How can Finance influence economic activity? I'm not sure how to put it. I'm currently reading Blanchard's Macroeconomics. In a chapter, he explains how for example an unexpected shift in monetary policy, or in consumption or in fiscal policy, can affect the stock values, and the yield curves of bonds, but not how for example a financial bubble (stock/bond overpricing) can affect the economic activity of consumption, investment, etc. The perspective presented in the book seems a bit too one-way. I'm interested also in the other direction, from finance to economic activity.

Is there any bibliography that presents, in a academic way, this other perspective of finance affecting the economy?

This question, as mentioned, in incredibly broad. So, of course, this answer will not be complete. Also, I am unsure what you mean by "financial". I will try to answer this question, assuming that by "financial" you mean, specifically 'stock/bond' market.

Here is one link from NBER which should help you get started, kinda, since it only scrapes the surface.

There are two sections to consider:

  Theoretical: As far as traditional, not necessarily classical, economic theory is concerned, stock and bond markets are corollaries and ancillaries of several factors of economic activity, e.g. capital market, money market, investment, employment etc.. That is, the financial market should just be an indication and investing mechanism based on real economic factors.

and,

  Practical, Modern: Now, since so many different corporations and businesses invest and are invested in the stock/financial markets, volatility in the stock/financial market will affect them directly, or indirectly.

    Directly: If these companies invest and are invested in, their valuation and/or income will be affect by market swings. For example, many of the financial firms which went under in the crisis.

    Indirectly: The shifts in the market can affect the global position of investing. Attitude is perhaps the largest impact felt from the shifts in financial markets. If the general attitude on investing shifts, it makes it harder for new companies to gain investors, i.e. capital.


How to get hang of mathematical language that is so extensively used in economics? For last couple of weeks I am trying to read "Game Theory" from Fudenberg and Tirole and "Microeconomics" from Jehle and Reny. But the kind of maths they use for their theorem-proof-theorem analysis, is just not getting into my head. What book can I use to easily master such kind of Real Analysis that can help me to understand these books?

If you don't have any background in Real Analysis, I suggest you to read "Analysis I" written by Terence Tao.
I was in a similar situation that you a year ago. I studied Economics at college but we never had to do rigorous proofs (as a matter of fact, I did not know what was a theorem, a mathematical proof, or mathematical logic until I read the book). We only learned some "rules" of derivation and integration, and to manipulate algebraic equations in order to get some important results in Economics. However, a professor suggested me to apply to a PhD program and to take a real analysis course. It was really hard because I had never seen something like that. The books recommended by the analysis professor were the common books you will be recommended here: Baby Rudin, Kolmogorov and Fomin, Ok, Abbot, Apostol, etc. I read some of them (specially Baby Rudin) and I found them too difficult.

The problem was that I found difficult "thinking as a mathematician". Therefore, I started to search for the "best book" in real analysis, and I found this one written by Terence Tao. It was amazing, not only because the deep understanding and the outstanding expository skills of the author, but because he started from the very beginning: he answers some important questions (what is analysis and why to do it?) and starts explaining what are the natural, integer, rational, and real numbers (and also the Peano axioms, and some operations). He also starts explaining what sets are.
Then, he develops the most important concepts of analysis: sequences, limits, convergence, series, etc.

I think the most important feature of the book is that it is completely focused on building mathematical skills: how to prove a proposition, different ways to do it, how to use your intuition to develop a proof, etc. And also, it gives you a complete understanding of the topic. This makes it starkly different from other books such as Baby Rudin (which assumes that you know lots of results that, in fact, you don't), which is useful as a reference book and also when you have some well understanding of the topic (I moved easily from Tao to Rudin when the analysis course I took required me to do so). Another important characteristic of  the book is its appendix: it gently introduces you to the basics of mathematical logic: what mathematical statements are, the structure of proofs, (nested) quantifiers, etc; and gives several examples of proofs.

I often see questions like this and I have always found puzzling why no one recommends this book. It is maybe the best mathematics book I have ever read (as it may seem obvious, I love that book I have fond memories of me learning how to make proofs and what real numbers and analysis really are). Also, it is strange because Terence Tao is unarguably the most important mathematician alive and a very kind person. You can see his blog and the books he has published in the following link: https://terrytao.wordpress.com/books/. I hope this recommendation would be useful.


Set of Bayes Correlated Equilibria when complete information is not available Model

Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world.

The state of the world has support $\mathcal{V}$.

When DM chooses action $y\in \mathcal{Y}$ and the state of the world is $v\in \mathcal{V}$, she receives the payoff $u(y,v)$.

Let $P_V\in \Delta(\mathcal{V})$ be the DM's prior.

The DM may also process some signal (formalised by the concept of information structure) to refine his prior and get a posterior.

Question

Let us define the concept of 1-player Bayesian Correlated Equilibrium provided in Bergemann and Morris (2013,2016,etc.).

$P_{Y,V}\in  \Delta(\mathcal{Y}\times \mathcal{V})$ is a 1 player Bayesian Correlated Equilibrium if

1) $\sum_{y\in \mathcal{Y}}P_{Y,V}(y,v)=P_V(v)$ for each $v\in \mathcal{V}$

2) $\sum_{v\in \mathcal{V}}u(y,v) P_{Y,V}(y,v)\geq \sum_{v\in \mathcal{V}}u(k,v) P_{Y,V}(y,v)$ for each $y$ and $k\neq y$.

Theorem 1 in Bergemann and Morris (2016) claims  that the set of 1-player Bayesian Correlated Equilibrium is equal to set of optimal behaviours under a range of possible information structures (this result holds in fact for any n-player game, thus also for $n=1$ as in this case).

Such information structures can go from the degenerate information structure (i.e., no information whatsoever on that state of the world and, hence, prior is equal to posterior) to the complete information structure (i.e., full revelation of the state of the world).

My question is: can we characterise the collection of 1-player Bayesian Correlated Equilibria for the model above under the assumption that the complete information structure is not available to agents (i.e., agents are not able discover the exact value of the state)? If yes, how? I believe it should amount to inserting a third constraint in the definition above but I can't see which one.

Does Theorem 1 in Bergemann and Morris (2016) still hold in that case?

You can certainly do it. However, keep in mind that the BCE will not be a lot "smaller". This is because there are many information structures that are almost perfectly informative, or that fully reveal some states but not all of them. Therefore, by disallowing the complete information structure you are simply removing one element in the boundary of the set of BCE's. Keep also in mind that this set has, in general, infinitely many elements. Since it is a convex set, any convex combination of two elements in it is also in the set, for example.

Going back to your question, there are many ways to rule out complete information structures. The one that comes to mind stems from the fact that a fully informative signal will correspond to a BCE where for each $y\in Y$, the support of $P_{V|Y}$ is a singleton. Notice that if this is the case, learning what action you should take implies learning the state of the world.

Therefore,  the extra constraint would be that $P_{Y,V}$ must satisfy that there exists a $y^*\in Y$ such that the cardinality of the support of the conditional probability of the states given that action is bigger than 1, i.e. $|P_{V|y^*}|>1$. This is consistent with the idea that at least in some cases the DM remains uncertain about the state of the world after receiving the recommendation to choose action $y^*$.

Notice that a signal that fully reveals all but one state of the world, and instead induces a posterior belief for such a state of $99.999\%$ will not be ruled out by the extra constraint, so including the constraint will have very little effect.


Where to find more detailed data for International Comparison Program 2011? According to the World Bank PPP conversion factors, in 2014, 0.86 SGD could buy as much stuff in Singapore as could 1 USD in the USA (presumably Averagetown, USA).

The market exchange rates in 2014 varied from 1.24-1.32 SGD per USD. This means that according to the World Bank, 0.65-0.69 USD could buy as much stuff in Singapore as could 1 USD in the USA. In other words, price levels were 31-35% lower in Singapore than in Averagetown, USA.

Anyone who has lived in both countries recently will find that impossible to believe, at least based purely on personal anecdotes.

So I was trying to find the data on which these numbers are based. In particular, detailed data like prices of specific goods that were used to form these PPP comparisons.

It seems like they come from the International Comparison Program (ICP) 2011. But the most detailed data I could find about the ICP 2011 was this Excel spreadsheet, which has no such information.

Anyone knows where I can find the detailed data (prices of specific goods, how they were weighted, etc.) on which these World Bank PPP conversion factors are based?

These data are not publicly available. According to Section VI of this PDF, the more detailed the data, the more restricted they are.

For the less restricted data, there is ostensibly some painful application process that researchers can go through in order to get access. But in practice, unless you're a big shot or someone who has connections with the World Bank, they will be reluctant to share the data with you. (That was my personal experience — I went through the whole long application process, there was some back and forth for about a month, and eventually they decided not to share the data with me.)

And for the most heavily restricted data:

  Access to Sub-National Data and Individual Price Observations with supporting metadata is restricted in general. However, users may address applications of access to these data directly to the countries in question.


Bolzano-Weierstrass Theorem and Pareto Efficient Allocation Wikipedia says 'The Bolzano–Weierstrass theorem allows one to prove that if the set of allocations is compact and non-empty, then the system has a Pareto-efficient allocation.'
However, I couldn't find a compelling simple proof for this theorem anywhere. Could someone provide a proof for the theorem in a simple fashion that is understandable for Undergrad students in Economics who have done a course in Analysis?

What one needs are two facts:

Scalarization/Sufficiency for Pareto Optimality
Suppose the economy has finitely many agents $u_i$, $i = 1, \cdots, I$, with feasible allocations given by some $X \subset \mathbb{R}^I$. If
$x = (x_1, \cdots, x_I) \in X$ solves the problem
$$
\max_{x \in X} \sum_{i=1}^I \lambda_i u_i(x_i),
$$
where $\lambda_i > 0$ for all $i$, then $x$ is Pareto optimal. This maximization problem is called the social planner's problem with social weights $\lambda_i$.
(The converse is not true. In other words, not all Pareto allocations arise as such, not even when $u_i$'s are concave.)
Continuous functions map compact sets to compact sets. (The Bolzano–Weierstrass gives a characterization of compactness on $\mathbb{R}^n$---closed and bounded.)

So if the preferences are continuous and feasible set $X$ is compact, existence of Pareto optimal allocation follows immediately. Choose any social weights $\lambda_i > 0$. A solution of the resulting social planner's problem is a Pareto optimal allocation.


