly appreciated.

Edit: clarified the notation and question.

This is just an extended remark:

Let $\Delta$ be the space of Borel probability measures on $[0,1]$. An equilibrium can be represented as an element of $\Delta^2=\Delta\times\Delta$. A two player game with continuous payoff-functions with action spaces $[0,1]$ can be viewed as an element of $C[0,1]^2\times C[0,1]^2$, where $C[0,1]^2$ is the space of continuous functions (here representing payoff functions) from $[0,1]^2=[0,1]\times[0,1]$ to the reals, endowed with the topology of uniform convergence, given by the $\sup$-norm $\|\cdot\|_\infty$ defined by
$$\|f\|_\infty=\sup_{x\in [0,1]} |f(x)|=\max_{x\in [0,1]} |f(x)|.$$
One defines $C[0,1]$ similarly.

There is also a well-behaved metrizable compact topology on $\Delta$, the topology of weak convergence (or weak*-topology); the coarsest topology such that the function $\mu\mapsto\int f~\mathrm d\mu$ is continuous for each $f\in C[0,1]$. In this context, convergence in this topology is convergence of cumulative distribution functions at continuity points. We let $\Delta^*$ be the set of Borel probability measures on $[0,1]\times [0,1]$, similarly endowed with the topology of weak convergence.

We can then define an equilibrium correspondence $$\eta:C[0,1]^2\times C[0,1]^2\to 2^{\Delta\times\Delta}$$
such that $\eta(v,u)$ is the set of equilibria given the payoff-functions $u$ and $v$. The correspondence has nonempty values by a theorem of Glicksberg. Since $\Delta\times\Delta$ is compact, we can show that $\eta$ is upper hemicontinuous by showing it has a closed graph.  The function $p:\Delta\times\Delta\to\Delta^*$ that maps mixed strategies to their independent product is continuous (see Billingsley's book on weak convergence). It follows, using a bit of analysis, that the "expected payoff"-function $k_i:\Delta\times\Delta\times C[0,1]^2\to\mathbb{R}$ is continuous for $i=1,2$. Now for each $\mu\in\Delta$, let
$$E_\mu^1 \{(v,u,\nu,\tau)\in \Delta\times\Delta\times C[0,1]^2\times C[0,1]^2\mid k_1(\nu,\tau,v)\geq k_1(\mu,\tau,v)\}$$
and
$$E_\mu^2 \{(v,u,\nu,\tau)\in \Delta\times\Delta\times C[0,1]^2\times C[0,1]^2\mid k_2(\nu,\tau,u)\geq k_1(\nu,\mu,u)\}.$$ Each of these sets is closed and the graph of $\eta$ is simply
$$\bigcap_{\mu\in\Delta}E_\mu^1\cap \bigcap_{\mu\in\Delta}E_\mu^2,$$
a closed set, so $\eta$ is upper hemicontinuous.

Now this doesn't tell us anything about what happens if payoff functions converge pointwise and not uniformly!!! The only useful information is that strategy spaces are compact, so there will still be a convergent subsequence. If you can show that this subsequence must converge to your candidate equilibrium- this will require making use of the details of the game, you should be good to go.


GDP projections for the fifty American states I'm looking for GDP projections for the fifty American states (up till 2040, or 2050). Are these available online, or in any economics papers?

I've found GDP projections for America, and historical GDP data for the fifty states. While GDP projections are not reliable, I need this for a project that I'm working on.

Official forecasts seem not to be available. The Bureau of Economic Analysis did produce these forecast in the past, but not anymore.

Forecasts from academic economists are scarce. US studies are usually only available for employment and not for GDP (for example, this paper). A working paper from late 2014 reviews the literature on regional forecasting (not only for the US) and the state-of-the-art methodology of such exercises. You can see in Table 1 a summary of studies between 1975 and 2015. None of them focuses on GDP for US states. Notice however that there are such studies for Germany (Wenzel, 2013) and Europe (Baltagi et. al. 2014), so maybe in the future an equivalent for the US will be produced.


When there is a third degree price discrimination, why is the total MR curve kinked at the top? I know that the total MR = MR of student + MR of adult, but wy is it kinked at the top?

I believe this is just a horizontal sum. At the very top of your graph, only adult has a part of its curve above 10.25. So when your summing horizontally student =0  Adult = x, This changes once you are below 10.25, then all of a sudden you have student = x  and adult = x. This additional amount from student causes the kink. If pretend student was always =0 then the total on the right would be identical to adult.

I hope this helped. I'm sorry if it's not phrased better.


Would a Federal Job Guarantee hurt the economy? I've been reading about how a job creation program would disrupt the private sector. One of the main things I kept seeing was that the a FJG will result in the elimination of thousands of jobs. So, consequently it would hurt the economy. But a FJG would create jobs that pay higher than minimum wages as well. Wouldn't that increase consumer spending, cancelling out the negative impact?

Conventional economics research is not very kind to the idea of job guarantee (see discussion in highly cited works of  Palley, 2001;  Sawyer, 2003 and Seccarecia 2004). In general most of the profession agrees that job guarantee program (i.e. program where government is some sort of employer of last resort/provides employment) is generally not efficient from either macroeconomic or microeconomic perspective, with emphasis on the macroeconomic perspective.
The problem is not that it would destroy jobs on a net basis. The whole aim of such program is to create government jobs for anyone that is unemployed so on net basis it would increase the number of jobs. The problem is that especially if the wage for these jobs is set at above minimum wage, or more specifically market wage at each individual sub-market it would crowd out productive jobs from the economy and instead create less productive government jobs (see the papers cited above).
Next unless this is founded by debt or high powered money it will not increase consumer spending on net basis. This is just elementary macroeconomics, if government runs balanced budget government spending multiplier will be exactly equal to 1 meaning it will not create any additional stimulus for the economy and even that assumes government funds itself with non-distortionary lump sum taxes so in reality it would likely depress demand (see Blanchard et al. Macroeconomics: a European Perspective).
Now, in principle there is nothing wrong with government running deficit or financing projects with high powered money but both are not suitable for some large permanent program. When it comes to financing projects with high powered money there is virtually unanimous agreement in the profession that only limited amount of real spending can be financed in such way (see this poll among top US economists). There is also issue that amount of real spending that government can finance with high powered money depends on macroeconomic situation (e.g. more of it can be financed when interest rates are zero and less otherwise). When it comes to deficit it is generally considered desirable to run budget deficits in recessions, but in the end government needs to respect its intertemporal budget constraint so in expansion it also should run surplus (technically thanks to economic growth there is some leeway as if we assume there are no 'end times' when debt has to be repaid, government could run deficit equal to rate of growth and keep its debt-to-GDP ratio stable - but with GDP growth rates most developed nations have this would only give extra leeway of about $1-2\%$ hardly enough to fund some ambitious program).
Lastly, issue with job guarantee program is that anything it promises to do can be done better in some other way. If you want to raise welfare of the poor then there is a plethora of relatively more efficient redistribution policies. If your aim is solely boosting employment then there are many other policy instruments such as earned income tax credit, which in combination with minimum wage can boost employment while creating also some floor below which peoples' earnings can't fall. If your goal is to stimulate economy then simple fiscal stimulus to households would be more efficient etc (you can see overview of this in the above cited literature). Hence, most conventional economists would reject job guarantee on the grounds that there are more efficient alternatives.


Does learning economics lead to richness? I have started to learn economics from Adam Smith's "Wealth of nations" because I think that learning economics (or narrow fields of it) will allow me to become rich.

Does knowing economics allow me to make money?

First things first, we must dispel the misconception that you will find in economics some magic formula to "beating the stock market" or some other way to make easy money. I explain why why here.

Learning economics can help you to become more wealthy in several prosaic ways:

In the same way that learning to be a doctor or lawyer can make you rich. If you have useful skills then people will pay you to use your skills to help them. Professional economists are employed in the government, academia, and the private sector and are generally well-paid.
Learning economics will also teach you to be a more logical and systematic thinker, which is likely to make you better at all kinds of intellectual tasks—including those not directly connected to economics. Again, this is likely to improve your future earnings potential.
Many ordinary people do truly stupid things with their money. Economics will not generally teach you about these things (better to read about personal finance, as Arthur Tarasov suggested), but it will teach you to be more savvy in matters of money and help you to avoid the pitfalls.

