Economics: inductive or deductive? Verificationism or falsificationism? Question 1: Are economic theories and models developed using induction or deduction?

My view: If we gather historical evidence and figure "so, people tend to be like this and that so let's call this the Law of somethingsomething", then the answer is clearly induction.

Question 2: Are economic theories judged using verificationism or falsificationism?

My view: It seems to be verificationism: if the theories and models seem to be at least somewhat in accordance with reality, then it is considered a verification of the theory.

As regards the induction/deduction division, economics uses both, and they usually start by some induction followed by mathematizing it and then using deduction.

In the older days, economists were based more on their own personal experience and observation as to how people behave economically. Just browse any classic economics book from the 18th, 19th and even pre-war 20th century and this becomes obvious. They then embarked on lengthy verbal arguments to connect these instances of experience (in the modern era this approach has partly survived, but formalized into the "representative agent" analytical framework).

In modern days, both stages have changed:
At least for fundamental advances, what can be detected as long-term trend is that solid empirical evidence (being statistical or other), that can claim some generality, has become a required springboard for induction and a new theoretical economic model. Just one example of a seminal such paper,

Aiyagari, S.R. (1994). Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics, 109(3): pp.659-684.

is a paper where the author packs considerable statistical evidence and theoretical and empirical references in two pages before presenting his model of (what the paper title says), as a way of validating his approach.

The second stage has become mainly mathematical rather than verbal: one lets its model roll and see what results it will produce (this is the deduction step). This synthetic approach is necessitated because social phenomena do not have the repeatability observed in the natural world (although I would dare to say that there are many aspects of economic behavior that have remained virtually unchanged for at least all written history, and around the globe).

Of course since nowadays science is produced in an industrialized way, a million economics papers out there are purely works on existing theoretical frameworks, so this strand is pure deduction.

As regards the verificationism/falsificationism contrast, it appears that the OP uses the words in a rather relaxed manner, away from their stern meaning and the philosophical schools behind them. In that sense then, yes, economics looks for "adequate representations of reality", i.e. it sides with "verificationism": an inside joke is that "no economic theory was ever abandoned because it did not conform with the data"...

For such matters, Mark Blaug's inside polemic The methodology of economics: Or, how economists explain has not lost its bite.

The helpful comment below suggested also looking at abductive inference for how economists go methodologically about understanding the world.


How can I obtain State level Investment in the US? How can I obtain investment level data by state in the US?

I want to analyse how Public investment vs Private Investment responded to TFP shocks on a state level, so I am looking for Gross Private Domestic Investments, Residential and Non Residential investments for each state.

This is a great question that I think you should bring up to the US Census bureau.
I believe at one point they did explore how to come up with capital measures by state; however, nothing ever happened.    At this point and at the time of this posting the measurement of capital measures by state does not exist.  It would appear this would be the "Holy Grail" of economic measurement.
There may be some capital data on equipment and structures at the state level from the Survey of Manufactures data (ASM) from the census bureau but that would be for only one sector in the economy.
There have been some studies about state level investment but the data used for the analysis are mostly state shares from  aggregate US totals.  The ratio used to come up with these types shares usually comes from the researchers assumptions, which is the best practice available.
Below is an example of a report:
https://www.cbpp.org/research/state-budget-and-tax/its-time-for-states-to-invest-in-infrastructure
If there is capital data at the state level someone please post the source here.


Effect of changing MC on monopolists' maximised profits Let a monopolist have constant MC = c, with no fixed costs. If $p(c)$ and $q(c)$ are the profit maximising price and output as a function of MC and the market demand schedule is given by $q = D(p)$, how does the monopolists' profit vary with a small change in MC? This is what I have so far:

Maximised profits is given by:

$$
π = p(c)q(c) - cq(c)
$$

Differentiating w.r.t c:

$$
\frac{dπ(c)}{dc} = q(c)[p'(c) - 1] + q'(c)[p(c) - c]
$$

The first term $q(c)[p'(c) - 1]$ is clearly positive because $q(c) > 0$ and for a monopolist $[p'(c) - 1]$ is also positive because:

$$
p(c) = \frac{c}{1+\frac{1}{Ɛ}}
$$

$$
p'(c) = \frac{1}{1+\frac{1}{Ɛ}}
$$

and for there to be a profit maximising level of output, $Ɛ < -1$

$$
p'(c) =  \frac{1}{1+\frac{1}{Ɛ}}> 1
$$

For the second term, $q'(c)$ is clearly negative since higher MC leads to higher price and therefore lower quantity. $[p(c) - c] > 0$ since for a monopolist $p > MC = c$.

At this stage, the effect on profits of a rise in MC is ambiguous since both terms have opposing effects (one is positive, other is negative) and how profits change depends on the magnitude of the two terms. How can we quantify the effects or at least know the relative magnitudes of both terms to find how profits will change to an increase in MC?

If MC increases, profits need to go down. Let $\pi (q(c))$ and $\pi' (q(c'))$ denote profits before and after the cost increase. Observe that producing $q(c')$ was feasible when the marginal cost was low and, therefore, it must be the case that

$$ \pi (q(c))=[p(q(c))-c]q(c)\geq[p(q(c'))-c]q(c').$$

In addition, we have that

$$[p(q(c'))-c]q(c')>[p(q(c'))-c']q(c')=\pi' (q(c')),$$

which gives us $\pi (q(c))>\pi' (q(c')).$


Marginal Utility Meaning I'm revisiting some old topics from introductory economics and I am not quite sure I have convinced myself of the theory behind marginal utility. I have a few simple questions if anyone could please help me with.
On a demand curve, if we move from point 1 to point 2:
the increase in demand is due to two classes of buyers:

Buyers who would've bought at a higher price but are now buying even more at a lower price (marginal utility of second quantity now greater than new price at P2)

Buyers who were not buying at all at the previous price and are now buying (marginal utility of first quantity now greater than new price at P2)

In general, is the increase in demand attributed more to buyers of class 1 or class 2? Intuitively, I always thought it would be class 2. In my personal experience, decisions for buying or not buying tend to be more binary in an all or nothing fashion so the marginal utility theory applied to class 1 has not held as strongly as it has in class 2.
If theres no simple answer, is there a topic I should look into to get a better understanding?

That's an entertainingly specific question to ask! I don't know the answer, but my thoughts are this.
You're looking at an aggregate demand curve, which is a result of all the demand curves of individuals in this economy. Now, individual demand curves are fairly easy to understand. Each individual takes prices to be fixed, and then they maximise utility. When the price changes, for instance because the economy moves from point P1 to point P2, everyone adjusts their consumption behaviour. How much they'll change their consumption is then a question of their utility functions, and hence is specific to the product and to the economy.
So, this is my answer: I think either could be true, it just depends on the product, prices, and utility functions.


How did the Plaza Accord revalue the Japanese Yen? In September 1985, Japan, the US, and three other nations agreed to the "Plaza Accord," which appreciated the Yen and Deutsche Mark. The value of the Japanese Yen appreciated from 200 Yen per Dollar to 100 Yen per Dollar.

How was this implemented? What of the free market? Did interest rates in Japan double? What are the mechanics by which an external intervention like this is made to hold in the "free" market (especially the FX market which is renowned for being so liquid and so "free").

Thanks

The Plaza Accord was implemented through market mechanisms. According to Wikipedia Central banks of the signatory nations spent $10 billion dollars. They exchanged these dollars for other currencies. This increases the supply of dollars and may even decrease demand if so far the central banks have been purchasing dollars. Due to the higher supply and not higher demand the 'price' or exchange rate of the dollar fell. At the same time the countries also implemented policy changes. This would effect the mid to long term exchange rates.

The Japanese interest rate did indeed fall.
http://www.tradingeconomics.com/japan/interest-rate
 Mind though that the US interest rate also fell
http://www.tradingeconomics.com/united-states/interest-rate


Economies of Scale explanation? I am from non-economic study background.

I recently came across this line by J.C. Hosten

  "To Lower costs per unit of output, people usually increase the size of their operations"

I read the wiki page of the Economies of scale.
And saw the diagram that as the size of operation/production was increasing the cost a decreasing.

My Question is, Why it happens?

The short answer is that average costs fall because fixed costs get averaged across more units.

In more detail:

Costs have two components: fixed costs (which do not vary with produced quantity) and variable costs (which do vary with produced quantity).

For example, if you produce newspapers your costs might include

paying journalists to write and edit the content of the newspaper
renting a building for the journalists to work in
paying to print each copy of the newspaper.

Notice that you only have to pay the journalists and the rent once, no matter how many copies you print (so these are fixed costs). The cost of printing (paper and ink) will increase as you produce more copies of the paper because you will need more of these inputs, so these are variable costs.

Suppose it costs \$10,000 to pay a team of journalists to produce an issue of a newspaper (fixed cost), and \$1 to print a copy of that paper (variable cost).

If you sell one thousand copies then the total cost is $$\$10,000+(1,000 \times \$1)=\$11,000.$$
That means the average cost of producing each copy is $$\$11,000/1000=\$11.$$

Now suppose production increases to 2,000 units. Now the cost is $$\$10,000+(2,000 \times \$1)=\$12,000.$$ The average cost per unit is $$\$12,000/2000=\$6.$$

So output increased and the result is that the average cost per unit has fallen. This is a situation in which there are economies of scale. The reason this happens is that, as output increases, the fixed cost (here the \$10,000) gets spread over more units so that the average fixed cost per-unit decreases even if the variable cost does not. In particular, notice that in the first case the fixed cost gets averaged over 1000 units (a fixed cost of \$10 per unit), whereas in the second it is averaged over 2000 units (a fixed cost of \$5 per unit).


Efficient Market Hypothesis and constant ex-ante real interest rates? According to Hayashi's Econometrics (page 151), efficient market hypothesis is a joint hypothesis combining:

Rational expectations $\rightarrow$ expected inflation$= \mathbb{E}(\pi_{t+1}|I_t)$, where $I_t$ is the information available at the beginning of the period.

Constant Real Rates $\rightarrow$ The ex-ante real interest rate is constant.

Why is the second one also included? I've searched the wikipedia, but I didn't find anything helpful.

Any help would be appreciated.

To test market efficiency, you always need to specify the market's model of price formation

Tests of the efficient markets hypothesis must always include a model of how the market forms prices. One of Fama's big contributions was that you cannot separate these two things in a test. Tests of efficient markets and models of price formations are inherently linked. So, in this case, the assumption of constant real interest rates is merely an assumption of how the market forms prices. Only after assuming this, can we test market efficiency. You might disagree with the model---more sophisticated models will repeat this experiment in that way---but the point is that you have to assume some model for price formation.