Does the minimum of short-run average cost equal the minimum of long-run average cost in the long run for perfect competition? I was recently reading this resource (http://www2.econ.iastate.edu/classes/econ101/hallam/Comp_LongRun_HND.pdf) which states that in the long run for perfect competition, price is equal to both the minimum of the long-run average cost and short-run average cost.

I am unsure of what this is implying. The resource states that because short-run average cost equals price, it shows that there is zero economic profit, while the fact that long-run average cost equals price implies that no identical firms will want to enter or exit. Why is this so? Why does the short run average cost equaling price imply that there is zero economic profit (and not long run average cost equaling price), and why does long run average cost equaling price mean that firms will not have the incentive to enter or exit (and not short run average cost equaling price)?

Furthermore, I am unsure of whether the minimum of the short-run and long-run average cost are equal. I read online that each short-run average cost is tangential to the long run average cost at one point. What is exactly meant by by the short-run average cost curves being "tangential" at one point, does this mean that each short run average cost touches the long run average cost at one point (what exactly is meant by tangential)? And why isn't the minimum point on the short run average cost the point on the long run average cost curve, not the tangential point?

URL

So to understand why the long run average cost curve and short run average cost curve  have the same minimum in perfect competition, as well as some of the other stuff you ask, you have to understand the different assumptions that underlie the models you're working with.

Let's start with what the short run and long run mean here. In this context, the short run is when a firm is stuck with some fixed costs. It may be able to vary labor or raw materials, making those things variable costs, but some other things (e.g. contracted salaries, rental rate of capital) are fixed costs. It may be hard to expand the size of a factory quickly or find a new place to move production.

So here we see 3 different short run average cost curves. Each of these factories of course want to minimize cost per unit produced (average cost), and then set a price equal or above that (otherwise they'd be losing money!), so you have 3 different quantities that the firms will want to produce. You will notice that some of these firms will have to set a higher price than that firm with the production in the middle, so you can imagine which firm is going to get the customers in perfect competition.

Why are the SAC's shaped like this U shape? It is because generally there are economies of scale up to a certain point before things get too big to handle. A school can more efficiently allocate teachers by bumping up classroom size from 1 to 5 for example. But if you try to give the teacher a 1000 child classroom, you would expect things to be absolute chaos.

So now what happens in the long run? In the long run all these things we would normally consider fixed costs are actually variable costs. We can change the amount of capital we rent or other such things.

So given enough time, firms can change how much they want to produce along this line (LAC). We assume everyone moves along the same line because in perfect competition, we assume firms are identical, so that includes the technology and efficiency the firms have to produce the goods. So firms will naturally want to set production to the minimum of the long run average cost curve, so that they can set those low low prices meant to attract customers.

At least...that's what we would expect naturally, right? The last piece of putting it all together is seeing that the marginal cost equals average cost when average cost is minimized. I give a boring mathematical proof here. I assume you need no explanation for why firms set price equal to marginal cost.

  So, price equal to short run average cost means that the firm produces its goods, sells each of them for the price, and breaks even. Thus we say no economic profit. Price equal to long run average cost means that all firms want to expand or contract their production so that they all produce the same amount of goods and basically all look identical. So all firms compete and push price down to the minimum of the long run average cost curve. They neither make nor lose money. So firms are indifferent between operating and not operating. It doesn't really make a difference to them. Thus, firms don't really want to enter or exit.

Edit: To answer the last part, why is the long run cost curve not tangent at the minimum of each short run cost curve, consider the following: For almost all cases, we should expect the minimum of the short run cost to lie above the long run average cost curve. In the short run, you can vary only some inputs, and in the long run you can vary all inputs. So for any given quantity you are trying to produce, it's easier to find a cheaper combination of inputs in the long run than it is in the short run.

This particular question on the tangency has been asked before, with a good top answer here.


Can a commercial bank lend money from transaction/checking account as it would from a deposit account? Transaction/checking accounts are highly liquid - M1

Deposit accounts are less liquid - M2

Per fractional reserve system, banks lend deposited money as credit to clients provided they keep a reserve requirement.

Does this apply to both transaction accounts and deposit accounts? If yes, is the reserve requirement percent the same for both?

Per fractional reserve system, banks lend deposited money as credit to clients provided they keep a reserve requirement.

This is a misleading statement. A bank loan creates a deposit, which can be transferred to other forms of deposits.

  Does this apply to both transaction accounts and deposit accounts?

As the above explained, this is not applicable.

  If yes, is the reserve requirement percent the same for both?

Each country has its own rules. Countries like Canada abolished reserve requirements in the 1990s. The United States was the main countries with reserve requirements, but I believe those were suspended during the 2020 Crisis. Before the suspension, reserves depended upon the type of account, and so were somewhat incoherent (e.g., banks would “sweep” deposits between accounts at the end of the day to reduce reserve requirements).


connection between foreign assets and trade surplus / deficits I am reading Piketty's "Capital in the 21st Century" and in Chapter 5 he writes

"Furthermore, the evolution of a country's net foreign asset position is determined not only by the accumulation of trade surpluses or deficits but also by very large variations in the return on the country's financial assets and liabilities."

I am having difficulty understanding this statement. Specifically I do not see why there is necessarily a relationship between foreign assets and trade surpluses / deficits. It seems that country X needing nothing from the rest of the world can make a lot of coffee and sell it to country Y, running up a large trade surplus. This activity does not seem affect in any way the balance sheet of foreign assets. Nation Y buying the coffee does not own anything in country X, since the coffee sits in country Y upon completion of the purchase. Some goes for country X, since the currency it receives from Y would sit in country X.
Does possession of country Y's currency by country X constitute a foreign asset owned by country X?

Piketty  is correct, this is well known mechanism thats discussed in any international economics 101 textbook.
I think the best way how to see how this work is to forget about money for a second. Ultimately all economic transactions  are not about money but about exchanges of real goods and services. Money are just facilitators of transactions, they solve the double coincidence of wants. For the purposes of this discussion you can think of money as just technology that makes transactions easier and go faster like internet which allows you to send letters faster and easier compared to post office, but what really matters is the content of a message.
So lets forget about the money for now and consider a barter economy where you have your country X that does not want anything from country Y but country Y wants coffee from country X. In such situation country X would either:

export the coffee for nothing in return essentially making the coffee foreign aid - a noble act for sure but alas most people/countries will not just generously give away their  products or services for nothing.
the country X exports the coffee in exchange for country Y promising to pay them some goods and services back at some time in the future (i.e. for debt). Now debt is an asset for country X (for the creditor) and liability for country Y (borrower) so their net foreign assets position changes.

If you introduce money the same thing occurs except the debt is denominated in money terms rather than in some goods and services. In addition if we introduce not just money but also assume both country X and Y have their own separate currencies, dollars and pounds lets say then also some important exchange rate effects come in the play.
For example, if country X is the exporter country Y must always go through forex market to exchange their pounds for dollars to pay for X exports as people in X want dollars (since they dont want anything from Y and you can’t buy things in X with pounds). This will increase the demand for dollars at the same time as increasing supply of pounds. Hence the value of dollar rises (ceteris paribus) and value of pound decreases (ceteris paribus). This change of relative value of currency makes all foreign denominated assets and liabilities worth more so if the country is a net debtor currency depreciation increases its foreign currency debt burden making the net asset position even worse.
In addition this goes little bit beyond the scope of the question but eventually running trade account deficit leads to higher interest rates relative to those that run surpluses which encourages people to actually invest (i.e. purchase assets) in the country running trade deficit to the point where the flow of foreign investment is high enough to force exchange rate to equate the real returns in home and foreign country. An important caveat is that there are also other factors at play for example Batra & Belad (2013) show that thanks to USD being reserve currency US managed to keep low interest rates even though running huge trade deficit. This being said this is how, in general, the mechanism works in the long run and then some special circumstances can create exceptions.


Consider the utility function U(x,y) = y√x Draw the indifference curve for U= 10, U=15, U=20.

My knowledge of algebra has deteriorated over the last few years of being out of school and I am really unsure of how to answer this.

The X value is going up in the standard 1 to 10.

Hint: This suggests $y=\dfrac{U}{\sqrt{x}}$

so draw the three curves in the usual way

$y=\dfrac{10}{\sqrt{x}}$; three of the points are $(1,10)$ and $(4,5)$ and $(9,3.333)$
$y=\dfrac{15}{\sqrt{x}}$; three of the points are $(1,15)$ and $(4,7.5)$ and $(9,5)$
$y=\dfrac{20}{\sqrt{x}}$; three of the points are $(1,20)$ and $(4,10)$ and $(9,6.667)$


Income Offer Curve In Basic Microeconomics Can anybody explain to me the income offer curve? Is it a relationship between $x_1$ and $m$? If the budget equation is $p_1x_1+p_2x_2=m$? With income being the variable $m$?

It is the change in the demand of $x_1$ and $x_2$ for different levels of income $m$ (when we shift the budget curve out). Intuitively, how will your consumption of the two goods change when income changes. If we let $x_1$ be bus tickets and $x_2$ taxi rides, then if your income increases, we might expect that you will takes the bus less and the taxi more often.


Will Chinese yuan be a key international currency someday? IMF adopted Chinese yuan as international currency the other day. Will Chinese yuan be a key international currency someday?

"SDR inclusion does not mean... that the renminbi will rival the dollar as an international currency, at least not any time soon. The dollar is widely used globally in trade, in international borrowing and lending, and as the principal currency for official reserve holdings (about sixty percent of global reserves are held in dollars). Importantly, the dollar’s global status is a market outcome, not the result of a decision by any international body or of an international agreement. Private investors and governments freely choose to hold dollars because the markets for dollar-denominated assets are, by far, the deepest and most liquid of any currency; because the United States imposes no restrictions on capital flows in or out of the country; because of the quality of U.S. financial regulation; because the Federal Reserve has kept inflation low and stable for the past thirty years; and because the United States is large, prosperous, and politically stable."

This is the quote from Ben Bernanke's blog. Ben Bernanke is the former chairman of the Federal Reserve.


Growth Rate of Solow Model Conside the following Cobb-Douglas Production Function:
$$Y_t=\bar AK_t^{1/3}\bar L^{2/3}$$

The growth rate of per capita GDP for this equation in continuous time is $\frac{y'_t}{y_t}= \frac{1}{3K_t}$ where $y_t=\frac{Y_t}{\bar L}$

Using the Law of Motion of Capital:

$$\Delta K_{t+1}=\bar sY_t-dK_t \implies \frac{\Delta K_{t+1}}{K_t}=\bar s \frac{Y_t}{K_t}-d$$

where $\bar s$ represents the savings rate.