Note that none of these three things are specific to economics. You would do just as well to learn medicine and read a beginner's guide to investing. Some advice in my capacity as an 'old guy' rather than an economist: if you want to become rich then find a career that pays good money and that you will enjoy and work hard at it.

Final remark: If you really want to learn economics then reading Adam Smith is probably a pretty bad way to start. That is like trying to learn English by reading Shakespeare. Much better to start with a modern introduction to the subject (I am fond of "Intermediate Microeconomics: A Modern Approach" by Hal Varian).


Intuition behind Engel Aggregation and Cournot Aggregation Could anyone provide a possibly intuitive and friendly explanation to the Engel Aggregation $(\sum s_i \eta_i = 1)$ and Cournot Aggregation$(\sum s_i \epsilon_{ij} = -s_j)$? Here, $s_i = \frac{p_i,x_i}{I} \ge 0$ is the income share, $\epsilon_{ij}, \eta_i$ are price and income elasticities, respectively. I was not sure how this theory of aggregation of consumer demand tell us about the consumption behavior. Thank you in advance for your help!

These expressions can be easily derived formally by taking the derivatives of Walras' law w.r.t $I$ (Engel aggregation) and $p_j$ (Cournot aggregation).
The Engel aggregation means that not all goods are luxuries ($\eta_i>1$), or necessities ($\eta_i<1$), or inferior goods ($\eta_i<0$). The Cournot aggregation says that the budget share $s_j$ of the good $j$  is small when the good $j$ has many substitutes ($\epsilon_{ij}>0$), and big when it has many complements ($\epsilon_{ij}<0$), or their respective budget shares are large.


How does trading create value? Let's say village A has all the something S they need, and village B has all the something T they need. The properties of S outweigh the benefits of T.

Village A and village B start to trade S for T.

After trading, is the value V of S + T now different?

The net value of the two villages increases because value is in the eye of the beholder. If commodity S is more valuable to village A than to village B, and commodity T is more valuable to B than A, then, when they trade, both villages gained something of more value to them and the relative wealth of both villages increased.

Value comes from the valuator.

This is why--one of the reasons, anyway--Marxism was doomed. Value doesn't come from labor at all. Only cost comes from labor. For example, if I go stand in the middle of the road and labor all day pointing at the sky, I've worked hard but created no value, because no one else values my sky-pointing. Similarly, if I build two houses and put exactly the same amount of labor into both of them, but one is on a mountain with a beautiful view of the city, and the other is next to the city dump, the first will be far more valuable because people would value the location of the first, "envaluating" the house.


When countries industrialise, why do jobs from agriculture shift to manufacturing? This is a historical trend whether it may 18th century Britain or 19th century America or what's currently happening in China. What I am confused is  by the fact that manufacturing jobs such as working on an assembly line are not that well paying. Still the trend holds true.

I want to know what are the causes for the shift.

This is a common area of study in Development Economics. There is for example the Dual-sector model, first developed in 1954. It is very well explained in the link provided, but basically:

[the] agricultural sector is typically characterized by low wages, an abundance of labour, and low productivity through a labour-intensive production process. In contrast, the capitalist manufacturing sector is defined by higher wage rates as compared to the subsistence sector, higher marginal productivity, and a demand for more workers. Also, the capitalist sector is assumed to use a production process that is capital intensive, so investment and capital formation in the manufacturing sector are possible over time as capitalists' profits are reinvested in the capital stock. [...]
The primary relationship between the two sectors is that when the capitalist sector expands, it extracts or draws labour from the subsistence sector. This causes the output per head of labourers who move from the subsistence sector to the capitalist sector to increase. [...]
The agricultural sector has a limited amount of land to cultivate, the marginal product of an additional farmer is assumed to be zero as the law of diminishing marginal returns has run its course due to the fixed input, land. As a result, the agricultural sector has a quantity of farm workers that are not contributing to agricultural output since their marginal productivities are zero. This group of farmers that is not producing any output is termed surplus labour since this cohort could be moved to another sector with no effect on agricultural output. [...]
The end result of this transition process is that the agricultural wage equals the manufacturing wage, the agricultural marginal product of labour equals the manufacturing marginal product of labour, and no further manufacturing sector enlargement takes place as workers no longer have a monetary incentive to transition.

In other words,, low productivity in agriculture due to unlimited land and workers and low use of capital means low agricultural wages, whereas high productivity in new capital intensive industries means high wages, thereby leading to a migration process that continues until wages equalise.
It might be worth noticing that this model was also used by Simon Kuznets to explain why industrialised countries saw a non-monotonic evolution of wage inequality between 1870 and 1950 (i.e. an increase and then a decrease in inequality), pattern that came to be known as the Kuznets Curve. As the article above states:

The Kuznets curve implies that as a nation undergoes industrialization – and especially the mechanization of agriculture – the center of the nation’s economy will shift to the cities. As internal migration by farmers looking for better-paying jobs in urban hubs causes a significant rural-urban inequality gap (the owners of firms would be profiting, while laborers from those industries would see their incomes rise at a much slower rate and agricultural workers would possibly see their incomes decrease), rural populations decrease as urban populations increase. Inequality is then expected to decrease when a certain level of average income is reached and the processes of industrialization – democratization and the rise of the welfare state – allow for the trickle-down of the benefits from rapid growth, and increase the per-capita income.


Prediction Interval for $E(y|X_0)$ when model is in $ln(y)$ Let's suppose we have linear regression with dependent variable $ln(y)$. How would one find a prediction interval for  $E(y|X_0)$ ?

If we have $PI(E(ln(y)|X_0))$, is there a way to reach $PI(E(y|X_0))$?

Any help would be appreciated.

I got hold of this link from Journal of Statistics Education

Using the notation in it, let $X\sim \log N(\mu,\sigma^2)$, i.e. $Y=\log(X) \sim N(\mu,\sigma^2)$.

Hence, $E(X)=E(e^Y)=e^{\mu+\sigma^2/2}$. An estimator for $\log(E(X))$ is $$\bar Y+\frac{S_Y^2}{2}$$. Also, $Var(\hat\log(E(X)))=\frac{\sigma^2}{n}+\frac{\sigma^4}{2(n-1)}$, which gives $$\hat Var(\hat\log(E(X)))=\frac{S_Y^2}{n}+\frac{S_Y^4}{2(n-1)}$$.

For large samples, using the CLT, we have $$\frac{\hat \log E(X)-\log E(X)}{\sqrt{\hat Var(\hat\log(E(X)))}}\sim^a N(0,1)$$

Thus, one possible CI from this perspective is $$CI(E(X))=\left]e^{\bar Y+\frac{S_Y^2}{2}\pm z_{1-\alpha}\sqrt{\frac{S_Y^2}{n}+\frac{S_Y^4}{2(n-1)}}}\right[$$.
According to the link, this is the Cox method, while the modified Cox method substitutes the standard normal quantile for a $t(n)$ quantile. They simulate more than just the these two intervals. They also simulate the naive approach.

If we look at table 5  of the link, we can see that the best method is the modified Cox, since for small samples, and large ones, the covering probability is the most close to the nominal level.

Alecos answer, if I understood correctly, suggests adding a correction term to the naive approach, resulting in $CI(E(X))=\left]e^{\bar Y+\frac{1}{2}\frac{S_X^2}{(\bar X)^2}\pm t_{1-\alpha}\sqrt{\frac{S_Y^2}{n}}}\right[$.

I've simulated his answer with the following code in Mathematica:

sim[n_] := Module[{},
  ct = 1;
  res = 0;
  While[ct <= 10000,
   data = RandomVariate[LogNormalDistribution[5, 1], n];
   y = Log[data];
   my = Mean[y];
   s2y = Variance[y];
   mx = Mean[data];
   s2x = Variance[data];
   qt = Quantile[StudentTDistribution[n], 0.975];
   If[E^(my + 0.5*s2x/mx^2 - qt*Sqrt[s2y/n]) < E^(5 + 0.5) <
     E^(my + 0.5*s2x/mx^2 + qt*Sqrt[s2y/n]),
    res++];
   ct++;
   ];
  res = res/10000.
  ]

The only difference is that I've done 10000 replications whereas the link only does 1000.

