How can the Fed enforce exit criteria if they begin yield curve control?

History and Theories of Yield Curve Control (20 pages)
https://www.boj.or.jp/en/announcements/press/koen_2017/data/ko170111a1.pdf

Lastly,  as  the  fourth  issue, I  would  like  to  touch  upon  the  relation  between  fiscal  management  and  yield  curve  control.  As  I  noted,  yield  curve  control  by  the  Bank  differs  from  the  government  bond  price-supporting  policies  once  implemented  in  the  United  Kingdom and the United States. While these policies aimed to minimize financial costs of the government, the Bank's current policy aims to overcome deflation and achieve the price stability  target.  Given  that  the  policy  directly  sets  the  long-term  interest  rates  as  its  operational   target,   however,   it   is   undeniable   that   the   area   deeply   related   to   fiscal   management expands. Not surprisingly, therefore, there are voices of concern and criticism that  the  current  policy  coincides  with  money  finance  or  monetization,  or  that  the  exit strategy of  the  policy  will  be  constrained  by  consideration  for  fiscal  management.  It  is  therefore   important   that   the   Bank,   bearing   in   mind   those   voices   as   well,   gain   the   understanding  of  the  markets  and  the  public  by  releasing  more  carefully  than  ever  the  information on the purpose and ways of thinking about monetary policy implementation.

Quantitative Easing: Entrance and Exit Strategies (16 pages)
https://files.stlouisfed.org/files/htdocs/publications/review/10/11/Blinder.pdf

Because many of the Fed’s unorthodox quantitative easing policies put taxpayer money at risk, these policies constituted quasi-fiscal operations — equivalent to investing government funds in risky assets.

I would argue that there was less spare capacity in the economies after World War 2 due to destruction of assets in many countries and due to wartime restrictions of consumption and investment. Also the household sector in the United States emerged with a relatively clean balance sheet where collateral assets were not saturated with private debt. By contrast the economies with QE today have spare production capacity and assets saturated with greater burden of private debt. I am not aware of any econometric series that compares the private debt to government debt. Rebel economist Steve Keen publishes some charts making these comparisons of private to public debt but I have not drilled down into his sources of data.


When to use the market and when to use central planning?

There is a school of thought that says that people unconsciously use cost-benefit analyses in their relationships with other people. In this idea, people show kindness only because they anticipate getting rewarded for those acts, so it is in their own self-interest to do so.

Monetizing small tasks takes time, and then collecting money for tasks done takes more time. So people do this mentally instead, moreso by feelings than rational calculation. At the level of an interpersonal relationship, words and feelings matter whereas in a business relationship, only tasks and services or goods rendered matter. Thus, monetizing the countless miniscule interactions that take place in a personal relationship would be impossible and there needs to be some degree of trust to replace that.

At the level of a firm, an employment contract stipulates generally what somebody is being paid for. It is more efficient for the company to let individuals decide what to do in a day, or to instruct them to undertake certain tasks (depending on the organizational structure of the firm) than to spend time haggling for a price at which they should be paid in order to carry out various parts of their jobs. As other users have commented, when a firm gets too large, there are diseconomies of scale as it becomes too difficult to control a large number of workers. Then work tends to be contracted out to other firms and the use of money comes in.

However, token economies work well in situations such as mental asylums, to encourage those people to undertake tasks and follow rules.


Demand curve is same as Marginal Benefit curve?

Nuance matters:
In the comments under 1muflon1's answer the quote given is

The demand curve represents marginal benefit. The vertical distance at each quantity shows the mount consumers are willing to pay for that unit. Willingness to pay reflects the benefit derived from each unit.

So the actual claim is not that the demand curve is the same as the marginal benefit curve, but that it represents it in some way. To be even more precise, the inverse demand curve represents marginal benefit. The demand and inverse demand curves are often conflated as these mappings are represented by the same graph.


How to interpret Employment Elasticity in this text?

I'm citing the first two lines of the article you refer to (emphasis mine):

  The debate among researchers about the employment effects of minimum wages remains intense and unsettled. There is clear variation in the magnitude of estimated employment effects across studies, with the debate often being between an elasticity for low-skilled groups equal to (or indistinguishable from) zero, or an elasticity in the range of −0.1 to −0.2.

Mechanically, you can always compute elasticities of any two variables w.r.t. each other at an initial point $b$, which is defined as

$$\eta_{a, b} = \frac{\partial a(b)}{\partial b}\frac{b}{ a(b)}$$

Simply googling employment elasticity gives you

$$\eta_{employment, X}$$

where $X$ is the unknown. What is it, that employment is elastic towards?

The article makes clear that indeed, $a$ in this context is the employment rate, while $b$ is the level of the minimum wage.

Instead of googling, you could have looked at any of the studies cited in the article. The first sentence in Dube et al (2010) actually states that

  We use policy discontinuities at state borders to identify the
  effects of minimum wages on earnings and employment in restaurants
  and other low-wage sectors.

So they're interested in two related elasticities, one of which was the one you initially suspected. Their table 2 will give you some estimates of those elasticities.


Are bank reserves part of M1 or only part of M2, and why?

Using the Federal Reserve's definition for M1 (warning, M definitions can vary between countries, so always check the local definition):

  "M1 is defined as the sum of currency held by the public and transaction deposits at depository institutions (which are financial institutions that obtain their funds mainly through deposits from the public, such as commercial banks, savings and loan associations, savings banks, and credit unions)."

Note, reserves are not counted as part of M1. The explanation for that is in the answer here:

How does a cash deposit change the M1 Measure of the Money Supply

So in question 1) we are told that Toyland earns cash and uses it to pay down a short term loan from Bank One. Critically we are not told where Toyland has its account. Note, we can't assume that Toyland doesn't have a bank account, since the bank would have insisted on it having one to receive the loan. We'll assume to make things simple it was Bank One.

If it receives cash from the public that was not in the banking system, then Bank One's cash reserves would increase. At the same time so would Toyland's deposit account, so there is no change to M1 at that point in time. The decrease in the 'cash held by the public' outside the system is matched by the increase in the deposit account at Bank One.

Now Toyland pays off its loan. There is no change to the cash reserves, Bank One simply decreases its loan book, and removes the money from Toyland's deposit account. So M1 decreases, because the loan is repaid and the liability deposit money is removed from the banking system. M2 is essentially M1 + some savings deposits and money market funds, so M2 will decrease as well.

2) Bank of America takes $25k from its cash reserves and makes a loan.

Actually, Bank of America doesn't do that. Bank of America makes a loan by creating a liability deposit account/entry for that amount, and a matching entry in its loan book. Creating that deposit money increases M1 (and M2). Whatever Sissy does with the money subsequently is irrelevant.

Bank Nerd Trivia... 10% is the figure used for reserves in the example Keynes wrote for the 1931 Macmillan report, which has been subsequently copy and pasted into the textbooks. I've never seen an actual banking system that uses 10% - in 1930's reserve ratios were usually 20%+, whereas these days they are down to 1-2% in Europe. Although the US has a 10% reserve rate on "Net Transaction Accounts", it has a 0% rate on all other accounts, which makes the actual rate open to account classification decisions by the US banks.

Keynes has a lot to answer for btw., the textbook description is horribly confusing, and also partially incorrect. (Try applying loan repayments to the examples it uses.)


Graphically detecting heteroscedasticity in OLS

You can visually inspect for heteroscedasticity in the disturbances by plotting the regression residuals against the fitted values and then checking if you can discern some pattern to the spread of the residuals in the scatterplot. The idea here is that the variance (spread) of heteroscedastic errors $\varepsilon_i$, conditional on the explanatory variables $X_i$, is not constant:

$$ Var(\varepsilon_i | X_i) \neq \sigma^2.$$

You can also explicitly test for heteroscedasticity in a linear regression by using statistical tests such as Breusch-Pagan or White.


Why do graphic card prices rise due to bitcoin miners?

I thought someone would have answered this by now.

Folks will argue but bitcoin is still a relatively new currency. A couple of regulations here, some stolen money there, and a lot of people may stop using it.

NVidia and AMD's target market (gamers and graphics designers) have a fairly predictable demand. This bitcoin thing is a new category and no one knows where it will be a few years now. Chip manufacturing (unlike say software development) is a heavy investment industry. Investment in factories, people and minerals.

It takes a while to ramp up production in order to satisfy the demand of this new category of coin miners. What if, by the time, the ramp up is completed, the miners have left?

This uncertainty is probably why they are taking it slow. let the market adjusts itself while they ramp up slowly.


There is no universal definition of a modified IS-LM framework. There are several modifications out there. Some such modifications include adjusting the model to capture the last financial crisis or opening the economy with the BP curve as you said, or more explicitly considering the role of banks. Another modification is the IS-MP model, which represents a more realistic version of monetary policy.


Why don't shipping businesses own their own shipping containers?

First, it appears there are historical reasons: it was the initiative of the producers to standardize the way their goods were transported, already from the factory. And it involved transportation by rail initially, rather than ship. See interesting information here.

Second, I see an economic rationale: overseas commerce is rather volatile, especially at individual-shipping-company level. In such a situation, it would be difficult for each individual shipping company to optimize the number of containers owned. But if there are companies that lease out containers to all the shipping industry, fluctuations dampen and overall capacity is more easily optimized.

Another approach can be found here, where on the subject the authors write

  “Own or lease?” The question has long lain at the heart of container-shipping strategy. From our analysis, the industry typically
  relies too much on leasing. While leasing may be the only option for
  many cash-strapped liners that already have substantial debt, other
  lines should take advantage of this by owning more of their fleet.
  Leasing does provide a little more flexibility to change vessel
  deployment. But that breathing room often comes at too high a price.

The "substantial debt" usually comes from building/buying new ships.


In competition policy (part of microeconomics), market power is often defined as the ability of a firm to raise and maintain prices above the levels that would prevail under competitive conditions (with obvious adjustments if the market power is held by a buyer).  Having market power does not necessarily mean it is used or abused, just that it can be

See for example:

https://stats.oecd.org/glossary/detail.asp?ID=3256
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/284400/oft415.pdf


Does labor negatively affect output (from empirical perspective)?