And Capital-Output Ratio in Steady State:
$$\frac{K^*}{Y^*}=\frac{\bar s}{\bar d}$$

where $\bar d$ represents the depreciation rate

Prove that the growth rate of per capita GDP is equal to
$$\frac{1}{3} \bar s \frac{Y^*}{K^*} (\frac{(K^*)^{2/3}}{K_t^{2/3}} -1)$$

I have no idea how am I supposed to get the equation from $\frac{y'_t}{y_t}= \frac{1}{3K_t}$, because it seems like this is not derived by substitution.

After some work, I realised that the following equation looks somewhat like:

$$\frac{1}{3} \bar s \frac{Y^*}{K^*} (\frac{(K^*)^{2/3}}{K_t^{2/3}} -1) =\frac{1}{3} \bar d \frac{\Delta K_{t+1}}{K_t}$$

Appreciate it if anyone can provide me with some advice on how I should go on further! Many thanks!

I do not directly see what intuition you are supposed to get from this growth rate equation, and the resulting math exercise but here is a sketch of the proof.

First determine the steady state capital by setting $\Delta K_{t+1}=0$ and solving for $K^*$.

Substitute this value for the $(K^*)^{(2/3)}$ in the fraction. Replace the $ \frac{Y^*}{K^*}$ in the same expression with the value that you get capital-output steady state ratio, and work the $d$ into the parentheses.

The expression you have now can be shown to be the same as the growth rate of $y_t$ that can be found from the production function.


Isn't buying currency with high interest rates a double whammy? I will give an example of what I mean and please tell me what I'm missing because this can't be correct. For the sake of simplicity I will only use USD and EUR.
So let's say that the central bank in the US raises interest rates. You buy USD with EUR and leave it there for let's say 1 year. You get your nice interest, and decide you want to buy a house in Europe, so you need euros.

Now what happened with the price in that time? Let's suppose the initial ratio was eur/usd=1. Because of the high interest rates on usd, it's value appreciated and eventually the ratio became say eur/usd=0.5. At that point you decide to sell your dollars for euros. Now, not only did you earn money because of the interest you got on USD, but now the exchange ratio also went your way, so isn't this a double whammy?

To use some numbers:
you have 100 euros, you buy 100 usd.
Interest is 100%, now you have 200usd. You earned money.
You decide to buy euros again. Since eur/usd=0.5, with 200usd you buy 400 euros. You earn money again!

I know this is oversimplified but I would like to know the key point that I'm missing. Is it the uncertainty?

Yes, it’s the uncertainty. If you tried hedging the currency, the hedge would be generally such that there would be a loss that offsets the interest advantage. (This is known as covered interest rate parity. In oractice, there is a spread that causes behaviour to deviate from that -the currency basis. So you can lock in a small spread, but it is typically on the order of 10 basis points or less. During a financial crisis, the basis can get relatively large.)

If you do not hedge, the volatility in the currency rates over one year is normally greater than the interest rate differential. Buying a high interest rate currency is known as a carry trade. It is profitable until it isn’t. For an example, look at the Japanese yen in the early to mid-2000s. In that period, Japanese interest rates were the lowest in the developed world. It was thus a popular currency to short. It would then have periodic bursts where its value would shoot up, forcing shorts to cover.


Why are asset pricing models equilibrium models? I have several times heard scholars refer to asset pricing models (such as the CAPM) as a type of equilibrium model. Why exactly is this the case? Does this simply mean that equilibrium is a necessary condition we need to accept for the model relationship to hold? Can this be shown formally?

An equilibrium asset pricing model is one in which the asset prices jointly satisfy the requirement that the quantities of each asset supplied and the quantities demanded must be equal at that price. It is as opposed to a partial equilibrium model where the price of the asset (or at least some assets) are determined outside of the model.


Why would microeconomics be considered more "objective" than macroeconomics? I can imagine the following reasons for this:

conflation of positive vs normative economics in macro
micro phenomenon is less complex (or smaller): thus easier to create reliable models for

Thanks

I used to think that microeconomics was relatively more scientific than macroeconomics. Early macroeconomics, in particular, suffered from choosing models of agent behavior that made modeling easier but bore little relationship (or at least a highly disputed relationship) with reasonable behavior of individual agents. This led to the microfoundations effort, which attempted build macroeconomic models from the ground up by modeling the behaviors of the economic agents in line with microeconomic theory (rational expectations, utility functions, life cycle effects, market power, and so on). Aligning macroeconomics with microeconomics strongly implies that microeconomics "has it right" and macroeconomics does not.
However, that's not the end of the story.  In a nice essay called The Macroeconomic Foundations of Microeconomics, macroeconomist Mark Thoma says that microeconomics has a lot of hidden macroeconomics lurking in the background, and it is important to recognize this and formalize the role of macroeconomics in microeconomic theory. For example:

One of the lessons from macroeconomics is that prices do not always
move fast enough to keep markets in balance, and this observation --
this macroeconomic foundation -- needs to guide microeconomic
theorists. The Walrasian auctioneer is a convenient theoretical
assumption, somehow prices always magically move immediately to clear
all markets and attain the highest possible societal welfare (and it's
useful for comparing long-run outcomes). But that assumption is not
very useful as a foundation for macroeconomic models that try to
explain short-run swings in the macroeconomy. Microeconomic and
macroeconomic models ought to be consistent with each other, but the
microeconomic foundations need to have realistic assumptions about the
ability of price changes to clear markets.

More generally, microeconomics usually assumes that microeconomic agents are embedded in a functioning macroeconomy. An economy with functioning markets for other goods, property rights, production functions and industrial organization that makes supply curves, demand curves that are well defined, and the like. This joint dependence on the assumptions of the other family makes the two major schools of economic thought closer to peers than the microfoundation revolution suggests.
That said, microeconomics has done a lot more to bring experimentation (field and laboratory) into their research. This has helped inform their modeling and econometric work in a positive way, including this year (2019's) Nobel winners. For ethical and financial reasons it is much harder to do this in macroeconomics. This could be a reason to think that, in general, microeconomics might be a bit more objective. However, the majority of microeconomic research is non-experimental, so we shouldn't go too far with this argument.
I also recommend Raj Chetty's essay Yes, Economics Is a Science for a comparison of the scientific bona fides of the field of economics with other scientific endeavors, particularly medicine.

It is true that the answers to many “big picture” macroeconomic
questions — like the causes of recessions or the determinants of
growth — remain elusive. But in this respect, the challenges faced by
economists are no different from those encountered in medicine and
public health. Health researchers have worked for more than a century
to understand the “big picture” questions of how diet and lifestyle
affect health and aging, yet they still do not have a full scientific
understanding of these connections. Some studies tell us to consume
more coffee, wine and chocolate; others recommend the opposite. But
few people would argue that medicine should not be approached as a
science or that doctors should not make decisions based on the best
available evidence.
... Nonetheless, economists have recently begun to
overcome these challenges by developing tools that approximate
scientific experiments to obtain compelling answers to specific policy
questions. In previous decades the most prominent economists were
typically theorists like Paul Krugman and Janet L. Yellen, whose
models continue to guide economic thinking. Today, the most prominent
economists are often empiricists like David Card of the University of
California, Berkeley, and Esther Duflo of the Massachusetts Institute
of Technology, who focus on testing old theories and formulating new
ones that fit the evidence.
This kind of empirical work in economics might be compared to the
“micro” advances in medicine (like research on therapies for heart
disease) that have contributed enormously to increasing longevity and
quality of life, even as the “macro” questions of the determinants of
health remain contested.


Any study on performance gap between optimal mechanism and linear mechanism? In mechanism design, the optimal mechanism is usually not linear in the agent's type. However, linear mechanisms are easy for implementation. Are there any studies on the performance comparison between optimal and linear mechanisms. I guess a theoretical comparison is probably hard, as the payoff in the linear mechanism does not have closed-form, but a numerical analysis is not very difficult. Thanks.

Robustness and linear contracts by Carroll says that linear is optimal (in his class of environments). Tim Roughgarden from Stanford also studies `the price of anarchy' related to using simple but suboptimal mechanisms.


How are fund managers usually compensated against benchmark? I have heard that fund managers who invest clients' wealth are usually compensated according to how well they perform against a benchmark.

What exactly is the (most typical) payoff function for fund managers as compensated against benchmark? E.g. the 20, 2 rule for hedge funds, what is the exact number over which they get 20 percent? Is it the amount that they earned more compared to what they would have earned if they just inveated in a benchmark index?

The format varies. Many firms just charge a straight fee as a percentage of assets, and/or as a percentage of in/outflows e.g., mutual funds.

For fund managers that are not hedge funds, returns are compared to index returns if there are any incentive bonuses. Individual fund manager’s bonuses are often based on this relative performance, even if the client is not charged. Better returns presumably brings in more clients for the fund, and so the fund firm is more profitable, even if it does not charge performance fees.

The hedge fund 2/20 model was 2% of net asset value, plus 20% of returns in excess of some target (discussed next). There would be other mechanisms, such as a “high water mark” rule, which would means that the variable compensation would not be paid until any losses are recovered. The 2% fixed fee always needed to be charged to keep the expensive hedge fund operation going. Since hedge funds typically used leverage, the 2% would have been smaller as a percentage of assets.

The exact terms would be negotiated, the stories that I have seen is that typical terms are now less generous than the 2/20 numbers, but that varies from fund to fund. Very popular hedge funds might charge more.

Hedge funds were supposed to diversify from equity market risk, so the return target was often either fixed (e.g., 8%), or a money market rate plus a spread (e.g. Treasury bill returns plus 5%). That would change based on the structure of the fund.

As an example, if the target rate of return is 8%, and the fund returned 13% (5% more), the fund would get 20% of the 5%, which is 1%.


What is the justification for it being a problem if loans are not paid back? As far as I could understand, the loan system applied by banks which is based on a fractional reserve system works as follows:

Assumptions:

The bank has initially 1000$.
The fractional reserve is currently 10%.
For simplicity, we assume that all deposits are made only on this bank, instead of having multiple banks. It has been argued in many places that, for the overall view of the money system, that this is a justfied assumption.