Further reading

For more information about this, check out Fama's website. You'll find some links to some books of his. It would be helpful to read at least the first two sections of chapter 5 of his book, "Foundations of Finance."

The argument that he makes in that chapter is approximately the following (borrowing his notation, but changing $\phi$ to $I$).
The point that he makes is that we want to test if the information sets are equal
$I_{t-1}^m = I_{t-1}$, where $I_{t-1}^m$ is the information that the market possesses. But because we can't test this directly, we would like to test
whether the distributions of prices are the same
$$
f_m(p_1,...,p_n \mid I_{t-1}^m) = f(p_1,..., p_n \mid I_{t-1}).
$$
However, this is impossible too. The equality possesses no testable content because we only observe $f(p_1,..., p_n \mid I_{t-1})$ and not $f_m(p_1,...,p_n \mid I_{t-1}^m)$ (see the top of page 137 of the linked chapter). I do not observe the latter because I do not know what $I_{t-1}^m$, except that $I_{t-1}^m \subseteq I_{t-1}$, and I do not know how the market uses this information. For this reason, we specify a model for how the market takes information and turns it into prices. Thus, we specify $f_m$ ourselves (in turn, also specifying what information $I_{t-1}^m$ the market uses). That is, we specify what data the market uses and the way in which it uses that data.

On page 134, Fama says

  the statement that prices in an efficient market "fully reflect" available information conveys
  the general idea of what is meant by market efficiency, but the statement is too general to be
  testable. Since the goal is to test the extent to which the market is efficient, the proposition
  must be restated in a testable form. ... this requires a more detailed specification of the process of price formation, one that gives testable content to the term "fully reflect."

Why assume constant rates in the example in Hayashi?

I think it's just an assumption made in that particular example. If you read a little further into the linked chapter, you'll see that Fama discusses 4 different models of market equilibrium. The first two are ridiculous, but he's doing it just to demonstrate the concept. (Part of the reason is that some of the previous ideas about market efficiency had some bizarre consequences, which he demonstrates through those examples.) The point is that any test of market efficiency is always tied to the model that is assumed. If the test fails, you know one of two things: either the market is inefficient or your model of the market is wrong. The unfortunate truth, however, is that you will never know which one it is.


when a=0, would economy accumulate more physical capital? Why? Utility function is

$U(c_t,l_t)=(1-a)ln(c_t)+aln(l_t)$

$l_t$ is leasure time

$c_t$ is consumption

Production function is $y_t=k_t^e(1-l_t)^{1-e}$

$k_{t+1}=i_t+(1-\delta )k_t$

where k is capital delta is capital depreciation rate. i is investment.

My question is

when a=0, would economy accumulate more physical capital? Why?

——

I think that, when a=0, agents get utility only from consumption. They don’t get utility from leisure time so they have a more tendency to work. So output increases, which leads to capital accumulation.

Does this make sense? How can more correctly interpret this?

—-

In addition to interpretation, I have essentially following question

I derive optimal physical capital equation for delta=1and for the maximization problem

$$v(k_t)=max\sum B^tu(c_t,l_t)$$

$$k_{t+1}=Bey^*_t$$

But I could not demonstrate this is locally stable.

Please give me a hint. Thanks.

If you want, I can write my solution in detail.

From the looks of this question, it seems like a typical consumption-saving problem with possibly endogenous leisure.
I am assuming the production function is constant returns to scale. I am assuming that $a\in[0,1]$
The problem is:

$\underset{\{c_t,k_{t+1},l_t\}} {Max} \sum_{t=0}^{\infty} \beta^t U[c_t,l_t] = (1-a)ln[c_t]+aln[l_t]$

subject to $k_{t+1} = f[k_t,l_t]+(1-\delta)k_t-c_t$

The Bellman Equation:

$V[k_t] = U[c_t,l_t]+\beta V[k_{t+1}] $

Differentiating w.r.t $k_{t+1}$ and using the envelope condition you will find the Euler as:

$\frac{c_{t+1}}{c_t} = \beta (f_{k_{t+1}}+(1-\delta))$

Which at steady state gives you:
$k^* =(1-l^*)(\frac{e}{\frac{1}{\beta}-(1-\delta)})^{\frac{1}{1-e}}$

If a = 0, there is no labor selection problem and $l^*=0$ leading to full use of available time for labor. Clearly, there is more capital in the steady state equilibrium.


Is the mode of wage distribution a meaningful economic indicator? The Central Statistical Office of Poland publishes a report every two years, in which it diagnoses the labor market. Among other indicators, they publish the mode of the distribution of wages, in painful detail (up to a grosz, worth around a quarter of a cent). For instance for 2017 it was 2074.03 PLN worth at the time of writing 548.6 USD (source tweet in Polish).

These statistics always resonate strongly with a lot of my friends, however I have doubts. Having a background in statistics but none in economy, I criticize this indicator as being excessively susceptible to noise. I expect very low correlation between the frequency of wage equal X PLN and X+0.01 PLN and as such conveying very little information about the labor market as a whole. I could see this indicator useful if applied to a reasonably quantized histogram (which however raise the question where should the bin edges be). On the other hand, if somebody does not wish to look at the market as a whole, I could imagine some creative uses of this value.

I would like to ask the community if it is aware of any meaningful uses of the aforementioned in economic research, and if so, at which degree of quantization.

Yes, it is a very useful indicator.  You are correct that it has greater noise, but, depending upon how it was calculated it can be a very useful measure.

Statistical efficiency is a nice thing, but it implies a very specific loss function.  Let us imagine you are a government.  For the US government, the mean wage includes individuals like Bill Gates.  The implicit loss function is quadratic loss.  However, is this a politically useful measure?

You want to get over 50% of the votes, and this is a highly skewed distribution.  That does not attest to the well-being of the middle of the body politic.  For that, you want to look at the median, which minimizes absolute linear loss.  It is less efficient. It tells you the experience of the median voter, provided votes are roughly distributed randomly across the income spectrum. However, since voting is an all-or-nothing proposition, you don't just want to know the health of the middle.

This brings us to the all-or-nothing loss function.  It is the populist loss function.  It is the most common experience of your people.  Hillary Clinton and David Cameron managed median voter theory perfectly; they both lost.  This is a problem that, in politics, used to be called the "farm-block," problem.  The median is not representative if any one large body can move the vote.  The body most likely to do this are the individuals at the mode.  If they act together, they move an otherwise tied election, and almost all elections are close to being tied if competition is real.  Voting is an all-or-nothing proposition.  The mode minimizes the all-or-nothing loss function. To ignore the mode is to watch a government collapse.

Do not think of this as an attempt to find the center of location.  Think of it as a gamble that no government wants to lose.

Don't use bins, find the supremum of a kernel density estimate.


Why is corporation tax regarded as a direct tax? I understand that the classification of taxes is on ability-to-pay principle and is partly determined by the demand elasticity of the commodity or service.

That's how I understand income tax is direct, while customs tax is indirect.

But I can't really wrap my head around why corporation tax is also considered a direct tax. Can't the corporations simply raise their prices in order to shift away the incidence of tax burden?

The classification of direct vs indirect taxes is outdated and has nothing to do with the effects of taxes on behaviour. This classification is mostly due to historic reasons.

Direct taxes are taxes on property, businesses or people. They tax entities directly and not through their behavior. This doesn't mean, however, that these taxes don't have behavioral effects.

Indirect taxes are taxes on transactions and exchanges, since they are not taxing entities themselves, but their behaviour.

The classification is not very meaningful nowadays. For example the estate tax is direct (it directly taxes the estate), whereas the inheritance tax is indirect  (it taxes the transaction from parent to child). However, these two taxes are economically equivalent.


Is it valid to compare cryptocurrencies by using their smallest divisible unit? I'd like to compare the relative value (in USD) of three cryptocurrencies: Bitcoin, Ethereum, and IOTA. (See spreadsheet below.) Specifically, I'm comparing the price of each currency's smallest unit of division. And I'm taking that a step further to compare the "unit price" and the "smallest unit price" over the current circulating supply.

(Note, although these currencies have big differences with respect to their feature sets and target markets, and I don't want to consider that for the purposes of this question.)

The Problem: Currency Differences

Unit Subdivision

These three cryptocurrencies vary dramatically by the amount a single unit can be subdivided. A single bitcoin (BTC) can be divided by 1/10^8. That is the smallest unit that can be recorded on the blockchain and is sometimes called a Satoshi. A single Ethereum unit is called an ether. It can be divided by 1/10^18 and this smallest unit is called a Wei. A single IOTA cannot be subdivided, unlike the BTC and Ether units, which were chosen to give sub-unit precision rather than large whole numbers.

Circulating Supply

Also, the current circulating supply of each currency is dramatically different. At the time of this writing there are 16,451,325 BTC in circulation, 93,329,609 Ether in circulation, and approximately 2.8E+15 IOTA in circulation (which unlike BTC and Ether, is fixed and will never increase.)

Solution Premises

Use Smallest Unit of Currency for Price Comparison

The first premise of my question, which may be incorrect, is that we can get closer to an apples-to-apples comparison of price by calculating the price of the small unit of currency. For example, I don't think it would be accurate to compare the price of BTC ($1,918.41 at the time of this writing) and the circulating supply of 16,451,325 BTC against the price of an IOTA (0.17) and it's circulating supply of  2,779,530,283,000,000.

Use Price over Supply to Show Value

The second premise, which may be also be incorrect, is that after we have a price-per-smallest-unit for each currency, we can further estimate value by dividing that number by the existing circulating supply.

For example, if a baker slices a single pie into 4 slices and sells each for two dollars apiece, and a second baker slices a pie into three slices and also sells for each for two dollars apiece, I can see that I can more "value," for my money by dividing the cost of a single slice by the number of total slices. In the case, a value of .5 for the quarter slices and a value of .67 for the pie sliced in thirds.

I'm considering the available supply in this case to be fixed, which is true with IOTA. The circulation of Bitcoin and Ethereum will increase to give a slow inflationary rate, but I don't think I want to consider that in the context of this question.

Summary

This is a screenshot of a spreadsheet where I've done the above calculations (click to enlarge):

In the last three columns we see very different results. In column G, the price of the smallest unit for the currency, the Ethereum unit "Wei" is cheapest by far.
However, in column I--which takes the price of the smallest unit of currency divided by the circulating supply of that smallest unit--the IOTA (larger numbers are better here) seems to be a better value.
And finally, in column H, we abandon the idea that using the smallest possible unit is important and simply divide the unit price by its circulating supply. That result suggest that bitcoin is a better value.

I feel that the calculation in column H, where we don't reduce the currency price/circulation to it's smallest possibly unit is wrong, especially if we're considering IOTA in the set. But I'm also unsure, due to my lack of economics knowledge, that the degree to which the currency can be subdivided is important.