The negative coefficient could imply decreasing returns to scale under some specifications. For example, Miller & Upadhyay (2002) show that under certain assumptions (see the paper for details) the Cobb-Douglass functions of a form $Y =AK^{\alpha}L^{\beta}$ could be rewritten as:
$Y =AK^{\alpha}L^{\alpha +\beta-1}\implies \ln Y = \ln A + \alpha \ln K + (\alpha+\beta-1)\ln L$
The authors even find some negative estimates for coefficient on labor, although most of them not statistically significant. However, the study above is done on a panel with short $T$ and might not necessarily be applicable to time series setting that you seem to imply you are having by only including $t$ subscripts.
Moreover, if you just directly applied the specification you are showing above most likely your coefficients are biased so that could be an explanation for this result.
As pointed out by @Bertrand in his +1 comment there is likely to be an endogeneity present, and hence it is common to use methods that address that. For example, the Wooldridge method that relies on GMM is becoming very popular in the literature (see . Wooldridge, 2009), and some older but still popular approaches include the
Levinsohn and Petrin (2003) or Olley and Pakes (1996)  approaches. Also,  Van Beveren, I. (2012). Total factor productivity estimation: A practical review and sources cited therein provide good overview of different estimation methods.
Furthermore, if you are estimating the production function on datasets with long $T$ you need to take into account possible unit-roots (or use some cointegration models) and in addition to the stochastic trends also deterministic ones. If you run this on a time series data I would find it very likely that the result is just due to some stochastic or deterministic trend that was not properly taken into account.


Hypothetical: If a nation produces absolutely no good or service, would the currency notes it has have any value?

I'd say no. No production is required for a money to have value. Money can be valuable  because it facilitates trade. That is, whatever good is used as money can be more valuable than its intrinsic value because it is an liquid instrument that can be used in trade with others to solve the double coincidence of wants problem. Even pure endowment economies can utilize money for this purpose as long as people are not endowed with bundles that are also their equilibrium bundles and the economy is one in which money has a use (see Starr (2003) for several examples of how this can happen). Essentially, money is needed in circumstances where barter and good specific debt is costly or impossible.

For a famous example of an economy without production that did use money consider Radford (1945),
The Economic Organisation of a P.O.W. Camp. In this paper Radford documents how the POW inmates, despite having no production to speak of, with all goods provided by either the captors or the Red Cross, use loose cigarettes as money to price goods and solve the double coincidence of wants problem.


In Smith's theory, what is the difference between the "nominal price" vs. "market price" and "real price" vs. "natural price"?

Adam Smith in his writing defines the nominal as the price of something at a given time counting prices out of market equilibrium. He refers to it as the price at what something is exchanged between two individuals not taking into account general market conditions or particular affairs at given time.

It's just the price in monetary terms at what something it's exchanged and can or cannot represent the fair trade for one or both parties at a given period.

Market price for Adam Smith is the price at what something is generally traded in the market at given time. It is different than the nominal price and sometimes it's rare when they are the same but nominal price should tend to market price if certains conditions are met in a most free and untroubled markets.
Adam Smith also writes about free market irregularities, monopoly in labor , capital or land markets.

He also makes an extended analysis and compares a market price for gold and silver and how it is different in terms of time periods or given countries due to; coin making fees, coin metal compound, weighting devices and standards, easyness of purity verification or just shortage and abundance of metal resource among others.

The real price he writes is what something costs to produce purely by it's labor value required to obtain it, via exchange or by producing it. I quote "The real price of everything is what anything costs for the person whom wants to posses it, the effort and the fatigue that his adquisition requires."

The natural price for Adam Smith is the price that justly covers the average cost rates of, land leasing, labor wages and capital gains destined to produced it and sell it on the market, and nothing more. Then he writes we could say something is exchanged by it's natural price when that price represents the minimum or cero gains for the factors required to produce it.

I make the observation that those are the 3 main factors that make posible the exchange of a product or service in terms of the classical economic view established by Adam Smith and his contemporary collegues.


Inclusion of firms on the efficient frontier of a Production Possibility Set

Though I echo many of the sentiments posed by @AlecosPapadopoulos, maybe this would be helpful for your understanding. Ultimately, we can consider the efficiency frontier as the firms that make up the most efficient ways (or methods of production) of generating a particular output. For example, if our initial bundle of inputs was (listing them in $(x_1, x_2)$ pairs) $(2,5)$, the only firm that can generate a unit of output is firm E, hence its inclusion on the efficiency frontier.

But what about any bundle like $(4,3)$ or $(5,2)$? Clearly firms A and D can produce one unit of output with the first bundle, and firms D and F can generate one unit of output with the second bundle. However, in both cases, only firm D is the most efficient producer.

(Why do we care? Perhaps if we're trying to consider the firm that satisfies a cost minimization problem. Suppose the price of each unit of $x_1$ is $1$ and the price of each unit of $x_2$ is $2$. Which firm will produce with the lowest cost? Firm D's production costs are only $\$8 $ per unit of $y$ (while both C and E's costs are $\$10$ per unit of output!), and hence if all goods are undifferentiated the cost curves are constant, firm D will dominate the market).

Hope that clarifies a bit- let me know if I totally misunderstood your confusion.


If $S_Y$ is the amount saved by $Y$ in the first period, and $T_X$ is the amount transferred by $X$ to $Y$ in the second period, then $X$'s payoff as function of his choice $T_X$, taking as given $Y$'s choice $S_Y$ is
$$\ln(I - T_X) + a\left(\ln(I-S_Y) + b\ln(S_Y+T_X)\right)$$

$X$ will choose $T_X$ by solving the following problem :
$$\max_{T_X \geq 0} \ \ \ln(I - T_X) + a\left(\ln(I-S_Y) + b\ln(S_Y+T_X)\right)$$

First-order condition for optimality is:

$$\frac{1}{I-T_X} =\frac{ab}{S_Y + T_X} $$

Solving it for $T_X$ we get,

$$T_X = \frac{abI-S_Y}{ab+1}$$

This is the best response transfer function of $X$.

Now we solve $Y$'s utility maximization problem in period 1, taking as given $X$'s best response function of period 2.

\begin{eqnarray*} \max_{S_Y\geq 0} & & \ln(I - S_Y) + b\ln\left(S_Y + \frac{abI-S_Y}{ab+1}\right)\end{eqnarray*}

which can be rewritten as

\begin{eqnarray*} \max_{S_Y \geq 0} & & \ln(I - S_Y) + b\ln\left(I+S_Y\right) + b \ln\left(\frac{ab}{ab+1}\right)\end{eqnarray*}

Solving it we get
$$S_Y^* = \max\left(\frac{(b-1)I}{b+1}, 0\right) $$

Since $b \in (0, 1)$,
$$S_Y^* = 0$$

Consequently,
$$T_X^* = \frac{abI}{ab + 1}$$


How to make a timeline in given problem?

End of the 14th year is essentially the same as the start of the 15th year. As in, you need to apply the interest for the 14th year before you withdraw the $309.

This problem has several steps and is most easily solved in reverse. First you need to figure out what principal A you need to withdraw $309 for 5 years. Second, you need to figure out what principal B you need with 8% interest over 2 years to reach principal A. Lastly, you need to find what annuity payment needs to be made each year for 12 years to reach principal B. That will be your answer.


Numeraire negativity to avoid boundary solution

Consider $u(x,y)=2\sqrt x+y$, and the budget constraint is $x+y\le 0.5$.

If non-negativity is imposed, i.e. $x,y\ge0$, then optimal solution to the utility maximization is $\bar x=0.5$ and $\bar y=0$. Note that under this solution, the FOC holds with strict inequality. So we need to discuss various complementary slackness conditions before arriving at the solution.

If we allow $y$ to be negative, then the optimal solution is $x^*=1$ and $y^*=-0.5$. Under this solution, FOC holds with equality, and both $x^*$ and $y^*$ can be solved directly from the FOC (and the budget constraint).

From the perspective of characterizing solutions, it is thus more convenient not to impose the non-negativity constraint(s).


What is the difference between a power law exponent and the Pareto exponent?

A random variable $X$ has a Pareto distribution with Pareto exponent
  $\theta$ if  $$\text{P}(X>x)=\begin{cases}
 \left(\frac{x}{x_m}\right)^\theta \quad \text{ if } x\geq x_{min}\\  \
 \ 1 \quad \quad \quad  \text{ if } x<x_{min} \end{cases}$$

In this case, the Pareto exponent is $\theta = \alpha - 1$. Remember that $P(X>x)=\int_x^\infty p(x')\mathrm{d}x'$.


Is printing money to pay government expenses regressive or progressive taxation?

It rather depends on what happens to wages and interest rates, a ceteris paribus issue, and who you identify as "rich" or "poor": for example current workers borrowing to buy a house tend to be richer than the unemployed but poorer than those with large savings.

If wages fail to rise then existing workers may lose from this with their pay falling in real terms (while new workers resulting from the increased expenditure could gain)
If interest rates fail to rise then existing holders of money may lose with the value their assets falling in real terms (while existing borrowers may gain as they have to repay less in real terms)

If both rise to reflect the impact of inflation, it is much harder to identify who is bearing the cost

Incidentally, the extent to which moderate unfunded increases in government expenditure actually affects inflation is an empirical question and the evidence is not conclusive


To profit from rolling, mustn't you be much more bullish or bearish than before?

If markets are efficient, the option premium will equal the expected return on the option. This is independent of the past history of the underlying security.
In order for the past history to matter, you will need to demonstrate market inefficiency. It is possible to demonstrate some market inefficiencies (e.g., the fixed income pricing literature is generally premised on the existence of a term risk premium, the issue is how to estimate it). However, future returns getting a risk premium based on recent historical price movements would be equivalent to proving that technical analysis can reliably outperform (on a probabilistic basis). Finding validation of such a possibility has been a major challenge for researchers.


tl;dr:
That quote refers to conditions for currency area/monetary union to work optimally. Even sub-optimal monetary union can exist. Furthermore, the gold standard existed in era of relative stability, low government spending and actually in era where movement of labor and capital was virtually unrestricted. As soon as that era ended gold standard collapsed. So it was able to exist because at the time conditions were favorable for it.
Full Answer:

was gold standard not monetary union?