The following happens now:

1) Guy A makes a loan for 900\$. The bank keeps 100\$ (more than 10%, thus ok).

Total loans owned by bank: 900$
Total deposits owned by bank: 100$

2) Guy A pays guy A', which deposits the money on the bank again.

Total loans owned by bank: 900$
Total deposits owned by bank: 1000$

3) Guy B makes a loan for 800\$. The bank keeps 100$ as a new reserve (more than 10%, thus ok).

Total loans owned by bank: 1700$
Total deposits owned by bank: 200$

4) Guy B pays guy B', which deposits the money on the bank again.

Total loans owned by bank: 1700$
Total deposits owned by bank: 1000$

This repeats itself a couple of times, until we arrive at:

Total loans owned by bank: 5000$
Total deposits owned by bank: 1000$

From the deposits, 500\$ are reserves of the bank, which belong to the bank, and 500\$ are money which is owned by the last guy that got money from another guy.

Ok, so this is, as far as I understood, the beginning of the "loan process with a fractional reserve system", with a couple of loans. The bank has still enough reserves, so it did everything ok.

Now let's assume that Guy A comes to the bank and says "Hi, I'm sorry, I can't give you the money back, I'm broke".

Currently, the following thing happens: The bank says "ok, so you must give us your security to cover our loss" (for example the car).

Question: Why does this happen, what is the justification for taking the car from Guy A? Since the bank never lost anything...?

It appears that the OP confuses  money with property rights

A) It writes "deposits owned by the bank" which is simply wrong, since deposits are liquid assets belonging to the persons that deposited them. The bank leases the funds from them and then sublets them to the debtors.
B) Looking also at an OP's  comment to another answer, indeed the bank may create the money, but it creates the money as a medium of exchange and representative of value -it does not keep the property rights on the money itself it creates.
 C) Finally we should not forget that the bank is a distinct legal entity from its own shareholders.

Stopping at the four explicit amounts the OP gave (after person $B$ pays person $B'$ and person $B'$ deposits the money in the bank), the bank's balance sheet is as follows:

\begin{array} {| r | r | r |}
  \hline
\hline
  \text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\
  \hline
\text{Loans} & 1,700 & \text{Shareholders Capital} & 1,000\\
\text{Cash} & 1,000 & \text {Deposits} & 1,700\\
\hline
\text {TOTAL ASSETS} & 2,700 & \text{TOTAL LIABILITIES} & 2,700\\
  \hline
\end{array}

A Balance Sheet is just an inventory at a specific point in time, of Cash and Rights to Collect in the future ("Assets") and Obligations to Pay (also in the future) ("Liabilities").

It is important to understand the "Liabilities" (obligations to pay) side.
The initial USD $1,000$ with which the bank started, represent an "obligation to pay" for the bank towards its own shareholders. Second the bank is obliged to pay at any time USD $1,700$ total to persons $A'$ and $B'$ that deposited their wealth to the bank. The fact that the depositing transaction could happen because the bank in a previous instance has created the money, does not give the bank a property right on that money, just because it was its "creator".

That the bank has at the moment $1,000$ in Cash as when it started doing business, relates to the bank's "liquidity" situation. This is not unimportant, and in fact it is an index of financial health on its own right. But it has to do only with the short term horizon. For the long-term horizon though, it is property rights that matter. And so it is not the only financial criterion for the economic health of a bank.

So assume that person $A$ comes in and say "I cannot pay my loan of USD $900$". Certainly, in the short-term, this won't affect the liquidity of the bank -it will still have the USD $1,000$ that it now has. But if the bank writes-off the debt, it will do so against the Shareholders capital invested. So after the write-off the balance sheet will be

\begin{array} {| r | r | r |}
  \hline
\hline
  \text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\
  \hline
\text{Loans} & 800 & \text{Shareholders Capital} & 100\\
\text{Cash} & 1,000 & \text {Deposits} & 1,700\\
\hline
\text {TOTAL ASSETS} & 1,800 & \text{TOTAL LIABILITIES} & 1,800\\
  \hline
\end{array}

Assume things with debtor $B$ go smoothly, the bank will eventually (in the long-term) collect his loan, and it will be able to give to persons $A'$ and $B'$ their deposits back... so where is the problem? Well, the problem is that it will give to its shareholders only USD $100$ back instead of the initial USD $1,000$ investment.

And who might care?

First, we live in societies built upon the principle of private property rights. The shareholders have a right to defend their property rights, and the bank acting as their representative attempts to defend them by not simply writing-off the debt (but demanding another asset -the car- in its place), even if such a write-off may affect the property rights only of the shareholders, and not of the people that keep their wealth to the bank as deposits.

But again, does this creates a problem to the economy now? In terms of actual existing liquidity the answer is no. But the Present is affected by what we project for the Future. After the write-off, the future of the shareholders and of the bank looks worse, because their current wealth is less. And this will affect negatively what the bank and the shareholders will and can do in terms of their involvement in the economic activity now.
So to the question "who cares?" the second answer is "the whole economy".


How does the Fama and French 3-factor model explain stock covariance? Does it at all? If so, how?

It is understood that size and value play a role in determining returns and there are proposed explanation those these, but what about covariance?

It is not clear to what covariance this question refers to.

As in the CAPM model the covariance among assets is reduced to $\beta$, through the covariance with the market index.

$\beta_i=\sigma_{i,M}/\sigma_M^2$

Then, if CAPM is correct, we could explain the covariance relating the $\beta$s

$\sigma_{i,j}=\beta_i*\beta_j*\sigma_M^2$

In the context of multifactor models something similar occurs, since, in order to use those models, it is necessary to estimate $\beta$s, or sensitivities, related to each proposed factors.


ARCH Model - Expectation of Absolute Value I have a time series model:

$$y_t = \sigma_t \epsilon_t$$

$$\sigma_t = w + \gamma|y_{t-1}|$$

Where $\epsilon_t$ are i.i.d normally distributed with mean zero and variance one. Suppose t = $0, ±1, ±2, ±3, \ldots$ and that the process $y_t$ is weakly and strongly stationary.

a) What restrictions on the parameters w and $\gamma$ seem sensible?

b) Calculate $E|y_t|$ assuming that this quantity is finite, noting that $E|\epsilon_{t-1}| = \sqrt{\frac{2}{\pi}}$

(c) Write $|y_t|$ as an AR(1) process and hence calculate the autocorrelation function of absolute returns:
$$p_j = \frac{cov(|y_t|, |y_{t-j}|)}{cov(|y_t|, |y_{0}|)}$$

So for (a) I feel like: $\gamma \in [0, 1)$ should be reasonable as we expect periods of high-volatility to cluster. Do we need to assume w > 0 for a positive standard deviation? I think these make a difference on the answer for b:

$$ E|y_t| = E[|\sigma_t \epsilon_t|] = E[|\sigma_t| |\epsilon_t|]$$
$$ \text{as they are independent:} $$
$$ = E[|\sigma_t|] E[|\epsilon_t|] = E[|w + \gamma|y_{t-1}||]\sqrt{\frac{2}{\pi}}$$
$$ \text{as we assumed w and $\gamma$ are positive:}$$
$$ = E[w + \gamma|y_{t-1}|]\sqrt{\frac{2}{\pi}} = \{w + \gamma E[|y_{t-1}|]\}\sqrt{\frac{2}{\pi}} $$
$$ \text{as we have a weakly stationary series:}$$
$$ E|y_t| = \{w + \gamma E[|y_{t}|]\}\sqrt{\frac{2}{\pi}} \implies E|y_t| = \frac{w\sqrt{\frac{2}{\pi}}}{1 - \gamma \sqrt{\frac{2}{\pi}}} $$

Is this right or have I done some hocus pocus?

For (c) I'm stuck:

I get $|y_t| = \{w + \gamma |y_{t-1}|\}|\epsilon_t|$ but can't make anything useful out of the covariance.

Any help is much appreciated. I'm not too familiar with ARCH/GARCH models.

I don't believe $w>0$ is necessary or sufficient to get a positive standard deviation everywhere. I think you need $\sigma_0 \geq 0$ and $w\geq 0$ with one of the two inequalities strict.

If $\gamma  > 1$ then the series $\sigma$ will grow explosively if $w + \gamma \cdot \sigma_{t-1}  >0$ or behave explosively harmonic if $w + \gamma \cdot \sigma_{t-1} <0 $. Neither of those seems particularly desirable most for economic situations.


A question related to purification theorem I am stuck at some point in part b, I would be very happy if you could help. My calculations are below the question.

a)
P1 plays N with probability p. P2 plays N with probability q.
Mixed Nash: $((\frac{1}{2},N),((\frac{1}{2},N))$
b)
P1 plays N if $(1+x\epsilon_1)q+x\epsilon_1(1-q)>q0+(1-q)1$
$\epsilon_1>\frac{1-2q}{x}$
P2 plays N if $(x\epsilon_2-1)p+x\epsilon_2(1-p)>p0+(1-p)(-1)$
$\epsilon_2>\frac{2p-1}{x}$
The distribution is not necessarily uniform. pdf's are not specified explicitly, so I need to find a general solution.
$p=Pr(\epsilon_1>\frac{1-2q}{x})=1-Pr(\epsilon_1<\frac{1-2q}{x})=1-F_{\epsilon_1} (\epsilon_1<\frac{1-2q}{x})$
$q=Pr(\epsilon_2>\frac{2p-1}{x})=1-Pr(\epsilon_2<\frac{2p-1}{x})=1-F_{\epsilon_2} (\epsilon_2<\frac{2p-1}{x})$
I am stuck at this point.

