This assumption is usually considered as reasonable from a normative perspective. For instance, consider the following situations:

in situation A, you face an urn with 5 blue balls and 5 red balls. A ball is selected randomly and you can bet on its color. You receive a monetary prize if your bet is correct.
in situation B, you face an urn which contains 10 balls that are either blue or red. The number of blue balls has been selected randomly between 0 and 10 according to a uniform distribution. Once the urn is formed (you don't know its content), a ball is selected randomly and you can bet on its color. You receive a monetary prize if your bet is correct.

In the expected utility theory we usually consider these two situations as equivalent since the probability distribution over the final outcomes (the color of the ball) is the same: there is a 50% chance that a blue ball is selected, and a 50% chance that a red ball is selected. Therefore from a theoretical perspective it is hard to think of any reason why people would strictly prefer one situation to another.

However, empirically a substantial fraction of people exhibits a strict preference for the situation A rather than the situation B, for instance in
 this paper. According to my experience, most researchers are inclined to see this behavior as a mistake that reflects some difficulties with the computations of probabilities. Interestingly, this behavior is associated with ambiguity aversion, which is also sometimes considered as an anomaly. However, this is largely a matter of interpretation and other researchers prefer not to make any normative judgment on this behavior, as a matter of principle, and prefer instead to try to find rational explanations for it. It is for instance sometimes argued that the additional layer of uncertainty which is added in situation B would be a legitimate reason for risk-averse individuals to strictly prefer situation A.


What is the usefulness of approximating an optimal decision rule that close enough to steadystate in RBC model?

Side note: This is one way of solving it - the alternative would be formulating a Bellman equation and iterating on that.

If you assume that the real economy is on or sufficiently close to the steady state, you can also infer about responses to shocks. That is, you can look at the impulse response functions to a change in whatever interests you, and see how the model economy changes. Arguing that we're close enough to that steady state will allow you to see how the economy responds to certain shocks.

Also, in general, you can simulate the economy with (for example TFP) shocks, and look whether the simulated economy looks similar to the real economy. Using this comparison you could judge the model.

This needs arguing that we are close to the steady state - or that convergence happens really fast. Generally, the growth literature around Solow has provided arguments for this.

But your argument is very present in most extensions of the basic RBC model: especially when it is important how close we are to the steady state - when models are more nonlinear. There have been many papers showing that this is the case for standard Neo Keynesian extensions of the RBC model.


What is the calculable effect of counterfeiting on an economy?

I'm adding this as a separate answer because it's quite independent of my other answer.

We've agreed that if there are X dollars existing and you counterfeit Y dollars, then you've stolen Y/(X+Y) of the value of those X dollars.

This assumes you do your counterfeiting all at once, and without warning.

If instead you do your counterfeiting slowly over time, or if it can be anticipated, then there's an additional effect:  people try to rid themselves of money holdings in order to avoid being stolen from.  (That is, they try to trade dollars for goods before the dollars lose value.)

This is costly to the moneyholders, with no offsetting benefit to anyone.  One way to see that it's costly to moneyholders is that they now own less money, which makes their lives less convenient.  A different way to see that it's costly to the moneyholders is that the rush to trade money for goods bids up prices, which lowers the value of money.  (These are not two different costs; they are two different ways to think about the same cost.)

So in this case, you have stolen more than Y/(X+Y) of the value of originally existing money, but kept somewhat less (because by the time you get to spend your dollars, they're worth less than dollars were worth at the outset).  The difference between what you steal and what you keep simply dissipates.


Have Raj Chetty's Opportunity Atlas stats changed or been recalculated since early 2019?

I dont think it had been recalculated becouse his plans for the American drean is still on sight,to me he has dispel the myth for of social mobility than anyone else
and that of fruitvale in Oakland the income is highly disappointing for the black people which as such other might think is kind of a racist thing forgive me but is something to look at


Which measures are there to evaluate a country economical development?

Your question brakes down into:
- Alternatives to measure "economic development": there are several ways to interpret what development is, it can be social, intensity of money flows, or volume of "money flows".

If you look for social development and well-being, the HDI (Human Development Index) is a good start, but there are several others like the Genuine Progress Indicator (GPI)

If you look more to assess the level of financial risk that a government or country is exposed to (debt wise) in combination to the wealth generated in that country, you can take as an example what the European union measures for economical stability: a combination of Budget deficit to GDP and debt-to-GDP ratio.


Are there any major commodity markets with a public order book?

Major trading exchanges have order books that anyone can see, if they're willing to pay for the service. So in that sense, they are available to the public. For example, anyone can subscribe via a broker to the London Stock Exchange Level 2 data, which shows them the live order books for listed instruments.

Very few have "secret" order books. I think you mean dark pools; they do exist too, and wikipedia has a list.


Have any economists ever argued that the notion of opportunity cost should be done away with?

The concept of Opportunity Cost is not used in order to net the direct
  benefit of a choice, but in
  order to compare it to the direct benefit of alternative choices.

How do we go about using it in Economics?

1) We gather all available alternative choices, say $A, B, C$
2) We measure (in whatever way appropriate for the situation) the benefit from each choice, say $G_A, G_B, G_C$.
3) The opportunity cost of choice $A$, say $OC_A$ is defined as the maximum benefit among the benefits of the alternative choices :

$$OC_A \equiv \max \{G_B, G_C\}$$

If $G_A - OC_A <0$ obviously we will be better off by choosing something else, and not $A$. And that's that.

Standard example: you have some money and the only choices available are $A$ to put it in a bank account yielding $3\%$ interest and $B$ to put it in another bank account that yields $4\%$ interest.

The direct benefit of choice $A$ is $3\%$ and its opportunity cost is the direct benefit from the alternative choice $B$, i.e. $4\%$.

This does not mean that  $A$'s "net benefit" is $3\% - 4\% = -1\%$. This operation just tells us that we have better choices than $A$. Again, it does not, in any meaningful way, say something like "so the net benefit from choosing $A$ is $-1\%$. It only says "if we choose $A$ we will actually get $3\%$ direct benefit, but we would have get $1$ percentage point more if we had chosen $B$" (an even funnier fallacy here is to say, "so I got $3\%$ and I foregone $1\%$, so my "true benefit = gains (-) losses" therefore true benefit is $3\%-1\%=2\%$" -so sir, can you please hand me this $1\%$ the bank gave you on top of your true benefit? Thank you so much).

Turning to your example, the direct benefit of choosing $x^*=0$ is $3$. The highest opportunity cost of choosing $x^*$ will come from choosing $x'=\epsilon>0$. This will have direct benefit $3-\epsilon$, which is the highest opportunity cost of choosing $x^*$.

Perform if you want the subtracting operation, $3-(3-\epsilon) = \epsilon >0$. The important result is that we get a positive number: so the benefit from choosing $x^*$ is greater than the benefit from choosing any available alternative. It is not the case that the "net benefit" from choosing $x$ is $\epsilon$ (again, since you will get $3$, can you please give me the $3-\epsilon$ which is above your "net benefit"?)

My impression is that this confusion surrounding the correct use of opportunity costs has psychological roots together with the use of the word "opportunity" in a different context: the "feelings of disappointment"(disutility) from "missed opportunities", that one may experience when he learns that he could have gotten more, which appear to "subtract" from the utility gained from what he actually got. Indeed, but in such a case, the missed opportunity was not known/available as an alternative choice during the time of decision. One could attempt to construct a utility function accommodating such behavior, but this is a totally different issue, it has nothing to do with how "opportunity cost" is defined and used in Economics.


I think you have the inequality sign wrong. The inequality as you write it cannot hold. To see this, consider the numerical case where $y=4 > y'=3, d=1 < d'=2$ and $u= \sqrt(x)$. I let you do the calculation yourself.

I suppose the correct inequality is:
\begin{equation} u(y−d)−u(y−d') \leq u(y'−d)−u(y′−d′) \end{equation}

This equation holds true due to the curvature of a concave function. If you're on the upward sloping part of the function, the closer you are to the summit, the flatter the slope. So the vertical distance between the images of the two points in the domain on the left side of the equation is smaller than the same on the right side if $y>y'$ and $d \leq d'$, and equal if $y=y'$. On the downward sloping part it's the other way around. The set of inequality conditions imply each other. Changing one inequality requires changing the others. You can check this for yourself by picking points on a concave curve that satisfy the inequalities.

It is really just an elaborate version of $|x| \leq |y|$, where if $x \leq 0, y \leq x$ and if $x \geq 0, y \geq x$.
I hope this answers your question.


Question on General Equilibrium: how to write offer curves?

$EO_2BO_1$ is 2's offer curve and $EO_1A$ is 1's offer curve. Set of competitive equilibrium allocations is given by the intersection of the two offer curves that is the set of allocations on the line segment $O_1B$.


Examples of a good student's project with minimal economical knowlege

This question is quite broad, but I'll give 3 ideas I would have liked to do, and is of appropriate difficulty, while in undergrad.

Review a seminal paper - Wikipedia has a list of important publications in economics.  They could write a 10-20 page paper and give a deep analysis of what the authors did and why.  I.e. if there is a derivation they could explain why it is solved that way, if it is the only way, or if there is another way and suggest these alternatives.
Construct a new policy function - Let them argue their intuition in constructing a new policy function (e.g. why do you take log consumption?) and solve for the constrained optimization problem.  They should know how to use the method of Lagrangian optimization, but the courageous student could set theirs up as a Bellman equation.
At my school it was perfectly acceptable for a Bachelor's thesis to do a real world project instead of write a paper.  They could make some kind of event, I had a classmate present on the UN Millennium Development Goals and had a video message from Jeffrey Sachs.  They could find somebody (or a few people) local to come and speak.  Also they may have access to a small budget from their school, or can elicit donations from local restaurants, and can provide food (college students love free food)!