Technically they are not completely equivalent, but they are both very similar as they represent an extreme regime of fixed exchange rate. Consequently, many economists draw parallels between gold standard and monetary union. For example, Eichengreen & Temin (2010) in their paper Fetters of gold and paper also argue that gold standard and European Monetary Union (EMU) were virtually equivalent, so your professor is not wrong.

How come that the gold standard was able to exist?

Well first lets correct some incorrect premises. You write:

In past countries did not had fiscal unions and could not move around as easily as today.

The first part is generally correct, however the second part (where I assume the moving refers to movement of different factors such as labor/capital) is not correct. In fact prior to WWI people could move around the world relatively more freely than today. Most countries did not even have passports for their citizens. When it comes to capital arguably there were also less barriers to capital flows. For example, Keynes, who lived in the era of gold standard, argues in his book economic consequences of peace that:

“What an extraordinary episode in the economic progress of man that age was which came to an end in August 1914!
...
The inhabitant of London could order by telephone, sipping his morning tea in bed, the various products of the whole earth, in such quantity as he might see fit, and reasonably expect their early delivery upon his doorstep; he could at the same moment and by the same means adventure his wealth in the natural resources and new enterprises of any quarter of the world, and share, without exertion or even trouble, in their prospective fruits and advantages; or he could decide to couple the security of his fortunes with the good faith of the townspeople of any substantial municipality in any continent that fancy or information might recommend.
He could secure forthwith, if he wished it, cheap and comfortable means of transit to any country or climate without passport or other formality, could despatch his servant to the neighbouring office of a bank for such supply of the precious metals as might seem convenient, and could then proceed abroad to foreign quarters, without knowledge of their religion, language, or customs, bearing coined wealth upon his person, and would consider himself greatly aggrieved and much surprised at the least interference.
But, most important of all, he regarded this state of affairs as normal, certain, and permanent, except in the direction of further improvement, and any deviation from it as aberrant, scandalous, and avoidable.
The projects and politics of militarism and imperialism, of racial and cultural rivalries, of monopolies, restrictions, and exclusion, which were to play the serpent to this paradise, were little more than the amusements of his daily newspaper, and appeared to exercise almost no influence at all on the ordinary course of social and economic life, the internationalisation of which was nearly complete in practice.”

Furthermore, also empirical research shows that in the pre WW1 era there were large capital flows between poor and rich countries (see the sources provided in this answer). So the premise that factors could not move easily in the era of gold standard is false.
Next, the comment you quote was actually mine and note I was specifically talking about conditions for currency unions to work 'properly' i.e. to be optimal (sorry if that was not clear). A monetary/currency union does not need to be optimal to exist.
This being said note that gold standard did actually broke down because gold standard tended to exaggerate asymmetric macroeconomic shocks (see the previously cited Eichengreen & Temin) and it did broke down after WW2 where the kind of globalization and international mobility (which could mitigate the above mentioned shocks) was all but lost.   In fact as measured by value of exported goods as share of GDP, the world only as late as in early 1980s reached the same level of globalization as in 1914 and when it comes to international mobility arguably there are still more restrictions on it than in 1914.  Although in form of  Bretton Woods system Gold Standard technically lasted till 1970s, Eichengreen and Temin argue this was largely due to  ideological reasons, and generally the system was not considered successful.

Furthermore, one of the reasons why gold standard also broke down was that as government spending  and government debt increased after WWI and WW2. This put pressure on governments to monetize their debt and finance portion of their spending through seigniorage. The pre-WW1 gold standard era was also an era of relative stability (macro-economically speaking) as argued by Eichengreen & Temin and sources cited therein. In contrast the interwar and post WWII period was from macroeconomic perspective much more turbulent (Great Depression, Oil Shocks, recent Great Recession etc.). When times are ‘good’ it is much easier to sustain suboptimal monetary union then when economy is expecting macroeconomic shocks, especially asymmetric ones, as smoothing out asymmetric shocks requires countries to adopt different monetary policies or some sort of fiscal transfers (See DeGrauwe Economics of monetary union).


The yield on government bonds is not necessarily equal to fed fund rate. Fed fund rate is a rate at which other banks can borrow from Fed.

This being said the funds rate affects interest rates on all debts since if the banks can borrow more cheaply from Fed they can also offer better terms to their own creditors. Bonds compete on markets for loanable funds so if the interest rate on loans go down  the bond yield will also be lower.

If we are talking about risk free bond then it’s yield will be quite close to the funds rate but not necessarily equal. Also, yes the bond yield can be negative.


Why are there two formats for the Solow capital evolution equations?

The Solow-Swan has the two versions, one is in discrete time (first equation) and other in continuous time. Both give the same results, but you cannot mix them - as you did.

In the first equation (discrete time) you can take the first diference but never a derivative, since the variable is not continuous. The point above the variable means that it has been diferenciated with relation to time.

So the last equation does not make any sense because tried to mix both models.


Does the Federal Reserve buy and sell stocks?

No, the Fed is not allowed to buy stocks, they are allowed to buy government securities in open market operations in order to achieve the target rate for the federal funds rate. The guidelines for this are explained in the Section 14 of the Federal Reserve Act. You can find the Fed holdings in the Federal Reserve Statistics.

However other central banks, like the Bank of Japan, started buying stocks as a measure to support their financial institutions (their banks were subject to too much market risk because of their stock holdings). The have detailed their stock purchasing plan in their website.


Let $\pi$ be the fine that needs to be paid besides the parking fee (say, $\phi$) if he gets caught. Further, he may or may not get caught for not paying. So let $p$ be the probability perceived by John about whether he will be caught. Let $u(x)$ be utility function of paying for amount $x$, with $u(0)=0$, $u'(x)<0$.
If he pays the parking fee $\phi$ he has the assured utility of $u(\phi)$. However, if does not pay for parking, his expected utility is $p \cdot u(\phi+\pi)$
Now risk premium is defined as the minimum amount by which the return on risky choice must exceed the risk free choice to make the individual indifferent between the two choices. Let $\pi_m$ be such that: $$u(\phi) = p\cdot u(\phi+\pi_m)$$
So, for John, $\pi_m$ becomes the risk premium for this game. If $\pi>\pi_m$ then $u(\phi) = u(\phi+\pi_m)>u(\phi+\pi)$ and it would be irrational for him to not pay for parking and risk getting caught. If opposite, he takes decides to not pay for parking and risk getting caught.


Proof of Concavity of Cobb-Douglas Function

If you look at the case $x_1=x_2=\ldots x_n=t>0$, you have
$$F(x_1,x_2,\ldots,x_n)=t^{a_1}\cdot t^{a_2}\cdots t^{a_n}.$$
Verify that the function $t\mapsto t^{a_1}\cdot t^{a_2}\cdots t^{a_n}$ is not concave. This implies that $F$ is not concave either.


If you charge a single (indirect) tax rate, x% on all goods and services in a country, will you get x% back as tax revenues?

Depends on the type of tax, and on whether you assume the government gives the money to people back or just keeps them, but generally no. The exception would be any non-distortionary tax (lump-sum tax, Pigouvian tax etc). But if it is tax that is applied to all consumption then it will create distortions.

This is because while you can tax consumption of goods and services you generally can’t tax leisure (which can be viewed as another good - just sitting and enjoying yourself) so this tax will distort the marginal rate of substitution between consumption of regular goods and services  and leisure. The amount of distortion will depend also on whether you assume that for leisure you need to still consume some goods but generally there will be still distortions. So the tax will induce shift from consumption of goods and services (and consequently from their production and production determines the output/income or GDP) to leisure and the government should collect less than 10% of GDP.

Leakages like the fact that some sources of consumptions are hard to tax (like consumption of home production) just make this worse.

What I described above is the substitution (Hicksian) effect. If we assume that government redistributes the money back to people this is the only relevant effect.

If the government decides to keep the money on its account there will be second effect. This is so called income (Marshallian) effect. If the taxes are not returned to people they become poorer and as a result their decision between consumption of standard goods and services (and hence production) and leisure will get affected again by this income effect. In principle, depending on the parameters we would put on utility function, the income effect could cause people to consume more standard goods and services than previously. In that case GDP could actually increase (although overall utility would be lower - but GDP only looks at consumption of standard goods and services, consumption of leisure is not measured by it). Hence in case you assume that government keeps the money it would depend on how income effect would affect consumption of goods and services and leisure and whether this effect would be stronger or weaker than substitution effect.


If I shred a $20 bill, is society poorer? What is the effect on the real economy?

You have to make distinction between short-run and long-run.
Short-run: In short-run money is not neutral, meaning that in short-run money and other nominal variables can affect real output. A one example why this is true are sticky wages. In presence of sticky wages wages (for example due to nominal contracts that take time to renegotiate) a fall in money supply and deflation would lead to increase in real wages above the equilibrium level. This would cause excess unemployment and loss of output until wages would finally adjust.
So in short-run amount of money and nominal variables in general have a real effect on economy although this effect is not as simple and clear cut as saying that shredding one bill will lower output and printing one more will increase it as the effect of changes in money supply depend on macroeconomic conditions (for example at zero lower bound increases in money supply will be mostly offset by drop in velocity of money  see Krugman; 1998). However, discussing fully the reverberations money have in the short run is beyond the scope of SE answer. I recommend having look at Blanchard et al. Macroeconomics: an European Perspective chapters 3-10, 20-22 and 24 with emphasis on chapters 3-10 which have the core.
Long-run: In the long-run you get the classical dichotomy and money are neutral. This is almost definitional since long-run is in macroeconomics defined as a long period of time where among other things prices have time to adjust and are flexible.
This can be best seen from the AS-AD diagram below that I took from Mankiw's Principles of Economics:

As you can see short-run aggregate supply is increasing in aggregate price level so money are not neutral and can affect the level of production. However, the long-run aggregate supply is orthogonal on price level. No matter what the aggregate price level is the production will be always same and determined by the production possibilities of an economy (i.e. determined by real factors that affect the production possibilities of an economy).
This is intuitive as economy ultimately cannot produce more than it is possible given its production function and resource constraints. If an economy faces following production function $F(L) = 5\sqrt(L)$ and we have $100$ units of labor then we cannot produce more than $50$ units of output no matter how much money we print or destroy. Volume of money in circulation in the long-run does not make factors of production more productive nor it increases the stocks of factors production so by itself it can’t change how much economy can produce in the long-run.