I have never done such purification exercises, but I would approach it like that. As you state,
$p=Pr(\epsilon_1>\frac{1-2q}{x})=1-Pr(\epsilon_1<\frac{1-2q}{x})=1-F (\frac{1-2q}{x}),$
$q=Pr(\epsilon_2>\frac{2p-1}{x})=1-Pr(\epsilon_2<\frac{2p-1}{x})=1-G (\frac{2p-1}{x}),$
where $F$ and $G$ are the cdfs corresponding to densities $f=F'$ and $g=G'$. Because they are cdfs, they are weakly increasing. For simplicity, suppose they are strictly increasing so that their inverses clearly exist (i.e., I assume full support. If there were holes, you could still define appropriately some inverse for the flat parts).
Then, combine those two equations to
$1+x F^{-1}(1-p) - 2 G (\frac{2p-1}{x})=0$ (and another similar formulation for q). The LHS of this formula decreasing in $p$. Note that for $p=0$, we have $1+xF^{-1}(1)-2G(\frac{-1}{x})=1+x-0>0$ on the LHS such that the equation never holds, $p$ must be larger than zero. For $p=1$, have on the LHS $1+xF^{-1}(0)-2G(1/x)=1-2G(1/x)$ which can be more or less than 0. That is, for some $x$ there is a pure strategy equilibrium with $p=1$ and for others there is a mixed strategy equilibrium with $p<1$.
Now consider the same equation that solves for the mixed strategy and plug in $p=\frac{1-x}{2}$ such that the LHS above is $1+xF^{-1}(\frac{1+x}{2})- 2 G(-1)=1+x F^{-1}(\frac{1+x}{2})- 0>0$ for small $x$, meaning we have to increase $p$ to fit the equilibrium equation LHS=0.
Next consider the same equation that solves for the mixed strategy and plug in $p=\frac{1+x}{2}$ such that the LHS above is $1+xF^{-1}(\frac{1-x}{2})- 2 G(1)=x F^{-1}(\frac{1+x}{2})-1<0$ for small $x$, meaning we have to decrease $p$ to fit the equilibrium equation LHS=0.
Thus, for small $x$, the equilibrium $p$ is such that $p\in [\frac{1-x}{2},\frac{1+x}{2}]$, leaving only candidate $p\to \frac{1}{2}$ as $x\to0$.


Why is the tat-for-tat strategy a Nash equilibrium in infinitely repeated games? Why is the tat-for-tat strategy a Nash equilibrium in infinitely repeated games, but not a Nash equilibrium in a finite scenario? Specifically for this matrix:

Assume higher payoffs reflect higher utility. It's a prisoner's dilemma situation.

Since tit-for-tat assumes we start at (Honor, Honor), and play the strategy that the other player last played in future rounds, I don't really see why it's a Nash equilibrium in an infinite scenario and not a finite scenario.

In a finite scenario (e.g. one round), wouldn't the players end up at the NE (Cheat, Cheat) because they follow their self-interest? And in an infinite scenario, wouldn't they end up at (Honor, Honor) (not a NE) assuming the discount factor is high enough?

Any clarity appreciated!

(i) In the 1 round case, tit-for-tat is not a NE. To see this notice that the tit-for-tat strategy, as you describe, dictates that the players play $(H,H)$ in the first (and only) round---as you point out, this is clearly not a NE, since either player can increase her payoff by changing her strategy from $H$ to $C$. Perhaps what you missed is that the strategy includes proscription in first round, which does not cohere from the 1-shot Nash behavior.

(ii) In the $N$-round case, again tit-for-tat is not a NE. This is a little more subtle that point (i) but not much. If both players play according to the strategy, then they will make it to the $N-1$ round playing $H$. At this point, the strategy dictates they play $H$ in the $N^{th}$, and final, round. For the same reason as in (i) this is not a best response, hence not an equilibrium (note that forward looking agents would anticipate this, so the strategy would break down immediately, but analyzing the last round is sufficient to see it is not an equilibrium).

(iii) In the infinitely-repeated case, tit-for-tat can persist, but it depends on how agents discount future utility in comparison with current utility. The general logic is that since there is no final period where things begin to unravel, players are always willing to forgo current utility to maintain good standing (the tit part of the tit-for-tat?) and therefore a higher future (continuation) payoff. Of course, if the players care about today's payoff far more than tomorrow's, they will defect and play $C$. See here for more about NE in infinitely-repeated games.


The Myth of Exploitation According to the Labor Theory of Value According to the Labor Theory of Value, a good is worth as much as the labor put into it. We might then go further and assume that the labor put into it was as valuable as the goods used to fuel that labor (and so on and so on).
How then can a theory of exploitation be maintained? Since laborers by definition receive the worth of their labor as subsistence wages?

The whole point of the (specific) Labor Theory of Value that you apparently refer to, is that, what Labor "injects" as value into goods produced, is more than what Labor needs to consume in order to survive. This is a fundamental assumption/argument, in order to answer the question "how profits come about?".

Then, since the theory argues that profits spring solely from Labor, it follows that they should not be appropriated by the holders of capital (the holders of capital should only get the value of capital etc that goes into the goods produced, a value that does not "inject more" than what it already is). Simply put, after paying third parties for purchases etc out of Sales, and calculating depreciation (which is what the holders of capital should receive), the rest, that would appear as profits, should be distributed to the workers (because it is the workers that created this surplus, not the capital) and not retained by the capital holders. But because they are not thus distributed, the theory of exploitation emerges.

Even more simply, I need to eat one Kgr of bread to produce two Kgr of bread, in which production other goods, equipment etc have participated, whose value amounts to only half-Kgr of bread. I take as wage the one Kgr of bread, and all other factors of production take their half-Kgr of bread. Another half-Kgr of bread remains. It is taken by the owner of the bread business as "profits". It should be given to me, because it materialized solely because of the participation of my labor in the production process -or so the theory argues.

Therefore the phrase in the question

  "We might then go further and assume that the labor put into it was as
  valuable as the goods used to fuel that labor (and so on and so on)"

negates the fundamental premise of this theory, and leads to some other theory, one apparently incorporating a general principle of "preservation of value" (which by the way, is what the Accounting discipline is based on).


Bliss point utility doubt Why is the bliss point utility function convex even though it has concave portions to it ?

According to Nicholson and Snyder (authors of Microeconomic theory - Basic principles and extensions) a function has diminishing MRS and is convex only if it is quasi-concave. Accordingly, I checked quasi concavity for the bliss point utility function $U (x, y) = 12x + 16y –x^2 – y^2$, and it showed that the function is quasi concave throughout. This means that the function should be convex throughout, but that is not the case here.

Quasi-concave utility functions represent convex preferences. But that preferences are convex means that the weakly-better sets are convex, it is not about the convexity of any function.


Can we model risk with only probability? Sorry for the confusion! I am adding an example to see if it helps:
For example, consider a gamble A, with payoffs {a,b,c,d}, whose probability of each payoff being realized is equal (so 25% each); and another gamble B, with payoffs {a,b,c,d,e}, and the probability of each is 20%.
Now I would like to measure the risk difference between the two gambles A and B, but all {a,b,c,d,e} are unknown in the data; only the 25% and 20% probabilities, and the fact that payoffs of B include payoffs of A are known. So it would not be possible to estimate expectation or variance, and using only probability seems a lot more feasible. What will be the potential problems with using only the probabilities as the risk measurements? Is there any way to bypass using expectation or variance for this situation (the ultimate goal here is to measure marginal risk aversion)? Thanks a lot!

I don't think it even makes sense to talk about risk without specifying the payoffs.
Take your two examplary gambles and suppose that $a=b=c=d=e=0$. In that case, there is no risk involved at all. It is like flipping a coin and if it lands Heads, nothing happens, and if it lands Tails, nothing happens. This would not even be considered a gamble.
Alternatively, let $a=b=c=d=0$ and let $e>0$. Then gamble $B$ gives you the possibility of free money. Similarly, let $a=b=c=d=0$ and let $e<0$. Then gamble $B$ simply is a possibility to burn money with some probability. However, these two gambles $B$ are very different.
Alternatively, suppose that all $a,b,c,d,e$ are events. The first four are associated with some payoff and in event $e$ simply gamble $A$ is played. Then gamble $A$ is in fact gamble $B$. Without a specification of the events, you cannot compare the two.


How interest rates affect investment We know that a rise in real interest rates will cool down the economy in terms of investments. An increase in interest rate will provide higher incentive for saving rather than consumption. So people will start to save in banks and banks would be having a high stock of these savings. Now, effectively this stock should compel banks to lend more to the people needing it and hence it should drive down interest rates and raise investment levels. How is this fallacy arising ? Please explain

The price and quantity of a scarce resource are determined by supply and demand.  The quantity which would be offered at some imagined price increases with that price.  The quantity which would be purchased at some given price decreases with price.  The actual quantity and price of every transaction will then naturally be the level where the quantity offered equals the quantity demanded.

In the case of savings and investment, the price is the interest rate and the quantity is the amount lent and borrowed.

So there is no fallacy.  The interest rate is the one agreed to when a lender (saver) and a borrower make a deal.  The interest rate isn't the cause, it is the result of the agreement.  The interest rate bid and offered at a given moment are two different numbers.  There is no fallacy because there is no transaction.  At the moment of transaction, there is a single number: the "interest rate" itself. So again, no fallacy.


Hotelling’s Continuous Model - game theory Hotelling’s Continuous Model: Consider Hotelling’s model, in which citizens are a continuum of voters on the interval $A = [−a, a]$, with uniform
distribution $U (a)$.

Show that for a general distribution $F (\cdot )$ over $[−a, a]$ the unique Nash
equilibrium is where each candidate chooses the policy associated with
the median voter.

I know that the median is $a^m=0$ but I don't understand what does a general distribution mean and what does "associated with median voter" means exactly. If somebody could clarify what this exercise asks me to do that would be great!

Pick an arbitrary cdf $F$ that is supported on $[-a,a]$. The median, $m$, must satisfy $$\int_{-a}^{m}dF \geq \frac{1}{2}, \quad \text{and} \quad \int_{m}^{a}dF \geq \frac{1}{2}$$

Note that $m$ is not generally $0$.

The phrase you mention, "the unique NE is where both candidates chooses the policy associated with the median voter," simply means that the unique NE is where both candidates choose a policy located on $m$.

This is easy to show, think of "unraveling toward the center."


Derivation long run cost function of three inputs with Leontief-like characteristics Suppose that a firm produces a good using capital, skilled labor, and unskilled labor.  Let $K$ denote the amount of capital,$L_1$ unskilled labor, $L_2$ skilled labor. The production function is $f(L_1, L_2, K) = K^2 min\{L_1, L_2^{\frac{1}{3}}\}$. Furthermore, let capital rental rate, $r=200$, unskilled wage rate is $w_1=5$, and skilled wage rate is $w_2=6$.

Find long run cost function.

I am unsure as to how to approach this problem given the K^2 term in the function.  Thus, I tried when $K=1$.  However, I would like to know how to approach it for all $K$, where $K$ is a natural number.