Derive the Hicks demand function for $U(x_1,x_2) = x_1^{1/2}x_2^{1/3}$

Let $f(U)=U^{6/5}$. This is a positive monotone transformation of $U$ on $\mathbb{R}_0^+$. So the preferences represented by $U$ are also represented by $V(x_1,x_2):=f(U(x_1,x_2))=x_1^{3/5}x_2^{2/5}$. The utility function $V$ has Cobb-Douglas form and you can use the formula for the Hicksian demand for Cobb-Douglas utilities: $$x_1^*=\left(\frac{3p_2}{2p_1}\right)^{2/5}V,\quad x_2^*=\left(\frac{2p_1}{3p_2}\right)^{3/5}V.$$ Substituting for $V$ you get $$x_1^*=\left(\frac{3p_2}{2p_1}\right)^{2/5}U^{6/5},\quad x_2^*=\left(\frac{2p_1}{3p_2}\right)^{3/5}U^{6/5},$$ or $$x_1^*=\left[\left(\frac{3p_2}{2p_1}\right)U^3\right]^{2/5},\quad x_2^*=\left[\left(\frac{2p_1}{3p_2}\right)U^2\right]^{3/5}.$$


The theory is that if you have three types of production sectors in the economy:

Sectors which could export more with liberalised trade
Sectors which could import more with liberalised trade
Sectors which could see little change with liberalised trade

then increased trade could tend to increase wages in the first type of sector, reduce wages in the second type, while leaving the third type less affected.  In addition, greater efficiency associated with liberalised trade could tend to reduce overall consumer prices, boosting the real value of all wages.

So for an economy which has a comparative advantage in low-wage sectors, this theory might suggest that the relative wage gap could narrow with liberalised trade.  By contrast, the same theory might suggest that the relative wage gap could widen with liberalised trade for an economy which has a comparative advantage in high-wage sectors.

This is only a theory and would require empirical confirmation.  Other things may be happening at the same time, such as changes in the local skill-sets or liberalised labour and consumer markets, which mean that the theoretical effects of liberalised trade are overwhelmed by other effects and the predicted relationship may not be seen.

An example of this sort of discussion can be read at https://wol.iza.org/uploads/articles/378/pdfs/how-does-international-trade-affect-household-welfare.pdf


Difference between LMSR and Liquidity-Sensitive LMSR

The LMSR has a number of parameters which governs its function, but the LS-LMSR focuses, in particular, on the sensitivity function, AKA parameter b. This parameter determines how sensitive the market maker is to incoming orders. The higher the value, the less sensitive the market maker is, and the slower the price will change, because it requires more liquidity to increment the price.

It's up to market operators to set b appropriately, taking into account the amount of liquidity that's expected. However, this can be difficult to manage, as traders enter and leave the market. LS-LMSR outlines a programatic way to dynamically asses conditions and change the LS-LMSR accordingly, setting the value higher as the market thickens, and vice versa. Parameter b can be changed by the operator whenever the need arises, but LS-LMSR alleviates some of that management burden.

It probably would be a good idea for Augur and Gnosis to implement a dynamic way to manage liquidity, since relying on manual edits impedes scaling to large numbers of markets.

The LS-LMSR also describes a way to run the market maker at a profit. In many instances, operating at a loss isn't such a bad thing, at least to a pre-determined degree, since the initial liquidity is what attracts traders to enter the market. As with b, you can also edit this in time and bound losses to your liking (LMSR already supports this), but this paper provides a way to run profitably, or at least break-even.

As for whether to implement, this is a business model question. Exchanges will have to weigh the cost/benefit of sacrificing some money upfront to get participants to trade, with the desire to generate transaction revenue as the market intermediary. Both approaches are valid, but dependent what outcome you're trying to achieve.


What exactly is "quantity of money per unit of output"?

It is the quantity of money, measured by money supply of 'near money', divided by the real GDP. You can see that from reproduction of those tables in the:
The Collected Works of Milton Friedman, compiled and edited by Robert Leeson and Charles G. Palm.
Here is a link to chapter from that book which reproduces the lecture and the figure from the lecture. You can see the picture also below (the note under the table makes it explicitly clear Friedman is talking about quantity of money per real GDP.


More complex than simple and multiple regressions?

Welcome to the wonderful world of econometrics! Most introductory econometrics courses will extend Ordinary Least Squares (OLS) by considering binary outcomes models such as the logit and probit.

Whilst OLS is typically restricted to modelling continuous outcomes bound between $-\infty$ and $\infty$, in research one will often come across data where this is not the case. The most elementary extension is the binary (yes/no) outcome data.

This data takes the form of a yes/no (coded 1/0). Clearly, OLS runs into several problems. First and foremost (for your purposes) is the fact that you can predict outcomes outside of the range $[0,1]$. The simplest solution: logistic regression.

Logistic regression estimates the probability that $y=1$ conditional on your explanatory variables. It does this creating a mapping of your regression equation $\beta_0 + \beta_1 x$ on to the space $[0,1]$ by considering:
$$ \ln \left( \frac{P(y=1)}{1-P(y=1)} \right) = \beta_0 + \beta_1x $$
Depending on what data you can find (and what software you have available - for example EViews, R, Stata and SPSS all have built in routines for logistic regression) this might be an interesting way to proceed.


Graduate Level Textbook on Labor Economics and Macro-Labor

There's also Labor Economics by Pierre Cahuc, Stéphane Carcillo, and André Zylberberg. It's a broader labor econ book, but The "Unemployment and Inequality" fourth of the book covers these topics. I have not seen the second edition, but I expect that they did not alter that part for the worse.


It is my impression that the subject has seen its fair share of scholarly research already. Check the references in the wikipedia article for WWW-II (the article itself is not very good), and maybe the book The Economics of World War II: Six Great Powers in International Comparison.


Do any social welfare functionals, other than maximin, meet all of Arrow's conditions plus invariance regarding ordinal level comparability?

There are at least two other examples of SWFs that satisfy these conditions.

The first is a positional dictatorship.  Let N be the number of individuals (assume it is fixed).  For any k between 1 and N, the kth positional dictatorship SWF orders social alternatives in terms of the preferences of the "kth best off" agent.  Formally, given any social alternative x, let v(x), be the vector of utilities of all individuals for x, but ordered from lowest to highest.  The  kth positional dictatorship SWF is then defined by the kth component of the function v.  If k=1, we get the maximin.  If k=N, then we get the "maximax" ---what you call the "inverse" of the maximin.  If k=[N/2], we get effectively "dictatorship of the median individual".   The point is not that these rules are normatively attractive (they aren't) ---but they satisfy your axioms.

Another possibility is the so-called leximin or lexicographical maximin rule.  This is the lexicographical extension of the maximin, obtained by ranking social alternatives according to the vector-valued function v from the previous paragraph, but with coordinates treated lexicographically.  Thus, alternative x is better than alternative y if it has a higher minimum utility value. If x and y yield the same minimum utility, then we compare them by looking at the utilities of the second-worst off individual in x and y.  If these individuals also have the same utility, then we look at the third-worst off individuals, and so on.

This SWF is very similar to maximin, but it satisfies a stronger version of the Pareto axiom.

For more information, I suggest you look at the 2002 article by Claude d'Aspremont and Louis Gevers entitled "Social welfare functionals and interpersonal comparability", which is Chapter 10 of the Handbook of Social Choice and Welfare volume I (Arrow, Sen and Suzumura, eds.).  You could also look at Chapter 2 of the book Axioms of Cooperative Decision-Making, by Hervé Moulin (1988).  In particular, Theorem 2.4 on page 40 of Moulin's book might be useful to you:  it says (roughly) that the positional dictatorships and their extensions (such as leximin) are the only SWFs satisfying ordinal level comparability and a few other mild conditions.


Why should the cost of home ownership and home renting be equal in the long run?

Note that the "cost of home ownership" depends not only on the house and the market, but also the individual. For someone who moves every year, home ownership is generally not a good option - that person incurs closing costs every year, and most of their mortgage payments at the start of the loan go to interest, rather than building a meaningful amount of equity in the house.  It would be far better for that person to simply rent, rather than throwing away a few percent of their home's value every year in closing costs.

With this in mind, it's possible that the characteristics of the population make renting and home ownership roughly equal in cost, when averaged over a long period of time and the entire population. If you're not going to stay in a home for several years, it will generally be more favorable to rent, since you do not have enough time to recoup up-front costs associated with buying. I don't have hard numbers to show this equivalence, but it's worth pointing out that annual cost of home ownership vs. renting has a component that is unrelated to market value or interest rate - individual lifestyle choices play a role as well. Empirically, we might find that renting is the better financial option for about as many people as would be better off with home ownership.


Why did the Swiss National Bank end the currency peg?

From the Economist:

  The SNB suddenly dropped the cap last week for several reasons. First, many Swiss are angry that the SNB has built up such large foreign-exchange reserves. Printing all those francs, they say, will eventually lead to hyperinflation. Those fears are probably unfounded: Swiss inflation is too low, not too high. But it is a hot political issue. In November there was a referendum which, had it passed, would have made it difficult for the SNB to increase its reserves. Second, the SNB risked irritating its critics even more, thanks to something that is happening this Thursday: many expect the European Central Bank to introduce “quantitative easing”. This entails the creation of money to buy the government debt of euro-zone countries. That will push down the value of the euro, which might have required the SNB to print lots more francs to maintain the cap. But there is also a third reason behind the SNB’s decision. During 2014 the euro depreciated against other major currencies. As a result, the franc (being pegged to the euro) has depreciated too: in 2014 it lost about 12% of its value against the dollar and 10% against the rupee (though it appreciated against both currencies following the SNB's decision). A cheaper franc boosts exports to America and India, which together make up about 20% of Swiss exports. If the Swiss franc is not so overvalued, the SNB argues, then it has no reason to continue trying to weaken it.

I have only several things to add to this commentary, all contained here.


What is the game theory of retaliatory trade tariffs?

Indeed it's difficult to account for all the real-life complexities, but the basic game-theory model of trade wars is prisoner's dilemma, e.g.

https://leadersatwork.northeastern.edu/management/trump-tariffs-and-the-prisoners-dilemma/

  The concept of the Prisoner’s Dilemma is important to a number of business school subjects, including economics and negotiations. The current Trump administration provides a rich opportunity to explore this concept in the context of important policy deliberations. [...]