Why don't profitable firms use previous profits to offset current loss

The primary goal of most companies is to make money for its shareholders. They put money in, and they expect to either get dividends, or be able to resell their shares for a higher amount. It's the shareholders who own the company, and they are the ones deciding. And they want money. Otherwise they would give their money to charity.
So when a company makes a profit, they will do a combination of one or more of these:

Set aside some as reserves (in some cases there are mandatory reserves by law)
Re-invest some of the profit to make more money in the future (buy new equipment, buy companies, hire people, send money on R&D...)
Pay dividends to shareholders, or buy back shares (two ways of giving money back to shareholders)
And the rest will remain as cash.

Investors usually don't want the company to hoard profits. A safe reserve so it can go through difficulties, but that's it. Cash in the bank makes very little money, it's not a useful use of those funds for the investor: they'd rather get the money and invest it themselves according to their own risk profile.
If the company doesn't do what the investors want, then the shareholders will usually change management to make sure it complies.
So keeping employees on the payroll in tough times is not a primary goal of most companies. Of course, it's not a good idea to fire everybody at the first sign of trouble (it has an impact on the morale and performance of the other employees, it may cost a lot in severance, and when business picks up it will take time and cost money to hire and train new people), but if things are too bad, then it's the only option the company has to fulfil its obligation to shareholders.
There may be exceptions: a company and its shareholders may decide that their social responsibility is more important than making money. Cue all the "fair", "equitable", "social", "responsible", etc. keywords. But those are really the exception rather than the norm, and there's a limit to what can be done. Even if it made profits consistently and kept those as reserves, those reserves can't last forever while the company is burning through cash.
Remember that many companies have very small profits compared to the revenue and costs.
Consider a company with usual revenue of 1 billion pounds, but with tight margins: their expenses could be 900 million pounds, so the profit is 100 million pounds. They keep the profit year after year for 5 years, so they now have 500 million pounds in the bank, and the shareholders haven't complained yet (as if).
Now Covid strikes, and the revenue dwindles to 100 million pounds. If they keep all their costs the same, they're haemorrhaging 800 million pounds a year. They won't last a year like that! So yes, they will have to reduce costs, and part of this is laying off staff.
Don't think those figures are realistic? In 2019, Easyjet has revenue of about 6.385 billion pounds, but expenses of over 6 billion pounds! With revenue slashed to a fraction of what it was, they obviously can't keep spending like they did. They would have needed to keep profits of the last 20 years just to be able to get through this year.


Competitive vs complete and non-competitive vs incomplete marekts

Complete market is a market where every possible asset or good can be assigned a price and where you have perfect information, can make perfect contracts and zero transaction costs. Any market can be complete regardless of its market structure. So you can have complete market dominated by monopoly, or oligopoly or monopolistic competition etc.

Perfectly competitive market is a market where there are so many buyers and seller that firms become price takers and when the products are identical so there is a little scope for differentiation.

You can’t just call non-competitive market incomplete. For example, in standard undergrad treatment of monopoly you still assume complete markets, yet the market structure is non-competitive.

Yes when people talk about complete markets they do it in a pretty much same sense as Arrow-Debreu


Would saving money outside of banking system be able to reduce monetary base?

Options 1-2 do not reduce the monetary base. “Money in circulation” are all notes/coins that were issued to the private sector and not returned.

There is no way of measuring how many transactions notes/coins support (or whether they have been destroyed). So reducing “circulation” has no effect on published statistics.

Option #3 would reduce the monetary base if the money is returned to the central bank.


Economic theory journals for a refinement theorem about utility function representation

For theory you have in order of prestige... (I know subjective)

Journal of Economic Theory
Theoretical Economics
AEJ-Micro (only micro)
Mathematics of Operations Research (OR related)
Games and economic behaviour (only game theory)
Economic theory
Journal of Mathematical Economics
Social choice and welfare (only social choice)
Theory and Decision
Mathematical social sciences
$\ldots$

There are of course other journals that publish theory, like:

International journal of Game theory
Economic Inquiry
Economics Theory Bulletin

Feel free to add to the list.


Deriving and explaining the weighted cost of capital

If you are asking "Is the WACC the amount that the company expects to earn on the stocks and bonds that it holds.." then the answer is no.

The WACC, in very simple terms, is the amount of money a company pays to obtain financing for projects. These types of financing are clearly listed in the wikipedia article and clearly extend beyond stocks and bonds issued by the company.

A company can calculate the WACC to determine whether or not undertaking a project will be profitable. That is, a company can determine that it must earn some minimum return on a project before that project becomes profitable.

You, as a consumer, possibly have experience with cost of capital. Consider the interest paid on a car loan. That interest is the cost you incur for financing the purchase of your vehicle by borrowing funds from a financial intermediary.

As far as derivation goes - I'm not sure how to simplify these formulas much more. However, you can think simply about the first as the ratio of the interest paid out on sources of financing and the total market value of those sources of financing (so...some ration < 1) and the second is a more simple case of the first.

http://www.investopedia.com/walkthrough/corporate-finance/5/cost-capital/wacc.aspx

I think this website gives a decent walkthrough of the concept. Hope this helps some.


Hint: I won't give a full answer since this is a very specific question, but I can give you a long outline here. A Lagrangian is set-up with an objective function (in this case utility) plus or minus (depending on Kuhn Tucker constraints, which we won't worry about) a constraint function (in this case, income) which is set to zero and then multiplied by the Lagrange multiplier, which we will denote $\lambda$.

So we set up the Lagrangian function. (Plug in the utility function yourself.)

$$\mathcal{L} = u(x_1, x_2, x_3) - \lambda (p_1x_1 + p_2x_2 + p_3x_3 - m)$$

Solve for the partial derivatives $\frac{\partial \mathcal{L}}{\partial x_1}$, $\frac{\partial \mathcal{L}}{\partial x_2}$, and $\frac{\partial \mathcal{L}}{\partial x_3}$ and set them equal to zero (You can also solve for the partial of $\lambda$, but it just gives you back the budget constraint, which I skip to). For example, you get for your first derivative:

$$\frac{\partial \mathcal{L}}{\partial x_1} = \alpha (x_1 + z_1)^{\alpha - 1} - \lambda p_1 = 0$$

Once you solve the three partials, the easiest thing for you to do is solve for $\lambda$ with respect to the other variables for all three partials, and then figure out how to substitute them into the budget constraint. You should solve for each $x$ in terms of the prices, maybe some $z$'s, the greek letters $(\alpha, \beta, \gamma)$ and income $m$. (I tried working some of it out; enjoy your algebra.)


Under what conditions should the External Rate of Return (ERR) be used instead of Net Present Worth (NPW) and vice versa?

Investment protects are inherently risky, and when calculating either of these numbers many assumptions need to be made. From projecting what future inflows and outflows will be, to deciding what rate of return to use to discount these projects payoffs. As far as I know, usually both measures are calculated and considered when making a decision since they give a slightly different information.

For example, the NPW needs to assume some rate at which to discount payoffs, in your example you call it the MARR, the choice of such rate can be controversial, while the calculation of the ERR does not need to assume any rate. For example I can show you a project with a very high NPW, but this high number may only be due to the fact that I chose a very low MARR, this will be evident because the ERR will necessarily be low. The two measures give a more complete picture. Likewise, I can give you a project that has a very high ERR, but the actual level of the value of the project can be tiny, this will be reflected by the fact that the NPW will be a small positive number.

If the MARR is not controversial, the king of all measures is certainly the NPW, as it literally tells you how valuable is a project. But there are many ways to tinker with the NPW and make it look better so complementary measures give you a better picture of the quality of the project.


One of the original statements of this kind were Kaldor's Stylized Facts on growth, Kaldor's Facts, the most important of which are that:

Labor and capital receive approximately constant share of output (about 0.6 for labor and 0.4 for capital)
The rate of growth of output per worker is roughly constant (about 2%)
The rate of return on investment is roughly constant (if you look at long enough intervals, i.e. about 3%...)

More recently, the famous growth theorist Paul Romer came up with a renewed set of facts New Kaldor Facts paper. The most salient ones are that:

Market is constantly increasing its dominance as a way to organize economic activity.
The rate of economic growth has been accelerating for millenia.
Measured inputs explain only a small part of income differences across countries.
Human capital is constantly being accumulated, and yet, the human capital premia has not changed over time.

Also, a newly minted constant, as theorized by Minsky:

The nature of financial markets and risk taking implies periodic financial crisis.


Does labor mobility create a certain type of market failure?

Well, from the same paper (p. 5), it's not all that clear that the theory translates to actual market failure:

  There is very little reliable data on either the scale of
  poaching or its impact upon employers’ training
  decisions – despite this being frequently adduced by
  policy makers as the prime cause of market failure in
  training. One of the few recent surveys to touch on the
  issue (4) suggested that poaching was a serious problem
  for no more than about one per cent of the employers in
  the sample, whereas an earlier survey of employers
  suggested that the possibility of poaching had
  discouraged as many as 38% from investing in skill (5).

The references cited for data being:

  (4) J. Kitching and R. Blackburn. 2002. ‘The Nature of
  Training and Motivation to Train in Small Firms’, DfES
  Research Report RR330, Nottingham: DfES.

  (5) Training Agency. 1989. Training in Britain, London:
  HMSO.

I think this constitutes a partial answer, but I'm quite interested in more data, in particular from other countries.

And, yes, as I suspected, labor immobility is also a form (perhaps less controversial) of market failure. But this does in turn raise the interesting question whether you can fix one market failure without causing another (in the labor market).


