what results can be derived from the average cost curve? What is the practical use of knowing a firms average cost curve?

The reason why I ask is because computational problems that a firm faces are either with regards profit maximization or cost minimization and average cost curves are never used in computations.

If I can refine the question, what economic theory is derived from the average cost curve that are not given by marginal cost curve?

Assuming a firm is a perfect competitor in input markets, the long-run average cost curve, which traces out the minimums of short-run average cost curves, can be used to characterize economies and diseconomies of scale for a firm. This is definitely a practical concept in business and IO. In an industry where the long-run average cost curve is always decreasing, a natural monopoly will tend to emerge due to the increasing cost-efficiency of larger firms.

In a monopsony, the employing firm's average labor cost curve is equal to the supply of labor in the labor market. The marginal cost curve lies above the supply curve in this market because the firm's market power allows it to expressly set wages as a function of the quantity of labor. One reason this is practical is that it offers a potential theoretical explanation of why we do not see significant disemployment effects, or may even see an increase in employment, from establishing minimum wages in particular labor markets.


Indifference between 2 risky asset Consider the problem of an individual that must choose how much of his initial wealth
w0 > 0 to allocate to a risky asset X. The risky asset X has n ≥ 2 possible return rates,
namely r1, . . . , rn, and P rob(r = ri) = pi > 0 for all i ∈ {1, . . . , n}. The individual’s utility
function over wealth u is increasing, strictly concave and differentiable everywhere. Suppose now that there exists a second independent risky asset Y that has the same possi1ble return rates happening with the same probabilities as X..
Is the existence of Y beneficial to the individual?
When I first read the question, I think if they both have exactly the same probability and return value, it shouldn't be an advantage for us. But at the same time, I am wondering if there is any other situation that I am missing and that could take advantage of this situation. I wonder your comments.

It can be shown that under the assumption of strict concavity of utility function the investor will choose to split her wealth equally in the two assets. This happens because the variance on returns decreases by investing in two assets (assuming that the returns on two assets are independent).
We can consider two scenarios: first when the individual invests only in $X$ and the second where she splits her investment between $X$ and $Y$. It can be shown that in second case the variance of return goes down.
Let $r \equiv E(R_x) = E(R_y)$ and $\sigma^2 = Var(R_x) = Var(R_y)$
Assume that in second case, she invests $\alpha$ fraction of wealth in $X$ and $(1-\alpha) $ fraction in asset $Y$. Clearly $E(R) = r$. However:
\begin{align}
Var(R) &= Var(\alpha R_x + (1-\alpha)R_y)\\
&= (\alpha^2+(1-\alpha^2))\sigma^2 \tag{from independence} \\
&=(2\alpha^2+1-2\alpha) \sigma^2
\end{align}
The investor will choose $\alpha$ to minimize the term in braces which happens at $\alpha=0.5$ and so $Var(R) = \sigma^2/2$
Now it is a well know result that a portfolio with mean preserving spread is less preferred by risk-averse (concave utility) individuals. So the individual will choose to split her wealth equally among the two assets.


Preference relations defined by $x_1^n + x_2^n$ converge to $\max\{x_1, x_2\}$ In the problem set 2 of Rubinsteins Microeconomics (btw is there a comparably nice written book on macroeconomics?) there is the following question:
Let $\succ_n$ be the preference relations defined on $\mathbb{R}^2_+$ by the utility $x_1^n + x_2^n$. Let the preference relations $\succ$ be defined by the utility $\max\{x_1, x_2\}$. Show that $\succ_n$ converge to $\succ$.

Preference relations are said to converge if for $a \succ b$ we have that $a \succ_m b$ for sufficiently large $m$. I am indeed able to prove that.

Now w.l.o.g. $x_1 = \max\{x_1, x_2\}$ and $y_1 = \max\{y_1, y_2\}$. Assuming that $x_1 = y_1$ we have $x \sim y$. But the only case when $x \sim_m y$ is when also $x_2 = y_2$. In other cases we would have either $x \succ_m y$ or $y \succ_m x$ for all $m$ (depending on $x_2$ and $y_2$, the "smaller component". These are actually lexicographic preferences!)