  This also happens between countries and is playing itself out in many of President Trump’s recent actions involving tariffs. Bilateral agreements between the U.S. and its trading partners confront the “Prisoner’s Dilemma” when it comes to the issue of tariffs. Consider when the President said on March 8, 2018, “he” will impose tariffs on steel and aluminum imports within 15 days. Tariffs represent a situation where the “rational” decision would appear to be to raise tariffs on imports and hope the other side either doesn’t or cannot. The “rational” decision typically leads to retaliation as it does in many prisoner dilemma situations.

  Of course, President Trump doesn’t see tariffs as posing a prisoner’s dilemma type problem, at least in his public pronouncements: “When a country (USA) is losing many billions of dollars on trade with virtually every country it does business with, trade wars are good, and easy to win. Example, when we are down $100 billion with a certain country and they get cute, don’t trade anymore-we win big. It’s easy!” (March 2, 2018 Twitter)

  Not surprisingly, other countries threaten to retaliate. China, Canada, and the European Union have already said they would respond by enacting tariffs that could result in extensive American export losses affecting industries and farms that the President had claimed to protect. Most economists feel that a trade war is disruptive and will make the world as a whole poorer.

  Perhaps the President sees international trade as similar to the construction industry; i.e., as a forum where he can exert power and his will on the other party. What works in the construction industry where Trump gained his negotiation experience may not work in the very different world of international diplomacy. The President might have had leverage in dealing with contractors. But in international trade, the U.S. accounts for 9 percent of world exports and 14 percent of imports. This would not appear to be a position of domination.

  Of course, another characteristic of President Trump’s negotiation style is to stake out an extreme position (anchor) in order to both intimidate an opponent and to give room to make concessions or compromise, and this may be the case with his tariff pronouncements.

http://blogs.cornell.edu/info2040/2018/09/20/the-trade-war-between-the-u-s-and-china-a-prisoners-dilemma/

  In his [FT] article “Trade wars and the prisoners’ dilemma,” Gavyn Davies draws connections between this tit-for-tat tariff game and the classic example of the prisoners’ dilemma.

  Davies highlights the fact that, if the U.S. and China are truly engaged in a non-cooperative, prisoner’s-dilemma style game, they will likely end up in a “bad Nash equilibrium,” where both countries’ payoffs are worse than if they were to simply cooperate with each other. Specifically, assuming that each country continues to choose strategies that protect its best interests in a time of uncertainty, it’s likely that there will be 1-3% reduction in global output in the next several years.

  In its entirety, Davies’ article demonstrates that the game theory logic underlying the prisoner’s dilemma is omnipresent. Almost every economist and investor examining the impacts of the budding trade war has assumed that the two countries will continue to retaliate against one another without cooperation. Their models paint a dismal (albeit realistic) picture of this trade war’s global repercussions. Still, economists and investors might be better off employing the same game theory logic to illustrate the mutually beneficial benefits of cooperation. Perhaps the prisoner’s dilemma will help to show how cooperation, not just among inmates, but among countries can lead to better payoffs than self-preserving strategies.

https://www.bloombergquint.com/global-economics/game-theory-explains-why-the-u-s-china-trade-spat-is-worsening

  Experts surveyed by Bloomberg News lay out four scenarios for how the U.S. trade conflict with China could end: Both sides back down, which now seems unlikely in the short term; China blinks; the U.S. blinks; or both sides keep escalating.

  The “China blinks” scenario assumes President Xi Jinping won’t want to endure a downturn in the Chinese economy, which showed signs it underperformed in May. The “U.S. blinks” scenario assumes China calls Trump’s bluff, knowing how much he enjoys a strong economy, rising stock market, and the support of voters in farm states that China could target.

  The fourth scenario, in which neither blinks, is the most damaging. “We’re not there yet, but it’s scary, because it seems like we’re on a path toward major conflict, and it’s hard to see the offramp,” says Michael Smart, managing director at Rock Creek Global Advisors LLC in Washington and a former international trade director on the National Security Council.

  The World Trade Organization was created to prevent exactly this kind of bluffing and brinkmanship. “Trade agreements are a way of escaping from a prisoner’s dilemma in which each country acting rationally is stuck doing something that is bad for it individually, but they can’t get out of it without a collective agreement,” says Dartmouth College economist Robert Staiger.

  The Bagwell-Staiger Theory of Trade Agreements and the "Reciprocity Approach"

The WTO literature seldom fails to mention prisoner's dilemma (avoidance), e.g.:

  At the latest since the writings of David Ricardo and John Stuart Mill the welfare-enhancing qualities
  of international trade have been common wisdom in the realm of economics (Irwin, 1996). Reality,
  however, paints a different picture: Countries are often reluctant to open up their borders to foreign
  goods and services and unwilling to liberalize trade unilaterally. Yet, there are plenty of examples that
  countries have overcome what appears to be a mercantilist and protectionist stance and engage in
  bilateral or multilateral trade agreements. What is the rationale for such cooperation? Why do
  sovereign countries contract over trade issues?

  Starting with the seminal work of Harry Johnson (1953), economists have strived to address this
  question. The basic intuition that has guided much of the literature is that countries cooperate in an
  effort to constrain unilateral “beggar-thy-neighbour” policies. Trade protection by one country may
  reduce the welfare of trading partners; it provokes negative externalities, or spill-overs.
   The strategic
  set-up of a prisoners’ dilemma emerges. Excessive trade protection, albeit inefficient, becomes the
  dominant strategy for importing countries. The purpose of a trade agreement is to eliminate the
  inefficient restrictions on trade volumes that arise when policies are set unilaterally, and thereby offer
  governments a means to escape the prisoners’ dilemma.

  Theories of trade agreements based on externalities come in two variations.
   The best-known and
  most elaborate theory of trade cooperation is based on a terms-of-trade driven prisoners’ dilemma that
  (large) countries overcome by means of concluding an international trade contract. The terms-of-trade
  school contends that it is solely the ability of economically large countries to influence world prices
  for goods and services – and their potential to actively deteriorate other states’ terms-of-trade - that
  motivates governments to conclude trade agreements. Large countries realize that the unilateral
  setting of import tariffs creates inefficiencies that can be avoided by mutual trade cooperation. This
  theory is represented most prominently by Kyle Bagwell and Robert Staiger. Their research
  programme is the only one that formally integrates an explanation of why countries cooperate on trade
  matters with an explanation of how this can be done. In other words, it currently is the only approach
  in economics that can explain both the existence of the multilateral trading system and its architecture.

  The political externalities strand of the literature, which gained prominence through the writings of
  Wilfred Ethier (2004; 2004a; 2006), is critical of the terms-of-trade approach. It alleges that “a trade
  agreement serves governments to get credit for the reduction in foreign trade barriers. International
  cooperation is not about the elimination of economic (world-price) externalities, but about political
  externalities. The latter arise when politicians in one country believe that their political status is
  directly affected by actions of politicians of another country” (Hauser and Roitinger, 2004: 652).

  Different as these rationales for trade agreements may be concerning possible policy implications,
  their basic intuition is identical: Both schools rely on a simple game set-up, where two or more
  rational players are faced with a prisoners’ dilemma situation.

(Avoiding) prisoner's dilemma also applies to subsidies, not just tariffs:

  We begin our investigation of the role for retaliation by looking at export subsidies. Bagwell and Staiger
  (2001b) show how a subsidy agreement that limits government payments and avoids subsidy escalation
  can be of value to governments of exporting firms. Without such an agreement, each government is
  tempted to subsidize its exporters so as to create a competitive advantage in a third market – i.e., a
  prisoners' dilemma problem.

It's actually not clear to me if a more formal turn-based "beggar thy neighbor" rather than the simpler simultaneous version (prisoner's dilemma) has received much attention game-theory wise.

Since trade wars are back in fashion, perhaps we'll see more theoretical literature dealing with how they happen rather than how they are avoided...

The tit for tat strategy and the associated iterated prisoner's dilemma have been studied theoretically quite a bit; perhaps there's more literature relating them to trade wars...

Actually there is some literature from three decades ago how trade wars start and iterate, but it seems mired in controversy as far as modelling goes; the hypothesis  of rent-seeking by internal pressure groups adds another dimension to simpler model of the (external) trade war; this conflicting issue of modelling hasn't been fully resolved as of then:

  In Trade Wars, Professor John A.C. Conybeare, a political scientist,
  employs a game-theory approach in an attempt to formalize a predictive
  theory for when trade wars will occur.  While Conybeare praises the
  rent-seeking literature for rendering trade wars "more theoretically and
  empirically understandable," he finds the interest group explanation
  conveyed in that literature to be incomplete because it "has largely been
  confined to examining the interindustry structure of protection within
  countries and, with a few exceptions, has not made international comparisons." In other words, Conybeare takes the position that, while interest
  groups may set the internal political agenda within a particular country,
  no interest group explanation of trade wars can be complete without an
  understanding ofthe constraints facing that country due to its bargaining
  power vis-a-vis other nations. [...]

  In Chapter Five, he looks at the Anglo-Hanse trade wars to test his
  assertion that bilateral trade wars between large trading units will result
  in a prisoners' dilemma that will evolve into a cooperative equilibrium as
  the two sides learn to employ contingent retaliation. Unfortunately, four
  hundred years worth of trade-a sufficient time span to produce iterative
  opportunities for even the most exacting game theoretician-did not
  produce cooperation. By the author's own admission this was because
  "domestic rent-seeking in conjunction with a severe public good problem in the use of the tit-for-tat strategy of retaliation" caused "outbreaks
  of conflict to escalate."

  In Chapter Six, Professor Conybeare describes the Anglo-French
  trade wars beginning in 1664. These trade wars are used to illustrate the
  author's hypothesis that trade wars between two large countries should
  evolve into a cooperative interaction after some initial defection because
  such wars resemble iterative prisoners' dilemmas.3o Contrary to Professor Conybeare's general hypothesis, the trade wars lasted for over two
  hundred years and did not evolve into a cooperative equilibrium at the
  pace his model predicts. As with the Anglo-Hanse trade wars, the author
  is forced to admit that his own example "illustrates the ease with which
  the effects of iteration may be' disrupted." Once again, the cause of a
  protracted trade war can be traced to domestic rent seeking. [...]