Here is an example where the two are actually compatible: The consumer's utility function $U:\mathbb{R}_+\to\mathbb{R}$ is given by $U(c,1-n_ns)=c-n_s$, the initial labor endowment is $1$ and $F:\mathbb{R}_+\to\mathbb{R}$ is given by $$F(n)=n(1-e^{-n}).$$
This function has IRTS, but still turns a unit of labor into less than one unit of consumption at any amount of input. If you let the price of consumption be $1$ and $w\geq 1$, you have a competitive equilibrium in which nothing is produced and the consumer simply consumes their endowment.
Side rant: The usual definition of IRTS is that when the inputs are multiplied by a number larger than $1$, the resulting output increases more than proportionally. Under this definition, no production function for which an input of $0$ is feasible has IRTS. Even if one restricts oneself to nonzero inputs, the definition does not work the way people seem to think. The standard example of a production function with IRTS is a Cobb-Douglas production function in which the sum of exponents is larger than $1$. The standard definition of IRTS applied to an input combination with some, but not all, entries $0$ would show that IRTS does not hold here. It does work when we restrict ourselves to input combinations that produce a positive output, and the function in the example is of this kind.
However, one can show that no competitive equilibrium exists if one makes the assumption that the consumer prefers to turn some labor into consumption and the production function produces zero output with zero input and is continuous and increasing, and the consumer's utility function is strictly increasing on the interior. For example, with Cobb-Douglas utility, every bundle in which the consumer enjoys both consumption and leisure is better for the consumer than a bundle in which they enjoy only one of these in a positive amount. Since every competitive equilibrium is Pareto efficient by the first welfare theorem (whose assumptions hold here), some amount of consumption must be produced here, and this is not compatible with profit maximization. Indeed, suppose there is an equilibrium with $p$ the price of the consumption good and $w$ the wage. Since the consumer's utility function is strictly increasing on the interior, an optimal consumption bundle can only exist if $p>0$ and $w>0$. Let $c_e$ and $n_e$ be the equilibrium consumption and labor supply. Efficiency requires $c_e>0$ and, therefore, also $n_e>0$. Since the firm can always have a profit of $0$ by using no input, profit maximization implies that
$$pF(n_e)-wn_e\geq 0.$$
But then, $$p F(2n_e)-w 2n_e>p 2F(n_e)- w 2n_e=2\big(p F(n_e)-wn_e\big)\geq p F(n_e)-wn_e.$$ Here, the strict inequality comes from IRTS and the weak inequality from $pF(n_e)-wn_e\geq 0.$ We see that the production plan that use an input of $2n_e$ produces a higher profit than the production plan that uses $n_e$, in contradiction to the firm maximizing profit with a production plan with input $n_e$.


Name of robustness check where you exclude individuals?

Depending on the context this is sometimes called Jackknife resampling

  In statistics, the jackknife is a resampling technique especially
  useful for variance and bias estimation. The jackknife pre-dates other
  common resampling methods such as the bootstrap. The jackknife
  estimator of a parameter is found by systematically leaving out each
  observation from a dataset and calculating the estimate and then
  finding the average of these calculations. Given a sample of size n
  $n$, the jackknife estimate is found by aggregating the estimates of
  each $( n − 1 )$-sized sub-sample.

It may also be referred to as leave-one-out cross validation, which isn't exactly the same but very close.

  Leave-one-out cross validation is K-fold cross validation taken to its
  logical extreme, with K equal to N, the number of data points in the
  set. That means that N separate times, the function approximator is
  trained on all the data except for one point and a prediction is made
  for that point.

Well, that's the name for leaving out a single observation at a time. Strictly speaking, it isn't the name for leaving out each panel unit once. When you resample in way that accounts for the panel or time series structure, that is usually called Block Bootstrapping, in this case a kind of cluster bootstrapping.

Personally, I would call this block-jacknife or leave-one-block-out cross validation.


Is money supply affected by the stock market?

They may, but probably not much. Because stocks cannot be used as a substitute for money in most transactions there is no direct channel. However, because stocks can act as collateral for loans, and loans have the capacity to create money through the money multiplier mechanism they can have some effect, just as anything that relaxes borrowing constraints could increase the money supply.

Collateralized loans make up the vast majority of bank debt. Suppose, for example, that banks only made collateralized loans. Then when stock prices go up, some borrowers formerly at the limits of borrowing constraints due to limited collateral, would be able to take out additional loans. These loan proceeds could then be deposited in banks or spent, either way likely ending up in banks eventually where, through the mechanism of fractional reserve banking, they could be used to create additional money. However, as you can see in the figures below, margin debt is a very low fraction of GDP in contrast to say household overall debt. So in general this is not going to be a big channel.

Source: Ominous Sign as Margin Debt Continues to Rise

Source: Wikipedia Subprime mortgage crisis page


Did the financial crisis affect the retirement patterns of Baby boomers?

I don't know if you'd find these specific references helpful to look at, but I hope it's a good start. Quandl has a database called Social Security Administration and if you search "retirement" within the database, you will see datasets on number of retired recipients of social security, along with their spouses and dependents, and the average monthly amount they receive. Data goes back to the 1960s. Another database, Federal Reserve Economic Data, also shows retirement data such as federal employee retirement plans and funds. Data goes to back to the 1940s. You'd have to search for "retirement" within the database. Both these databases are free to access. Hope this helps. [Disclosure: I work for Quandl]


Maximizing units under a budget constraint and increasing costs

I think you are making this harder than this needs to be from a reasoning standpoint. Given a budget M, you are trying to maximize your total expenditure. You have just one input cost, being marginal material cost of the additional good. There is no trade-off between inputs, so "maximizing" in this sense just means how much you can buy given M, which will end up being simple algebra rather than some more difficult Lagrange calculus needed for multivariate constraint functions.

The issue with your LINEST model is that either your dependent variable is the marginal cost, not the total cost (as needed for your objective), or you are interpreting it incorrectly. If the former, rerun the regression with the data you referenced. If you used the two columns of data that you referenced then your interpretation I wrong and should be as follows: your coefficient β(1) would then just be the estimated price per item (an intercept shouldn't exist as no fixed costs are present), with the independent variable being the number of units, and the dependent being the total cost for that day. If you use this model, then your given M should be plugged into the left side of the equation and then solve for the number of units algebraically. Keep in mind that if you end up with, say, x=12.7, then you should round down, as 13 units would be unattainable under the constraint.

I would consider using the log function, however, due to the increasing MC like you mentioned above. For your log function, follow the same algebra as above, solving for x=units attainable under the y=M constraint. Use a calculator for that one, no one wants to do log base 1.77  of a number in their head.


Is there a go-to resources on the use of the scientific method in economics?

Economists often do something similar to what your physics teacher taught. One of my graduate econometrics teachers taught us to begin our empirical investigations by asking what the ideal experiment to test them would be. And a quick web search confirmed this is a widespread sentiment:

  Esther Duflo, PhD ’99, a prominent antipoverty researcher at MIT whom
  Angrist advised when she was a graduate student, says his relentless
  concentration on the problem of selection bias—for instance, the
  possibility that the better-rated high school is populated with better
  students—spurred her to go beyond his techniques and conduct actual
  field experiments. “Once you ask the question right, you can ask what
  the ideal experiment to answer it is,” she explains

The Natural Experimenter By Peter Dizikes on January 2, 2013

  For a long time I have maintained that economics is unfairly
  criticised for the use of unrealistic assumptions. (See Cartwright
  1989, 1998). I can summarise my view by comparing an economic model to
  a certain kind of ideal experiment in physics: criticising economic
  models for using unrealistic assumptions is like criticising Galileo’s
  rolling ball experiments for using a plane honed to be as frictionless
  as possible. This defence of economic modelling has a bite, however.
  On the one hand, it makes clear why some kinds of unrealistic
  assumptions will do; but on the other, it highlights how totally
  misleading other kinds can be – and these other kinds of assumptions
  are ones that may be hard to avoid given the nature of contemporary
  economic theory.

The Vanity of Rigour in Economics: Theoretical Models and Galilean Experiments by
NANCY CARTWRIGHT

  So what is, intuitively, an experiment? The key idea is control:
  experimenting involves observing an event or set of events in
  controlled circumstances. It is useful to distinguish at least two
  important dimensions of control: (1) control over a variable that is
  changed or manipulated by the experimenter, and (2) control over other
  (background) conditions or variables that are set by the experimenter.
  Both dimensions involve the idea of design or manipulation of the
  experimental conditions: the experimental laboratory is in some
  intuitive way an “artificial” situation compared to what is likely to
  happen in the “natural” or “real” world. 3 An experiment is usually
  designed with the aim of getting a clear-cut answer to a fairly
  specific scientific question. As we shall see, many different kinds of
  questions can be answered in the laboratory. But typically, such
  questions regard the mutual dependence of some variables or
  quantities, and in particular the causal relations holding between
  them.

Experimentation in Economics by Francesco Guala


How to evaluate whether the synthetic control is good enough

This is an excellent question, but unfortunately with no (yet) agreed upon answer.

Many authors such as in those seminal papers use cross-validation for this. This is basically what is implied in the ADH (2015) paper on German unification. If the synthetic control is good the MAPE (mean absolute prediction error) and RMSPE (root mean square prediction error) should be quite low. Additional cross-validation where the pre-treatment period is split into training and testing period is so far the common way to go, although there is no agreed upon value of how low the prediction errors should be, just that lower is always better.

Next it is also argued that examining if the trend in the countries from donor pool that are assigned non-zero weights and seeing if the pre-treatment trend in those donor countries seem to match the pre-treatment trend of treated country similar way as you would do for DiD (Difference in Differences) as argued here.

Lastly, as crazy as it may seem, yes visual inspection is actually recommended as well.

Beside the above you should also conduct sensitivity analysis by systematically trying to vary the number of countries in the donor pool and see if the resulting synthetic control has still a good fit. That's again also done by ADH 2015 and you will find it in almost all studies as well. Publishing your weights is also considered good practice.

Of course, doing a proper cross-validation is difficult if you have small pre-treatment sample. I was once working on a synthetic control study at one of the euro-system member's central bank with few colleagues where we had very short pre-treatment period due to data constraints. Instead of doing cross-validation we decided to just test whether the real pre-treatment series is statistically significantly different from the synthetic series using couple of non-parametric tests. When we presented the results and methodology at a workshop no objections to that were raised, and there were some very excellent econometricians present in the room. However, beside central bank's brief the study was not published because the results were not very interesting as placebo test showed results were not significant and we decided to abandon the project since we judged chance of publication to be low so the idea never got proper peer review, so take that as you will.