Running the code for the same sample sizes of the link, we obtain the following covering probabilities: $${0.8954, 0.8464, 0.7682, 0.7153, 0.6454, 0.4832, 0.3045, 0.073, 0.0068}$$.

AS we can see the correction increases the covering probabilities when compared to the naive method, but it still suffers from the same problem, i.e., the prob. tend to zero as the sample size increases.

All in all, the best course of action is to use the modified Cox approach.


What happens if an expensive thing goes into high supply for a limited time? Let's say we have this Product A and it costs $1000, it's incredibly useful so it's in high demand, and we got it from a very-short limited-time "event"

But then it goes available again in high supply for another same "event" but a bit more longer so now prices drop to let's say $400 and we have high supply of it now

What is the most probable way that it will rise in price again, if it just takes time how long do you think would it increase price. Let's just say the product is incredibly useful and alot of people really want it.

a lot of factors go into this. If a product in low supply and high demand suddenly becomes high in supply, with the same level of demand, as you mentioned, the price will in theory drop from \$1,000 to \$400. But the issue is the elisticity of demand, and the opportunity cost of selling the product at a lower price when demand rises. If the price is at \$400, and demand increases as supply dwindles, but there are substitutes to the product, consumers will simply buy the substitute. If there is no substitute however, demand is high, and price elasticity is high, the price can rise fairly quickly in that scenario.


What is the most general definition of “the core” in game theory? I’ve seen definitions of “the core” that rely on some specific assumptions, such as that the game is one of a transfer of resources, or that there is “transferability of utility” (presumably intending to capture the notion of money being the source of this).

But what is the most general definition of the core? Can we talk about the core of any arbitrary game, or does the concept fundamentally only work for specific types of games?

We can talk of the core for any arbitrary game. To explain how let me compare it directly to how we define non-cooperative games. In a standard non-cooperative game we define Players, $I$, action sets for each player, $A_i$ for each $i\in I$ and payoff functions that map any profile of actions to payoffs $u_i: A\rightarrow \mathbb{R}$, where $A=\prod_{i\in I} A_i$. Finally the solution concept, for example, Nash equilibrium, correlated equilibrium or rationalizability is a condition on these objects that we think are a good prediction of what will happen. For instance, Nash equilibrium predicts that every player is best responding to a correct belief about what other players are doing.

The  Core is another solution concept, however, the language developed so far is not sufficient, because the idea of the core is that it predicts that no group of people (or coalition) will have a profitable deviation. It is clear that now the unit of analysis are groups of people, so the "agents" in this setup are the elements of $P(I)$, the power set of $I$, which contains all possible groups of people, so you will need to define the action sets for each of these groups. A natural way could be that if $C\in P(I)$ then $A_C=\prod_{i\in I\cap C} A_i$, i.e. the coalition $C$ can choose the actions of all its players. It is clearly not the only possibility, maybe you want to allow for players to have some autonomy within the coalition, but let's say you define action sets that way.

You will also have to define payoff functions for each possible coalition. Again a natural way could be to define $u_C=\sum_{i\in iI\cap C} u_i$, i.e. the sum of utilities of players in the coalition. Note that your assumption on this coalition utility will necessarily come with some assumptions of how you substitute between players' utilities within the coalition.

Finally, you will have to define which coalitions are possible to co-exist. For example, can players belong to multiple coalitions or not? Again a natural way would be to rule out this possibility so that in equilibrium each player must belong to only one coalition, i.e. $C\cap C'=\emptyset$. This language will allow you to define that the core will be a situation where all players belong to a coalition, each coalition chooses an action for each of their players and there is no subset of players that will rather separate from their current coalition to form another one and choose a  different profile of actions.

Hopefully, I  have made clear that I needed to make several assumptions just to be able to define the core. Especially if I want to have some counterpart with the original non-cooperative game I started with. This is cumbersome.

I think this is why, to some extent, the way some of the literature developed was by not subordinating the definition of core (intrinsically a cooperative solution concept) to the terminology of a non-cooperative game. One way to do it is by directly defining a payoff function for each player from being part of a coalition $V_i(C)$ for each player where $C\in P(I)$ (this notation has implicit that being in a coalition can probably imply different actions on your part). The core is then a partition of players (each player belongs to a coalition, say $i\in C_i^*$) such that there is no coalition $C'\in P(I)$ such that for all $i\in C'$, you have $V_i(C')\geq V_i(C_i^*)$ and with strict inequality for some $i\in C'$.

Clearly, this last formulation has fewer assumptions than my first formulation. However, it is also clear that it does have assumptions. The main ones (at least for me) is that suffices to know what coalition you belong to figuree out your payoff (i.e. no externalities between coalitions). And the other important assumption is that players can only belong to one coalition. This is restrictive in many situations, for example, politicians that belong to multiple interest groups, etc.

Depending on what you are willing to assume about the nature of cooperation and deviations from cooperation, you will get a different-looking definition of core, but the general principle is the same. The core is the prediction that captures that no subgroup of players has incentives to coordinate and improve their condition. So the concept is not bound to specific kinds of games, but I think that there is no consensus on how to apply it universally to all kinds of games.


Understanding agents selecting among markets Let's say an entrepreneur can choose between starting a business in a competitive market with zero economic profit, and starting a business in a market that is not perfectly competitive with positive economic profit. We would perhaps expect in an equilibrium that there would be no competitive markets unless there were no opportunities for economic profit anywhere. Where could I find more information on the structure of markets in this regard?

If a market has free entry, then profit will tend to zero in the long run. Monopolistic competition and perfect competition are both characterized by zero long-run profit. Of course a firm would prefer to enter a market in which long run profits can be earned, but such markets are characterized by barriers to entry.

To better understand this, consider a market in which firms can enter with entry cost $c$. Then, in long-run equilibrium, the profit that will be earned by incumbent firms cannot exceed $c$, otherwise potential entrants would have an incentive to enter the market.


What kind of economic freeware exists for economics students? Can anyone recommend some free software for students studying economics for use in senior projects, theses, or dissertations?

I never understood why discussion about specialized software should be off-topic in the specialty's website. And of course I don't agree. So:

Before diving into R, which indeed appears to be the dominant (and rich) freeware for statistical computing, one can try Gretl. It is an Econometrics freeware, with a lot of functionality, a very good Random Number Generator, and has both menu-driven implementation but also code-writing by the user. It is easier for beginners - but it is serious stuff. The wikipedia page for Gretl lists some reviews about Gretl.

The other kind of "economics" (not mathematics) software apart from econometrics packages would be specialized simulation software, for say Dynamic Stochastic General Equilibrium Models, or micro-applications.  For DSGE, one such is Dynare.  A lot of DSGE-code for various other software can be found at International Network for DSGE Modeling, Monetary and Fiscal Policy.


Why is the derivative used to represent marginal cost instead of the difference? Marginal cost is defined as "the change in the total cost that arises when the quantity produced is incremented by one unit." And given a total cost function $C(q)$ that's differentiable, the marginal cost is the derivative, $C'(q)$. But if I were given $C$ and asked the cost that arises when the quantity produced is increased from 2 to 3, I would simply calculate $C(3)-C(2)$; no need to bring calculus into the picture.  In general, $ C(3)-C(2) \neq C'(2)$. For example, if $C(q) = q^2$, then $C(3)-C(2) = 5$, but $C'(2) = 4$.

Thus my question is:
Why is the derivative used to represent marginal cost instead of the difference?

Note: I thought this question must've been what's being asked here, but evidently not; there what's being asked is (essentially) why $C'(3) \neq C(3)-C(2)$.

The derivative is used in some contexts, but not all, when the cost function is differentiable. In those contexts, it tends to be assumed that supply is continuous, not discrete. This is a matter of convention and of analytic convenience. It has the advantage of being consistent, whether you're approaching the supply point from above or from below.

But in other contexts, given your cost function, assuming that the thing being supplied is discrete and not continuous (that is, it is possible to supply 2 units or 3 units, but not 2.9 or 3.5 or any other fractional unit) then the marginal cost of the third item is indeed 5, not 4.


Who owns German debt? I know that Germany has huge external debt. I don't know how to find out which entities own this and especially which country they belong to.

This Deutsche Bank figure from 2013 has some broad categories for German debt and compares it with other rich countries:

A newer chart, using slightly with more granular categories. Note that Germany is DE.