Is there a reason that the convergence of preference relations is done in this way to ignore such subtilities? In my opinion we should have that $\succeq = \lim_{n \to \infty} \succeq_n$ iff $a \succeq b = \lim_{n \to \infty} a \succeq_n b$.

I am assuming you're familiar with the concept of monotonic transformations.

Let $f(z)=z^n$ be a monotonic transformation. $f(z)$ is an order preserving transformation for all positive $n$. Let $v:\mathbb{R_+^2} \to\mathbb{R}$ be an utility function, where $v(x_1,x_2)=(x_1^n + x_2^n)^{1/n}$. The function $f(v(x_1,x_2))=((x_1^n + x_2^n)^{1/n})^n=x_1^n + x_2^n$ will represent the same preferences as $v(x_1,x_2)$. Therefore, $(x_1^n + x_2^n)^{1/n}$ should also converge to $\max\{x_1,x_2\}$.

To prove the same, consider $v(x_1,x_2)=\Big(1+\cfrac{x_1^n }{x_2^n}\Big)^{1/n}x_2$. Assume $x_2 = \max\{x_1,x_2\}. $Now, as $n \to \infty$, two cases arise.

1) If $x_2>x_1$, then $\cfrac{x_1^n }{x_2^n} \to 0$ as $n \to \infty$. In that case, $v(x_1,x_2)=x_2=\max\{x_1,x_2\}$.

2) If $x_2=x_1$, the limit can be calculated by taking log on both sides as follows-
\begin{align*}
\ln(v(x_1,x_2)) = \cfrac{\ln(1+\cfrac{x_1^n }{x_2^n})}{n} +\ln(x_2) \,\,\,\,-(1)
\end{align*}
Since $x_1/x_2=1$,we have $(x_1/x_2)^n=1^n$. Using this in equation $(1)$, we get
\begin{align*}
\ln(v(x_1,x_2)) = \cfrac{\ln(1+1^n)}{n} +\ln(x_2)
\end{align*}
As $n\to \infty$, the term $\cfrac{\ln(1+1^n)}{n}$ becomes $\infty/\infty$. This limit can be solved using L'Hospital's rule. The value of the limit(you may check it for yourself) comes out to be $0$.
Now we have $\ln(v(x_1,x_2)) = 0 +\ln(x_2)$, or, $v(x_1,x_2)=x_2=\max\{x_1,x_2\}$.


Risk with unknown probability distribution of the outcomes From Wikipedia:
"Risk aversion comes from a situation where a probability can be assigned to each possible outcome of a situation and it is defined by the preference between a risky alternative and its expected value."
"Ambiguity aversion ... is defined through the preference between risky and ambiguous alternatives, after controlling for preferences over risk."
What is the preference between an ambiguous alternative and a certain outcome referred to? For example, the choice between a certain reward and an unknown probability to win a larger reward.
I think it is not risk aversion, because an alternative's probability distribution of the outcomes is unknown, and not risk ambiguity because one alternative does not entail a risk.

A sure outcome is just a special case of a risky alternative with a degenerate probability distribution.
Under a set of appropriate conditions, the choice of a sure outcome over an ambiguous alternative can be attributed ambiguity aversion. But since different authors define ambiguity aversion somewhat differently, the "appropriate conditions" also differ. On the other hand, choosing a sure \$100 over an uncertain distribution over \$1 and \$2 can hardly be called ambiguity averse.


How did we arrive to 40 hr work week? I am interested in a (reasonably) quantified explanation of why the work week in most of the world is 40 hrs and not for example 20? How did we arrive to the number 40.

Another question is, and here I understand I can't expect quantification so much, is why there are more part time jobs available in the low income range (menial work) but not so much among knowledge workers? For example, I am a software engineer living in a major metropolitan area, still finding part-time work is very hard. Seems like everyone wants full-time employees or at least contractors.

I am perplexed by this state of the labor market and would like to learn some perspectives on this from schooled economists.