  The Chicken Wars began because of Regulation 22, promulgated in
  July, 1962, which curbed the export of frozen chickens into EEC countries. The Chicken Wars brought the powerful agricultural lobby in
  France into direct conflict with the powerful agricultural lobby in the
  United States. Not surprisingly, France, the largest poultry producer in
  the EEC, was unwilling to embrace a free trade policy whose benefits
  would be spread among consumers throughout Europe. The benefits of
  protectionism were concentrated in France and the costs were borne by
  consumers throughout Europe. Indeed, the stakes were sufficiently high
  that France might have quit the EEC had not French agricultural interests been appeased.

So a fuller (game theory) model of trade wars seem to need to account for internal groups as different players rather than treat countries as single entities. I don't know if more progress on this has been made since that book.

A somewhat more recent paper (only two decades old) on the US-Canada wars from more than a century ago:

  The classic analysis of retaliation with optimal tariffs by Johnson (1954) is shown to
  have empirical validity. The pattern of US–Canadian tariff interactions in the period
  1868–70 shows evidence of a retaliatory adjustment process of the kind described by
  Johnson. Both countries perceive they have market power and therefore think they
  can gain from applying retaliatory optimal tariffs. In the short run, changes in the tariff
  level of each country are seen to be Granger-caused by changes in the tariff of the
  other. An interpretation of that result is that a tariff innovation in one country due to
  exogenous political economic forces in one country, say a highly influential protection-
  ist lobby, is met with retaliation by the partner country which seeks to reverse the
  initial increase. This leads to a tariff war. The Granger causality tests capture the short-
  run reactions that give credence to this story.

  What is more interesting, however, are the questions about the long-run steady-state
  solution after the retaliation war ends. In the long run, the USA maintains and even
  increases the tariff shock that it initiates, while the Canadian policy tends to back down
  from the tariff shock that it initiates. This is consistent with the Kennan–Reizman
  hypothesis that big countries win tariff wars, no matter who starts it. A second long-run
  result is that the Canadian tariff demonstrates a permanent change following a US
  tariff shock; that is, the cross-country effect is positive. On the other hand, in the long
  run, the US tariff returns to its own internal equilibrium (retaliation component is
  significantly no different from zero), unaffected by innovations in the Canadian tariff.
  This result is consistent with Chan’s (1991) model of bargaining which emphasizes
  the availability of outside options. Since the USA has greater outside options, it
  chooses not to participate in a costly retaliatory war. However, since Canada is highly
  trade-dependent on the USA, its outside options are limited and the best it can do is to
  retaliate in an attempt to bring down the US tariff increase.

  Interestingly, an additional inference that may be made from the study is not one
  about retaliation, but about internal political economic factors. While Canadian retali-
  ation does not succeed in reversing a US tariff increase due to political economic
  factors, US retaliation is shown to succeed in at least partially reversing a tariff
  shock caused by political economic factors. Hence, not only is the size and lower
  trade dependency of the USA vis-à-vis Canada beneficial in non-cooperative or bar-
  gaining games, but the internal political economic factors in the USA seem to be more
  stubborn in the face of retaliation than are political economic factors in Canada. It was
  perhaps in the best interest of Canada to establish the Canada–US Free Trade Agreement in which the political importance of the issue was far greater in Canada than in
  the USA.

I have to say however that Chan's model (although based on game theory) seems pretty obscure; the paper only has 10 citation in Google scholar. The Kennan-Riezman hypothesis (that big countries win trade wars) seems a lot more discussed, with a few hundred citations; but it doesn't seem primarily based on based on game theory; it uses an Edgeworth box
 analysis to draw its main conclusion as to the bargaining power in a trade war.

A highly-cited 1993 paper by Grossman and Helpman does attempt to model national-level interest groups: it includes not only the global country utility but also (domestic) political contributions in the government's utility function when doing trade negotiations.

I think this is still pretty limited, since it only considered campaign finance contributions as part of the latter. Potential for votes is not distributed among groups, but only modelled via the general country welfare utility function. But even this results in a pretty complicated analysis. Only by the 34th page in their paper they get to introduce the competitive model including foreign governments, which is not developed a lot. The paper notes/conclues the obvious trade-off that a national government has to face between industry lobby groups and general population welfare with respect to tariffs, and also (obviously)

  Tariff rates are highest in industries with the largest stakes in trade policy (i.e., greatest output) and in industries where foreign export supplies and mohme import demands are most inelastic. [...]

  Industry groups that are politically stronger than their counterparts abroad will secure exceptions from across-the board tariff cuts or from reductions in the levels of export promotion.

But practically all of this involves equilibrium analyses rather than much game theory; there are no (game) iterations involved in this paper. These two authors have an even more highly cited paper title "protection for sale" which elaborates on the costs borne by lobby/industry groups.


You have most of the explanation here - the only missing piece is that as the de facto reserve currency of the world, almost all global trade is conducted in US dollars.  Typically what happens is that a buyer will convert local currency to \$USD, the \$USD will be exchanged in the transaction, and then the seller will convert that \$USD to their local currency.

There are two points in that chain where the United States can intervene - when the buyer converts to \$USD, and when the seller converts back to local currency.  The US' ability to impose credible sanctions rests on its ability to exert this influence, and historically it has had it by way of the \$USD being the reserve currency for the world.

In principle, nothing has ever stopped other nations from circumventing this mechanism.  What has made $USD desirable as a reserve currency has been the relative political and financial stability of the US economy, which allows the \$USD to act as a store of value.  The relative part is important - in a global exchange economy mediated by fiat currencies, there really are no non-currency safe-havens.  Every boat on the ocean rocks in a storm, but some rock less than others.  It is better to weather a bit of sea-sickness than to jump to a boat that may capsize.  US-imposed sanctions reflect a belief that nations would rather capitulate to US demands than skip over to the next boat.  For much of the globalization era this has been true for most nations.

However, there has been cause to question this relative stability in recent decades (especially since 2009) and so it's very telling that we are seeing these agreements.  They indicate that to some nations, whatever benefits have historically flowed from transacting in $USD are viewed as no longer being present.  Whether this is good or bad is open to interpretation - after all, it should be expected as other large economies "catch up" to the US in terms of economic activity, stability of institutions, etc.


I thought a little bit about the problem, and I came up with the following quick hack, that seems to work.
Here is the piece of code that should do the job in principle with integers:
function  [exch]=achange(p,coins)
s=size(coins);
c=zeros(1,s(2));
coins=sort(coins,'descend');
it=1:s(2);
isaninteger = @(x)isfinite(x) & x==floor(x);
if p<coins(end)
   return
end
if isaninteger(p)==0
   exch.coins=coins;
   exch.c=inf(1,s(2));
   exch.rest=inf;
   return
elseif any(isaninteger(coins)==0)
   exch.coins=coins;
   exch.c=inf(1,s(2));
   exch.rest=inf;
   return
end
rest=0;
while p>0
    trQ=mod(p,coins)==0;
    idx=it(trQ);
    li=length(idx);
    if isempty(idx)
       rst=1;
       rest=rest+rst;
       p=p-rst;
    elseif li>0 && li<s(2)
      ps=it(trQ)==0;
      idx2=idx;
      idx2(ps)=[];
      for k=1:li
          if p>0
             p=p-coins(idx2(k));
             c(idx2(k))=c(idx2(k))+1;
          end
      end
    elseif li==s(2)
     for k=1:li
         if p>0
            p=p-coins(idx(k));
            c(idx(k))=c(idx(k))+1;
         end
     end
    end
end
exch.coins=coins;
exch.c=c;
exch.rest=rest;
end

At least for the following example it works:
>> exch=achange(57,[10 25])
exch =
struct with fields:
  coins: [25 10]
      c: [1 2]
   rest: 12

>> exch.coins*exch.c' + exch.rest
ans =
57

or for:
>> exch=achange(51,[10 25])
exch =
struct with fields:
    coins: [25 10]
        c: [1 2]
     rest: 6

>> exch.coins*exch.c' + exch.rest
ans =
51

and finally my example from the comments:
>> exch=achange(60,[1 2 5 10 20])
exch =
    struct with fields:
    coins: [20 10 5 2 1]
        c: [1 1 3 4 7]
     rest: 0

>> exch.coins*exch.c'
ans =
60

If any input is not an integer, we obtain
>> exch=achange(57,[5 .10 25])
exch =
    struct with fields:
    coins: [25 5 0.1000]
        c: [Inf Inf Inf]
    rest: Inf

or similar
>> exch=achange(57.8,[5 10 25])
exch =
   struct with fields:
     coins: [25 10 5]
         c: [Inf Inf Inf]
      rest: Inf

UPDATE 21.11.2020
Due to the fact that the allocation of the species is not optimal by the above code, which can be seen, for instance, by first example, where the residual amount can still be allocated to some coins, I provide a small amendment that should produce better results.
The residual amount of the mentioned example is $12$ indicating that the structure of problem is unchanged, which allows us to solve the problem recursively. That is, we should replace the lines of code after the While-loop by the following If-construct to invoke a recursive call whenever it is necessary.
if any(rest>coins)
   exch2=achange(rest,coins);
   exch.coins=coins;
   exch.c=c+exch2.c;
   exch.rest=exch2.rest;
else
   exch.coins=coins;
   exch.c=c;
   exch.rest=rest;
end

Then we can reduce the residual amount of the first example from $12$ to $2$, as we can see through
>> exch=achange(57,[10 25])
exch =
   struct with fields:
     coins: [25 10]
         c: [1 3]
      rest: 2


Why should $dp_2=dm =0$ in this problem?

The assumption $dm =0$ says that we examine the behavior of the consumer under a fixed nominal income, and this is something interesting to study, because it aligns to a large degree with the observed reality of many people that have approximately constant income.
The assumption $dp_2=0$ assumes away general equilibrium effects, since we are looking at changes in $p_1$ which is price in one market, while $p_2$ is the price in another market, presumably of a different good. So while formally the justification here is that "we do partial equilibrium analysis", the vindication of partial equilibrium analysis is that the effects from changes in one goods market to another goods market take some time to materialize, so partial equilibrium analysis has relevance to the real world.
So we see that the assumption $dm=dp_2=0$ is not "necessary to find the correct solution" (there is not one correct solution, but solutions each consistent with the corresponding assumptions made). But it is neither an "arbitrary" set of assumptions, on the contrary, it has a specific logic and purpose for which it is imposed.
The OP asked in the comments

"Then why not also assume that $d\lambda=0$"?