In the end, a stock (or cryptocurrency) is just worth what someone is willing to pay for it. And value is more than just price. But are the above calculations a valid way to compare cost of these currencies?

No, the above calculations are not a valid way to compare cost of these curencies, for exactly the reason you state:  a cryptocurrency is just worth what someone is willing to pay for it.

They don't have intrinsic value. Cryptocurrencies are inherently wealth-destroyers, they are not wealth: they require resources to construct, and then just act as ponzi schemes thereafter. So their only value derives from the number and purchasing power of the people that can be fooled into buying them.


How do I solve the Envelope Theorem condition in Microeconomics? I am preparing myself for a MSc in Economics and don't understand why, according to the Envelope Theorem, when deriving a utility function $ u(θ, q(θ), r(θ)) = B(q-r) - C(\frac{q}{θ})$, its derivative with respect to $θ$ is $(\frac{q(θ)}{θ^2})C'(\frac{q(θ)}{θ})$.

I'm guessing your inquiry is concerning the chain rule of total derivatives.
In the special case that $B(q-r)$ is for some reason omitted out of the expression, the derivation sequence would be this.
$$\frac{\partial{u}}{{\partial\theta}}= \frac{\partial{u}}{{\partial{C}}}\frac{\partial{C}}{{\partial\theta}} = -1*\frac{\partial{C}}{{\partial\theta}}=-\frac{\partial{\frac{q(\theta)}{\theta}}}{{\partial\theta}}C′(\frac{q(θ)}{θ})=-(-\frac{q(θ)}{θ^2})C′(\frac{q(θ)}{θ})$$
If your problem is with the latter part of the expression above, I'd suggest you read through derivation rule of composite functions.
As @Giskard has pointed out, it is unclear from the question why the term $B(q-r)$ would be omitted and perhaps you'd like to provide additional information on that.


Demand function for good x $U(x,y) = x + 4y$, I tried to find demand function for good x, so I did utility maximization.
max $U(x,y)  = x + 4y $ subjects to $P_x.x + P_y . y = I$
and I found the $Px /Py  = 1/4$, so $4Px = Py$.
Plug it in budget constraint I found $P_x.x+4P_x.y = I$
My Question is when I write demand function for good x, should it be $x = I/P_x$ because I said $y = 0$
So, Can I say that there is corner solution?

In your case there could be multiple solutions to the problem not just $y=0$. Any combination of $x$ and $y$ that would satisfy the budget with equality would be optimal in this case.
Hence I think it would probably be best just express demand for $x$ as:
$x=\frac{I}{P_x} - 4 y$
In fact this also gives you all potential optimum solutions to the problem since you can verify that for some parameters for example $I=100$ and $P_x=1$, when you consume 0 units of $y$ (implying that $x=100$) you get exactly the same utility as when you consume $x=96$ and $y=1$, or $x=92$ and $y=2$ and so on. So the $x= \frac{I}{P_x}-4y$ gives the combination of all possible optimum solutions. I personally don't see an reason to just assume that $y$ should be zero in such situation (unless this is for a classroom setting and that was recommended by instructor in these situations).


Change in optimal savings due to increased risk Currently I am working out advanced micro problems that deal with household's optimal savings behavior. Although I think I understand the material quite well, I am not sure about the specific detail of the solution of the following (shortened) problem.

Let $u: \mathbb{R}_+ \to \mathbb{R}_+, c_i \mapsto c_i^2$ be the (consumption) utility function for the two time periods $i \in \{1,2\}$. Assume that the income $y_2$ is risky with riskiness represented as $\beta$ and $\beta$ being a mean-preserving spread. What can you say about the change in optimal savings if $\beta$ increases?

My thoughts about this are as follows. What we are looking for here is the sign of $$\frac{ds^*}{d\beta}$$

where $s^*$ denotes optimal savings. In the lecture we showed that its sign only depends on the sign of $$K = \frac{d\mathbb{E}[u']}{d\beta}$$ Since $\beta$ is a meaning-preserving spread we then said that the sign of $K$ only depends on the sign of $u'''$, i.e. that $K < 0$ if $u''' < 0$ and vice versa but we omitted the case $K = 0$. But since $u(c_i) = c_i^2$ it is $u''' = 0$.

My questions are thus

What is the conclusion if $u''' = 0$? Is it the same as the positive (> 0) case?
Why exactly do we, if $\beta$ is a MPS, only need to care about the argument's second derivative in order to determine the sign of the expectation?

Your question is essentially about precautionary savings, i.e. the response of savings to risk.

What determines precautionary savings is the coefficient of relative prudence: $CRP=-\frac{U'''}{U''}C$, where $U$ is the utility function, $C$ is consumption and primes denote derivatives. As we always have decreasing marginal utility in economics, i.e. $U''<0$, then the sign of the savings will depend on the sign of the third derivative, as you mentioned.

Think of this coefficient as similar to the risk aversion coefficients. The difference is that prudence means that agents act in anticipation of risk by saving more, whereas risk aversion reflects how agents react when presently faced with risk.

With quadratic utility, the coefficient of relative prudence is zero and there are no precautionary savings. Hence there is no effect of risk on savings. With such utility we therefore have certainty equivalence, which is quite convenient and hence often used. Mean preserving spreads don't matter then. So no, it is not the same as in the positive case, where savings would go up in resonse to risk.

What is crucial here, as you noted, is the third derivative. The coefficient really only uses the second derivative as a normalization.

A mean-preserving spread keeps the mean/expected value of consumption the same. However, it does not neccssarily keep the derivatives (marginal utility) the same, which are what matter for (savings) decisions. If the marginal utility is linear (quadratic utility), then a mean-preserving spread keeps the expected marginal utilities the same as well. Hence, there are no precautionary savings (no reaction) in that case.

If the marginal utilities are convex, then the mean-preserving spread changes things in a way that matters, i.e. it becomes beneficial to save more. This follows from Jensen's inequality. If it is concave, the opposite is true. So the relevant function to look at is $U'$, as this is how the agent makes decisions. When we want to see whether a function is convex or concave we look at the second derivative. So the second derivative of $U'$ is $U'''$, which is why the third derivative matters here.


Can repeated game sustain a discounted average payoff that is not individually rational? Look at the following payoff matrix, there are two stage Nash equlibria, and we consider a infinitely repeated game with discount factor $\delta\in(0,1)$, can players sustain an average payoff of (2,2) under any strategy? (I am confused because the individually rational(i.e. minmax) payoff is (3,3)) If not, why?

I'm inclined to say $(2,2)$ is not sustainable, though I don't have a formal proof at the moment.

To achieve an average payoff of $(2,2)$, the players must play $(H,H)$ in some stages. But then a player can deviate to playing $L$ and avoid any subsequent punishments by ensuring that he can always get at least $3$, which is better than $2$.


Is optimal labour zero when (i) capital fixed and (ii) elasticity of substitution less than 1? I am getting some "weird results". I find that in a CES, with short term fixed capital and elasticity of substitution smaller than one, it is optimal for firms to hire zero labour, which seems at odd with the idea that the marginal product of labour is always positive (except in the extreme case of Leontief, where $\rho = -\infty$).

Assume a simple CES production function:

$$Y = A\left( \alpha L^{\rho} + (1-\alpha)K^{\rho} \right)^{\frac{1}{\rho}}$$

Assume that capital is fixed in the short term, so the firm only optimises over  $L$. Importantly, the firm must pay the cost of capital anyway. Therefore, as long as $p>0$, the firm is always better off by producing something. Thus, the key question is how much labour to hire.

Under competitive markets, optimal labour comes from:

\begin{equation}
\frac{\partial Y}{\partial L} \equiv \alpha A^{\rho} \left(\frac{Y^*}{L^*}\right)^{1-\rho}  = \left(\frac{w}{p}\right)
\end{equation}

Importantly, notice that MPL is (i) always positive, (ii) for $\rho<1$ (including negative values) and $L^*=0$, it is infinity!. In other words, whenever there is imperfect substitution of factors, and the wage rate is non-infinity, you want to produce with some labour.

Replacing output into the above yields a single equation with only one unknown ($L_i^*$), which solution is:

$$ L^* = K \Omega^{\frac{1}{\rho}}  $$

where

$$ \Omega = \left(\dfrac{(1-\alpha)}{\left(\frac{w}{A p \alpha}\right)^{\frac{\rho}{1-\rho}}-\alpha}\right) $$

Now, discard the parameterisations where $\Omega<0$. These are corner solutions where $L^*=0$.

So far so good. Except for some strange result when $\rho<0$. To see this, let us replace optimal labour into the production function. After some rearranging, you get:

$$ Y^* = AK\left(\alpha\Omega + (1-\alpha)\right)^{\frac{1}{\rho}} $$

Now, compare this with the case of zero labour. Let us call this $Y_0$. Here, output is:

$$ Y_0 = AK(1-\alpha)^{\frac{1}{\rho}} $$

Now, we want to know under which parameterisation the firm is better off producing with zero labour. Profits with optimal labour and with zero labour are respectively:

$$ \pi = pY^* - rK - wL^* $$

$$ \pi_0 = pY_0 - rK $$

Thus, the firm will produce with no labour iff $\pi_0> \pi$, which is:

$$ wL^* > p(Y-Y_0) $$

So, if the labour costs do not compensate for extra profits, the firm will choose $L^*=0$. Here is where the problem arises: for $\rho<0$, $Y-Y_0$ is always negative! Which means firm will produce with zero labour.

To see this, let us find the conditions under which $\Delta Y=Y-Y_0<0$. This is,

$$ AK\left[\left( \alpha \Omega + (1-\alpha)\right)^{\frac{1}{\rho}} - (1-\alpha)^{\frac{1}{\rho}}  \right] <0 $$

$$ \left( \alpha \Omega + (1-\alpha)\right)^{\frac{1}{\rho}} < (1-\alpha)^{\frac{1}{\rho}} $$

Noting that $\rho<0$ will invert the components, you get:

$$ \frac{1}{\left( \alpha \Omega + (1-\alpha)\right)} < \frac{1}{1-\alpha} $$

Which is clearly true for:

$$ 0< \alpha\Omega $$

So, for "normal" parameterisations where $\Omega>0$, we can see that $Y-Y_0<0$ is always true.

I have confirmed this in R. The following code produces delta in output = -15:

rm(list=ls())

rho       <- -0.5
alpha     <- .6
A <- 1
p <- 1
w <- 0.7

K <- 2.756729
omega = (1-alpha)/((w/(alpha*A*p))^(rho/(1-rho))-alpha)
L = K*omega^(1/rho)

ll = alpha*L^rho
kk = (1-alpha)*K^rho
tr = (1/rho)
Y = A*(ll+kk)^tr
Y0 = A*(kk)^tr

delta_output = Y-Y0

delta_profits = p*(Y-Y0)-w*L

if I change $\rho$ to 0.5, you get the desired result (that using labour does increases output).