My Attempt

Assume $K=1$.  Then we have $$f(L_1, L_2, 1) = min\{L_1, L_2^{\frac{1}{3}}\}$$

From here we can see that in order to minimize cost at a particular level $q$, we have $L_1=L_2^{\frac{1}{3}}=q$ which leads to $$L_1=q$$ $$L_2=q^3$$.  Thus, $$c(q)=200+5q+6q^3$$

Your reasoning that $L_1=L_2^{1/3}$ is valid for any $K$. Indeed if this equality does not hold you can lower the cost by reducing the excess input of either skilled or unskilled labor. Thus you can rewrite the cost minimization problem in two dimensions instead of three

\begin{equation}
\min_{K,L_1}{200 K + 5 L_1 + 6 L_1^3}
\end{equation}
subject to
\begin{equation}
K^2 L_1 = q
\end{equation}

From the constraint you can replace $L_1$ by $q/K^2$ in the objective function, which becomes a minimization problem with one variable $K$ and a parameter $q$. Solving it will give you the cost function as the value function of the problem.


Johansen cointegration and VECM? I am confused about how to proceed about testing for cointegration. I am interested in testing for cointegration between 3 stock indices.

I was instructed to use returns and not prices. So my question is how do I proceed about identifying a cointegrating relationship since the definition is finding a combination of I(1) variables that is I(0). Since returns are I(0) because they are the first differences, can I still use the Johansen test?

Cointegration testing usually goes in this way:

Have very clear which is the "long-run" relationship among variables your theory predicts. The point about cointegration is that there is at least one common trend among the variables. In your case, you would expect that the price of the three stocks move in tandem, based on some underlying market phenomena like economic growth, volatility, etc. In this case, the long run relationship between variables  in likely to be in levels (price of stocks).
Test for unit root on each variable in levels. There are plenty of tests here (ADF, KPSS, etc). You want to find that these variables are I(1) or maybe I(2).
Perform the Johansen cointegration test. If you reject the null hypothesis of cointegration ($r=0$), then there is not a common trend among the variables, and they are not cointegrated. Do not run regressions with them in levels, as any result will be spurious. If you do happen to find cointegration ($0<r\leq n$), then estimate the VECM, from where you can get the cointegration vector(s) that define the common trend(s).


Maximize utility given an arbitrary number of goods and the condition that exactly X number of items must be bought How does one maximize the utility given some budget restriction, an arbitrary number of different goods (with varying utility and prices) and the added condition that exactly X number of items must be bought?

I guess this must be done algorithmically, but I have no idea how.

Utility maximization problem is
\begin{eqnarray*} \max_{x_1, x_2, \ldots, x_n} && u(x_1, x_2, \ldots, x_n) \\ \text{s.t.} && \sum_{i=1}^n p_ix_i \leq M \\ && \sum_{i=1}^n x_i = X \\ && x_i\in\mathbb{Z}_+ \ \ \forall i\in\{1,2,\ldots, n\} \end{eqnarray*}

If we ignore the budget constraint, the equation $\sum\limits_{i=1}^n x_i = X$ has ${X+n-1\choose n-1}$ solutions. List them, sort them from high to low by utility, and then identify the highest one in the sorted list that also satisfy the budget constraint.

If $u$ is strictly increasing, differentiable and quasi-concave on $\mathbb{R}_+^n$, then one can solve the utility maximization problem in the usual way by ignoring the $\sum_{i=1}^n x_i = X$ constraint, and then inspect the integral solutions of $\sum_{i=1}^n x_i = X$ that surrounds the solution of the utility maximization problem, and choose the best amongst them to get the final solution.


The "permanent portfolio" content I am considering the idea of "Harry Browne's permanent portfolio". I seen a few versions of this strategy where the different parts consists of funds which in turn have some costs associated with them.

Then why not just buy one ETF(which only contains the corresponing asset) for each of three parts consisting of government securites and gold and for the last forth just a large stock fund for the stock part?

I hope I understood your question correctly. In case this helps:

1) you can probably cover even the stock part with a combination of just a few ETFs.

2) traditional funds (as opposed to ETFs) will always be promoted much more aggressively, because their providers earn high fees. ETFs are much less profitable for their providers and are often not promoted at all even if they represent a superior solution. This might explain why you see versions with traditional funds, but not ETFs.

I think you are right in thinking that you can construct a "permanent portfolio" type investment portfolio out of ETFs with a superior cost structure. Probably the best way to do it. Industry players who have a vested interest in traditional portfolio management won't tell you this though.


How to account income from the informal sector? Some context here.

I'm from India and over here around 80% of the public work in the informal unaccounted sector.

Yesterday, the main opposition party said that if they're elected, they'd compensate each individual who's earning less than 12K per month.

For example, if someone earns 5K, govt will add 7K or if someone earns 10K, govt will add 2K

But as almost 80% of the people belong to the unaccounted informal sector, how would govt come to know the exact figures?

Okay 1 easy way to guess would be how much money an individual spends, how much money in the bank etc but don't you think people will have an incentive to show lower incomes?

How would the govt know the exact figures then.

PS- I'm not concerned from where the govt gets the money to balance, I'm only concerned regarding the validity of the income figures.

Thanks!

Check this interesting report of the International Labor Office on Measurement of the Informal Economy. They raise and discuss the Key Challenges:

The paucity of data
Why is measurement important?
Conceptualizing the informal economy (Employment in the informal sector and informal
sector enterprises)


Tariff long term effects China imports $14B of soybeans from the US annually.  In response to US Tariffs, China has put Tariffs on US soybeans and is switching to Brazil for their beans.

In the long term and based on history, can one expect that Brazil will retain China's business after the tariffs are sorted out between the US and China? Or is their some economic force (price?) that would shift the soybean market back from Brazil to US farmers/

We don't know.  Consider the following possibilities:

The tariff lasts long enough that the United States soybean farmers switch from soybeans to some other crop.  When the tariff is dropped, they don't change back.  Brazil keeps the business.
Brazilian farmers open new land and buy equipment specifically for soybeans.  When the tariff ends, Brazil and the US split the business in some fashion (implicitly via market actions).  Some farmers in both countries may go out of business or switch crops as a result.
Brazilian soybeans that had shipped to Europe are now shipped to China.  Europeans buy soybeans from the US that they had bought from Brazil.  Transport costs may climb, but both the US and Brazil continue to produce soybeans at about the same rate as they did prior to the tariff.  When the tariff goes away, business patterns may go back to the previous pattern.
The US uses soybeans to make biofuels or otherwise finds new ways to use soybeans.
Chinese consumers might replace some soybeans with some other food in their diet.  Maybe they decide they like the new food better and they never eat as many soybeans as they did previously.
Producers and consumers engage in long term deals.  So once the market is changed, it stays changed even after the impetus for change is gone.

We might know how much of the soybean market is dominated by long term deals, but other than that, we don't really know how things will change.  It's quite possible that all these things happen to some level.

When something like this happens, it may make both permanent and temporary changes.  Someone might be able to work out a model whereby we can speculate as to how much of the change would be permanent and how much would be temporary.  But any such model is going to be somewhat of a guess.


Sources of data for GDP and BoP accounts When an American buys a coffee within the US, how does that 3.50 dollars worth of consumption expenditure make it's way to the US GDP account? Is the information obtained from the company's tax records? When a French citizen buys the same 3.50 dollar coffee in the US how does that information get reported so as to make it into the US and French Balance of Statements? I don't see coffee shops asking customers for passports when these order coffee so how does the coffee shop know how much it sold to whom? How does the French government get information about this coffee purchase by one of its citizens in the US to know to reflect it on its Balance of Payments statement?

When an American buys a coffee within the US, how does that 3.50 dollars worth of consumption expenditure make it's way to the US GDP account?

It would be personal consumption expenditures which primary data source is from the:

BEA’s Benchmark Input-Output (IO) Accounts, which are based primarily on the Census Bureau’s Economic Censuses

BEA’s International Transactions Accounts;

Census Bureau’s Annual Retail Trade Surveys

Service Annual Surveys

Quarterly Services Surveys

Monthly Retail Trade Surveys  (the coffee purchase would most likely come from here)

Bureau of Labor Statistics’ Consumer Price Indexes

https://www.bea.gov/sites/default/files/methodologies/nipa-handbook-all-chapters.pdf#page=90   page 5-7

When a French citizen buys the same 3.50 dollar coffee in the US how does that information get reported so as to make it into the US and French Balance of Statements?

This questions seems to be difficult to answer; however, after looking at the BEA’s Balance of Payments methodology on data sources it seems that this information is easily collected  from the BEA’s Quarterly Survey of Payment Card and Bank Card Transactions Related to International Travel (BE–150)

[As long as they are paying with a credit/debit card].

(https://www.bea.gov/sites/default/files/methodologies/ONE%20PDF%20-%20IEA%20Concepts%20Methods.pdf#page=8)  [page 13-5] (section 13.23)

This survey is filed by U.S. companies that operate payment and bank card networks. The survey captures information on credit, debit, charge, automated teller machine, and point of sale transactions between U.S. merchants and customers holding foreign-issued cards and between foreign merchants and customers holding U.S.-issued cards.

When a French citized buys the same 3.50 dollar coffee this transaction would be collected (if the person uses a credit or debit card) by the persons bank card company.  Then the bank card company would fill out the survey and indicate that their card user bought coffee at a US firm for 3.50 dollars.