Response to edit:

as with classical DiD there is always an issue of potentially delayed effects or anticipation effects that would bias the result. However, in this case the authors argue that the increase after the reunification was actually part of the effect and not delayed effect. As the authors say:

  Our estimate of the effect of the German reunification on per capita GDP in West Germany is given by the
  difference between the actual West Germany and its synthetic version, visualized in Figure 3. We estimate that the
  German reunification did not have much of an effect on
  West German per capita GDP in the first two years immediately following reunification. In this initial period, per
  capita GDP in the synthetic West Germany is even slightly
  lower than in the actual West Germany, which is broadly
  in line with arguments about an initial demand boom
  (see, e.g., Meinbardt et al. 1995). From 1992 onward,
  however, the two lines diverge substantially. While per
  capita GDP growth decelerates in West Germany, for the
  synthetic West Germany per capita GDP keeps ascending
  at a pace similar to that of the prereunification period.

However, arguably this is a weak point of the paper.

Otherwise, if there would be a genuine delay in the effect you would have a problem that could be solved similarly as with DiD by identifying the 'correct' date where the treatment started to have an effect and identify the pre and post treatment period based on that.


What gives value to precious, luxury things?

Only a surplus on demands will make things "valuable".   So it is about the price level accepted by those who demands it, and the demands can be from essential needs to status show-off.

If you read Netherland history, you will notice there is a period of non-existence luxury goods, due to the shape of religious culture that forbids show off.

OTH, there is also terrible rent seeking like monopoly that make essential goods pricey.


Why aren't lengthier expirations offered, especially when a competitor offers it?

I am not sure of the exact procedure, but it is not purely an administrative decision of the exchange - they need market makers who want to support the product. Given the rise of algorithmic trading, one could imagine that any conceivable product could be created, and hope that people set up algorithms that create a two-way market. However, exchanges have rules about margin calls, and so sketchy financial products raise the concern of entirely artificial squeezes.
The revealed preference is that not many entities want to trade long-dated equity options, and so we return to the previous point. This is not a general property across all financial products; fixed income supports long-dated option trading (swaptions) as a side effect of hedging embedded call options in bonds/mortgages.


In the Solow growth model, does labor grow like technology at the steady state?

In deterministic growth models of closed economies with exogenous constant growth drivers (here, population and labor efficiency), the steady-state of the economy is in "growth rates", or under the newer terminology, it is a "balanced growth path".

The growth rate of the economy can only be the sum of the growth rates of these exogenous growth drivers. So in the balanced growth path, aggregate magnitudes grow at $n+g$, per capita magnitudes grow at $g$ and magnitudes per efficiency unit of labor are constant.

One can see this directly through the production function by considering

$$Y_t = K_t^\alpha (A_t L_t)^{1-\alpha} \implies \ln Y = \alpha \ln K_t + (1-\alpha)\cdot [\ln A_t + \ln L_t]$$

$$\implies \frac {\text{d}\ln Y}{\text{d}t} = \frac {\dot Y}{Y} = \alpha \frac {\dot K}{K} + (1-\alpha)\cdot \left[\frac {\dot A}{A} + \frac {\dot L}{L}\right]$$

$$\implies \frac {\text{d}\ln Y}{\text{d}t} = \frac {\dot Y}{Y} = \alpha \frac {\dot K}{K} + (1-\alpha)\cdot (g+n)$$

To have a balanced growth path, we must have equal and constant growth rates (so ratios like $Y/K$ etc remain constant), therefore

$$\frac {\dot Y}{Y} = \frac {\dot K}{K} = \gamma$$

$$\implies \gamma = \alpha \gamma + (1-\alpha)\cdot (g+n)$$

$$\implies \gamma = g+n$$

Note the importance of constant returns to scale, in order to obtain this result.


How would a firm increase price in such a scenario?

It could work (it would depend on model parameters) if you would assume that it is impossible for firm to enter the market once firm exists. This is actually quite complex and long problem so I will provide only partial solution.
This would be a sequential Bertrand competition problem (since you assume that firms only can compete on prices). Here in first round company A (the one with lower marginal costs $c_A<c_B$) would have a choice - either set its price $p_A=p_B$, split the market between itself and second firm B and just get the extra profit thanks to its marginal costs being lower and do this in both period 1 and period 2.
So you would have strategy of 'tolerating B' (T) giving profits:
$$T: \pi_{A,t=1}+\delta \pi_{A,t=2}= (p_A -c_A) \frac{q(p)}{2} +  \delta (p_A -c_A )\frac{q(p)}{2}$$
where $p_A =p_B =c_B > c_A$ and $\delta$ is a discount factor for future profits.
Then you could have second strategy of 'contesting B' (C). In this strategy firm A would  undercut firm B in the first stage allowing it to get monopoly profits in the second stage so the strategy profit would look like:
$$C: \pi_{A,t=1}+\delta \pi_{A,t=2} = (p_{A,t=1} -c_A) q(p_{A,t=1}) +  \delta (p_{A,t=2} -c_A)q(p_{A,t=2})$$
Where now parameters would have to be such that $p_{A,t=1}<p_A$ (i.e. the first period price has to be lower in strategy C compared to strategy T) and then the second period price $p_{A,t=2}$ would be monopoly price in that period. Whether, strategy C or T makes sense will depend exactly on parameters of this model, depending on your assumptions on discount rates, marginal costs differential between the firms and consumer demand you could end up with either T or C being dominant strategy. Also, this requires assumption that if firm B gets loss in the first round it will immediately exist and won't be able to ever enter again.
Regarding your second question inelastic demand is in principle consistent with even perfect competition. You can only make some inferences about market power once you assume what the competition is (for example monopoly market power is inversely proportional to the elasticity of demand). However, it would be beyond scope of SE answer to list effect of inelastic demand on competition across all market structures. You can have look at  Paul Belleflamme &  Peitz Industrial Organization: Markets and Strategies for overview of this.


Why does quadratic utility function imply $\mu-\sigma$ preference?

If you have quadratic preferences then your utility function is:
$$ U(W) =  W - \lambda W^2$$
this implies your expected utility function looks like:
$$ E[U(W)] =  E[W - \lambda W^2] =  E[W] - \lambda E[W^2]$$
$$ =  E[W] - \lambda E[W^2 - E[W]^2 + E[W]^2]$$
$$ =  E[W] - \lambda E[W^2 - E[W]^2] + \lambda E[E[W]^2]]$$
$$ =  \mu_w - \lambda \sigma_w^2 + \lambda \mu_w^2$$

Therefore, we have established that expected utility depends only only the mean $(\mu_W)$ and variance $(\sigma^2_W)$ of wealth and the risk parameter $(\lambda)$.


I don’t think crisis itself has set definition as opposed to recession, unless you attach some clarifier to it as the examples you mention. Generally the word is even in academic work thrown around quite loosely.

For example in Romer advanced macroeconomics in the subject index for word crisis you will find:

  crisis; see debt crisis; economic crisis of 2008-; recessions

Hence the word crisis is at least in macroeconomics used very loosely. However, when it comes to for example debt crisis or financial crisis you get more precise definition.

For example consider these definitions of the terms you mentioned (excluding health crisis since for that I think we have to go outside economics and also you tagged it with macro so I will focus on that) by leading authors:

Financial Crisis: according to the Mishkin and Eakins popular textbook financial markets and institutions a financial crisis is defined as “a major disruption in financial markets, characterized by sharp declines in asset prices and failures of many financial and non financial firms”.

Debt Crisis: which is also used as a synonym for fiscal crisis in Romer advanced macroeconomics it is argued that debt/fiscal crisis is a situation that involves “a sharp contraction in fiscal policy, a large decline in aggregate demand, major repercussions in capital and foreign-exchange markets, and perhaps a default on foreign debt.”

To further add to the confusion many authors have their own slightly different definitions of debt crisis. For example Reinhart and Rogoff in their now infamous research on debt crises define two kinds of debt crises external debt crisis defined as debt crisis that “involve outright default on a government’s external debt obligations—that is, a default on a payment to creditors of a loan issued under another country’s jurisdiction, typically (but not always) denominated in a foreign currency, and typically” and internal debt crisis defined as default that do not involve powerful external creditors.

If we look at the meaning of crisis as recession we find that they are defined as a drop in economic output. For example according to Blanchard et al macroeconomics an European perspective a recession is “a period of negative GDP growth. Usually refers to at least two consecutive quarters of negative GDP growth.”

Hence I don’t think there is any precise definition of crisis in macroeconomics and I would say in economics in general. A crisis is just used as an umbrella term for times of economic distress or fall in economic activity. Sometimes even within the field some authors might have different definitions.


The way I would think of this is as follows. Let us write the value
of the first company as $V_{A}$and the second as $V_{B}.$ Given
your definition, let me know if you agree with the following argument:
$$
V_{A}=s_{AA}\sum_{t=0}^{\infty}\pi_{tA}+s_{AB}\sum_{t=0}^{\infty}\pi_{tB}
$$
 Where $s_{AA}$ denotes the time invariant share of company A that
comapny A owns and $s_{BA}$ denotes the share of the company B that
A owns. Moreover, $\pi_{t}=A_{t}-L_{t}$ or the equity of each company.
By a symmetric argument, we have that :
$$
V_{B}=(1-s_{AA})\sum_{t=0}^{\infty}\pi_{tA}+(1-s_{AB})\sum_{t=0}^{\infty}\pi_{tB}
$$

Now, consider company $A.$ Taking differentials:
$$
dV_{A}=s_{AA}\sum_{t=0}^{\infty}d\pi_{tA}+s_{AB}\sum_{t=0}^{\infty}d\pi_{tB}
$$
Ceteris Paribus,you claim that $\sum_{t=0}^{\infty}d\pi_{tA}=1$
and the other term equals 0. So what you have then is:
$$
dV_{A}=s_{AA}\times1
$$
and
$$
dV_{B}=(1-s_{AA})\times1
$$
The answer is fairly intuitive- the change in value of each firm is
the change in profits that one of the firms has experienced times
the share of the profitable firm owned by either.
If each firm owned half, then the change in the value of each firm for an increase in $1 would be half, since each firm would have half the claim on the firm whose profit has increased by a half.