You can also see the plot of delta output here. It is clear that the delta output is always negative, and asymptotically zero for $x=\infty$, which is when $L^*=0$.

Ok, rather embarrassing, but the problem was in the formula for $Y_0$. In effect, for $\rho>0$, it is true that

$$ Y_{_{L=0}} = AK(1-\alpha)^{\frac{1}{\rho}} $$

However, for the case of $\rho<0$, the limit of $Y$ is zero. The proof is trivial. Rewrite the CES as:

$$ Y = AL\left(\alpha + (1-\alpha)\left(\frac{L}{K}\right)^{-\rho} \right)^{\frac{1}{\rho}} $$

Then, it is trivial to see that:

$$ \lim_{L\rightarrow 0} Y = A0 \: \alpha^{\frac{1}{\rho}} = 0 $$

With this, we can see that $\Delta Y = Y > 0$. This solves the inconsistency.

PS: as it turns out, the marginal product of labour at $L=0$ is not infinity. Apparently, the Inada conditions do not hold for the CES with $\rho<0. Actually, the marginal product of labour seem to be zero! (check slide 15 here). This is a major revelation to me.


Demand Curves for Stocks i am currently working on a paper on demand curves for stocks and have some questions.
I've read that many models (CAPM, APT, Modigliani-Miller theorem) assume demand curves for stocks to be flat. Can you tell me why?
Now research suggests that they actually slope down. Why is this relevant and what implications does this have?

In a framework such as CAPM, agents are assumed to be rational, and usually to have identical preferences. All agents have access to the same information, and agree on the level of riskiness of every particular stock. As returns are a reward for taking risk, the price of every asset do not depend on the supply but on its riskiness. Thus, the demand curve is flat: no matter how much of asset A their is on the market, nobody wants to pay a premium which would lead to have a lower reward for a same level of risk.

This models have very strong and restrictive assumptions, which is why we end up with this weird infinitely price-elastic demand curve. More complex models, with less restrictive assumptions, might produce downward sloping demand curves.


Where can I find a complete list of goods affected by NAFTA? I am looking for the list of goods that NAFTA, preferably in the format of what is subject to tariff reduction.

I have found a few potential leads, but none seem to be exhaustive:
https://www.investopedia.com/terms/n/nafta.asp

https://fas.org/sgp/crs/row/R44875.pdf

https://aic.ucdavis.edu/pub/briefs/brief21.pdf

https://aic.ucdavis.edu/2003/02/01/role-of-nafta-in-california-agriculture-a-brief-review/

Here is the agreement in full (if someone is familiar, perhaps they could point me to a specific chapter?):

https://www.nafta-sec-alena.org/Home/Texts-of-the-Agreement/North-American-Free-Trade-Agreement?mvid=2

As highlighted by @Bkay, these linked documents are likely to rot. For future users, the keyword I was missing when searching for these documents was 'tariff schedule'. The below links to 2019 tariff schedules. I suggest that in the future a user search:

'YEAR tariff schedule COUNTRYOFINTEREST'

It may also be useful to specify the trade agreement of interest.

For USA: Harmonized Tariff Schedule 2019 Revision 2

Link: https://hts.usitc.gov/current

For Canada: Customs Tariff by Chapter (Customs Tariff 2019-1)

Link: https://www.cbsa-asfc.gc.ca/trade-commerce/tariff-tarif/2019/html/tblmod-1-eng.html

For Mexico (and all three): Mexico Import Export Codes

Link:http://www.siicex-caaarem.org.mx/

Chapters of interest will vary by personal use.


How exactly does a stock price gap overnight? I read Bob Baerker's answer.
I'll exemplify with KODK.   The NYSE has

Extended Hours: 4:00 pm to 8:00 p.m. ET

Opening Session: 4:00 a.m. to 9:30 a.m. ET

Pretend that on July 28 2020, KODK  last traded on the NYSE at 7:59 PM for \$9. Pretend that on July 29 2020, KODK first traded on the NYSE at 4:01 AM for \$15. How did KODK jump overnight by +6? Is the reason merely because the first trade on July 29 2020, a buyer accepted the sale price of $15?
Many thanks to user "Bob Baerker" for this chart!

A stock price is the price where two entities are willing to transact. The prices are often affected by new information. If a company has a major announcement to make during the day, trading is often halted, and then the price can be radically different after trading resumes, since investors may have revised their valuations.


GDP in expenditure approach GDP calculated using expenditure apporach is like this:
GDP=C+I+G+(X-M)
However on this site:
http://www.singstat.gov.sg/statistics/visualising-data/charts/share-of-gdp-by-expenditure

The data is avaialable for C, G and net exports, but there are two variables: Gross Fixed Capital Formation and Changes In Inventories. Since there is no 'I' variable, can I assume that the sum of those two variables are equal I?

The authoritative source here is the United Nations System of National Accounts, SNA.

Change in inventories are indeed part of what we normally call Investment. First, for clarification, the definition of "change in inventories", taken from page 108 of SNA, version 2008:

  The basic principle underlying the measurement of changes
  in  inventories  of  finished  goods  is  that  output  should  be
  recorded at the time it is produced and valued at the same
  price  whether  it  is  sold,  otherwise  used  or  entered  into
  inventories for sale or use later. In effect, goods only enter
  inventories when they are not immediately used
   for sale or other use in the period they
   are produced. Similarly, goods are  withdrawn  from  inventories  when  the  demand  for  the
  goods exceeds the amount produced in a period. No output
  is recorded when goods produced previously are withdrawn
  from  inventories  and  sold  or  otherwise  used  unless  a
  storage activity as described be low in section F takes place.

Second, the components of "Investment" (officially called Gross capital formation), as stated in page 282 of the aforementioned document is:

  There are three types of capital formation to be examined,
  gross  fixed  capital  formation,
    changes  in  inventories  and
  acquisition less disposal of valuables.

This and following pages go about explaining each of them, and how to measure them.

Finally, the document provides a worked example of the table of "uses of output" (the expenditure approach of GDP). Here is a screenshot of a section of that worked example, presented in page 291. You can see that change in inventories are indeed treated as part of "Gross Capital Formation":


Nash Equilibrium and Dominant Pure Strategy when payoffs identical What happens if the payoff is the same across strategies? I have some thoughts but I am not sure.

$$
\begin{array}{c|cc}
 &C&D\\
\hline
A& 1,1& 1,1\\
B& 0,1&1,-1
\end{array}
$$

Dominant strategy
By definition, a player's strategy X is dominant over his other strategies if strategy X is the best strategy regardless of what the other player chooses as his/her strategy.

For player 1 (Row), is ‘A’ a dominant strategy for player 1? I'm not so sure here. Yes, A is the best response if player 1 plays C, but both A and B are the best responses to player 1 when he plays D. In this case, should strategy A be considered a dominant strategy for player 1?

Same goes for player 2, if player 1 plays A, then player 2 can respond with either C or D. If player 1 plays B, then player 2 respond with C. Can i say C is a dominant strategy for player 2 then?

Nash Equilibirum
Nash Equilibrium is defined such that no other player can do better by unilatarally change his strategy.

Is (A,C) Nash Equilibrium? By definition its Nash Equilibirum since player 1 will not change from A to B since payoff of 0 is not better than 1. player 2 will not change from C to D, since payoff of 1 and not better than 1. (Is this thinking correct?)

Is (A,D) Nash Equilibrium? By definition its Nash Equilibrium since player 1 will not change from A to B since payoff of 1 is not better than 1. player 2 will not change from C to D, since payoff of 1 and not better than 1. (Is this thinking correct?)

Thanks.

First, make sure you have a definition of strategy clear. Strategy describes the actions a player chooses conditional on information etc. In your case it's a one-shot game so perhaps the distinction between an action and a strategy is not that important.

In game theory there is the notion of a "weakly" or "strictly" dominant (or equivalently "weakly" or "strictly" dominated) action. Nash equilibrium does not allow for any strictly dominated action to be chosen. It can be, however that a weakly dominated action is chosen. Hence you cannot cross out a whole row or column because an action is weakly dominated.

Your thinking regarding to NEs is correct. In both AC and AD no player can be strictly better off by changing his/her action conditional on opponent's action being held constant.

Finally, game theory done properly is rigorous enough (at least at undergraduate and graduate level), that there is never grey area. The definitions you gave are not stated mathematically and not 100% correct either, hence they seem a bit vague.


How can the share price of a company be less than its (theoretical) liquidation value? A recent article from Bloomberg states that Deutsche Bank's share price is less than half its theoretical liquidation value.

According to Investopedia, liquidation value is defined as:

  The total worth of a company's physical assets when it goes out of business or if it were to go out of business.

This means, that the liquidation value does not include intellectual property, goodwill and brand recognition. Which would be reasonable factors why a share price can exceed the total worth of a company's physical assets.

Now, a company's total value, which includes intangible assets, is represented by the company's stock price.

Wouldn't this imply that:

If one bought all shares of Deutsche Bank and sold all its physical assets could make a fortune? (assuming that such action would not affect the share price)
If a company's total value is less than that of its physical assets, the company's intangible assets are negative?

So the question that I would have asked is: How is it possible, that the stock price of Deutsche Bank is less than half of the worth of its physical assets?

A company can have a positive book value and still be in trouble because of insolvency.  This is very common with banks.  Banks operate by borrowing short term to buy long term assets.  This is inherently risky and vulnerable to a liquidity crisis.  A bank can show a profit and positive book value and still be in a world of trouble.  If investors feel that a bank will not be able to rollover their short term debt, then the bank will be in trouble.  Selling their long term assets will not be the answer because long term assets are by their very natural not very liquidable.  You can never trust a bank's balance sheet nor their income statement.  A more accurate assessment of a bank would be of their cashflow, maturity mismatching and credit rating.


extensive vs intensive labor in US in recent decades Total Hours worked is a mix of extensive (to work or not, the usual standard working week) and intensive (how many hours to work).

I'm interested in how this balance of extensive and intensive margins worked in the US over time, particularly from the 1980s onwards, and over the financial crisis.

Can anyone suggest a source carrying out such an analysis?

This should serve as a starting point, although it's too early to cover the crisis. Maybe you'll find something when looking in papers citing this one via Google Scholar.


Are there countries with free banking? Are there any countries in which banks do not need to follow any special regulation other than the regular business regulations. If not, are there any countries that come close?
For more information https://en.wikipedia.org/wiki/Free_banking?wprov=sfla1 .