Basic New Keynesian Model: Why variables are defined by integral equations In the basic New Keynesian Model most variables are described as an integral equation. Lets for Instance look at labour demand which is defined as:
$$N_t=\int_{0}^{1}N_t(i)di$$

What is the intuition behind that. How does the $N_t(x)$ function look like and why do we integrate it interval $[0,1]$?

I am reading Gali's book.

First of all, this is not something special to "the basic New Keynesian Model". It is a commonly used technique when modeling an economy with competitive environment.

In your case, the author wrote that there is a continuum of differentiated goods represented by the interval [0,1] and each firm is producing one of the goods. You can imagine that there are uncountably many different kinds of good in the market. As a result, the size of each firm is negligible (just a point on the [0,1] interval) compared to the entire economy. Each firm indexed by $i$ solves its individual profit maximization problem to obtain its labor demand $N(i)$. Then, the aggregate labor demand is simply the "sum". In this case, the sum is replaced by the integral because the variety of different firms is the whole unit interval.


Multivariate implicit differentiation (Samuelson, 1948) I am studying "The Simple Mathematics of Income Determination", by Paul Samuelson (from book is called "Macroeconomia (artigos selecionados)", by APEC-CAEN. It is the 1st chapter of the book, the 13th page), and I am having some troubles in understanding a calculus passage.
First, Samuelson states the income equation:
$(1)$ $ Y =  C (Y - \bar{W}) + \bar{I} + \bar{G} $
Where $Y$ corresponds to income, $C$ corresponds to consumption, $\bar{W}$ corresponds to taxes (actually, I don't exactly know the odd reason why the letter W was picked as taxes instead of a more common letter as T), $\bar{I}$ corresponds to investment and $\bar{G}$ corresponds to government spending). For purpose of simplification, these three last variables are treated as constants.
Then, $Y$ is differentiatied in $\bar{G}$ (which I suppose it is an implicit differentiation, in the form of $\frac{dy}{dx} = - \frac{F_x}{F_y}$):
$(2)$ $\frac{dY}{d\bar{G}} = \frac{1}{1 - C'(Y - \bar{W})}$
But my doubt emerges in the following passage:
$(3)$ $\frac{dY}{d\bar{(-W)}} = \frac{C'(Y - \bar{W})}{1 - C'(Y - \bar{W})} = \frac{dY}{d\bar{G}} - 1  $
I realize that Samuelson did the same implicit differentiation as in step 2 and I can visualize that
$\frac{C'(Y - \bar{W})}{1 - C'(Y - \bar{W})} = \frac{1}{1 - C'(Y - \bar{W})} * C'(Y - \bar{W}) = \frac{dY}{d\bar{G}} *  C'(Y - \bar{W})$
but, how does $\frac{dY}{d\bar{G}} *  C'(Y - \bar{W})$ turns to $\frac{dY}{d\bar{G}} - 1  $?
I mean, how did this $-1$ replace the multiplying term $C'(Y - \bar{W})$
I tried to get it, but unsuccessfully. I hope you could shed some light on it.

We start from the equation:
$$
Y = C(Y - \overline{W}) + \overline{I} + \overline{G}
$$
First, we totally differentiate with respect to $(-\overline{W})$ (taking into account that $Y$ is a function of $\overline{W}$, $\overline{I}$ and $\overline{G}$)
$$
dY = C'(Y - \overline{W})dY + C'(Y - \overline{W}) d(-\overline{W}).
$$
Bringing the $dY$ terms on one side gives:
$$
(1 - C'(Y - \overline{W}))dY = C'(Y - \overline{W}) d(-\overline{W}),\\
\to \frac{dY}{d(-\overline{W})} = \frac{C'(Y - \overline{W})}{1 - C'(Y - \overline{W})}
$$
Next, we totally differentiate with respect to $\overline{G}$:
$$
dY = C'(Y - \overline{W})dY + d \overline{G}
$$
Again gathering terms gives:
$$
(1 - C'(Y - \overline{W})) dY = d \overline{G}\\
\to \frac{dY}{d \overline{G}} = \frac{1}{1 - C'(Y - \overline{W})}
$$
Therefore:
$$
\begin{align*}
\frac{dY}{d \overline{G}} - 1 &= \frac{1}{1 - C'(Y - \overline{W})} - 1,\\
&=\frac{1 - 1 +C'(Y - \overline{W})}{1 - C'(Y - \overline{W})},\\
& = \frac{C'(Y - \overline{W})}{1 - C'(Y - \overline{W})},\\
&= \frac{dY}{d(- \overline{W})}
\end{align*}
$$


How does the Contract Law definition of 'consumer surplus' relate to the Microeconomics definition? O'Sullivan & Hilliard's The Law of Contract (2018 8 ed). 16.23 starts on p. 387, 16.35 on p. 391.

Right: Pindyck, Rubinfeld. Microeconomics, Global Edition (2017 9 ed). p. 152.

Richard and Damian Taylor. Contract Law Directions (2019 7 ed).

  Difference in value or cost of cure? (Section 11.3.1)
  The £2,500 award made in Ruxley for Mr Forsyth’s ‘loss of amenity’ can be interpreted as
  damages for non-pecuniary loss, based on the fact that the contract was a consumer
  contract for enjoyment (see the opinions of Lords Clyde and Hutton in Farley v Skinner
  (2001)). However, the award may also be interpreted as a response to the need for a
  wider principle of recovery based on the loss of ‘consumer surplus’. Consumer surplus is
  the difference in value between what a thing is worth commercially and the higher value
  at which a consumer subjectively values it. So, whilst an extra few inches on the swimming pool added no financial value, the £2,500 represented Mr Forsyth’s consumer surplus:
  to him, and him alone, the pool was a more valuable asset if it was deeper (i.e. if his
  contract was fully performed). He had contracted for this extra depth and it had not been
  provided, so you could argue that the award of £2,500 was compensation for loss of this
  consumer surplus.

I'm not a microeconomist, but these terms appear to be defined wholly differently? Or am I overlooking something similar that underlies  them?

O'Sullivan & Hilliard write: Consumer surplus is a "type of non-financial loss" and

  can be defined as the amount by which the particular plaintiff values performance of a particular obligation over and above its market value.

This is identical to the economist's definition of consumer surplus.

Using Pindyck and Rubinfeld's example: If a student was willing to pay as much as $\$13$ for a rock concert ticket (this is the value she places on the "performance of a particular obligation") but only had to pay $\$12$ (this is the price or the market value of the ticket), then her consumer surplus is $$\$13-\$12=\$1.$$


Interest rates and economic growth Are interest rates the cause of economic growth?

For example there is no money in the system and bank a is lending company A a loan Y with X interest.

how can company A pay back the loan Y with interest X when the system is just loaded with loan Y?

My conclusion is the Loan Y can only be paid back with interest when the economic is growing by other loans?

Let's consider a simpler example.

You have 10 apples. With that, you can eat $x$ apples and "invest" in the rest $10-x$ apples, plant them, and each would yield two apples tomorrow. Let's say that with some optimization, you decided to eat 4 apples, saving the other 6 apples so that you could have 12 apples tomorrow. GDP would grow by 2.

Is this a result of "interest rate"? No. There's not even a bank here.

Now imagine that there is a bank that ask you to deposit your apples there for a day. What would you demand in return? 2 apples tomorrow for every apple you save today. That's the interest rate. The assumption is that the borrower can do something at least as productive with the money he/she borrowed, and the apples would go to those who can most efficiently use them.


Relevance of government liabilities to GDP After Malaysia's national debt was [reassessed][1], its totaled $250bn along with other government liabilities.

Now, I'm having trouble understanding the direct relevance of the ratio of goverment debt to gross domestic product, in Malaysia's case.

Namely, in the article it is stated that its 80 percent of Malaysia's gross domestic product. Why is this statistic important? That is, why should I care about the total government liabilities of Malaysia's being 80% of its gross domestic product.

In the case of Turkey, [it][2] is mentioned that companies based in Turkey are suffering under the weight of the foreign debt amounting to some $300bn. The comparison to the countries GDP is then made again; "\$300bn is more than a third of GDP".

Again, what gives a measure on the relevance of that the foreign debt is more than a third of GDP?

How does this measure differ from country to country?