But the optimal value of lambda is endogenous to the model, and it summarizes aspects of the consumer's optimal behavior. So whether it changes or stays constant is for the model to tell us.


Here was my attempt at a proof:

First let us look at the "if" case.

Assume $\succcurlyeq$ on $X$ is rational, continuous, additive, monotonic, and non-trivial.

BUT

Case 1: $x \succcurlyeq y$ and $p \cdot x < p \cdot y \ \forall p$

Suppose $p = \{\frac{1}{s} \cdots \frac{1}{s}\}$

$$p \cdot x < p \cdot y \implies \frac{1}{s} \sum^s_{i=1} x_i < \frac{1}{s} \sum^s_{i=1} y_i \implies \sum^s_{i=1} x_i < \sum^s_{i=1} y_i$$

So $x \succcurlyeq y \iff x \geq y$ by monotonicity

$x \geq y \iff x_i \geq y_i \ \forall i$ by definition

but then $\sum^s_{i=1} x_i \geq \sum^s_{i=1} y_i$ which is a contradiction.

Case 2: $p \cdot x \geq p \cdot y$ and $y \succ x \ \forall p$

Similarly, pick the same $p$.

$$p \cdot x \geq p \cdot y \implies \sum^s_{i=1} x_i \geq \sum^s_{i=1} y_i$$

$y \succ x \iff y > x$ by monotonicity

but then $\sum^s_{i=1} x_i < \sum^s_{i=1} y_i$ which is a contradiction.

Now, let us look at the "only if" case.

Let $u(x) = p \cdot x$ and $\exists \ p$ s.t. $\forall x,y$ then $x \succcurlyeq y \iff p \cdot x \geq p \cdot y$

Now we wish to show our five properties hold and the uniqueness of $p$.

The above implies that

$\exists \ p$ s.t. $\forall x,y$, then $x \succcurlyeq y \iff U(x) \geq U(y)$

This we have utility function representation, by definition. It is a basic proof from the beginning of your class probably that representation implies rationality.

We can also say if $U(x)$ is continuous in $X$ and $U(x)$ represents $\succcurlyeq$ on $X$, this implies the preferences are continuous.

$x \succcurlyeq y \iff p \cdot x \geq p \cdot y \iff p \cdot (x + z) \geq p \cdot (y + z) \iff x + z \succcurlyeq y + z \quad \forall x,y,z \in X$

So that shows additivity.

Now suppose monotonicity does not hold. Suppose $x \succcurlyeq y \implies p \cdot x \geq p \cdot y$

but additionally, $x < y$
$\implies p \cdot x < p \cdot y$ which is a contradiction.

Suppose non-triviality does not hold. Suppose $x \sim y \ \forall \ x, y$, where $x \neq y$, so $x$ and $y$ are unique. But we have monotonicity now.

but $x > y \iff x \succ y$
and $y > x \iff y \succ x$

For the uniqueness of $p$, building off of the outline you gave pick $x, y \in X$ where $x \sim y$ for both $p$ and $p' = (p + \epsilon, 1-p- \epsilon)$

This can only be true if $\epsilon = 0$ or if $x$ and $y$ are not unique, that is, $x_i = y_i \ \forall i$. We will rule out the trivial case where $x$ and $y$ are not unique and show $\epsilon = 0$ (and thus $p = p'$)

$$px_1 + (1-p)x_2 = py_1 + (1-p)y_2$$
and
$$(p+\epsilon)x_1 + (1-p-\epsilon)x_2 = (p+\epsilon)y_1 + (1-p-\epsilon)y_2$$
The second equation implies
$$px_1 + \epsilon x_1 + (1-p)x_2 - \epsilon x_2 = py_1 + \epsilon y_1 + (1-p)y_2 - \epsilon y_2$$

Subtract the first equation from this equation.

$$\epsilon x_1 - \epsilon x_2 = \epsilon y_1 - \epsilon y_2$$
$$\epsilon (x_1 - x_2) = \epsilon (y_1 - y_2)$$

Consider if $x_1 + \delta = y_1$ and $x_2 + \delta = y_2$ for any $\delta > 0$.

Then the differences $x_1 - x_2$ and $y_1 - y_2$ are equal, but bundle x will have higher monetary outcomes in whichever state occurs, so $x \succ y$. Contradiction.

Similarly, if $x_1 = y_1 + \delta$ and $x_2 = y_2 + \delta$, then $y \succ x$, which is again a contradiction with $x \sim y$

Thus $\epsilon = 0$.

$\square$


Game theory for showing interest and availability when dating

Sending costly signals may work, at least when the recipient is less attractive than the sender.
There's also a nice popular science book by Paul Oyer called Everything I Ever Needed to Know About Economics I Learned from Online Dating that covers some of this ground, including the paper linked above.
Another theoretical paper suggests that costly signals that are worthless to the recipient work nicely, because the cost signals to the recipient that the donor has resources and values her highly, but by being worthless, it screens out "gold-diggers" that merely want the gift. Perhaps setting a pile of cash on fire would do the trick?


Show that there is no continuous utility function which represents the lexicographic preferences

Hint:

To ensure the existence of utility function representation, we must have continuous preferences (and this is a sufficient condition). From the Mas-Colell book:

The preference relation $\succeq$ on $X$ is continuous if it is preserved under limits. That is, for any sequence of pairs ${(x^n, y^n)}^\infty_{n=1}$ with $x^n \succeq y^n$ for all $n$, $x = \lim_{n \to \infty} x^n$ and $y = \lim_{n \to \infty} y^n$, we have $x \succeq y$.

We then look at the definition of utility function representation.

The function $U$ represents $\succeq$ on $X$ if $\forall \ x,y \in X, x \succeq y \iff u(x) \geq u(y)$, where $u: X \to \mathbb{R}$.

Though it may be easier just to show that the preferences themselves are not continuous, and thus there is no utility function representation, continuous or not.


Do outputs of a country produced outside its borders contribute to its citizens' well-being?

GDP stands for Gross Domestic Product: this is the amount of activity that happens within the borders of the country itself, irrespective of source.

What you are thinking of is GNP: Gross National Product- which ideally would be the amount of economic activity worldwide attributable to citizens or corporations or the government of a particular country.

Historically, countries liked the idea of GNP and it used to be the 'favoured' way of reporting economic activity. However from a practical perspective as the world has become more and more globalized, it turns out that GDP is easier to estimate and is somewhat more realistic when trying to assess the level of economic activity happening in a geographic area.

Ultimately who cares who owns the factory, the fact that it exists where it is and not somewhere else is a huge boost to the local economy. Many industries have profit margins of 5% or less, guess where much of the expenses are being spent?


How does one do a hypothesis test for elasticity?

Do you agree with the way I have set up this hypothesis test? If the estimate were less than 1, I would have stated $\mathrm H_0: \beta_{\ln m} \geq 1$ against the alternative $\mathrm H_1: \beta_{\ln m} < 1$.

Setting up null and alternative hypotheses is the first step in a t-test.  You should not set them up after computing your estimates.  In your specific example with income elasticity of demand, you set up the null and alternative correctly, meaning that you want the alternative hypothesis to be the statement about what you are trying to prove.  You should use that null and alternative regardless of what the data then tells you.

P.S. You should report the one-sided p-value from your one-sided hypothesis test, not just the test statistic.


Utility theory and portfolio optimization: utility of what exactly?

In mean-variance optimisation I have typically seen the below quadratic utility function where $[]$ is the expected return (or mean return) of a possible portfolio, $\sigma^{2}$ is the return variance of that portfolio and $A$ is a parameter that the determines the sensitivity to variance.

$$=[]−\frac{1}{2}A\sigma^{2}$$

As an aside, maximising % return, also maximises $ return, log return and total wealth. They might not be equivalent when optimising for mean and variance though.


ECB bond buying from national banks, what are the national banks expected to do?

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


Is there an economic theory of why people like to hold on to wealth?

You could consider unspent money to be a call option. The set of future investment opportunities is unknown, so if you're optimistic about future opportunities it could be a valuable call option.

So saving money can be a profit/preference-maximizing behavior.


In the event of a company's bankruptcy, how does a SPV continue operations if it can no longer collect payments on collateral

Servicing and origination don't have to be done by the same firm. It is quite common that the financing company contracts out the servicing rights on the loans they originate.
Servicers, like many other kinds of firms, can continue to operate after bankruptcy. Bankruptcy is what happens when a firm can't pay its bills which includes debt, it doesn't mean that the firm needs to be liquidated. For example, existing debt holders are not getting paid and sue to put the firm into bankruptcy. The equity holders are wiped out, the debt holders become the new equity holders, and with the reduced debt costs the firm can often cover its costs and be profitable (even though the debt holders took a loss on their investment).
Servicing can be reassigned after servicer bankruptcy. In fact, not only does this happen but it is common for a servicer to change when a loan is sold. So transfer of servicing rights is commonplace.


Explaining why Hicksian demand is more inelastic to intermediate micro student

Here's a "no maths" explanation (including the inferior goods case, because I think it helps to understand what's going on):

Suppose we have a normal good, $x$, and we increase its price. Marshallian demand decreases thanks to two effects (i) consumers substitute away from $x$ towards cheaper alternatives; (ii) because prices are higher, consumers can afford less stuff, so it's as if their income were lower. Both of these effects point towards lower demand for $X$.

Now consider Hicksian demand, which shows the effect of a price change after we compensate consumers to eliminate the income effect. Instead of having two effects (income and substitution) pointing in the direction of lower demand, now there is only one (substitution). So Hicksian demand changes less with prices.

Note that on p83 of MWG, the authors note that the figure is drawn for the case of normal goods.

But let's look at the case of an inferior good. By definition, when the price of an inferior good increases Marshallian demand tends to fall due to the substitution effect, but increase due to the income effect. In other words, there is one negative effect and one positive effect on demand. These two effects cancel each other out to some extent, so that the overall effect of price on Marshallian demand is muted.