I'm going to stick my neck out and say that the answer is no, not because I have a specific reference (people tend not to publish papers stating that something doesn't exist) but monetary systems has been a keen interest of mine for the past decade and if free banking was currently being practised somewhere I would almost certainly know about it.

It has however been practised historically, perhaps most notably in Scotland 1716 - 1845.

You can find many proponents of free banking in the Austrian School of economics, for example George Selgin.


To what extent can cryptocurrencies be influenced by monetary policy? Background
In modern economies, at least up until ~10 years ago, it was assumed that a currency would be technically able to be subjected to monetary policy, that is, where more money is created or removed via typically monetary policy means.
However, certain assets/currencies whose quantity is determined purely through software and cryptography may not be able to be subjected to the same monetary policies.
Question
To what extent can a typical cryptocurrency whose quantity is deterministic be influenced by monetary policy on that currency?
My thinking

Technically, an organisation (e.g. a central bank), or even individual, could technically hoard a cryptocurrency in very large quantity, and then affect some sort of monetary policy by:

spending more of their currency holdings to cause inflation (depreciation of the currency's worth against goods and services), or
buying more of the currency to make it less abundant and promote deflation as appreciation causes goods and services to be cheaper.
Note: the orchestrator would have to control a significant sum in order to have a detectable effect.
Also: although an orchestrator couldn't create more of the currency, they could permanently destroy or decrease the supply (if they were willing to pay to do so) by destroying their cryptographic account keys, which creates an interesting asymmetry in capabilities.

However, no organisation/government could simply print or create more of the currency, at least not in a way that wasn't predetermined by the software.

One other thing
If the practical word 'cryptocurrency' throws anyone, please substitute it with 'a currency whose quantity is deterministic'.

Well first if actually the cryptocurrency we are talking about would be created by central bank, then the rules that were used to create it would be by definition monetary policy even if supply of money would be fixed, since monetary policy is central bank’s control of money supply either directly or via interest rate (see Yeyati, Sturzenegger (2010), or Friedman 2001). Keeping supply of currency completely fixed at all times is a valid (although arguably very disastrous) monetary policy. Hence, to an extent that some monetary authority consciously sets up rules for cryptocurrency, that set of rules will, by definition, be monetary policy.
If we are talking about some independent cryptocurrency then the cryptocurrency is equivalent to being a foreign currency from a perspective of central bank. In such case we can’t talk about central bank directly conducting monetary policy for cryptocurrency as by the definition of monetary policy monetary authority has to be able to change supply of money, but despite of that monetary policy set for its own currency can still affect the exchange rate between domestic and cryptocurrency and thus it can affect the value of cryptocurrency.
A loose monetary policy ceteris paribus, would depreciate USD/Bitcoin exchange rate making bitcoins more expensive (for more detailed overview of how monetary policy affects exchange rate markets see  Exchange Rates and International Finance).
Central bank could decide to do what you suggested buying/selling that cryptocurrency - which is equivalent to an foreign exchange intervention. This too is technically monetary policy since this is done through control of the money supply of central banks’s currency (e.g. central bank has to create more of its currency in order to get more of the foreign currency as reserves, and conversely when it reduces the foreign currency reserves it will get the previously created money back and thus reducing money supply). Even if a central bank has no control directly over money supply of other countries this allows central banks to also to certain degree control value of other currencies. For example, in past China’s central bank was partially keeping dollar overvalued and yuan undervalued by keeping large USD reserves.


Is there a proven, quantitative link between food wastage and food prices? Reducing food wastage should in theory reduce demand for food, thereby driving food prices down. However, there are a lot more factors involved here (for example, the reduction in price of a product x due to lesser wastage in region A may not actually lead to lesser prices in region B because transportation costs may fully offset the price decrease).

Has there been a study that quantitatively links food wastage and food prices?

As far as I know, there are no economic studies studying the effect of food waste on food prices. In part, this may be due to difficulties in measuring food waste, as noted by a commenter. However, a more fundamental difficulty stems from a lack of 'exogenous' variation in food waste. The amount of food waste may vary significantly between places and times, but so do other factors (taxes, technology, consumer demand) which also influence the price of food.

In light of the lack of empirical studies on this topic, allow me to discuss it from a more theoretical point of view. You write

  Reducing food wastage should in theory reduce demand for food, thereby
  driving food prices down.

There are therefore two questions here:

If people cut back on food waste, will their demand for food fall?
If demand for food falls, will food prices fall?

In my view, the answers are 'yes' and 'maybe, maybe not'. Let me address these questions in turn.

Question 1

Alecos has produced an interesting argument as to why a reduction in food waste could have no effect (or even increase) demand for food. Essentially, he models a reduction in food waste as an exogenous decrease in the price of food. When the price of food falls, we consume more of it. However, for a given level of consumption, our demand for food falls. With logarithmic utility, these factors cancel out; but in principle, either factor could be more important (so food demand could increase or decrease).

While this is an intriguing argument, I find it rather unconvincing. First, many people cut back on food waste precisely to reduce the amount of food they buy. It would be perverse to claim that such people 'respond' to their reduction in food waste by buying more food. Second, in modern economies, people are already satisfying (and often exceeding) their calorific requirements. Hence, the binding constraint on the quantity (not necessarily quality) of food purchased is how much food they want to eat, not the amount of food they waste. Third, as a modelling choice, I think we should view 'food waste' as an active choice which consumers make as opposed to some parameter to which consumers optimally react. I doubt that Alecos' conclusion would hold once recognise that wasting food is a choice, though of course we could check this.

In my view, things are more simple. If people waste less food, their consumption of food will not significantly change. As a result, their demand for food must fall.

Question 2

However, I am not so confident that a fall in demand will lead to a fall in prices. To simplify, let us suppose that food is produced by identical perfectly competitive suppliers in a market with free entry. In that case, it can be shown that each producer will produce at the level that minimises their average cost; and that the market price will equal this average cost. Hence, the market price does not depend on demand.

Naturally, this is just market structure and it may be useful to think about others (e.g. oligopoly). However, I think that you will find that the effect of demand on prices is often ambiguous and depends on the economies of scale that are present in the industry.


Should coefficient on interaction term be positive or negative? I have the following model for housing prices

price = $\beta_0$ + $\beta_1$ sqrft + $\beta_2$ bedrooms + $\beta_3$ sqrft $\times$ bedrooms + $\beta_4$ bathroom,

where sqrft is square feet.

I am confused regarding the interaction term. Should $\beta_3$ be positive or negative? I think that the effect of additional bedroom on house price is higher for larger houses. Is this correct?

I think that the effect of additional bedroom on house price is higher for larger houses. Is this correct?

As @emeryville said, if your question is about what the result should look like, different people may have different theories.  I think one can make a reasonable argument that going from 1 bedroom (small house) to 2 bedrooms should have a larger impact on the price than going from say 5 bedrooms (large house) to 6 bedrooms because the marginal value of adding an extra bedroom is larger in that case.

This is maybe outside the scope of your question, but based on the wording of your question, it sounds like you have a hypothesis which may not be supported by the results of your model.  So I just want to add that this could mean that your theory was wrong, but it could also mean other things, like that there is some outlier in the dataset that greatly influences the results, or that the model was misspecified in that it does not accurately reflect the true relationship between your variables.  If your estimated result was a negative $\beta_{3}$, but the true of value of that parameter is positive, that could mean that you have some omitted variables that resulted in a biased coefficient.  For example, perhaps the neighborhood location is associated with whether the effect of adding a bedroom is higher or lower for larger houses (and location is also correlated with price).  In a downtown location, both price and size could depend on different factors than a house in a suburb and the value of additional bedroom could be different.  So you would need to add location to the regression equation to obtain an unbiased $\beta_{3}$ coefficient.


The economic impact of corruption I know nothing about the 'economics of corruption' literature, whether in the medium(fluctuations) or long-run(growth)... Although I've found many surveys (mostly +5 years, and from journals I don't recognize), since I known nothing about this subject, I have no idea with which ones I should start,.
I'm looking for two pointers

One to a survey/literature review from a well-established journal (QJE, etc.)
A book on this subject, but similar in difficulty to those books for the general public like "Nudge", "Irrational Exuberance", "Trade Talks", "The Triumph of Injustice", etc.

Thanks in advance.

A very nice survey from a now well-established journal is

Olken, Benjamin A., and Rohini Pande. "Corruption in developing countries." Annual Review of Economics 4, no. 1 (2012): 479-509. Here is the ungated NBER version.
It is not new and focuses on developing countries, but it is very influential. They try to answer three questions:

what is the degree of corruption?
What are the consequences of corruption in terms of efficiency?
and what determines the level of corruption?


Socio-Economic Consequences of Nation-Wide Vegan Diet An advice I often hear regarding our environmental impact is to 'stop consuming meat and dairy products'. This is stated as the number one way to reduce your ecological footprint, according to multiple sources. Whether this is true or not, obviously much of our economy and society depends on the meat and dairy industry, ranging from farming and transport to butcheries or supermarkets.

If everyone in the United States would stop consuming meat, dairy and eggs within the next twelve months, what would be the economic consequences?
How much of a hit would the economy take?
What percentage of farmers could realistically replace their current products with vegan alternatives?
What other unintended socio-economic consequences would this scenario have?

I think your questions are very interesting. I am no expert on US farming data sources. However, I have briefly pursued these questions for the UK. As currently this question has no responses, I'll post my findings below verbatim along with my data sources.

I encourage you to pursue these research questions further, perhaps using a similar framework to below.

"My response uses DEFRA data to examine the extent of the agri-food economy that must change, in equilibrium, to complete a transition to a Vegan Economy. Although in the short run Rural Unemployment may rise, once we distribute the gains from a Vegan Economy, we can raise rural incomes and reduce rural unemployment.

Output Data

DEFRA's Food Statistics in your Pocket reveals that the Agri-Food Industry made up 6.3% of Gross Value Added in 2016. However, a Vegan Economy only entails removing animal products, which in equilibrium is unlikely to influence the distribution, retail, or catering sectors negatively; people under the vegan norm must consume sufficient calories to be healthy.

Note: The Vegan Norm assumes that people spend, counterfactually, the same proportion of income and that they eat a healthy, varied Vegan Diet. We also assume that UK Welfare can distribute any economic gains from a Vegan Economy.

Only Agriculture, Fishing, and Food Manufacturing remain relevant, which has ~2% GVA contribution. This figure overestimates the contribution of Animal Products as plant-based firms can partially fill in for Food Manufacturing. Also, these figures fail to distinguish between animal and non-animal products. The ratio of the value of plant to animal products for imports or exports is 2 to 1, calculated from Observation of Economic Complexity (OEC) data, which seems a reasonable prior for domestic production too. This data also indicates that the UK balance of trade does not suffer.