[1]: Malaysia leader on a mission (Hannah Beech and Richard C. Paddock, Sa-Su 16th of June 2018)

[2]: Pillow talk; surrender your dollars, urges President Erdogan (The Economist, 16th of June 2018)

The government debt represents the total liabilities outstanding that the government must (at some point) repay to investors. Generally to do so, governments tax their populace, either now, or at some future point.

The often cited Debt to GDP ratio figure is one shorthand for understanding how difficult it will be for any given government to raise the revenue necessary to cover its debts, and/or decrease government spending. If country "A" had \$100 billion in outstanding debt, and country "B" had \$400 billion in public debt, which would be in worse shape (that is, which would likely have a harder time raising the necessary funds)? Ultimately, it depends on a variety of factors, one of which being "how much can the country realistically raise in revenue?" If country "B"'s GDP is ten times the size of country "A," then even with a higher debt load, it represents a smaller relative amount owed, and might then be easier to pay back.

Of course, this is just one common, convenient shorthand statistic often used to quickly assess how sustainable a country's debt is. There are many other factors which must be considered if you're trying to comprehensively measure "default risk." But Debt/GDP is a pretty easy, useful one that has become popular over time.


Justification for my Random Effects estimation I need to defend my use of the Random Effects (RE) estimator in my economics project. I've been told in cross validated that the proper place for the question is here.

The causal effect of the exchange rate on shopping in the neighbouring country, is estimated using the following equation:

\begin{eqnarray}
\ln(\text{Traffic})_{i,t} &=& \beta_0+ \beta_1 \ln(\text{Exchange rate})_t + \beta_2  \ln(\text{Distance})_i \\&& + \beta_3 \ln(\text{Exchange rate})\cdot\ln(\text{Distance})_{i,t}+ \text{Month}_t \\&& + \beta_4(\text{Consumer confidence})_t + \epsilon_{i,t}
\end{eqnarray}

-$i$= 16 roads, $t$= day (2010-14)

-Exchange rate: foreign currency per unit of domestic currency

-Distance: distance between road and border

-Month: month dummies

-Consumer confidence: consumer confidence indices

Here are the reasons I can think of so far to argue for the validity of my specification:

Fixed effects is not viable. I do not have the full population/large sample of roads. D-I-D is not possible either, as there is no control group. RE is an alternative.
RE’s allows me to exploit the spatial dimension i.e. distance, which is really important for causality. Distance would be wiped out by alternative specifications that include road dummies.
All roads are the same classification of major road, there are not large differences between roads e.g. different speed limits are not altering the volume of traffic flow.
I can’t think of any unobservable in the residual that is correlated with the explanatory variables. The only one is maybe that larger shopping areas attract more cross border shoppers, and so some roads are affected more than others by the exchange rate. But in my case I know that people go the nearest shopping area, not the biggest.
All shoppers/roads receive the same shock/exchange rate. And shoppers are affected by national factors e.g. those contained in consumer confidence. So there’s no reason to have controls for each road.

Random effects scares me, so any advice is greatly appreciated! Thank you.

Your first point is valid for not using fixed effects as you are interested in the entire border not just these 16 roads.  Random effects can be advantageous when you have such a small sample compared to the population for your treatment group.  Also note, if the unobserved effect has a large variance or T is very large then RE will be close to FE anyway.  You can try both and do a Hausman test to see if the two models are different.

Your second point is not convincing.  I don't see this as being a justification for using random effect.  Don't lose site of what you are looking for, the effect of exchange rates on shopping across the border of your two countries.  You don't care about the effect of roadway length on the roadway traffic, so why bother with the idea of holding on to it in your results.  The one thing your distance variable can do is act as a sort of robustness check for you since that is one of the fixed effects you want to control for.  Now I can understand your interaction term with distance as there is probably some sort of cost and benefit for people considering the exchange rate vs the distance they have to drive, but in FE models, your interaction will remain.  Also note, that road dummies would be very similar to FE with your model specification.

I would probably likely try a First Difference approach as well since you are going to have serially correlated errors.  You have controlled for some time-variant factors like seasonality with your months and some economic conditions with consumer confidence, but there could be other factors that change over time: road constructions, localized new regulation, new store openings on one side of the border, etc.  These would create serial correlation in your error term.

As long as you have a good justification for each modeling approach, I would try them all and compare your results.  Just use a straightforward pooled OLS model as your baseline, and then proceed from there.  Don't just blindly try everything, but be thoughtful and understand the assumptions you make in each approach.


Exercise 4.7 in SLP (dynamic programming) Exercise 4.7 (b) : Show that under Assumptions 4.10 and 4.11, $T:H(X) \to H(X)$.

$H(X)$ is the set of continuous and homogeneous of degree one functions and $Tf(x) = \sup_{y \in \Gamma(x)} \{F(x,y) + \beta f(y)\}$. The continuity follows from the theorem of maximum. I am a little confused with showing $Tf$ is homogeneous of degree one. According to the solution,
\begin{equation}
\begin{split}
Tf(\lambda x)& = \sup_{\lambda y \in \Gamma(\lambda x)} \{F(\lambda x,\lambda y) + \beta f(\lambda y)\}\\
& = \lambda \sup_{y \in \Gamma(x)} \{F(x,y) + \beta f(y)\} \\
& = \lambda Tf(x).
\end{split}
\end{equation}
$\lambda$ can be taken out of functions because they are homogeneous of degree one. But, how can we justify the change from $\Gamma(\lambda x)$ to $\Gamma(x)$? More precisely,
\begin{equation}
\begin{split}
Tf(\lambda x)& = \sup_{\lambda y \in \Gamma(\lambda x)} \{F(\lambda x,\lambda y) + \beta f(\lambda y)\}\\
& = \lambda \sup_{\lambda y \in \Gamma(\lambda x)} \{F(x,y) + \beta f(y)\} \\
& = \lambda \sup_{y \in \Gamma( x)} \{F(x,y) + \beta f(y)\} .
\end{split}
\end{equation}
I do understand the second equality, but I do not understand the third equality.
Assumption 4.10 and 4.11 are as follows:

It follows from Assumption 4.10.
Let $\lambda y \in \Gamma(\lambda x)$ be the solution.
Let $\delta = \frac{1}{\lambda}$.
By Assumption 4.10,
$$
\lambda y \in\Gamma(\lambda x)
$$
implies
$$
\delta \lambda y \in \Gamma(\delta\lambda x)
$$
in other words
$$
 y \in \Gamma(x)
$$


Is Malthusian theory of population growth being realized? You probably are familiar with Malthus' Theory of Population Growth.

If you are not, Malthusian model has the following mathematically form:

$$P(t) = P_0e^{rt}$$

A basic graphic representation is:

Note that population is growing in a exponential form where as the resources are growing only linearly. By resources, I do not only mean food resources, but they also include water, energy, land and anything else that support the continuation of expansion of human societies.

Malthusian theory of population growth has been subjected to criticism, mostly, IMHO,  a reaction for the theory being too pessimistic.

But let's have a look at the real population growth for the past couple of thousand years:

Now, let's smooth the graph out:

Do you see what I see?

Still not convinced? Let's zoom in for the more recent times (vertical axis is in billions):

Those are the figures from wikipedia, on which I have calculated percentage change per five years:

Note that even at the current stage, we are still at an above the average trend for over the past 211 years (since 1804 when the world population hit 1 billion):

$$1.0095^{211} = 7.35$$

There are, currently 7.35 billion people on earth.

The average of annual population increase is 0.95% per year, but we are increasing at a rate of more than 1% per year.

Is Malthusian theory of population growth being realized? If this is true, are we going to hit the point of crisis soon because of the limited resources?

If not, why not?

Please support it with number and figures, I would appreciate a more scientific than opinion based discussion.

The annual growth rate of the global population has been in decline since about 1967 (five decades ago).

The absolute annual growth peaked in 1987 (three decades ago).

Malthusians claim that:

population growth is geometric or higher; and
food production growth is arithmetic or lower.

If either of those do not hold, then Malthusian theory does not hold. And it turns out that neither of them hold:

Population is not growing geometrically (not even arithmetically); and
food production turned out to be capable of greater than arithmetic leaps in growth: food production per capita grew by 45% between 1961 and 2013 (source: UN Food & Agriculture Organization FAOSTAT Food Production Indices for the world, element code 434, domain code QI, Area code 5000, Item code 2051, Agriculture (PIN);)

Some relevant factors: cheap, reliable, ubiquitous contraceptives; education and emancipation, particularly for women; cheap and plentiful crop fertilisers; mechanisation of farming; and selective crop breeding, by taking the old practice of eating the best of each crop and sowing the worst, and doing the exact opposite.