Hicksian demand eliminates the (positive) income effect, so  that the only remaining effect is the unambiguously negative substitution effect. Thus, Hicksian demand for an inferior good is more sensitive to price that Marshallian demand.


A down-to-earth explanation (including why) that I found: https://www.thebalance.com/who-owns-the-u-s-national-debt-3306124

FRED blogs are also helpful.


Pure exchange economy with two consumers and non differentiable utility functions

I would suggest that ask yourself the following questions (hopefully, this should help you figure out how to solve the problem) :

If good $z \in (x,y)$ was free, what would be the demand for both agents?
Is the conjunction of these demands feasible given the endowments? (this should allow you to rule out one of the cases)
If the demands are feasible, which price(s) for the other good would support such demands? What could be the equilibrium(a) allocation(s)?

Notice that if good $z$ is free, one of the agents is not able to consume the other good, and she is therefore indifferent between consuming any quantity of good $z$.

Hope this helps.


Note that I am not 100% sure. But in my understanding, we have

Year 1

Price for a product in the US :  $p_{US}=v$ \$
Exchange rate: $x$ pesos for $1$\$
Price of the product in the Philipines: $p_{Ph})=v.x$ pesos

Year 2

Price for the same product in the US : $p^\prime_{US} = (1+\alpha_v)v$ \$. The price increased due to the inflation $\alpha_v$.
Nominal exchange rate: $(1+\alpha_x)x$ pesos for $1$\$. A drop in value means you need more pesos for one USD.
Inflation in the Philipines: $p^\prime_{Ph} = \frac{P_{Ph}}{1+\alpha_p}$. Due to the inflation, the acquisitive power of the pesos is reduced.
Price of that product : $p^\prime_{Ph}=[(1+\alpha_v)v].[(1+\alpha_x)x].[\frac{1}{1+\alpha_p}] = \frac{(1+\alpha_v).(1+\alpha_x)}{1+\alpha_p}.v.x$

Variation

The effective variation compared to the previous year is thus, $\frac{(1+\alpha_v).(1+\alpha_x)}{1+\alpha_p}$, which corresponds to a rise in effective exchange rate of

$$\frac{1+\alpha_p}{(1+\alpha_v).(1+\alpha_x)}-1=2.7\%$$


If the country converts the reserves to 250 million per year, then in 4 years it will convert 1 billion and 15 billion will be exhausted in 15x4 years.


Why a current account surplus is bond to lead to an appreciation of a currency?

We have the following cases:

1) No capital mobility:
If there is no capital mobility, the trade balance is necessarily zero in equilibrium i.e. exports equal imports. When there is a trade surplus, there is an excess of demand for domestic currency over supply of domestic currency. In equilibrium, this surplus must be eliminated to ensure that demand equals supply. So the exchange rate must appreciate, reducing exports and increasing imports for the domestic country until the trade balance is in equilibrium. It doesn't matter if the demand is increasing or not, any excess or deficit must be eliminated by a change in the exchange rate.

2) Capital mobility:
In this case, the Balance of Payments must be zero in equilibrium. This includes the current account(exports and imports) and the capital account (trade in assets with the foreign country). Here a trade surplus or deficit can exist as long as the capital inflows balance it out. If there is a deficit, there must be net capital inflows (borrowing from abroad) and vice versa.

Hope this helps.


Type of good that can be owned but not consumed when used

As I understand it, the best way to answer your question is to translate your description in to the language of economics and to understand the way that economists talk about these things.

To put this in to the language of economics, these would likely be "durable goods" with very low rates of depreciation. "Capital goods" (or just, capital) are a type of durable good. It is usually assumed that all durable good depreciate at least at some positive rate. This isn't a terrible assumption as, in your example, a hammer might rust over time---even if that time period is very, very long.


Contract curve for firms with linear utility functions

1.) An economy with two agents who both have linear preferences will always have Pareto optimal points along either the right and bottom edges or the left and top edges of the Edgeworth box. Edges are dictated by the ratio of MRSa,MRSb.

2.) The contract curve is the locus of Pareto Optimal points.


The degree of precision with which the various terms for these economic aggregates are used may vary with the context.

But if one is trying to be strictly correct, three distinctions should be borne in mind:

Gross v Net: net meaning net of a deduction for depreciation of capital.
Domestic v National: national being inclusive of net property income from abroad (ie income earned by nationals from assets located abroad, less income earned by foreigners from domestically located assets) and also, as Kenny LJ points out, similar net international flows relating to employment income and taxes and subsidies.
At factor cost v At market prices: the latter being inclusive of indirect taxes.

In terms of these distinctions: GDP is clearly gross and domestic.  National income, without further clarification, could be either gross or net, but it is clearly not domestic.  So GDP and national income are conceptually distinct, although they could be numerically the same if national income is measured gross and the property income and other flows as above from and to abroad happen to net to zero.


Violation of completeness axiom (simple everyday examples)

There is a problem in how you translate completeness into behavior. Let $R$ be any binary relation, representing preferences, on a set $X$ of alternatives and $A\subseteq X$ be a nonempty set of alternatives available. The usual assumption is that the decisionmaker chooses an alternative $a\in A$ optimally according to the relation $R$. Here are three ways to interpret this:

$a R b$ for all $b\in A$.
$b R a$ for no $b\in A$.
$b R a$ implies $a Rb$ for all $b\in A$.

One usually uses 1. for weak (reflexive) preference relations, 2. for strict (irreflexive) preference relations, and 3. works in both cases. If we define $R'$ by $xR'y$ iff $\neg(yRx)\vee(xRy)$, then $R'$ is complete and satisfies 1. iff $R$ satisfies 3. If $R$ is irreflexive, $R'$ satisfies 1. iff $R$ satisfies 2. So completeness in itself has no behavioral implications from this perspective. It can interact with other properties. For example, transitive and complete is more restrictive than transitivity alone- completeness forces transitive to be applicable to more comparisons.

Now one can try to make a distinction between indifference and incomparability. But such a distinction necessarily uses a different framework than the usual maximization paradigm.


Does investment directly influence demand?

As mentioned by @Henry: investment is itself a demand for capital goods (physical, human, etc.).

If I decide to buy trucks this manifests itself as an increase in demand to the truck factory.


This index is derived solving the cost minimization problem
$$\min_x \{ p^\top x \lvert \bar u(x) \geq \bar u\},$$
where $p=(p_1,...,p_J)$ is price vector and $x=(x_1,...,x_J)$ is the consumption bundle. The problem can therefore also be written as
$$\min_{x_1,...,x_J} \sum_{j=1}^J p_j x_j \\[8pt]
s.t. \ \ u(x_1,...,x_J)\geq \bar u.$$
One interpretation of this problem is that the underlying question asked and answered by solving the problem is:

How much money is the consumer required to spend at the price $p$ in order to achieve the utility $\bar u$?

Solving the problem you get the Hicks demand functions
$$x^\star(p,\bar u),$$
and inserting these in the budget equation $p^\top x$ you get the expenditure function
$$E(p,\bar u) = p^\top x^\star(p,u) = \sum_j p_j x_j^\star(p,u)$$

It is worth noting that the problem are analogous to the cost minimization problem for firms

Firms minimize cost of producing output $y$ given a production technology captured by production function $f(x)$, hence the firm solve the problem
$$\min_x \{p^\top x \lvert f(x) \geq y\},$$
here prices are now factor prices. The solution here is conditional demand functions $x^\star(p,y)$ and the cost function $C(p,y) = p^\top x^\star(p,y) = \sum_j p_j x^\star_j(p,y)$.
Deriving the unit cost of utility with CES preferences
I will now show how to derive the unit cost of utility given CES preferences. As noted about this is the same as deriving the cost function of firm using CES production technology. I will not show that this is a price index, which would require setting up the formal properties of what a price index is, which is not trivial.
So the problem to be solved is
$$\min_x \sum_j p_j x_j \lvert u(x) \geq u$$
where
$$(1) \ \ u(x) = \left(\sum_j x_j^\alpha\right)^{1/\alpha}$$
To solve the problem I set up Lagrangian function and find FOC thereby arriving at the result that relative prices equal MRS. The Lagrangian is
$$\mathcal L(x,\lambda) = \sum_j p_j x_j - \lambda(\bar u - u(x)),$$
with FOC
$$\frac{\partial \mathcal L(x,\lambda)}{\partial x_k} = p_k + \lambda \frac{\partial u(x)}{\partial x_k} = p_k - \lambda \left(\sum_j x_j^\alpha\right)^{\frac{1}{\alpha}-1} x^{\alpha - 1} =  0,$$
this implies - using that constraint is binding so $\lambda > 0$ - that
$$\frac{p_k}{p_j} = \frac{x_k^{\alpha - 1}}{x_j^{\alpha-1}}\phantom{xxx} \Leftrightarrow \phantom{xxx} x_k = \left(\frac{p_k}{p_j}x_j^{\alpha-1}\right)^{\frac{1}{\alpha - 1}},$$
which is inserted in the constraint $u(x) = \bar u$ to get
$$\bar u = \left(\sum_k \left( \left(\frac{p_k}{p_j}x_j^{\alpha-1}\right)^{\frac{1}{\alpha - 1}}\right)^\alpha\right)^{1/\alpha} = \left(\sum_k \left( \frac{p_k}{p_j}x_j^{\alpha-1}\right)^{\frac{\alpha}{\alpha - 1}}\right)^{1/\alpha},$$
the sum index is running over $k$ so not binding $x_j$ and $p_j$ in the expression and these can therefore freely be moved outside the sum to get
$$\bar u = \left(\sum_k \left( \frac{p_k}{p_j}x_j^{\alpha-1}\right)^{\frac{\alpha}{\alpha - 1}}\right)^{1/\alpha} = \frac{x_j}{p_j^{\frac{1}{\alpha-1}}}\left(\sum_k p_k^{\frac{\alpha}{\alpha-1}} \right)^{1/\alpha},$$
which gives us the result that
$$x_j^\star(p,\bar u) = \frac{p_j^{\frac{1}{\alpha-1}}}{\left(\sum_k p_k^{\frac{\alpha}{\alpha-1}} \right)^{1/\alpha}} \cdot \bar u,$$
which is Hicks demand. To get expenditure function use
$$E(p, u) = \sum_j p_j x_j^\star(p,u) =\sum_j p_j  \frac{p_j^{\frac{1}{\alpha-1}}}{\left(\sum_k p_k^{\frac{\alpha}{\alpha-1}} \right)^{1/\alpha}} \cdot \bar u =  \frac{\sum_j p_j^{\frac{\alpha}{\alpha-1}}}{\left(\sum_k p_k^{\frac{\alpha}{\alpha-1}} \right)^{1/\alpha}} \cdot \bar u = \left(\sum_j p_j^{\frac{\alpha}{\alpha-1}} \right)^{\frac{\alpha - 1}{\alpha}}\cdot \bar u,$$
where it is easy to see that $\bar p:= \left(\sum_j p_j^{\frac{\alpha}{\alpha-1}} \right)^{\frac{\alpha - 1}{\alpha}}$ is the cost of each utility point since the derivative of $E(p,u)$ with respect to $u$ does not depend on the level of utility.
It is perhaps worth adding a final property, namely that the Hicks demand can be reexpressed in terms of the price index:
$$x^\star_j(p,u) = \frac{p_j^{\frac{1}{\alpha-1}}}{\sum_j p_j^{\frac{\alpha}{\alpha - 1}}}u \bar p = s_j(p) u \bar p = s_j(p)E(p,u),$$
where $s_j(p):=\frac{p_j^{\frac{1}{\alpha-1}}}{\sum_j p_j^{\frac{\alpha}{\alpha - 1}}}$ is denoted with "s" to indicate that it is a share in the sense that it is a positive numver in (0,1) and $\sum_j s_j(p) = 1$.