Yet, the Vegan Economy also sees growth in GVA from old and new Vegan Alternatives to Animal Products. The market for alternative products is growing rapidly across the agri-food chain. We reference The Vegan Society who have collated such evidence on their website. As such, we can expect this market to fill in the anticipated output gap.

Thus, in equilibrium, the Vegan Economy may see at most a 1% reduction in Gross Value Added from eliminating Animal Products from Agriculture and Food Manufacturing. Trend GVA growth may even rise thanks to alternative products.

Employment Data

DEFRA's Pocketbook indicates that we employ 820,000 people in Agriculture, Fishing, and Food Manufacturing. Animal Products are more labour intensive but likely make up only a third of GVA. So, perhaps half of these workers (~1% of UK Labour Force) have their employment at risk under a Vegan Economy.

A sectoral shift towards crops and alternatives could fill in the output gap, suggesting that the general equilibrium effects on employment are likely negligible.

Yet, even for those who do lose their work, we can redistribute the benefits of a Vegan Economy. These benefits include increased government revenue from higher GVA growth, reduced healthcare costs and improved productivity from healthier workers. We also avoid costs associated with accelerated climate change.

Our options for helping those farmers or manufacturers out of work include but are not limited to:
incentives to switch to crop farming
start-up programs to encourage new land use such as afforestation or sanctuaries
incentives for transport, retail, accommodation, or local government to provide training or apprenticeship schemes for those out of work. They are often the main employers in rural areas."

UK Economic Data Sources:

DEFRA (October 2018), Food Statistics in your pocket 2017 Summary
url: https://www.gov.uk/government/publications/food-statistics-pocketbook-2017/food-statistics-in-your-pocket-2017-summary

Page 7 of Rural productivity and Gross Value Added (GVA) statistics, DEFRA (2019)
url: https://www.gov.uk/government/statistics/rural-productivity

Observation for Economic Complexity (2017), United Kingdom
url: https://oec.world/en/profile/country/gbr/

The Vegan Society (2019), The Vegan Society Statistics: Business/Food Sales
url: https://www.vegansociety.com/news/media/statistics

Public Health Evidence

Chen, J., Peto, R. Pan, W., Liu, B., Campbell, T.C. Mortality, Biochemistry, Diet and Lifestyle in Rural China. Geographic study of 69 counties in Mainland China and 16 areas in Taiwan. Oxford University Press, 2006
url: https://nutritionstudies.org/the-china-study/

Academy of Nutrition and Dietetics (2016), The Position of the Academy of Nutrition and Dietetics: Vegetarian Diets
url: https://www.eatrightpro.org/-/media/eatrightpro-files/practice/position-and-practice-papers/position-papers/vegetarian-diet.pdf

British Dietetic Association (August 2017), British Dietetic Association confirms well-planned vegan diets can support healthy living in people of all ages
url: https://www.bda.uk.com/news/view?id=179

Environmental Evidence

Poore and Nemecek (2018), Reducing food’s environmental impacts through producers and consumers

CH5 page 77 Figure 5.12 of
Climate Change and Land: an IPCC special report on climate change, desertification, land degradation, sustainable land management, food security, and greenhouse gas fluxes in terrestrial ecosystems (IPCC 2019)
url: https://www.ipcc.ch/srccl-report-download-page/


Alpha interpretation in Solow growth model Consider the Solow model (without technology):
$Y = F(K, L) = K^\alpha L^{(1-\alpha)}$
What's the economic interpretation of $\alpha$? Prove and argue the result.

I see it as a share that goes into capital and $1-\alpha$ is the share that goes into labour, but how do I prove this mathematically?

I don't quite understand what you mean by "share that goes into capital", but the common interpretation is that $\alpha$ is the share of income/output spent on capital.

You can show that the following way:
Since the factors will be compensated according to their marginal products, under the assumption of competitive markets, we have (for capital):

$$
\frac{\partial Y}{\partial K}= \alpha K^{\alpha-1}L^{1-\alpha}=\frac{r}{p},
$$
where $\frac{r}{p}$ is the real rent.

So the amount of income spent on capital is equal to price times quantity, which in this case is,
$$
\frac{\partial Y}{\partial K}\frac{K}{Y}= \alpha K^{\alpha-1}L^{1-\alpha}\frac{K}{K^{\alpha}L^{1-\alpha}} \\
\frac{\partial Y}{\partial K}\frac{K}{Y}= \alpha
$$

Click here for more detail.


How are trade deficits financed? The usual answer is either "foreign debt" or "Foreign Direct Investment". But:

Why does that make sense?
And why wouldn't be financed otherwise like from importers taking out bank loans domestically rather than from foreigners?
Finally, it is said that a trade deficit can be financed by Foreign Direct Investment because the domestic currency given in exchange for the imports can only be spent back into the importing country. How does this work when whoever we're importing from is paid in THEIR currency rather than the domestic currency of the importer?

I hope someone more knowledgeable can help me out. Thanks.

Natural resources and gravity determines trade. How the balance of payments is settled is not really important. But there are a few possibilities

a country has a lot of debt and defaults or refis it down to a very low rate to go negative indefinitely;
foreign aid;
moneyprinting that isn't adequately adjusted in foreign exchange;
selling overpriced domestic assets that are not properly accounted in the bop records;
stealing things

An example of 1 would be any debt crisis.

For 3 for example, Zimbabwe was trade deficit during it's episode

For 4, US startup equity is boosting it's balance of payments. It is not fdi or portfolio investment and includes travel expenses and things not adequately tracked;

For 5, any sort of anti western government expropriating assets, like Zimbabwe, uses that to fund it's balance of payments.


CES First order Condition with two labour types I am struggling to derive a first order in this model with Cobb-Douglas production function and CES labour aggregator with two types labour (here male and female, but could be equally low and high skill).
Setup: Cobb-Douglas production function
$$
Y = A K^{\alpha}L^{(1-\alpha)} \tag{1}\label{1}
$$
where $K$ is capital and $L$ is labor, and $A$ the TFP. There are two types of labor $i \in \{F,M\}$ that are aggregated with constant elasticity of substitution
$$
L = \left[(1-\lambda) (a_M M)^{\frac{\sigma-1}{\sigma}} +\lambda(a_F F)^{\frac{\sigma-1}{\sigma}} \right]^{\frac{\sigma}{\sigma-1}} \tag{2}\label{2}
$$
where $\sigma$ represents elasticity of substitution between $M$ and $F$, $a_M$ and $a_F$ are productivity terms, and $\lambda$ is the share parameter. Combining these two equations gives
$$
Y = A K^{\alpha} \left[(1-\lambda) (a_M M)^{\frac{\sigma-1}{\sigma}} +\lambda(a_F F)^{\frac{\sigma-1}{\sigma}} \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}} \tag{3}\label{3}
$$
Solution: Setting marginal products of labour equal to wage should give
$$
W^{F} = (1-\alpha)\lambda a_F A K^{\alpha} (a_FF)^{-\alpha} \times \left[ (1-\lambda) \left( \frac{A_MM}{a_FF}\right)^{\frac{\sigma-1}{\sigma}}+\lambda \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1} \tag{4.1}\label{4.1}
$$
$$
W^{M} = (1-\alpha)(1-\lambda) a_M A K^{\alpha} (a_MM)^{-\alpha} \times \left[ (1-\lambda) \left( \frac{A_FF}{a_MM}\right)^{\frac{\sigma-1}{\sigma}} \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1} \tag{4.2}\label{4.2}
$$
Steps: So, I wanted to get the foc of equation $ \eqref{3} $ to get the marginal product of each type of labor and doing double chain rule for each powered bracket, but my result seems not to simplify to what it should.
$$
\frac{\partial Y}{\partial F} = (1-\alpha) \lambda a_F  A K^{\alpha} (a_FF)^{\frac{-1}{\sigma}} \times  \left[(1-\lambda) (a_MM)^{\frac{(\sigma-1)}{\sigma}} + \lambda(a_FF)^{\frac{(\sigma-1)}{\sigma}} \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1}
$$
Edit: Edited the FoC for the mistake. And to close this, I am putting here the simplification as suggested in the answer (hopefully without typos):
$$
 = (1-\alpha) \lambda a_F  A K^{\alpha} (a_FF)^{\frac{-1}{\sigma}} \times  \left[\left((1-\lambda) (a_MM)^{\frac{(\sigma-1)}{\sigma}} + \lambda(a_FF)^{\frac{(\sigma-1)}{\sigma}}\right) \times \frac{(a_FF)^{\frac{(\sigma-1)}{\sigma}}}{(a_FF)^{\frac{(\sigma-1)}{\sigma}}} \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1}
$$
$$
= (1-\alpha) \lambda a_F  A K^{\alpha} (a_FF)^{\frac{-1}{\sigma}} \times  \left[(1-\lambda) \left(\frac{A_MM}{a_FF}\right)^{\frac{\sigma-1}{\sigma}}+ \lambda \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1} \times (a_FF)^{\frac{1-\alpha \sigma}{\sigma}}
$$
$$
 = (1-\alpha)\lambda a_F A K^{\alpha} (a_FF)^{-\alpha} \times \left[ (1-\lambda) \left( \frac{A_MM}{a_FF}\right)^{\frac{\sigma-1}{\sigma}}+\lambda \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1}
$$
Sources:
Cahuc, P., Carcillo, S., & Zylberberg, A. (2014). Labor economics. MIT press. Chapter 3
Acemoglu, D., Autor, D. H., & Lyle, D. (2004). Women, war, and wages: The effect of female labor supply on the wage structure at midcentury. Journal of political Economy, 112(3), 497-551.

Simply multiply and divide one $\left(a_{F} \boldsymbol{F}\right)^{\frac{(\sigma-1)}{\sigma}}$ in the bracket and then take one outside the bracket. And by the way your FOC is incorrect in that $\frac{\sigma}{(\sigma-1)}$ should be cancelled out.


Sen's Liberal Paradox Economist and philosopher Amartya Sen posited that no social system could guarantee:

A minimal sense of freedom in social choice
Pareto efficiency

His original article can be found here.

In his original motivating example, he gave an example of two people faced with a scandalous book. One person thinks it's hot garbage and would prefer no one should read it, but would rather put themselves through the book than see the other person read it and enjoy it. The second person, while preferring to read the book than it be destroyed with no one reading it, would think it'd be hilarious if the first person were forced to read it.

In this scenario, suppose you let each person have some degree of choice in the matter of who ends up reading this book. So the social planner will consider whether each person would rather they themselves read the book, or throw it away. Their choices will be directly put into the social planner's preferences.