The 2015 Economics "Nobel": Angus Deaton

Deaton's "Understanding Consumption" (1993) was one of the major sources I used when doing seminar work for my master's. In the end I decided to write my thesis about a different (somewhat related) subject after realising the empirical difficulties with what I planned on doing.

I have since chosen a different research subject, but Understanding Consumption is a book I have spent many hours with. It's a bit dated now, but still a decent read if you want to know about consumption and saving.


Implicit Differentiation & Profit Function

I will only set up the first part of your question. See if you can move on from there.

If you try and set revenue as $p \cdot x$ immediately, you will get

$$p \cdot x = p \cdot (\gamma ap + b + R(y))$$

which as you note means $x$ will not be in this term. Profit could technically still be expressed in terms of $x, y$ in this case, but...

$$\pi(x, y) = p \cdot (\gamma ap + b + R(y)) - (cx + y + d)$$

is awkward since $x$ can be expressed in terms of $p$ and vice versa, so why would we have both in our equation?

So instead, solve for the inverse demand function:

$$x = \gamma ap + b + R(y) \implies \boxed{p = \frac{x - b - R(y)}{\gamma a}}$$

So you can solve for $p \cdot x$, but instead of substituting for $x$, you substitute for $p$. Once you solve for your first order conditions, you should be able to solve for $y$ as a function of variables including $b$.

Hope this helps.


Instead of proposing specific equations, I will point to two concepts that lead to specific equations for specific theoretical set ups:

A) Equilibrium
The most fundamental and the most misunderstood concept in Economics. People look around and see constant movement -how more irrelevant can a concept be, than "equilibrium"? So the job here is to convey that Economics models the observation that things most of the time tend to "settle down" -so by characterizing this "fixed point", it gives us an anchor to understand the movements outside and around this equilibrium (which may be changing of course).

It is not the case that "quantity supplied equals quantity demanded" (here is a foundational equation)

$$Q_d = Q_s$$

but it is the case that supply tends to equal demand (of anything) for reasons that any economist should be able to convincingly present to anyone interested in listening (and deep down they all have to do with finite resources).

Also, by determining the conditions for equilibrium, we can understand, when we observe divergence, which conditions were violated.

B) Marginal optimization under constraints
In a static environment, it leads to the equation of marginal quantities/first derivatives of functions.
Goods market: marginal revenue equals marginal cost.
Inputs market: marginal revenue product equals marginal reward (rent, wage).
Etc. (I left "utility maximization" out of the picture on purpose, because, here first one would have to present what this "utility index" is all about, and how crazy we are (not), by trying to model human "enjoyment" through the concept of utility).

Perhaps you could cover it all under the umbrella "marginal benefit equal marginal cost" as other questions suggested:

$$MB = MC$$

Economists live in marginal optimization and most consider it self-evident. But if you try to explain it to an outsider, there is a respectable probability that he will object or remain unconvinced, instead usually proposing "average optimization" as "more realistic", since "people do not calculate derivatives" (we don't argue that they do, only that their thought processes can be modeled as if they were). So one has to get his story straight about marginal optimization, with convincing examples, and a discussion about "why not average optimization".

In an intertemporal setting, it leads to the discounted trade-off between "the present and the future", again "at the margin" -starting with the "Euler equation in consumption", which in its discrete deterministic version reads

$$u'(c_{t})=\beta(1+r_{t+1})u'(c_{t+1})$$

...and one cannot avoid the theme of utility, after all: $u'()$ is marginal utility from consumption, $0<\beta<1$ is a discount rate and $r_{t+1}$ is the interest rate

(don't consult wikipedia article on Euler's equation in consumption, the concept behind it is much more generally applicable and foundational than the specific application that the wikipedia article discusses).

Interestingly, although dynamic economics are more technically demanding, I find this more intuitively appealing since people seem to understand way better "what you save today will determine what you will consume tomorrow", than "your wage rate will be the marginal revenue product of all labor employed".


Perfect Substitution with a Continuum of goods?

Seems like the problem specified as specified right now should have as solution $C(\omega)=\frac{\delta(\omega)}{P(\omega)}$ if $P(\omega)=\min_{\omega'} P(\omega')$ and zero otherwise. The solution proposed cannot be optimal because the budget constraint is not depleted. If we let $\omega^*$ be the index of the cheapest good, the indirect utility would be then $U^*(P(w))=1/P(\omega^*)$.


Does Medicaid or Medicare represent a higher risk to the Federal Government Solvency and Debt going forward?

Yes, both presents higher fiscal risks up to the future, as they imply in a higher Federal deficit. The hability to adjust depends, unfortunately, not only on the program itself, but in a political risk as the congress could refuse to reduce the revenue to these programs as this would be not appealing for voters. At least USA does not have something like "free healthcare for everyone" written in it's constituition like countries such as Brazil have.
The broader the extent of the program itself determines it's costs.


Problems with economic modelling: good textbooks/articles/papers?

I recommend reading Dani Rodrik's new book, Economics Rules: The Rights and Wrongs of the Dismal Science. Rodrik supports the use of mathematics as bringing clarity of meaning, and argues that the subject is far more applied and empirical than its detractors realize.

The final couple of pages have Rodrik's Ten Commandments for Economists. Numbers one and two are: Economics is a collection of models; It's a model, not the model. And also Ten Commandments for Non-Economists, which include: maths is useful; economists are not all alike; economists typically do understand how markets work.

All the Commandements with Dani Rodrik's comments can be found here. This review can also be useful for clarifying some of the commandments.


Does each stock exchange only trade in one currency?

An exchange can handle more than one currency, but this would be uncommon for equities.  An example is the ICE futures exchange in Europe.

Multiple currencies doesn't cause any particular problems - transactions are carried out in currency and it is up to you to convert to whatever currency you prefer.  Usually done by fx sweeps by your custodian bank.

For margin purposes combined exposure (e.g risk netting) can be calculated at prevailing fx rates.

Each security only trades in one currency, and each security trades basically like a mini exchange so there isn't really any problem.  Think of it like two exchanges run by the same company.


The use of the natural $\log$ permits to obtain approximations of percentage changes instead of unit changes (assuming linear regression). For instance, the parameter associated with $\log$ of GDP per capita would give you the changes in education (in the unit you measured it, e.g., years) as a result of an increase of 1% in GDP per capita. Notice that if your dependent variable is also a $\log$ transformation, you'll obtain elasticities.
To conclude, it should be straightforward for you to understand that there is no reason to apply a logarithm on unordered variables, or on binary variables. Its use on ordered variables is up to you, as the economic signification of choice of the estimates is dependent on your interests.


I need to prove how an increase in output p increases profit-max. Can someone help to understand why IFT implies that z is a unique maximizing point?

The uniqueness of z comes from the ND of $D^2f$ I believe. Let $z^*(p)$ be the solution of the problem at price $p$. Define the function, $G(p,z):=p \nabla f(z)-w$. From uniqueness we have $z=z^*(p)$ if and only if $G(p,z)=0$. That is, $G(p,z)=0$ is an implicit equation which tells us how $z^*(p)$ changes when $p$ does. The IFT gives us a way to find the derivative of this function
$$\frac{\partial z^*_i}{\partial p}=\frac{-\frac{\partial G}{\partial p}}{\frac{\partial G}{\partial z_i}}=-\frac{1}{p}H^{-1}\nabla f(z)$$
Where $H$ is the hessian of $f$.
So $\sum_i\frac{\partial f}{\partial z_i}\frac{\partial z^*_i}{\partial p}>0$ as $-H^{-1}$ is positive def.
The derivaitve of the profit function wrt to $p$ is $\frac{d}{dp}pf(z^*(p))=f(z(p))+p\sum_i\frac{\partial f}{\partial z_i}\frac{\partial z^*_i}{\partial p}$


Why are the 10 year German bunds and 10 year US treasury yield highly correlated?

Because they are the so called "Fly to Quality". When markets turmoil investors look where to safely invest their money to avoid volatility and risk. This lead to a depreciation (because of the more demand in bonds, the less bond rate) in rates. After the QE, as you said, the left risk about the already solid Germany was cut out because of the unlimited coverage by the ECB on European Bonds. Germany and US are considered the two solid major economics of the World and every rational investor who wants to do not run too risk (because it is impossible to avoid it entirely, see "idiosyncratic risk" for further information) prefers to invest there. A similar but slightly different chapter is for gold, considered a "Fly-to-Quality" good as well. Concluding, part of the correlation is due to economic relationships that there are between US and EU and it also accentuates the effects of important macroeconomic news of one or the other party.

TIP

Do you know why, sometimes, it is possible to see negative rates (as Danish or Switzerland or some Scandinavians)? Because sometimes, even if the rate is negative (you have to pay the issuer) the cost of carry is higher and then investors just leave their money there, paying less than to disinvest and invest again in another kind of security. This happened for some days to German rates too!


Can the function of the Central bank become automated?

It is conceivable that one of the functions of a Central Bank, of being a regulator of money supply, could ultimately be automated, if artificial intelligence were to advance enough. However, that role is much more complicated than merely feedbacks on flow of money, inflation and fractional reserve. So for the foreseeable future, that's a role filled by a panel of human experts.

And no, it will not be a distributed ledger,  because that's a hopelessly inefficient way to record Central Bank transactions. The Central Bank maintains its own ledgers, and will continue to do so. It is not the case that each transaction creates a new ledger. Instead, each transaction creates corresponding entries in two ledgers - that is the essence of double-entry book-keeping.


Tactical voting when the voting rule is unknown

You use the term 'deterministic' several times to refer to Gibbard-Satterhwaite, and a related question might specify preferences over risk for voters, and then ask whether there's a non-deterministic voting rule for which truth-telling is incentive compatible. I think this paper, by Gibbard from 1977, is relevant to that question.

As for the question you actually asked, if I understand you correctly, 'truth-biasedness' seems pretty strong. A voter misreports only if both (a) there are no voting rules under which misreporting would hurt her and (b) there is at least one voting rule under which misreporting would help her. So what's wrong with the following?