This information would be submitted into the mandatory survey that the BEA collects for their balance of payments direct investment (chapter 13 of BEA BOP methodology).  https://apps.bea.gov/itable/itable.cfm?reqid=62&step=1


Linearization and the effect of a change There is the following system of four equations and four endogenous variables $(K,L,w,q)$. Assume $F$ is a concave function.
$\partial F(K,L)/\partial K = r + (1-p)$
$\partial F(K,L)/\partial L = w$
$F(K,L)-rK-wL-q-(1-p)K = 0$
$v(w,p)=\bar{v}$
It seems to linearize the system around the equilibrium values to get $\frac{\partial K}{\partial p}$ and $\frac{\partial L}{\partial p}$ and it seems that these equations become
$\frac{\partial K}{\partial p} = \frac{-F_{LL}-F_{KL}\partial w/\partial p}{(F_{KK}F_{LL}-F^2_{KL})}$
$\frac{\partial L}{\partial p} = \frac{F_{KK}\partial w/\partial p + F_{KL}}{(F_{KK}F_{LL}-F^2_{KL})}$
I tried to Taylar expansion but I could not get these equations. How do we get these last equations? These equations are from p.85 Kousky et al. (2006)

Start from the first order conditions:
$$
\begin{align*}
&F_k = r + (1- p)\\
&F_L = w\\
\end{align*}
$$
Now totally differentiate with respect to $p$:
$$
\begin{align*}
&F_{KK} dK + F_{KL} dL = - dp\\
&F_{LK} dK + F_{LL} dL = \frac{\partial w}{\partial p} dp\\
\end{align*}
$$
This is equivalent to:
$$
\begin{align*}
&dK = \frac{- dp - F_{KL} dL}{F_{KK}}\\
&dL = \frac{\frac{\partial w}{\partial p}dp - F_{LK} dK}{F_{LL}}
\end{align*}
$$
substituting the second into the first gives:
$$
\begin{align*}
&dK = \frac{(- dp)F_{LL} - F_{KL}(\frac{\partial w}{\partial p} dp - F_{LK} dK)}{F_{KK} F_{LL}},\\
\to &\left(1 - \frac{F_{KL} F_{LK}}{F_{LL} F_{KK}}\right) dK = \frac{-F_{LL}dp- F_{KL}\frac{\partial w}{\partial p} dp}{F_{KK} F_{LL}},\\
\to &dK = \frac{-F_{LL} - F_{KL}\frac{\partial w}{\partial p}}{F_{LL} F_{KK} - (F_{LK})^2} dp
\end{align*}
$$
This gives:
$$
\frac{\partial K}{\partial p} = \frac{-F_{LL} - F_{KL}\frac{\partial w}{\partial p}}{F_{LL} F_{KK} - (F_{LK})^2}
$$
The expression for $\frac{\partial L}{\partial p}$ can be derived in a similar way.


How does the Uber's pricing model work? I'm working on a paper on the sharing economy, and in particular on its economic implications.

I am aware of the surge pricing model that Uber adopts, and of how it works. But I'm wondering on what criteria and how Uber estimates the base fares of each city.

I would like, ultimately, to understand whether and why this artificial pricing model is better than the "natural" pricing models of other peer-to-peer services (e.g. AirBnB), that allow the users to set their own rates.

It is important to distinguish between optimal pricing from Uber's perspective and optimal pricing from an efficiency standpoint. If Uber was the only company matching drivers and customers, it would adopt a monopoly pricing strategy on selling rides to consumers and buying rides from drivers. These rates may be very far from the efficient rates. It is therefore important to state what you mean by a "better" pricing model.

From the perspective of Uber/Airbnb, profit maximizing pricing strategies may differ because of many reasons. AirBnB is in a business where the quality of a service can vary greatly and is often unobserved to them. Uber in contrast matches customers with services that have little to no variation in quality (speed, safety), which are fairly well observable due to their GPS data. But even depending on expected company growth may lead the two companies to have optimal pricing strategies closer or further from efficient prices. Finally, the competition in each city may be very different for Uber, since cab rates are fixed by a central planner. The competition of AirBnB usually has decentralized pricing except where a hotel chain has a local monopoly.

Even from an efficiency standpoint, there may be large advantages from a centralized pricing strategy in the market for rides. Most urban areas have fixed cab ride rates to increase transparency. Anybody can get into a cab without worrying about being charged an unexpectedly high amount. This can greatly enhance market outcomes.


Definition of "simple situation" is ambiguous "Simple” situations (where it is easy to predict which strategies will be chosen by the different agents):

Each participant has a strategy that outperforms all others regardless of the strategies adopted by its partners.

How can everybody have a strategy that outperforms everybody else's strategy?

Consider the typical prisoner’s dilemma,

$$
\begin{array}{|c|c|c|}\hline
&{\rm confess}& {\rm lie} \\ \hline
{\rm confess} & \color{red}{-8},\color{blue}{-8} & \color{red}{0},\color{blue}{-10} \\ \hline
{\rm lie} & \color{red}{-10},\color{blue}{0} & \color{red}{-1},\color{blue}{-1} \\ \hline
\end{array}
$$

In this case it is easy to predict that each player should play confess, regardless of the the selection made by the other player. Or in the words of the problem:

  The best strategy (the one that outperforms other strategies) is to confess regardless of the strategy adopted by other players


Weird Leontief production function I am solving some micro related exercises and I came across this weird Leontief production function: $$Q =\left(\min\{K, L\} \right)^b$$

I am not sure how to solve it. I have to find the inputs' demand, cost function etc.... Should I solve it as $K^b=L^B=Q$ and then proceed as usual with the standard Leontief?

This is not a weird case, but a Leontief production function which is not homogeneous of degree one, but homogeneous of degree $b$. You can see this if you use the connection between a C.E.S. production function and the Leontief one.

Consider
$$Q_b=[a K^{-\rho} +(1-a) L^{-\rho}  ]^{-\frac{b}{\rho}},\;\; b>0$$

$$\Rightarrow Q_b = \frac 1{[a (1/K^{\rho}) +(1-a) (1/L^{\rho})  ]^{\frac{b}{\rho}}}$$

Take the limit when $\rho \rightarrow \infty$. Since we are interested in the limit when $\rho\rightarrow \infty$ we can ignore the interval for which $\rho \leq0$, and treat $\rho$ as strictly positive.

Without loss of generality, assume $K\geq L \Rightarrow (1/K^{\rho})\leq (1/L^{\rho})$. We also have $K, L >0$. Then we verify that the following inequality holds:

$$(1-a)^{b/\rho}(1/L^{b})\leq  Q_b^{-1} \leq (1/L^{b}) $$

$$\rightarrow (1-a)^{b/\rho}(1/L^{b})\leq  [a (1/K^{\rho}) +(1-a) (1/L^{\rho})  ]^{\frac{b}{\rho}} \leq (1/L^{b}) \tag{1}$$

by raising throughout to the $\rho/b$ power to get

$$(1-a)(1/L^{\rho}) \leq a (1/K^{\rho}) +(1-a) (1/L^{\rho})  \leq (1/L^{\rho}) \tag {2}$$
which indeed holds, obviously, given the assumptions. Then go back to the first row of $(1)$ and

$$\lim_{\rho\rightarrow \infty} (1-a)^{b/\rho}(1/L^{b}) =(1/L^{b})$$

which sandwiches the middle term in $(1)$ to $(1/L^{b})$ , so

$$\lim_{\rho\rightarrow \infty}Q_b = \frac {1}{1/L^b} = L^b = \big[\min\{K,L\}\big]^{b} \tag{3}$$

For more, see this answer.


Two part tariff-income effects I understand that a monopolist optimally sets a two-part tariff by pricing at marginal cost and then extracting CS as a lump sum fee.  However, wouldn't the lump sum fee induce a decrease in consumer demand?  Is the typical assumption made in two-part tariff problems that there is no income effect?

In the typical textbook treatment of the two-part tariff model, income effect is ignored/assumed to be negligible.
Goldman, Leland, and Sibley (1984) provided detailed comparison of optimal nonlinear pricing strategies (of which two-part tariff is a special case) with and without income effect. Their conclusion is

When [income effects] are absent, the aim of optimal pricing is to raise a given amount of profit with the least possible distortion to individual's consumption plans. Therefore increments of consumption are priced according to the  Ramsey rule. When income effects are present, the optimal pricing problem is equivalent to the optimal taxation problem, and the goal is optimal income redistribution.


Why is that when one person or group gets a good or service, someone else will have to live without it? !

There's this statement in my Applied Economics book that I don't understand. Why is that when one person or group gets a good or service, someone else will have to live without it? I hope you answer this question. Thank you.

That statement is not generally true.

It is true of rivalrous goods (e.g. when I take a slice of a pizza, there's that much less left of the pizza for you).

It is false of non-rivalrous goods (e.g. when I step into the sunshine, there is usually* no less of the sunshine for you).

*Unless of course I somehow also block the sunshine for you.


Solow growth model - analytic proof that Inada conditions imply steady state capital is increasing in the savings rate Let's take the example of a generic Harrod-neutral (labor-augmenting) production function $f(k)$; all letters denote the growth rates they usually would. In the regular Solow growth model with the Inada assumptions, it is a result of its comparative statics that, since $sf(k^*)=(n+\delta+g)k^*$ is the steady-state condition, if we assume $k^*$ is a function of the savings rate then $\frac{\partial k^*}{\partial s}>0$. Total differentiation gives us that
$$ \frac{\partial k^*}{\partial s} = \frac{f(k^*)}{(n+g+\delta)-sf'(k^*)},$$
and in my class the professor claimed that this last expression is strictly positive because the numerator is (fine) and the denominator is too. Basically, it boils down to the fact that $\frac{n+g+\delta}{s} > f'(k^*)$, and that this is a fact implied by the Inada assumptions.

I have tried messing around with the statement about the limiting behavior of the derivative at 0 (infinity) and as k tends to infinity (zero); all to no avail. If someone could please offer some hints or an explanation or a proof of this fact I would deeply appreciate. This was not a question posed for an assignment or anything of the sort, just personal interest (having some background in analysis).

We want to prove that

$$\frac{n+g+\delta}{s} > f'(k^*)$$

Replace the left hand side with the equivalent from the expression $sf(k^*)=(n+\delta+g)k^*$, and you get:

$$ \frac{f(k^*)}{k^*} > f'(k^*) $$

Cobb-Douglas case

Without loss of generality, assume $$f(k^*) = {k^*}^{\alpha}$$

Then, the above inequality is:

$$ {k^*}^{\alpha-1} > \alpha{k^*}^{\alpha-1} $$

This is:

$$ 1> \alpha $$

This condition represents a production function with decreasing marginal returns to capital, necessary for the Inada conditions to hold.

General case

A concave function has the following property, for any $x$ and $y$ in the domain:

$$f(y) \leq f(x) + f'(x)(y-x) $$

Rearranging, this is:

$$ \frac{f(y)- f(x)}{y-x} \leq f'(x) \hspace{1cm}, \text{for } y>x $$

This is, the derivative of $f(x)$ at point $x$ is no smaller than the slope of the segment between $x$ and $y$. For the case of a strictly concave function (which is needed for the Inada conditions to hold), the inequality is strict ($<$), except in the trivial case of $x = y$.

For further confirmation, apply the above when $y=0$ and $x=k^*$ (notice here $y<x$ so the sign of the above inequality reverses). Since $f(0)=0$, you get:

$$ \frac{f(k^*)}{k^*} > f'(k^*) $$

which is what we wanted to demonstrate.