Here are two charts, using the global historic data from the US Census organisation for 1800-1950, and the UN data for 1950-2014.


Ln differenced price level times 400, why 400? I am replicating a 2001 Journal of Economic Perspectives methodology paper on Vector Autoregression by James H. Stock and Adam Watson. The paper can be found here: http://faculty.washington.edu/ezivot/econ584/stck_watson_var.pdf

I'm having a slight problem with the log differencing. In the paper the researchers state that they multiply the ln differenced price levels by 400.

I have no clue why this is done. The price level data is quarterly chain-weighted and seasonally adjusted implicit GDP deflator of the US. I would understand if they would multiply by four to get the annual inflation figures, but this is unclear. Any suggestions?

You already accounted for multiplication by 4. Further multiplication by 100 to make the units of measurement percentage points? I.e. inflation is usually referred to as 3%, not as 0.03.


Auction with "buy-it-now" option Consider the buy-it-now price often included in online auctions. Suppose that 2 bidders in an ascending oral (English) auction bid for an object. Each has values i.i.d uniformly on $[0,1]$. Suppose the auction has a buy-it-now price of $B \ge 1/2$; either bidder can end the auction by paying $B$. Assume that there's an equilibrium when the bidding reaches $p(x)$ that a bidder with value $x\geq B$ will pay $B$ (i.e. $p(x)$ is the cutoff when a bidder with value $x$ pays the buy it now price). Also assume also that $p'(x)<0$. i) What price, conditional on winning, does a buyer with valuation $x$ expect to pay (as a function of $x$ and $p(x)$)?

It seems reasonable to assume that bidders will not bid more than $p(x)$. Hence, $b_1,b_2\in[0,p(x)]$. Then, it makes sense to consider two cases: where $x<p(x)$. Here the expected payment is simply the expected payment of the lower valuation bidder, namely, $\frac{p(x)}{2}$.

Secondly, we should consider the case where $x>p(x)$: the expected payment is here, the probability of facing a below-$p(x)$-valuation opponent, times their bid, plus the probability of facing an above-$p(x)$-valuation opponent times the probability of winning (ties are broken randomly) times $p(x)$

$$p(x)*\frac{p(x)}{2}+(1-p(x)*\frac{1}{2}*p(x))=\frac{1}{2}p(x)$$

  ii) Assuming risk neutrality, using the fact that the expected payment
  with valuation $x$ is the same without the buy-it-now option (namely,
  $1/2x$), what is $p(x)?$ (Note: you should get a quadratic equation; one root will be $p(x)=x$, but this is not the solution, given $p'(x)<0$)

I'm not sure how to solve this part, and I'm doubting my answer to the first part given that I don't know how it enables me to derive $p(x)$.

Here is how I would approach the first question:

We are conditioning on the fact that you have won. Given the symmetry, this implies that your valuation $x$ is greater than your opponent's valuation $y$.
Given that you have won, you either pay the 'auction price' or $B$. If you don't pay $B$, you pay somewhere between $0$ and $p(x)$. The expected auction price is the expected value of the second highest draw, so actually $p(x)/3$ - not $p(x)/2$ as you seem to be saying (intuitively, the expected valuation of the lowest bidder must be below the unconditional expected valuation).
The probability that you pay the auction price is the probability that your opponent's valuation $y$ is below your cutoff $p(x)$. This is because your opponent will drop out of the bidding as soon as the price exceeds her valuation. $Pr(y < p(x)) = p(x)$ since $y$ is uniform on $[0, 1]$.
Therefore, assuming you win, the probability that you pay $B$ is $1 - p(x)$.
Putting these claims together, I conclude that your expected payment conditional on winning equals: $(p(x)/3)p(x) + B(1 - p(x))$.
To check the plausibility of this, set $p(x) = 1$ so effectively the buy it now option disappears, and yields an expected payment of $1/3$. This is the standard result for $2$ buyers and a uniform distribution.


Would you consider airport parking to be a monopoly or a monopolistic market? If you look at it one way and group the different companies that offer parking, it could be a monopoly as that is the only place you can park. On the other hand, the different companies offer different prices and consumers can substitute.

If there are different companies offering with different prices, but not so many companies that it is perfect competition, then it is monopolistic and not a monopoly.


What is the exact difference between the $\hat{u}$ in PRF vs SRF? I've been confused about the exact difference between PRF and SRF is.

I know that it has to do with other variables that influence the regression that is not accounted for, but what is the difference in the models?

PRF: Population Regression Function
SRF: Sample Regression Function.

Population Regression Function (PRF) is the relation between conditional expectation of population $Y_{i}$ conditional on population $X_{i}$, versus the corresponding $X_{i}$, which is also a random variable (to be precise, a matrix of random variables) with some specific given values, say $x$, that is, $E(Y_{i}|X_{i}=x)= f(X_{i})$, which is PRF. For linear regression, $f(X_{i})=\beta_{0}+\beta_{1}X_{i}$.

For a specific value $X_{i}=x$ in population, there could be multiple corresponding $Y_{i}$. (Similarly, imagine when we have a sample dataset and we sort by $X$, we can find multiple corresponding $Y$). Thus, using the relation we get above, we have: $Y_{i}=E(Y_{i}|X_{i}=x)+\mu_{i}$ (Note: it's $\mu$, the deviation of population $Y_{i}$ from its conditional expectation value, rather than $\widehat{\mu }$, which is an estimated value from a specific sample). In other words, PRF captures the perfect, or ideal situation where if $X=x$ happens, we get $Y=y$. But remember both $Y_{i}$ and $X_{i}$  are random variables that may deviate from the perfect situation. Given $X_{i}=x$, the model uses an error term $\mu_{i}$ to capture the deviation caused by other random factors other than $X_{i}$.

Sample Regression Function (SRF), on the other hand, is the estimated relation between estimated $Y_{i}$, denoted as $\widehat{Y_{i}}$, meaning it is calculated by SRF, that is, $\widehat f(X_{i})=\widehat\beta_{0}+\widehat\beta_{1}X_{i}$, and $X_{i}$. (Note that $X_{i}$ and $Y_{i}$ here are actual values from sample, rather than from population, although we usually use the same denotations). $\widehat\beta_{0}$ and $\widehat\beta_{1}$ mean they are calculated or estimated from sample, rather than the actual relation between population $Y_{i}$ and $X_{i}$. Also, $\widehat f(X_{i})$, $\widehat\beta_{0}$ and $\widehat\beta_{1}$ are estimated parameters/relation based on sample, in order to "guess" the true parameters/relation in population. The estimated error term $\widehat{\mu}$, is the difference between the sample $Y_{i}$ and the calculated value $\widehat{Y_{i}}$ using the model we specify, and is the estimator of population ${\mu}$.


Can anyone help me understand the budget constraint of an investor in complete market? In the problem below, u is a utility function; $\beta$ is a discount factor; pc(s) is the price for a contingent claim for state s. c is initial consumption and and y is initial wealth. s represents a specific state.
$$max \ u(c) + \Sigma_s\beta\pi(s)u[c(s)]$$
$$ s.t. \ c + \Sigma_s pc(s) c(s) = y + \Sigma_s pc(s)y(s)$$

Can anyone help me understand the budget constraint?

So in an Arrow-Debreu market, there is a price for every asset/claim for every state of the world. The states $s$ refer to this.

For your utility maximization problem, you are maximizing a combination of what you consume, $u(c)$, and the expected profit from your portfolio of claims, which can then be put into future consumption.

$\pi(s)$ describes the profit in state $s$, and that is multiplied by the utility of consumption in that state $s$. In this case, I guess the maximizer does not seem to worry about variance, so maximizing sum of those possible outcomes in all states of the world suffices. Finally, $\beta$ represents the fact that you prefer to consume immediately instead of investing and waiting to see the state of the world.

So the budget constraint can be roughly described as such: whatever you decide to consume now plus the cost of buying claims that will give you money to consume later must equal whatever money you start with plus whatever money you get from buying those cool claims.