Why are population projections so inaccurate?

This is because most of these projections are based on extrapolation (in fact almost all forecasting is based on extrapolation) which is inherently extremely inaccurate.

Consider this simple example:

Let’s say that we know that person who gets breast feeding for 3 months will have height 150cm person with 4months 160cm and 5months 170cm. Now based on this it is very easy to estimate that the relationship in this small sample would be:

$$H=120+10M$$

Where $M$ is months of breastfeeding and $H$ height in centimeters. Now based on this relationship we could let’s say expect that someone with 3,5 months of Brest feeding will have 155cm and that would be quite accurate. But see what happens if we start to extrapolate that is to plug there numbers further and further out of our sample.

Let’s start with 6 months that would give us height 180 - reasonable. Let’s try 8 months it would give us 200 still reasonable but let’s try 20 months it would give us height 320 which for human might not even be possible.

The takeaway is that the relationships can change. Between 0-8 months the relationship can be nice and linear but at some point the relationship flattens so extrapolation too far outside the sample will lead to wrong prediction.

The same hold for population growth. If you predict population growth 12 months in advance then that can be easy as the relationship should not change that quickly. However, 10 years ahead it is very likely that the relationship that was estimated based on past birth rates simply changes. This could be due to the fact that the previous estimations were done from past observations at smaller total population (since birth rates can be different at different population levels). Or also because preferences of people changed in unpredictable manner. Or also because many of these projections can use some auxiliary forecasts of for example GDP growth that have their own margins of error.

Hence, it’s not really that surprising the projections were wrong. In fact I could even say given how difficult forecasting and extrapolation is its surprising they are not even more off then they actually are.

Also to really make sure the forecasts were wrong you also have to go to those reports and check their margin of error if one of the sources forecasts that birth rate will be 4% with margin of error of 3% then you can’t say real birth rate 7% was off as it’s covered in margin of error. Statistics is in end only exercise in probability no estimate is certain it’s always just a distribution.


Why isn't "long-run aggregate demand (or LRAD)" a thing?

The main reason why long run aggregate supply is vertical is that in the end the production capacity of every country is limited. In the end there is always some maximum number of number of stuff we can produce (of course, there can be economic growth which expands our production possibilities but the LRAS is basically given by the production possibility frontier that will at every point in time be finite).

However, there is no such restriction on people’s demand. One of the basic assumptions of economics is non-satiation. More is always better than less. However, another basic principle in economics is that marginal utility of consumption is increasing but at a decreasing rate. That is more is always better but the more you have of something the less valuable the thing to you becomes. This is what makes demand decreasing function of price. The thing is that this holds both in short and long term. It’s not like people are only non-satiated in short run, and also it’s not like the marginal utility of consumption increases at decreasing rate only in short run.

Vertical demand curve would basically imply that consumers would never want to buy more of the aggregate product which is certainly not true.

So to sum up, LRAS is vertical because of physical limitation on our production. At some point no matter what’s the price it is not possible to produce more. For example, a writer can only write so much hours in a day so even if someone would offered the writer million euros per hour he or she can never work more than 24h per day (and considering that would kill the person probably I should say not more than max 18h) so the supply will be at some point completely vertical given by the production possibility of the economy. However, no such restriction exists on people’s demand. People’s needs are endless and people will always prefer more to less if the price drops sufficiently (since utility is not increasing at constant but at decreasing rate).


Monetary Policy and the Yield Curve PART ONE

You've asked a lot of questions, so I will have to keep my answers rather brief.

  As I understand it the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations.

This is incorrect in a few ways:

The discount rate is a tool, but it's not a tool that is used to conduct monetary policy in normal times. It is, instead, a "penalty rate" in the sense used by Walter Bagehot.
The Fed Funds rate is not a tool, it is a target. The Fed Funds rate is calculated from market transactions, and the Federal Open Market Committee will often instruct the Federal Reserve Bank of New York to engage in open market operations to move the Fed Funds rate toward a particular level.
These are not the only tools at the Fed's disposal. It also has, for example, the reverse repurchase program, which enables it to set a floor under short-term secured borrowing rates.

  Are expectations regarding overnight fed funds rates reflected in the 1 month yields?

Yes, they are related, though the yield on a  1-month Treasury bill will in practice differ from the compounded Fed Funds rate for a number of reasons. One notable reason is that the Fed Funds rate, being a market rate, does vary, while the yield on a 1-month Treasury is effectively fixed at the time of purchase. The relationship between the expected values of a fixed rate and a floating rate is expressed through Overnight Indexed Swap values, and 1-month OIS on the Fed Funds rate is the best direct indication of the expected value of compounded overnight borrowing in the Fed Funds market.

  ...stuff about the discount rate...

No, as I said above. On an average day, bank borrowing from the discount window should be zero. Commercial paper represents medium-term borrowing by private companies.

  Finally I understand that changes in the curve at longer maturities may reflect the governments 'open market operations' and their buying and selling of US securities.

Yes, but that's also true of the short end of the curve. In fact, sometimes the Fed has sought to change the relationship of the short and long ends of the curve, as in "Operation Twist".


Symmetric Cournot equilibrium: suffciency without second order conditon

How can it be a minimum or saddle since for every $q_2$ the profit function is strictly concave? If anything, the implicit non-negativity constraints might be binding, for example, if $q_2\geq 1/2$.

When the objective function is strictly concave, the first order conditions are necessary and sufficient, and the maximum is unique.

Not sure if I'm answering your question, but hopefully it helps.


The ratio of relative prices $P^*/P$, where $P^*$ is foreign and $P$ home price level respectively,  is used in order to adjust the nominal exchange rate for changes in relative price levels in two countries. I think a good way of understanding it is to use analogy with real GDP. A real GDP $Y_r$ will be defined as: $Y_r = Y_n/P$ where $Y_n$ is nominal GDP where we would divide by $P$ in order to adjust for the effect of inflation (change in price level).
The real exchange rate is basically the same concept you are trying to adjust the nominal exchange rate for changes in price level, but you cannot just divide by $P$ because then you would be ignoring the changes in foreign price level.
You can see this more clearly if you look at the equation in terms of inflation (as in Copeland's Exchange Rates and International Finance textbook). Start with the definition for real exchange rate:
$$Q=S\frac{P^*}{P}$$
where, $Q$ is the real exchange rate and $S$ nominal exchange. Now take logs of the variables and to clean up the expression I will be using lowercase letters to denote logs (i.e. $\ln X = x$):
$$q = s + p^* - p$$
Now the above should hold across multiple time periods so lets examine the changes between $t-1$ and $t$ where $\Delta x_t = x_{t}-x_{t-1}$:
$$\Delta q_t = \Delta s_t + \Delta p_t^* - \Delta p_t$$.
Now finally by definition inflation ($\pi_t$) is the change in price level so $\pi_t\approx \Delta p_t$ so lets substitute that in:
$$\Delta q_t = \Delta s_t + \pi_t^* - \pi_t$$.
Hence the change in real exchange rate reflects the change in nominal exchange rate adjusted for inflation in foreign country and home country.


It is not quite true; the expenditure function is affine in utility, not linear. This is Stone-Geary utility, and I use the result that demand is given by
$$x_i^*=m_i+\frac{a_i}{p_i}\bigg(w-\sum_j m_jp_j\bigg).$$
One can interpret $\sum_j m_jp_j$ as "subsistence expenditure" and $w-\sum_j m_jp_j$ as "non-subsistence expenditure." Plugging this into the utility function, one can show that utility is an increasing linear function of non-subsistence expenditure. The inverse of a linear function is linear again, so we can write non-subsistence expenditure as $l(u)$ with $l$ linear (in the relevant range). This means then that total expenditure is
$$l(p)+\sum_j m_jp_j,$$
which is an affine function as the sum of a  linear function and a constant.


How to Calculate the productivity multiplier?

Let $y=Y/L$ and $k=K/L$ be the per-worker levels of output and capital. Observe that $y=Ak^\alpha$.