Say you have 3 voters, and consider 3 voting rules, one for each voter. Voting rule $i$ is: "Choose voter $i$'s most preferred alternative, unless the other two voters both prefer the same alternative and it is not the same as voter $i$'s most preferred alternative."

If the other two voters report truthfully, then a truth-biased voter can't gain from deviating: If voting rule $i$ is in effect and the other two voters differ in their most preferred alternative, then she cannot gain from misreporting because she gets her favorite alternative. If the other two voters both prefer the same option, then regardless of the voting rule that option will be chosen. In the former case there is one voting rule under which misreporting hurts her, in the latter case there are no voting rules under which misreporting helps her.


Say's law stated in terms of general equilibrium theory?

How about Walras's law?

  Walras's law is a principle in general equilibrium theory asserting that budget constraints imply that the values of excess demand (or, conversely, excess market supplies) must sum to zero.


Does Not Having a Fractional Reserve System Cause More Inflation?

Canada abolished bank reserves in 1992. Canada has had very similar inflation rates as the United States since then.

Increases in house prices do not improve bank equity. Banks make a profit based on being paid a rate of interest above their cost of funds. Increasing house prices just reduce losses in the case of default. Threfore, the relatively steady profits that come from interest rate spreads slowly builds up equity, with the result that bank balance sheets only exhibit moderate growth rates (similar to nominal GDP growth rates).


Software to simulate the effects of interest rates on an economy?

Unfortunately, the answer is so broad I'm not sure how useful it may be.

First things first, you'd need a model for the economy. There are various around, in the last few years DSGE models like RBCM and NKM are popular. Pick the one that you think is the most appropriate.

After that, procure data from the past for calibrating the parameters of your model. The interest rate, of course, will be set by you.

Finally, you can use R, Matlab or Octave to simulate, given your model and parameters, a set of outcomes and provide a result for each interest rate.


Behavioral Game Theory Reference Request

I know a bunch of people who teach behavioral economics using Erik Angner's book.
I love Rani Spiegler's book on behavioral economics in IO called "Bounded Rationality and Industrial Organization." Both books will introduce models that can be applied to poker.
Perhaps a little lighter but still scientific readings would be Kahneman's "Thinking, Fast and Slow" or Ariely's "Predictably Irrational."
As already suggested, a "handbook" is always a good place to start: Handbook of Behavioral Economics - Foundations and Applications.


You could use the fact that $\sum_{i=1}^{n}e_i=y$ (adding-up property) to see which parameter values are compatible with the above specification and this identity.
Before proceeding, you should replace on the RHS $\sum_{i=1}^{n}\beta_{ij}p_i$ by $\sum_{j=1}^{n}\beta_{ij}p_j$.


Beyond what is written in this Economist article, the general principle is an estimation based on statistical data. The 4 major aspects are private consumption, government consumption, investment and net exports.

I've worked as an auditor and cooperated with colleagues from the national bank of Portugal, which collected and cross-checked financial data to be able to calculate the GDP. Looking at the individual components:

The private consumption can be assessed by surveying individuals, making  assumptions in connection with the tax information and financial aggregated data from banks (who are obliged to report to the National Banks)
Government consumption is publicly available
Investments are estimated by looking at company data and company tax filings
Exports and Imports are calculated by crossing the info on  private consumption, investments, and bank data on payments sent overseas


How would you call a market for kidney donors and recipients?

Generally, these types of markets are called matching markets. That's also the same term given to a variety of economic decisions and market structures, from school choice to some types of marriage problems.


In a way EBQ (also known as EPQ) EPQ is an extension of the EOQ model, the difference being

In EPQ the company will produce its own parts
In EOQ parts are produced by another company

Note that if you produce stuff you need to store it somewhere, which comes at a cost. This is explicitly included in the EPQ model via the holding cost variable


Why does a homothetic function have constant ratio of marginal products along rays?

A homothetic function can be characterized as follows:
Let $f(\mathbf x)$, $\mathbf x \in \mathbb R^n$ be a function homogeneous of degree $r$. Let $g()$ be a function with $g'\neq 0$. Then

$$G(\mathbf x) = g[f(\mathbf x)]$$
is homothetic. Since $f(\mathbf x)$ is homogeneous of degree $r$ we have that

$$f(\lambda \mathbf x) = \lambda ^ rf(\mathbf x) $$

Then

$$G(\lambda \mathbf x) = g[\lambda ^ r f(\mathbf x)]$$ and so

$$\frac{\partial G(\lambda x)}{\partial x_i}=g'[f(\lambda  x)]\cdot \lambda ^r \frac{f(x)}{\partial x_i}=\lambda^r \cdot\frac{g'[f(\lambda x)]}{g'[f(x)]}\frac{\partial G(x)}{\partial x_i}$$

Evidently, we will also have

$$\frac{\partial G(\lambda x)}{\partial x_j}=g'[f(\lambda  x)]\cdot \lambda ^r \frac{f(x)}{\partial x_j}=\lambda^r \cdot\frac{g'[f(\lambda x)]}{g'[f(x)]}\frac{\partial G(x)}{\partial x_j}$$

which leads to the "constant MRS along rays" characterization of homothetic functions,

$$\frac{\partial G(\lambda x) / \partial x_i}{\partial G(\lambda x) / \partial x_j} = \frac{\partial G (x) / \partial x_i}{\partial G( x) / \partial x_j}$$

(see Simon and Blume 1994, p. 503).


Who regulates the balancing of the books for commercial banks? How? Is it public information?

It's public information, and you can take courses, and even university degrees in it.

The double entry book keeping technology used by banks is essentially designed to tackle exactly this problem, and all banks and commercial customers use it. The system itself provides a single error detection/correction mechanism, that guards against human error, and also originally required updates in two separate books, maintained by two separate clerks - which was deliberately done to make fraud more difficult. Essentially if the books don't balance, this is a red flag to find the mistake/fraud that caused this to occur and correct it. These days it's all computerised, but the underlying operations are identical.

The entire accountancy profession's job, is essentially to supervise this process, and periodically audit both banks and companies in order to make sure that the books are balanced, and that nothing illegal is being done.


Is the trade deficit driven by lack of domestic savings?

And we are back to Triffins' Paradox, apparently one of the most under studied and relevant concepts of our time which would answer many of these questions.

when one nation's fiat currency is used as the world's reserve currency, the needs of the global trading community are different from the needs of domestic policy makers. That is the reason we have a trade deficit.

Understood in this light, rising U.S. trade deficits in the 1990s and 2000s were required to provide enough dollars to lubricate rising global trade:

So, what does it mean if our trade deficit begins to decline? From the point of view of this professor, it would mean that we Americans are now saving money, but once again, we live in the age of globalization and we have the worlds reserve currency, so our economy is the whole planet not just within our borders.

Meaning, a declining trade deficit sounds good because we individualize our thinking about economics, oh boy, we are becoming savers, instead of spenders. We do not seem to care that it means fewer dollars are being exported. Who cares, right?

Well, consider that the global economy is about 60 trillion, of which about 25% is the U.S. economy. Into this vast sea of trade, the U.S. "exports" about 400-500 billion in U.S. dollars via the trade deficit. Put in perspective, it isn't that big compared to the machine it is lubricating.

So what happens when there are fewer dollars being exported? Demand for existing dollars goes up, pushing the "price" of dollars up--basic supply and demand, again, it sounds good, until you consider how it affects U.S. corporate profits.

No, their profits don't go up. Most large U.S. global corporations already earn 60+% of their revenues overseas, in other currencies. As the dollar weakened during massive QE, global corporate profits skyrocketed as earnings in euros, yen, etc. rose when stated in dollars.

As the U.S. dollar strengthens, overseas profits will decline when stated in dollars. Shrinking trade deficits means fewer dollars exported into the global economy, which means demand for dollars for trade, reserves and to pay debts denominated in dollars will face shrinking supply. That will drive the "price" of dollars higher.

As the price of dollars rise, U.S. corporate profits will decline as all the goods and services sold overseas in other currencies are converted (at least for accounting purposes) into U.S. dollars.

So let your professor know to be careful what he wishes for as shrinking trade deficits may appear to be positive for the domestic economy, but they won't be positive for a stock market dependent on profits generated by global corporations who earn 50%-60% of their revenues overseas.


The situation in Greece is complicated because it is part of the euro area, and NATO. It would presumably receive external aid.

But if you want a historical example, you could look at the tail end of the Depression in the 1930s. Although debt levels were not high by modern standards, governments had difficulty because of the Gold Standard. As countries moved to build up their militaries, they broke their pegs to gold. This gave them the ability to run large deficits to pay for the military spending.

Eichengreen’s “Golden Fetters” gives an overview of that era.

(The problem Greece faces that it is locked into an exchange rate system,like the Gold Standard, but it is even harder to get out of.)

In summary, the usual response is to break any existing currency pegs, default on foreign currency debt, and use deficit finance (and inflation) to handle the emergency.


Who were the economists who made lots of money in the financial markets?

At university classes, I always learned that the only economist who ever became rich was Ricardo. However, Ricardo was already rich before becoming an economist.

This article seems support this claim. It also gives an explanation for the lack of rich economist:

  If becoming wealthy is your goal in studying economics, you may be disappointed.  Although most economists make a good living, few have become rich from their knowledge of economics. In fact, if economists had some secret for making money in, for example, the stock market, they would likely be using those secrets to their own financial advantage [...] In short, economics won’t necessarily make you richer, but it may keep you from making some decisions that would make you poorer.


The demand for a key currency, like the USD - in contrast with other national currencies - is based not only on the domestic economy, but the global word economy. As the USA is viewed as a superpower and a global leader in economy, accordingly the US currency is generally viewed as a stable monetary asset which can be used as a global currency in international trade, or a clearing unit in international transfers and a value safeguard.
Some other currencies are tied to the value of the USD as well, which makes global trade much more calculable. As a result of this collective perception, the demand does not depend that much on the US economy, but the global economy and other global processes. This is obviously beneficial for the US economy and government as well, as it has much more wiggle room in becoming burdened with debts, while able to keep the value of its currency.