Convexity of indifference curve The convexity of an indifference curve results from the fact that the absolute value of its (negative) derivative, which is the marginal rate of substitution is decreasing. But why do we say that it's convex to the origin?

What is an implicit function that is convex and concave to the origin?

I think what people mean when they say "convex to the origin" (or to any point $p$) is that the function is convex when looked at in a new basis, namely the basis resulting from a rotation such that the new x axis (call it x') is, up to a constant, tangent to the IC and the distance $|p-IC|$ is minimized by that point of tangency ($w$).


Issues with an application of definite internal and marginal utilities I'm going to state the problem without much context because it is an issue of the math I'm doing, rather than any specific econ concept.

Condition. I'm trying to prove this.
$$ V(q_l) - \theta_l*q_l  > V(q_h) - \theta_h*q_h$$

Given
$$q_l>q_h$$
$$\theta_l < \theta_h  $$
$$V'() > 0$$ $$ V'' < 0 $$
$$V'(q_l) = \theta_l $$
$$V'(q_h) = \theta_h $$

I'm trying to use definite integrals to prove this. But I think I'm getting something fundamentally wrong here.

$$ \int_0^{q_i} V'(q)dq = \int_0^{q_i} \theta_i  $$
$$ V(q_i) - V(0) = \theta_i*q_i$$

This gives two equations, one for each $q_l, q_h$. Substracting these two equations from one another.

$$ V(q_l) - V(q_h) = \theta_l*q_l -\theta_h*q_h $$

I'm definitely doing something wrong here. Any help?

The mistake you are making appears to be treating $\theta_i$ as a variable while in reality it is a specific value of the derivative.

So
$$\int_0^{q_i} V'(q)dq = \int_0^{q_i} \theta_i dq \;\;\; i=l,h$$

is wrong, since $V'(q)$ equals $\theta_l$ evaluated at $q_l$ only (and equals $\theta_h$ evaluated at $q_h$ only).


Are symmetric equilibria continuous with respect to the payoff matrix? Assume a two player symmetric game where the payoff for the row player is given by:
$$
A = \left( \begin{array}{cc}
a_{1,1} & a_{1,2} &\cdots & a_{1,n}\\
a_{2,1} & a_{2,2} &\cdots & a_{2,n} \\
\vdots & \vdots & \ddots & \vdots\\
a_{n,1}&a_{n,2}&\cdots &a_{n,n}
\end{array} \right)
$$

We denote by $\Delta$ all probability vectors over $[n]$.

A symmetric equilibrium for the game is a vector $a\in \Delta$ such that
$$\forall x\in \Delta: x^tAa\leq a^tAa$$

Assume we increase the value of some specific coordinate $i,j$ by a variable $t$. Denote the new matrix by $A(t)$.

  Assuming $A$ is non-singular, is the change in the symmetric equilibrium continuous in $t$?

I'm aware that the question might not be enough well-defined, as there could be more than a single equilibrium for $A$, but is there necessarily a symmetric equilibrium for $A(t)$ which converges to the symmetric equilibrium for $A$ as $t\to 0$?

If I understand your question correctly then the answer is no. Consider

$$
A(h) =  \left( \begin{array}{ccc}
1 & 1 & 0 \\
0 & 2 & 0 \\
2+2h & 0 & 3 \end{array} \right)
$$
For the game defined by $A(0)$ the vector $a^t(0) = \left( \frac{1}{2}, \frac{1}{2}, 0\right)$ yields an equilibrium. For any $h>0$ however
$$
A(h) \cdot a(0) = \left( \begin{array}{ccc}
1 \\
1 \\
1+h \end{array} \right),
$$
so $a(0)$ is no longer an equilibrium. If play around with the probabilities you will see that nearby strategies do not constitute an equilibrium either. Hence if you have a positive sequence $h_1, h_2, ...$ such that $\lim_{n\to \infty} h_n = 0$ then you cannot select a sequence of vectors $a(h_1), a(h_2), ...$ such that they are equilibrium strategies of their respective games $A(h_1), A(h_2), ...$ and
$$
\lim_{n\to \infty} a(h_n) = a(0).
$$

In this counterexample I used that an action that was never played in $a(0)$ yielded the same payoff as actions with positive supports. If this is not the case then I think the answer to your question would be affirmative. Here is a proof for the case where $a>0$.

Since $a^t$ is a best response to $a$ we have
$$
A\cdot a = \underline{1} \cdot c
$$
where $\underline{1}$ is a vector with $1$ at all coordinates and $c \in \mathbb{R}$.
If $A$ is non-singular then
$$
a = A^{-1} \cdot \underline{1} \cdot c.
$$
As $a$ is a probability vector, $c$ is uniquely determined by $A$:
$$
1 = \underline{1}^t \cdot a = \underline{1}^t \cdot A^{-1} \cdot \underline{1} \cdot c
$$
I will use $A(h)$ to denote the perturbed matrix, and $a(h)$, $c(h)$ to denote the associated vectors. The original matrix and vectors occur at $h=0$. Since matrix inversion is continuous
$$
\lim_{h \to 0} c(h) = \lim_{h \to 0} \frac{1}{\underline{1}^t \cdot A(h)^{-1} \cdot \underline{1}} = \frac{1}{\underline{1}^t \cdot A(0)^{-1} \cdot \underline{1}} = c(0).
$$
Similarly
$$
\lim_{h \to 0} a(h) = \lim_{h \to 0} A(h)^{-1} \cdot \underline{1} \cdot c(h) = A(0)^{-1} \cdot \underline{1} \cdot c(0) = a(0).
$$
This is not an exact proof. To be exact you would have to specify the norm of a matrix, and then to prove that the above limits exist you would have to have a condition like
$$
\lim_{h \to 0} ||A(h)|| = ||A(0)|| \neq 0.
$$


Effect of changing Non Labor Income on Consumption-Leisure problem Given a Utility function $U(c,l) = c - \frac{1}{2}l^2$ , where $c$ is the consumption and $l$ is the number of hours of labour. Let $L$ be the maximum amount of labor, so the amount of leisure is $L - l$. The wage rate is $w$.

Assume a linear tax rate $r$, where $0 < r < 1$. Also, there is a fixed transfer of $R > 0$ to every individual that is irrespective of labor supply choice. Solve for labor supply l that maximises utility.

My solution:

$c = (1-r)wl + R$ therefore we maximise $U(l) = (1-r)wl + R - \frac{1}{2}l^2$.

Differentiating $U$ w.r.t $l$ we get $(1-r)w - l = 0$; therefore $l = (1-r)w$. So this shows that $R$ has no relation to $l$. However, it should make a difference due to the income effect, so I'm not sure what I'm doing wrong :/

Thanks!

This has to do with the form of the utility function. Assume instead that,say, we had

$$U(c,l) = c^{1/2} - \frac{1}{2}l^2$$

Does now $R$ affect the labor-supplied decision?

Solve it and explore. Check also the link offered in a comment to your question.


Microeconomic foundation of discrete choice model (1) Does the following result in a "valid" (in the sense of being consistent with the economic theory) market demand function?
A consumer $i$ maximizes a utility $u_{ij}$ in choosing one of J alternatives, $j=1,..,J$:
$u_{ij} = v_j - \alpha p_j + \epsilon_{ij}$
where $v_j$ is the utility of alternative $j$ without the effect of price (i.e. $-\alpha p_j$) and the logit error term $\epsilon_{ij}$.
The market demand results then as the choices of all consumers.

Is in accordance with economic theory to follow (1) and not assume a budget constraint but let the ultility of an alternative be directly affected by price?  And additionally assume that a consumer chooses one alternative (i.e., a corner solution follows directly from this assumption).  Does (1) result a  "valid" (in the sense of being consistent with the economic theory) market demand function ?

(2) Typically the theory of the microeconomic foundation of logit choice model (e.g.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1718571)  assumes that consumers maximize a utility function without the price effect but subject to a budget constraint. With a linear utility function, the maximization problem results in a corner solution of a consumer choosing only one choice alternative.
This setup (as outlined in the cited paper) leads than to the market demand.

Your first equation is an indirect utility function. The consumer chooses only one good and we assume that he can afford it. For simplification, the indirect utility discards the budget $m$ (often assumed be the same for all $i$).
Here, your demand function is perfectly inelastic. If the individual demand would not have been perfectly inelastic, the form would have been like $V=a-s(p)$, where $s'$ is strictly concave and increasing.