Steady state is given by: $$k^*=sy^*+(1-\delta)k^*,$$ or $$k^*=sA(k^*)^\alpha+(1-\delta)k^*.$$

Doing the algebra: $$k^*=\left(\frac{sA}{\delta}\right)^{\frac{1}{1-\alpha}}.$$

And: $$y^*=A\left(\frac{sA}{\delta}\right)^{\frac{\alpha}{1-\alpha}}=A^{\frac{1}{1-\alpha}}\left(\frac{s}{\delta}\right)^{\frac{\alpha}{1-\alpha}}.$$

I am not sure what is meant by the "multiplier on productivity". I would interpret this term to be the answer to the question, "Given a small unit change in $A$, what is the resultant change in $y^*$?" That is, the following expression: $$\frac{\partial y^*}{\partial A}=\frac{1}{1-\alpha}A^{\frac{\alpha}{1-\alpha}}\left(\frac{s}{\delta}\right)^{\frac{\alpha}{1-\alpha}}.$$

However, clearly, this does not correspond to your desired answer. So I suspect what is really meant is the elasticity of $y^*$ with respect to $A$: $$\frac{\partial y^*}{\partial A}\div \frac{y^*}{A}=\frac{1}{1-\alpha}.$$


Game Theory (continuous strategies, pure strategy)

I think I figured this out--I forgot to imposed the constraints on Alice and Beatrice, using the fact that they know this about Ashok and Bob and will strategize accordingly to maximize payoff.

Thus if

$$q_{A} = -\frac{1-2p_{A}+p_{B}}{3}$$

and

$$q_{B} = -\frac{1-p_{A}-2p_{B}}{3}$$

then Alice maximizes her payoff by

$$\frac{\partial B_{alice}}{\partial p_{A}} = \frac{\partial }{\partial p_{A}}\left(p_{A}\left[-\frac{1-2p_{A}+p_{B}}{3}\right]\right)$$

$$=-\frac{1}{3}(1-4p_{A}+p_{B})=0$$

With the same analysis given for Beatrice you get two linear equations in $p_{A},p_{B}$.


Relative risk aversion, a property of period or lifetime utility

Though this probably doesn't fully answer your question, given that it's been active for a little while with no other responses, this might hopefully be able to give some direction.

First, it's important to note that the Arrow-Pratt measures of risk aversion are just one possible measure of risk aversion. While it certainly has nice properties in many set-ups, if, for example, the agent doesn't follow expected utility theory, then the Arrow Pratt measure loses it's explanatory value.

When it comes to intertemporal risk aversion, it's generally worthwhile to consider risk aversion to be "how much an agent, in period $t$ would be willing to pay to avoid a particular gamble in period $t+1$?" For this, there seem to be several different derivations of measures of risk aversion, depending on the specific assumptions made about the within-period and between period utility function. Given that you've mentioned Epstein Zin, it's probably worth pointing out that their 1989 paper's focus was on divorcing intertemporal elasticity of substitution from risk preferences, and they take 15 or so pages to go through what risk aversion means in their non-separable framework, and how to define it. Perhaps more helpful is this recent work that considers a relatively general definition of risk aversion in a multi-period macro context, which can include some recursive inter-temporal aspects of utility. This paper also considers a model with non-additively separable utility, and shows that the CRRA coefficient is still the same as it is in the additively separable case. This might be another interesting paper since it also considers risk aversion over a planning horizon without separability.

That said, as this small set of lecture notes shows, if you're primarily interested in measures of RRA using a traditional measure, define it at period $t$ by taking the overall utility function's derivatives at the period of interest. There might be some non $t$ period consumption variables in that measure, but that's fine. This set also points out the interplay between risk aversion parameters and intertemporal substitution parameters.

If I find more I'll edit this response, but hopefully this provides at least a good start!!


Good question!

Qualitative methods (QM henceforth) have become more widespread in the recent decades, according to a 2014's survey in the Journal of Economic Surveys. QM include, among others, in-depth interviews, focus groups, case studies, ethnographic studies, and mixed-methods (quanti+quali). They are still not that popular though, and have been very often looked down by the field. This is evident from the JEL coding, which does not include a specific section for QM, but does include one for quantitative methods.

In contrast to BB King comment, these methods have been used in very hard-core economic issues like Macro (e.g. Blinder et. al. 1998), Labour Economics (e.g. Cregan 2005), International Organisation (e.g. Autor, Levy and Murnane 2002), Development Economics (e.g. Valente 2011), etc (for more examples, see Table 1 in survey above). Here is an article from an MIT economist commenting on his experience with using qualitative methods in labour economics research (excuse the fallacy of authority).

If you want to explore more, there is a 2016's book dedicated entirely to the subject. Also, Chapter 7 of this handbook focuses on QM used in Heterodox Economics.

Other references in which QM are used:

Health Economics
Introductory economics teaching
Measurement of poverty
Finance
Input-Output analysis
Economic modelling


What are the different patterns/quantity of employment according to demands of different income ranges?

So the phenomena you've identified is linked to a goods being labor intensive or not. Often ``craft'' goods required high-quality labor (think watches) to be built, while lower quality goods can be made using machinery. Now farming of all kinds used to be very labor intensive, but technology has replaced most of those workers.

So the substitutability of a worker matters a lot here and the skills that luxury goods need may be less substitutable.

Another factor is that when the good is more expensive, cutting costs (such as labor) at the potential expensive of quality is not always a goods idea - think how often you see ``handcrafted'' or pictures of the people working on the farm on organic products.


Does the Lucas (1978) asset pricing model feature complete markets?

It seems to me that we might as well say that markets are complete. It seems to me to be somewhat inconsequential since this is a representative agent model and that market clearing requires that the only assets that the agent may hold in positive net supply are the $n$ trees. The prices of all Arrow-Debreu securities may be inferred from shadow prices. Suppose the optimization problem is rewritten such that the agent may invest in the $n$ trees plus the set of all Arrow-Debreu securities. (There will be redundancies---I'm hand-waving a little.) The market clearing conditions say that, in equilibrium, the agent must have a unit holding in each of the $n$ trees and zero holdings in the rest of the assets and the price of each of these securities in equilibrium must be set to support these holdings. Since market completeness is a matter of whether or not the agent may trade in all of these securities, we may interpret the situation a two different ways: either the agent can invest in the Arrow-Debreu securities (as well as the trees) but the AD securities must be in zero net supply or the agent cannot invest in the AD securities (only in the trees). In either case, the result is the same.

On the other hand, if you had a model with more than one agent and they had different endowment processes, then the question of market completeness would matter for equilibrium outcomes.

Reference

Take a look at the notes here.

  We have used the equilibrium of the model to determine a single price,
  the price of a tree. With trading in trees, markets are complete.
  However we can introduce additional (redundant) assets and use the
  same approach to determine their prices.

Additional Note:

Your question is somewhat related to the question asked here: "Complete Markets in Continuous Time". See the solutions given there.

In addition, you can also find a discussion in these notes by Markus Brunnermeier:

  If the horizon is infinite, the number of events is also infinite.
  Does that imply that we need an infinite number of assets to make the
  market complete?

  List item

  Do we need assets with all possible times to maturity and events to have a complete market?

  No. Dynamic completion.

  Arrow (1953) and Guesnerie and Jaffray (1974)

The conclusion, which is in the slide titled "How many assets to complete market?", is that, in discrete time, it depends on the "branching number" (see the slides) and that, in continuous time, you can get complete markets simply with a risk-free bond and $n$ independent risky assets where $n$ is the number of independent Brownian motion underlying the economy.


There are economists who argue that market for organs would be efficient and would improve the allocation of cadavers saving lives. There also good arguments for them leading to Pareto improvements although you should note that market does not necessary have to be strictly pareto-optimal for it to be desirable. Often in public economics it is enough to show that a policy improves on the current state of affairs.
Hence there is significant number of economists who support such markets (but not all). For example, Gary Becker is an advocate of such markets (see Becker & Elias, 2007).  Another known advocate is Roth who supports such markets (see Roth (2015) Who Gets What — and Why: The New Economics of Matchmaking and Market Design). In fact according to IGM forum more than half of top US economists would be in favor of introducing market for kidneys in the US once the opinions are weighed by the confidence.
When economists consider efficiency of these markets kidnap or coercion (in its crude form) does not play big role. Even without any market for kidneys people can be kidnapped and it is completely possible that even with only voluntary donations of organs people get coerced (in fact it could be argued absence of market would actually make these issues more prevalent). Rather the market efficiency debate would depend on whether there are some market imperfections (asymmetric information, externalities etc.) and how exactly the market is organized.
Not all markets are created equal and it is important to create proper institutional framework for markets especially in such delicate issues as cadaver markets (see above cited Roth). Moreover, organ markets can be criticized on grounds that people might not be completely rational they might have inconsistent preferences and thus make choices that will end up not maximizing their utility (there is some evidence for people regretting donating/selling their organs see Goyal, Mehta, Schneiderman, and Sehgal, 2002; Zargooshi, 2001). This is why economists usually also argue such markets should be well regulated.
Furthermore, a worry exist that creation of market for kidneys could lead to crowding out of charitable donations of organs (Albertsen, 2020). Hence even if there would be overall benefit there might be some distributional and inequality issues (however, these are for moral philosophers to discuss). On other hand as argued by this previous answer here the prices on legal markets for organs are not prohibitively large and charities tend to sprung up to support poor people.


How can Factor Income paid to abroad be negative?

I suspect that you are looking at an economic description which contrasts factor incomes with current transfers.  That is slightly old fashioned, and the contemporary terms are primary income and secondary income in the balance of payments accounts (a similar change in the national accounts involved going from what was called GNP to GNI - gross national income)

For example, for the United Kingdom, you can find data in the UK Balance of Payments Pink Book, for  primary income in Chapter 4 and secondary income in Chapter 5

Primary income includes:

compensation of employees (e.g. pay of cross-border workers and short-term migrants)
earnings on direct investment (e.g. profits of foreign subsidiaries - in theory this can be negative if they are loss-making)
earnings on portfolio investment (e.g. share dividends and bond coupons)
earnings on other investment (e.g. interest paid on bank loans and deposits)
taxes and subsidies on products and production (only recently reclassified to primary income and possibly not in your factor income)

By contrast, secondary income (so presumably not in your factor income) includes:

remittances by long-term migrants and current transfers by others
insurance premiums and claims
cross-border taxes on income and wealth etc. and social security contributions and benefits
overseas aid
other intergovernmental current transfers and international organisations

Exports and imports of goods and services are treated separately: in the UK Pink Book, goods are in chapter 2 and services in chapter 3

In each case there are credits (income from abroad) and debits (income due abroad), leading to a net figure which can be positive or negative.  Add all of these up and you get the current account balance