When gradient of utility function is a zero vector In Advanced Microeconomic theory by Jehle and Reny is said that if $\mathbf{x^*}$ is a solution to the following maximization problem $\max_{\mathbf{x} \in \mathbb{R}_+^n} u(\mathbf{x}) $  subject to $\mathbf{p \cdot x}\le y$, then $\bigtriangledown u(\mathbf{x^*})=\mathbf{0}$
is possible but quite unlikely.

The question is why is it quite unlikely? I can think only budget constraint, but is it right?

This concerns the partial derivatives of the utility function with respect to goods, and not the partial derivative of the Lagrangian of the maximization problem.

So a zero derivative, and moreover at the optimum, would imply a threshold quantity after which utility diminishes.

In the real world, we all know that consuming excessively may result in utility reduction (think eating too much food too quickly).

In the theoretical world such utility functional forms have been used, especially "quadratic utility" in intertemporal representative consumer models in macroeconomics with a single good,

$$u(x) =ax - bx^2$$

In microeconomics, all abstract development of the theory usually assumes that utility is non-decreasing in each good separately. But in cases where one would want to allow for decreasing utility, then, indeed, the reason why we would not expect to find the optimum at the zero-gradient point, would be the workings of the budget constraint together with relative prices.


How was CES utility function derived? Is there any book/papers that I can refer to the proof (derivation) of the CES utility function?
Or if anyone could help me with the derivation, I will be so much grateful to you.

To understand the CES utility functions, which I guess is your question, a good starting point is the Wikipedia page on constant elasticity of substitution. In particular,

The CES aggregator is also sometimes called the Armington aggregator, which was discussed by Armington (1969).

Then, the CES utility function was popularized by Dixit and Stiglitz (1977) in their study of optimal product diversity in a context of monopolistic competition.
If you want to understand how the CES utility function behaves when $\sigma=\infty$ or $\sigma=1$ here is a nice discussion of the basics of the CES utility function, which is widely used in trade.
If you want a deeper understanding of the elasticity of substitution and a discussion of the special class for which the elasticity of substitution is a constant $\sigma$, here is an insightful discussion by Ted Bergstrom.


Pareto efficiency of organ markets Organ sale is legal in Iran. I was wondering: are organ markets Pareto efficient? Or could an argument be made for them being Pareto efficient? I have been thinking that both the buyer and the seller benefit from the transaction, thus no parties are made worse off. However, coercion/kidnap could occur. There has also been the emergence of black markets (which some scholars attribute to the lack of a legitimate market in almost every country in the world).

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.


Does migration exacerbate (albeit delay) the problem of aging, economically-inactive populations in Western societies? As a layman, I've always understood that there is a general consensus amongst economists that "immigration is economically beneficial" to rich Western countries (like Britain) who have aging populations because the influx of young economically active workers contributes to the economy (and tax coffers) and thereby supports the old economically inactive population.

But this seems quite obviously short-sighted.  Those immigrants will themselves grow old—and assuming that they remain in their new host countries, they will add to the economic burden of the elderly populations for future generations.

Is such immigration therefore not just kicking today's problems into the future, where it will have compounded and be exponentially worse?

I don’t really see the connection you are drawing. As @Fizz has pointed out, immigration usually happens over time and maybe when immigrants grow old there will be more immigrants to support all of the new old. Likewise, in many countries immigrants tend to have more children than non-immigrants, so that will attenuate the aging problem.

If anything it should be something to check case-by-case, but I don’t see any causal relationship between immigration and the “aging problem”. I see how just mechanically these two are related, but I don’t expect the relationship to have any particular systematic pattern.

It feels to me like you are saying that taking more exams is bound to lower your average grade. Of course more exams will impact your average grade, but it really can go up or down depending on many other factors.


Show that the elasticity of substitution is σ How do I show that elasticity of substitution is equal to σ from a CES utility function. I have derived the following:

$\frac{q(\omega)}{q(\omega ')}=\left(\frac{p(\omega)}{p(\omega ')}\right)^{-\sigma}$

And then I can use the following to show that the elasticity of substitution is equal to σ:

$\frac{\partial \ln\frac{q(\omega)}{q(\omega ')}}{\partial \ln\frac{p(\omega)}{p(\omega ')}}=-\sigma $

But how do I find: $\partial \ln\frac{q(\omega)}{q(\omega ')}$? What should I differentiate with respect to?

You cannot find $\partial \ln\frac{q(\omega)}{q(\omega')}$, it has no well defined meaning here. However, by the first relation you mention, it follows that $$\ln(q(\omega)/q(\omega'))=-\sigma\ln(p(\omega)/p(\omega')).$$ Taking the partial derivative on both sides with respect to $\ln(p(\omega)/p(\omega'))$ gives $$\frac{\partial \ln\frac{q(\omega)}{q(\omega ')}}{\partial \ln\frac{p(\omega)}{p(\omega ')}}=-\sigma.$$


Is there any work on equality in a market versus friction? This is a question about educational economics.

There is a phenomenon when studying countries like the USA and Chile (that have implemented voucher systems) that reducing the friction in a "marketplace" in education (e.g. choosing a school) results in a reduction in equality. It results in stratification of students into schools that match with social class.

It seems fairly obvious to me that this is a phenomenon that I'm sure has been studied or talked about in economics in a general way - I just don't even know where to look.

I'm looking for research into the idea that where there is some kind of inelastic good (e.g. health, housing, education) then reducing friction in a market will always have an effect of reducing equality.

Has anybody studied this? Any pointers to literature? Or if I'm just wrong in my observation of this being "fairly obvious" then I'd love to hear it.

The key theoretical work, at least in the area of education, comes from Milton Friedman and his "Theory of School Choice". Important references are:

Friedman, M. (1962), The Role of Government in Education. In Capitalism and Freedom. Chicago: University of Chicago Press.
Friedman, M. and Friedman, R. (1980). Free to choose. New York: Harcourt
Brace Jovanovich.

Check here for a not so old review of the literature on School Choice. Here is an interesting analysis of the Chilean education system, in the light of Friedman's ideas. Friedman had the idea that competition would increase quality across the whole spectrum of schools:

the quality of    all    schooling    would    rise    so    much    that    even    the    worst,    while    it    might    be
relatively    lower    on    the    scale,    would    be    better    in    absolute    quality”    (Friedman    and    Friedman 1980,    170)


The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them? I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality.

But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator and denominator when we take the MRS and thus gives us the same MRS as our old utility function. But this cancelling out can also happen with decreasing monotonic transformations. Then why bar them from use ?

The single most important feature that we care about a utility function is that if a bundle $X$ is preferred to a bundle $Y$ then $U(X)>U(Y)$ (with weak inequalities whenever appropriate). This is how we define a utility function. You can immediately see that if a function has that property, any monotonic increasing transformation of it will also have that property. However, if the transformation is decreasing, call it $V(X)=f(U(X))$ with $f'<0$, then $V(X)<V(Y)$ i.e. now $X$ gives less utility. Therefore, we see that $V$ cannot represent the same preferences.

What about the MRS invariance property? Well, once you understand that utility representations are not unique, (or unique up to monotonic increasing transformations), you can ask what is constant across all functions that represent the same preferences? The answer is: they have the same MRS.

You can clearly see that it is necessary for two functions to have the same MRS if they represent the same preferences, but it is not sufficient. As you pointed out, decreasing transformations also have the same MRS. Note however, that the interpretations of the MRS slightly changes when  considering monotonic decreasing transformations.


How Much Gold Did Weimar Have Pre-Hyperinflation? A few years ago, Peter Schiff and a few other Austrians (not all Austrians, as Mish was stating the opposite) were adamant about hyperinflation and Paul Krugman stated that it was like talking about fire problems during a flood, which made sense because of the credit crunch (the inverse problem).  However, Schiff kept pointing to Zimbabwe and the Weimar Republic as examples of hyperinflation and even now, we're seeing it in Ukraine.

As far as Ukraine and Zimbabwe are concerned, neither appeared to have much gold before their hyperinflation.  For instance, Ukraine has next to 0, if not 0 and Zimbabwe, from what I could find, had less than 5 metric tonnes.  When I was looking online to see if anyone knew how much gold they estimate the Weimar Republic had, I couldn't find a figure and was curious if anyone knew, or could find a historic estimate?

The reason I ask this is because the United States owns the most gold in the world (and it's not a close competition), assuming we don't believe the people who think it's not there, and thus it's hard to believe that, unless the U.S. begins to liquidate its position, that it would face hyperinflation like these other countries even without a currency backed by gold because people know that in a really bad situation, it could trash the dollar, create a new currency backed by its gold (note that I'm not saying this would happen, but the US is hardly a country comparable to Zimbabwe when you consider its gold holdings).

To address the first part of your question:

  "By July 10, Germany's free gold reserve had fallen to the equivalent of £35 million pounds, and all the Bank was doing had produced precisely the effect it was hoped to avoid. Another loss of 50 million gold marks was suffered during the week which ended on July 14 — the direct result of supporting the paper mark by rationing supplies of foreign currencies and having to cover indispensable imports from the gold reserve. If intervention continued at the then level of 10 million gold marks daily, bankruptcy would come within 60 days: the reserves had already taken as much as they could stand. If intervention ceased, on the other hand, it was broadly expected that the dollar would go to a million marks, the pound to over 4 million — and by the end of July that expectation was fulfilled. Merchants were still said to be borrowing paper marks to the value of 80 per cent of their stock, and exchanging them at the Bank for dollar Treasury bills needed ostensibly for imports. These bills were sent abroad to the merchants' buying agencies, and in most cases stayed there with no countervalue returning to Germany."

-A World of Possible Futures: German Weimar Republic in the early 1920s and the U.S. - Troubling similarities

The source itself appears to be of questionable value, but makes vague reference to:

"The Economics of Inflation (Routledge Library Editions-Economics, 84)" by Constantino Bresciani-Turroni (427 pages, Routledge, reprint edition, October 1, 2003, first published 1937

Judging from historical gold prices and exchange rates, we could estimate:

$$ 35M x 4.58 /  21.32 = 7.5M$$

So, 7.5 million troy ounces or 233 Metric Tonnes according to Google.

To address your second point, it seems to be exactly what the Weimar Republic tried.

I would not imagine the US would be keen to repeat something like that, though it seems far outside the scope of this SE to speculate on that.