Person 1 prefers not reading the book to reading it.
Person 2 prefers reading the book to not reading it.

So the social planner will therefore have the preferences:

$$\text{P2 reads} \succ \text{no one reads} \succ \text{P1 reads}$$

And the social planner will have the second person read the book. This is not a Pareto optimal result! Both people would rather the first person be made to read the book.

There are a few ways out of the paradox:

Let the two people make a contract to bargain their way to a better result.
Let them express their "preferences" sequentially, as a game.
Lighten the restriction on needing Pareto efficiency specifically
Only care about societies where everyone respects each others' choices and don't create weird externalities (societies that don't do this are the only ones that have this paradox).

So my general questions are:

  Are there other solutions to the Liberal paradox?
  Beyond abstract ideas of social justice, what practical implications could the paradox have on markets?

Another solution can arise if you allow for uncertainty and for the planner to provide private information to each player. See Bergemann and Morris, 2018 for a survey in what is called information design. In that way, it is not hard to see how each player can be convinced that the social allocation is its most preferred outcome with high probability such that from the ex-ante perspective, the outcome is Pareto-optimal.

Of course, I'm throwing a lot of details under the rug, but having asymmetric information seems like another solution to this conundrum.


Is there a term for a game whose pareto optimal solutions and nash equilibria are disjoint? Is there a term for a game whose pareto optimal solutions and nash equilibria are disjoint?

(e.g. prisoner's dilemma)

The term I often come across is 'inefficient Nash equilibrium' or 'Pareto-inefficient Nash equilibrium'. Here is an older well cited article discussing inefficient NEs: http://www.jstor.org/stable/3690047?seq=1#page_scan_tab_contents

Here is the frequency of the term 'inefficient Nash equilibrium' used in scientific papers:
https://scholar.google.com/scholar?q=%22Inefficient+Nash+Equilibrium%22&btnG=&hl=en&as_sdt=0%2C5

'Inefficient outcome' is also frequently used to describe NEs that are not Pareto-optimal: https://scholar.google.com/scholar?q=%22Inefficient+outcome%22&btnG=&hl=en&as_sdt=0%2C5
But it has to be put into game-theoretical context and specified that it is NE.


What's the name of this pairwise price-setting scheme? Two siblings inherit equal shares of a house. To decide who gets to live in it, they each bid what they think the other half is worth. The person with the higher bid gets it, and pays the other sibling halfway in between the bids. Therefore, everyone gets better than their bid: the seller receives more and the buyer pays less. Does this scheme have a name?

This is known as the "split-the-difference" mechanism, originally due to Samuelson (1985). See Section 6 of Gibbons et al. (1987) for a discussion of this rule. In particular,

this kind of rule only efficiently dissolves the partnership between the two siblings if they have equal (or sufficiently close to equal) shares in the house. Precisely, each sibling should own no more than 57.7\% of the house.
such a mechanism does not typically induce an equilibrium with sincere bidding (i.e., the siblings will report less than their true value for the house).


Confusion over shut-down point In my textbook, the shutdown point is defined as the intersection between the average variable costs curve and the marginal costs curve. Suppose Company A has total costs function $TC(q_A)=\frac{1}{2}q_A^2 + 6q_A + 10$. Then its marginal cost is $q_A + 6$ and its average variable cost is $\frac{1}{2}q_A + 6$. Setting those equal I only get zero, does that mean there is no shutdown point? This is part of a bigger exercise where the author says to pay attention to the shutdown points so I imagine it's not zero. What gives?

I think that potentially your teacher made a mistake (unless this is some tricky 'gotcha' problem) or if the problem involved actually creating the total cost function from some piece of text there might have been mistake in creating the total cost function. If you dont think that applies then read on.
1. Shut down point is at q=0
The first possibility is that indeed shut down point is simply zero. The shut down point is the point at which average variable cost ($AVC$) reaches its minimum - the minimum point can be either found by calculus (by minimizing the $AVC$ function) or indeed by equating $AVC$ to marginal costs MC $AVC=MC$.
The intuition for this is that normally the average cost curve will always decline when $AVC>MC$ and starts increasing only when $AVC<MC$ because marginal cost is the cost for the last product and intuitively if the last added variable to the sample is higher than average of sample then addition of that new variable increases the whole average and vice versa. As a consequence the minimum of average cost curve will be reached when $MC=AVC$ See the example below from Mankiw principles of economics:

However, in your case marginal cost is always above average variable cost ($MC>AVC$) except when $q=0$ when they are actually equal. You have a special total cost function which has average cost function and marginal cost function that looks nothing like the one in textbook. In fact I decided to model your cost function in R in order to drive the point. This is how your marginal cost (in blue) and average cost (red) look like:

As you can see in your case the marginal cost (blue line) is always above average variable costs (red line) except for when $q=0$.
2. Could your teacher possibly mean firm exit (long-run shutdown)?
It is not uncommon for teachers to call exit from the market long-run shut down (see one example here from Texas tech university lecture notes). In the case your teacher meant exit as a long-run shut down then long run shut down point would be given at an intersection of average total cost and marginal costs (see below example from Mankiw's principles of economics).

In this case $ATC=MC$ would equate at some non-zero $q$
3. The above only gives you $q$ coordinate of shut down or exit point
Note that in both examples provided above for firm to actually shut down or exit the price needs to be below the minimum AVC (shut down) or ATC (exit) respectively. The shut down quantity $q_{\text{shut down}}$ only tells you the $x$ coordinate at which AVC reaches its minimum. To see how firm will actually behave you need to always check whether the price (which will be on $y$ axis) that correspond to the shut down coordinate is actually lower than either minimum point on AVC (in case of shut down) or ATC (in case of exit) as shown in the pictures from the Mankiw's textbook.


Nash equilibrium - mistake in proof of paper? I have a question regarding the proof of Proposition 1 in Besley and Ghatak (2007) in Appendix A of their paper. It is a quite highly cited paper but I believe there is a mistake in the proof of their Proposition 1. The model is described in Section 2. of their paper. It is a very simple model that seeks to derive the Nash equilibrium of the market. In particular, they show that $\theta_c^*$ must satisfy $f'(n \theta_c^*) = \alpha$ in equilibrium. In their proof in the appendix they state:

However, I think there is a mistake because the package $(p', \widehat{\theta'})$ does not make each caring consumer strictly better off.

The new package $(p', \widehat{\theta'})$ gives utility:

$$b-p'+f(\widehat{\theta'} + (n-1)\widehat{\theta}) $$

The old package $(p, \widehat{\theta})$ gives utility:

$$b-p+f(n\widehat{\theta}) $$

The new package is strictly preferred to the old package iff

$$b-p'+f(\widehat{\theta'} + (n-1)\widehat{\theta}) > b-p+f(n\widehat{\theta})$$

$$ f(n\widehat{\theta} + \Delta \widehat{\theta}) - f(n\widehat{\theta}) > \Delta p$$

If we make the substitution as stated in the paper: $\Delta p = f'(n\widehat{\theta}) \Delta \widehat{\theta}$ and assuming we want a positive $\Delta \widehat{\theta}$, then the above becomes:

$$\frac{f(n\widehat{\theta} + \Delta \widehat{\theta}) - f(n\widehat{\theta})}{\Delta \widehat{\theta}} > f'(n \widehat{\theta}) $$

If we pick a negative $\Delta \widehat{\theta}$, then the above condition becomes

$$\frac{f(n\widehat{\theta} + \Delta \widehat{\theta}) - f(n\widehat{\theta})}{\Delta \widehat{\theta}} < f'(n \widehat{\theta}) $$

But $f$ is a increasing and strictly concave function, so the above inequalities are always false. So the new package is never preferred to the old package. Everything else in the proof is fine apart from this step and this is the most crucial step of the proof as it characterizes what $\widehat{\theta}$ should be in equilibrium, if this is wrong then many other results in the paper are also wrong.

So, is there a mistake in this part of the proof of the paper? And if so, is there a way to correct it so that the results still hold?

The objective is to show that, as long as $f'(n\hat\theta)\ne \alpha$, a firm can always engineer a package $(p',\hat\theta')=(p+\Delta p,\hat\theta+\Delta \hat{\theta})$ such that (i) a caring consumer strictly prefers this package, and (ii) the firm makes positive profits.

1) Your maths are correct: the inequalities are always false when f is increasing and strictly concave. In that case, the proof in the paper is unclear.
The package $(p',\hat\theta')=(p+f'(n\hat\theta)\Delta \hat{\theta},\hat\theta+\Delta \hat{\theta})$ does not satisfy (i).

2) You can show the proposition with the following reasoning.
Assume $f'(n\hat\theta)>\alpha$. Take any $h$ within the interval $(\alpha,f'(n\hat\theta))$.
For $\Delta \hat{\theta}$ small enough and positive, a firm that offers the package $(p',\hat\theta')=(p+h\Delta \hat{\theta},\hat\theta+\Delta \hat{\theta})$ satisfies (i) and (ii). With a first-order appoximation, we show (i): $$b-p'+f(\hat\theta'+(n-1)\hat\theta)>b-p+f(n \hat\theta),$$
and (ii):
$$\Delta p - \alpha \Delta \theta>0.$$

Assume $f'(n\hat\theta)<\alpha$, and take $h$ within the interval $(f'(n\hat\theta),\alpha)$.
For $\Delta \hat{\theta}$ small enough and negative, a firm that offers the package $(p',\hat\theta')=(p+h\Delta \hat{\theta},\hat\theta+\Delta \hat{\theta})$ satisfies (i) and (ii).


Is Debt Monetization Equivalent to transferring money from rich to poor? I'm reading Ray Dalio's "How the Economic Machine Works", and he says that there are four factors contributing to deleveragings in economies:

1) Debt Reduction

2) Austerity

3) Transferring wealth from the haves to have-nots

4) Debt Monetization

However, to me it seems like debt monetization is equivalent to transferring wealth from the haves to have-nots -- am I correct in my assumption?

Debt monetization leads to inflation which means that cash and Accounts Receivable get cheaper. That would mean that cash holders and creditors would get punished. Since creditors are wealthy people, aren't we basically reducing the dollars received by wealthy people and giving that money back to poor people through job creation?

Just want to make sure I'm understanding correctly.

Thanks!

In the US, broad debt monetization would produce the following losers:  owners of cash, bonds or equivalent fixed income securities- notably, China, Japan, and the other foreign US creditors, and entitlement holders such as pensioners.  The winners would be:  anyone who owns a real asset on a leveraged basis, such as property owners who have a mortgage, corporations who have borrowed a lot versus their cash flows.  This isn't really rich->poor, it's lender-> borrower.   This seems like an attractive policy for the US, although there's a very strong argument that the US dollar will permanently lose its reputation as a store of value if it were ever implemented.