See, for example, Palma/Anderson/Thisse.


What was the "free Coynage" referred to in Dudley North's (1691) Discourses Upon Trade? Dudley North (1691):

  I call to witness the vast Sums that have been coyned in England, since the free Coynage was set up; What is become of it all? no body believes it to be in the Nation, and it cannot well be all transported, the Penalties for so doing being so great. The case is plain, it being exported, as I verily believe little of it is, the Melting-Pot devours all.

What was the "free Coynage" referred to here? When was it "set up"? (Was it for example some specific law?)

It seems to refer to the free coinage act of 1666 introduced by British Parliament under the rule of Charles II.

The name of the act was:

  An Act for encourageing of Coynage.

But it is often referred to as free coinage act. The full text of the act can be read in this source.

According to the act:

  Gold and Silver to be coined gratis. For every Pound Troy of Gold or Silver brought, there is to be delivered a Pound Troy of Current Coin.; For every Pound Troy of Gold and Silver finer than Standard so much more than a Pound Troy delivered; and for baser Gold or Silver so much less.

So the act basically abolished seigneurage and allowed people to bring their silver/gold to the royal mint and having it minted into coins. Hence here the free literary means people did not had to pay for coinage of the coins.


Optimal posted price with uniformly distributed values A seller offers a price $P \in \mathbb{R}^{+}$. Buyers can have type $\theta$ distributed uniformly on  $ [0,1]$. If a buyer of type $\theta$ accepts, then he gets $\theta-p$, and the seller gets $P$. If he rejects, both the buyer and the seller get 0. Find all PBEs. Here is my solution:

Seller's expected utility from offering $p\in[0,1]$ is $(1-p)p.$ This is maximised at $p*=1/2.$ So in the PBE a seller will offer $p=1/2$ and all buyers of type $\theta>1/2$ will accept. Is this correct?

You are correct if there is only one buyer or one good for each buyer.
If there are $n$ buyers, but only one good, the seller maximizes
$$(1-p^n)p,$$
which has FOC $p^* = (\frac{1}{n+1})^{1/n}$.


Do mechanisms always result in a series of strategic games being played out? Mechanism design is an offshoot of game theory, and many call it "inverse game theory", since it involves the use of incentives to ensure that the end result of the game being played out is beneficial to the designer of the game.

That being said, is it always the case that whenever a mechanism is implemented, it results in a game being played out amongst the players?

My intuition says "no", since no game will take place if it is the dominant strategy for all players to reveal their true preferences. Am I correct?

I'm not sure what you mean by "results in a game".

When doing mechanism design, after you've fixed a mechanism, the resulting mathematical structure can be identified with a game which we solve using the tools of game theory. That is, the choice of a mechanism induces a game. I suppose you could take this to mean that it results in a game.

Just because that game has dominant strategies does not mean the game doesn't "take place". In fact, I don't even know how you can speak of dominant strategies when you don't (even if only implicitly) have a game in mind when doing so.


Optimizing Cobbs-Douglas given output I am trying to find L$^*$ and K$^*$ (Labour and Capital respectively) given the following:

  Q = $K^{1/4}$ $L^{3/4}$ where Q = 120, w=$24, and r=$128 (Not sure if you need w and r)

I know that if I can find either L$^*$ or K$^*$, I can find the other one easily.

I have found several questions relating to Cobbs-Douglas on here, but none where Q is given. A close example is this, but I don't have a budget constraint.

The problem is basically to derive the cost function of a firm. What you need to do is minimize costs given the output. That is
$$
\min\limits_{K,L} w \cdot L + r \cdot K
$$
subject to
$$
K^{\frac{1}{4}} \cdot L^{\frac{3}{4}} = Q = 120.
$$
You can solve this using Lagrange or the implicit function theorem (similar application as the MRS).


What happens on a banks balance sheet when the borrower submits loan payments? When the banks lends me money my demand deposits end up in his liabilities and my loan is on his assets. Lets say I paid that money to somebody who has an account at another bank. Lets ignore how the two banks settle that and just focus on that the bank has no liabilities to me and still has my loan on his assets. My employer pays me a salary via a bank transfer in my bank. No changes to my banks net liabilities - they just swapped owners. Now I make the loan payment. Does the bank just simply destroy my demand deposits? What happens to his asset side when I make that payment? What happens eventually to the loan on the banks assets when I finish paying my loan?

If you make a payment of \$X, then:

loan balance (bank asset) goes down by \$X, and
deposit balance (bank liability) goes down by \$X.

I.e., the bank balance sheet shrinks (as do money aggregates that  include bank deposits).

The bank may have held a loan loss provision against the loan, and so the loan may have been carried on the balance sheet at less than \$X. For example, a bank might think there is an expected loss rate on this loan of 2%, so the bank would have a provision of .02*\$X. The loan would be carried on the balance sheet at a value of .98X, not X. The creation of this provision generates a loss, causing a corresponding reduction of equity. (Note: how this is accounted for probably depends on the jurisdiction.) Note that there are no transactions associated with this loss, so it is a non-cash loss.

Since you paid off the loan in full, the provisioned loss did not materialise, and so it would be reversed. The value of the loan would be written up to \$X before cancellation. This would generate a non-cash profit, as equity would rise by the amount of the reversal of the loss provision.

In the comments, it was asked how banks make money on loans. They make money off the interest payments, which are supposed to be higher than the interest costs of the bank.


Bayes-Nash equilibrium and correctness of beliefs Define a Bayesian game as follows: $$G = \left\langle I, \left(A_i,T_i,(p_{t_i})_{t_i \in T_i}, u_i \right)_{i \in I} \right\rangle$$

$I$ is the set of players
$A_i$ is the action set for player $i$,
$T_i$ is the set of possible types for player $i$,
$p_{t_i} \in \Delta(T_{-i})$ is player $i$'s beliefs regarding the types of the other players. $(T_{-i}=\times_{j \ne i}T_j)$
$u_i : A \times T \rightarrow \mathbb{R}$ is player $i$'s utility function

Then a Bayes-Nash equilibrium is defined as follows:

  A (pure) Bayes-Nash equilibrium is a profile of choice functions (or
  strategies) $(\sigma_i:T_i \rightarrow A_i)_{i \in I}$ such that,
  $\forall i \in I, \forall t_i \in T_i, \forall a_i \in A_i$,

  $$\sum_{t_-{i}}p_{t_i}(t_{-i}) \cdot u_i(\sigma_i(t_i),
  \sigma_{-i}(t_{-i}); t_i, t_{-i}) \geq \sum_{t_-{i}}p_{t_i}(t_{-i})
  \cdot u_i(a_i, \sigma_{-i}(t_{-i}); t_i, t_{-i})  $$
  where, for every $t_{-i}, \sigma_{-i}(t_{-i}) = (\sigma_j(t_j))_{j\ne i}$.

And now my question: Am I correct that this implies that, in a BNE, every player (or rather, every type of every player) best responds given their beliefs about the types of other players, but that there is nothing in a BNE that pins down the beliefs a player (or type of player) has on the types of other players? That is to say, in a BNE, a player (or type of player) could have a degenerate belief (putting full probability on some $t_j^*$ for player $j$) in an equilibrium in which $t_j \ne t_j^*$? Put more simply, can a type of player's beliefs about the type of another player be wrong in a BNE?

I think your definition is incorrect, or at least incomplete.** Usually, in a Bayesian game, there is assumed to be a prior distribution on $T$ (where $T = \times_i T_i$). This distribution is called the "common prior" and it is assumed to be common knowledge that types are drawn according to this distribution. In this case, each player $i$'s belief $p_i$ is given by Bayesian updating on $T_i$ and this prior; and in BNE player $i$ must be best-responding to this belief.

The assumption of a common prior and Bayesian update rule (which is what gives this solution concept its name, after all) mean that players cannot be wrong, merely underinformed. In other words, a player with posterior belief $p_i$ is correct about the distribution of types of other players conditioned on her own, even though she does not know which realizations they have.

** Edit. Osborne and Rubenstein's text mentions that it is possible to define a more general game in which each player has a different prior distribution (there is no common prior). So your definition does match their most general definition. I suppose that in such a case two players may hold incompatible views, hence you could say that someone must be incorrect. That all being said, the vast majority of Bayesian games assume a common prior.