Market Power and Prices in the US I'm trying to get a measure of market power in the US. Here's what I'd be interested in, ranked from best (what I'm really after) to worst (stuff that kind of hints at my measure, but isn't really it.

Price distributions of similar goods in the US, by county/state
Average markups for different goods, by county/state
Average [other characteristic that correlates with higher firm market power], by county/state

Importantly, I'm after price distributions of goods consumed in state A, not produced in state A.

I guess I could use the Nielson data set to get some proxy of price distributions, but I don't think that's the strength of the data set. What else is there?

A paper just out of the oven provides a very comprehensive analysis of market power in the US for more than 50 years, using mark-up data from three different sources. The key graphs below:


Sources on Border Carbon Adjustment A large number of US economists have signed a Statement on Carbon Dividends, advocating a revenue neutral carbon tax as the best policy measure to reduce carbon emissions and so mitigate climate change.  The statement also advocates (para IV) a border carbon adjustment system to ensure that such a carbon tax would not encourage carbon leakage (ie transfer of production to another country with a laxer carbon regime) and damage US competitiveness.

What are good sources explaining how a border carbon adjustment system might work, the pros and cons of such a system, and lessons from attempts (if any, anywhere in the world) to operate such a system?

I found some references that might help you explore this topic. Other topics like game theory can also be applied to border carbon adjustments.
LSE: https://www.lse.ac.uk/granthaminstitute/publication/the-global-consumer-incidence-of-carbon-pricing/
This is an excerpt from the website: "the author investigates complementing the EU ETS with a carbon price on traded goods, through so-called Border Carbon Adjustments (BCA), and finds this would most affect the poorest as well as the richest consumers in the EU. This is the first estimate of the EU-wide consumer incidence of BCA to complement the EU ETS." They have a working paper you can download.
LSE: https://www.lse.ac.uk/granthaminstitute/wp-content/uploads/2012/04/Trade-climate-change-game-theory-border-carbon-adjustments.pdf
Here is an excerpt from the abstract: "This paper
advances two arguments. First, it argues that the conventional view of Border Carbon Adjustments (BCAs) as a “dirty” trade barrier should be turned on its head. Rather, the absence of a carbon price comprises an implicit subsidy to dirtier production in non-regulated markets. Second, BCAs could act as a gamechanger when climate policy negotiations move at a glacial pace, if at all. Materially stronger progress could be achieved indirectly from the threat of unilateral trade policies. The paper shows how this could come about, using a simple political game theory model."
Vivid Economics: https://www.vivideconomics.com/casestudy/border-carbon-adjustments-and-industrial-competitiveness-in-a-european-green-deal/
Here is an excerpt from the website: "Driving industrial decarbonisation while safeguarding international competitiveness is a major policy challenge. As part of the European Green Deal, the EU is considering the introduction of a Border Carbon Adjustment (BCA) to ensure that the price of imports into the EU more accurately reflects the environmental costs of their carbon content. BCAs could be an alternative to free allocation to emissions-intensive trade-exposed sectors as a measure to address the risk of carbon leakage in the EU’s ETS." They have a report you can download too.


Remove Linear Good From Quasi-linear Utility Function Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$,  $\beta > 0 $

What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) = f(x_1)$? If so, would the demand function simply be $x_1 = m/p_1$? I want to find the new demand function as well as the new indifference curves and draw these in a diagram, but I am unsure how to proceed. Surely I cannot graph them in $x_1, x_2$ space if there is no more $x_2$. Or would I still graph them in $x_1, x_2$ space as vertical lines?

I hope my question is understandable, thx for any help.

This is one possible interpretation. Good 2 being removed from the market can simply be interpreted as $x_2 = 0$. In an economic interpretation the good does not simply disappear from the utility function in the sense that preferences do not change, it is just the availability of the good that changes. This is an external condition, so you can simply think of this as a market constraint $x_2 = 0$.

Now, looking at indifference curves as the different bundles for which the consumer obtains the same level of utility, and defining this level as $k$. It is clear that for any $k$ when there is only one good, each "indifference curve" will consist of only one point (in particular $x_{1}|u(x_1,0) = k$). In a 2-D graph this will simply correspond some point ($x_1$,0) for each $k$ level.

The demand function should be quite straightforward.


Are stock trade commissions evidence of anti-competitive practice? A typical commission on a typical stock trade these days is $8. I don't understood how it can cost this much. It looks like the entire process is happening in software, electronically, and so the actual cost to the parties that supply this service should be near zero.

So I'm wondering, where does that money go? Is someone making a profit? Are they protecting that profit with exclusive dealing, collusion, or some other anti-competitive practice?

The money goes to banks/brokers. In fact most of the revenue in the financial sector comes from fees like that.

This is to compensate the bank/broker from taking the risk of carrying the opposite position on their books for a while, and the labor put into actually trading for you. A part of it is probably also profit. Since there are large entry costs, one would expect the financial sector to earn  profits.


Minimum wages - what is the effect? Does anyone know a good review on the debate on effects of minimum wages?
I am interested both in academic and non-academic sources. I have searched a lot but there is so much material written on minimum wages that it seems a bit like a jungle. Anyway, I have not been able to find any non-biased reviews of the research on the topic.

I will focus on academic literature reviews since they tend to be unbiased (or at least less biased) - academic literature reviews are often accessible even to non-specialists as they usually do not go deep into models as they try to provide broad overview of the topic:
Good (and highly cited) literature review on this topic are:
Neumark, D., & Wascher, W. (2006). Minimum wages and employment: A review of evidence from the new minimum wage research (No. w12663). National Bureau of Economic Research.
Card, D., & Krueger, A. B. (2015). Myth and Measurement: The New Economics of the Minimum Wage-Twentieth-Anniversary Edition. Princeton University Press.
Neumark, D., Wascher, W. L., & Wascher, W. L. (2008). Minimum wages. MIT press.
Manning, A. (2020). The elusive employment effect of the minimum wage. Journal of Economic Perspectives.
Doucouliagos, H., & Stanley, T. D. (2009). Publication selection bias in minimum‐wage research? A meta‐regression analysis. British Journal of Industrial Relations, 47(2), 406-428.
Neumark, D., Salas, J. I., & Wascher, W. (2014). More on recent evidence on the effects of minimum wages in the United States. IZA Journal of Labor policy, 3(1), 24
Maloney, W. F., & Nunez, J. (2000). Measuring the impact of minimum wages: Evidence from Latin America. The World Bank
However, note there is no full consensus in economics on minimum wages. For example, have a look at (this recent pol among the best US policy economists on effects of increases in the minimum wage on us employment) and you will find that most policy economist are uncertain, and the 'pro' and 'against' camp are almost equally split.
Consequently, you will see that some of the papers/books above are more cordial and some more critical of minimum wages - this does not mean the researchers are biased. Sometimes it is very hard to read empirical evidence and to reach some 'definitive' conclusion. For example, one reason why there is so much controversy is that in principle you should expect even relatively large increases in minimum wage to have smaller effects where original minimum wage was far below median wage and different ones when it is closer to median wage. This can often lead to situations where research in different places might yield contradictory evidence.
In such cases people will disagree and it is very hard not to tilt toward one side of an argument or the other but that is not necessarily evidence for  bias per se as people can emphasize different things. In the above list I strived to strike some balance among those economists who are less and more cordial toward minimum wage (although I think both sides of the debate try to be unbiased) so together it should make a balanced overview. Lastly, the above is just tip of an iceberg minimum wage is probably one of the most extensively researched economic policies but they should help you to orient yourself in the literature and also point toward solid primary research on the issue.


Help with undergrad econometric project I am working on undergrad research in econometrics and am seeking some advice/help in terms of finding data sets and picking variables. I have an idea chosen for my topic, but I need to make a official proposal including a rough linear regression equation to turn in to my teacher soon.
My topic idea is to observe the causes for recent decline in female labor force participation in the US. I am hoping this topic is not too broad. Initially, I was going to look at whether campaign spending impacted voter share in Senate races from 2012 data sets, but I find this idea a tad boring and would like to make my new idea work if possible.
My ideas for variables include the obvious: age & teen participation rates (16-24), race/ethnicity, educational attainment, children, martial status, avg weekly hours worked, etc. However, I wanted to also see if the increase in opioid addiction in the US could also be having an impact on labor force participation specifically for women, as well as paid family leave benefits in the US vs other countries and labor force participation of immigrant women.
So with all said, does anyone have any suggestions for me both as to whether this topic is viable as a project in my course, as well as where I could find the data for such a topic? I have been reading a lot of literature on the topic, but having a hard time finding actual data sets that I could use for regression.
Thanks!

Can you provide your research question in one concise sentence? It seems like you've proposed half a dozen topics some of which are peripherally related. You need a quantifiable dependent and independent variable as well as essential control variables.

The question needs to be quantifiable and have a wealth of data already available. I'd highly recommend for your undergraduate paper instead of asking a question and then searching for the data to back up the answer, you instead peruse some interesting data sources and ask a question based on what is available.

Check out sites like https://www.data.gov/open-gov/ which have a wealth of easily downloadable datasets that you can explore. Find datasets related to topics that you find interesting and go through the available data and begin to think of what can act as an independent or dependent variable. Base your question so that the dataset you have already found and think is interesting perfectly fits instead of the other way around.

Unless you plan to do original research it will be quite difficult to simply find data to fit your question unless you already knows it exists.


depreciation in income approach of GDP I have some doubt regarding gdp sector, while measuring gdp by income approach, we add depreciation. My doubt is: does the cost of goods that go into replacement of existing worn out capital is only treated as depreciation? Or do we also add the depreciation expense of all existing and serving goods, which have not worn out?

In theory, depreciation is a reduction of the capital stock. This includes capital assets that have actually been worn out and also capital assets that are not usable any more for any other reason (conceivably old machinery after upgrading to a new technology or so).

In practice, macroeconomic datasets infer depreciation either from what the firms in the economy in question say in their accounting or from changes in the capital stock that are not explained by any other influence (investment, dissolution and selling of the firm, ...); this is data that also comes from the firm's accounting. Note that this is not necessarily the same as the actual depreciation according to the theoretical definition since there may be any number of reasons for firms to write off capital assets early or late or at any given time. The formal rules for what practices in terms of write-offs are lawful or not are quite complicated and differ between legal systems (i.e. between countries).

Further, macroeconomic models sometimes simply assume a fixed depreciation rate which they then proceed to compute from averaging over the time series constructed from investments plus the differences in capital stock and dividing by the capital stock. This is, of course, not the way it should be done but nevertheless ...