The 40-week comes started with the movement of the 8h working day. The wikipedia article makes a quick summary of the historical progress of thinking from 12h work days in Britain during the industrial revolution to the nowadays 8h/day.
The quick summary is that after the first world war, the International Labour Organization (ILO) was formed and its first convention was defining limits for the work day:

Having decided (...) the "application of the principle of the 8-hours day or of the 48-hours week" which is the first item in the agenda

From Convention Limiting the Hours of Work in Industrial Undertakings to Eight in the Day and Forty-eight in the Week (ILO, 1919)
This meant that generally workers would work 8h/day as a maximum, with 1 day of rest per week. 52 countries have ratified this convention, although not immediately.
The change for the 40h week came in 1935, with another ILO convention, which explains the motivations in its preamble:

Considering that unemployment has become so widespread and long continued that there are at the present time many millions of workers throughout the world suffering hardship and privation for which they are not themselves responsible and from which they are justly entitled to be relieved;
Considering that it is desirable that workers should as far as practicable be enabled to share in the benefits of the rapid technical progress which is a characteristic of modern industry; and
Considering that in pursuance of the Resolutions adopted by the Eighteenth and Nineteenth Sessions of the International Labour Conference it is necessary that a continuous effort should be made to reduce hours of work in all forms of employment to such extent as is possible;
adopts (...) the following Convention, which may be cited as the Forty-Hour Week Convention, 1935:

From: ILO Forty-Hour Week Convention, 1935 (No. 47)
This later convention has been ratified by 15 countries only.
Further recommendations on the reduction of hours were made in 1962 (source ILO). The ILO also has a page summarizing the work done in the last 100 years on working time, which is a great resource to learn more.


Existing metrics for amounts of leverage used in financial sector My current understanding is that excessive leverage caused the Great Recession.

Are there existing metrics for measuring the levels of leverage currently used in the US financial sector (lending, investing, bonds, etc.)?

The first place to start is the Federal Reserve’s Flow of Funds report (Z.1) - link to Fed website.

It has aggregate balance sheets on an instrument and sector basis (including the financial sector, as well as its components). One can then look at growth rates, or scale relative to national income/GDP.

Although I have personal preferences on what data I would look at, someone else might be able to suggest studies on particular indicators.


How to find (document) the actual costs of a specific US government social program? I had an interesting discussion today while volunteering at a food bank program. The individual I spoke with was a retired math professor who stated his research makes him believe that significant money could be saved in regards to the foodstamp program.

Apparently the situation is that after the initial application for foodstamps, recipients on the program are required to file monthly or quarterly reports that document the minutia of their income (even things like a \$5 gift card from grandma) and if anything is deemed improperly documented the recipient is forced to file more paperwork or lose their food. The program is administered in county offices with waiting lines lasting 4-6 HOURS on average. All for approximately \$6 per day (\$185/month) through a special debit card that can only be used at authorized merchants.

The professor's contention was that money is being wasted and people are being dehumanized by the constant demand for proof-of-need documentation. He proposes that if we eliminated the monthly paperwork bureaucracy and just "gave" everybody who validly applied \$200 per month we would actually save money, even if the roster of recipients tripled. The only ways to get kicked off the program would be (A) dying - just like social security benefits, (B) requesting exit from the program, or (C) being convicted in a courtroom of committing fraud against the program (such as submitting fake applications for non-existent dependents) which would ban you for life.

On the surface is sounds practical: eliminate (actually repurpose - other agencies will find uses for these folks you can be sure) tens of thousands of high-pay civil service jobs) in exchange for just making an unquestioned monthly deposit. Note that the professor did support keeping the initial application screening process and also once a year requiring a simple "I still need help" affidavit. Mountains of paperwork monthly vs 1 sheet per year.

So my economic question is how can this "proposal" be validated? Where does one get the numbers for what is currently being spent on the program, broken down by both recipient costs and paperwork costs? Does such a source of data exist and is it available to average Joes like me for review?

PS: The professor also suggested putting a cap on the food card accounts of 90 days worth of benefits. If you don't use your benefits (say you are in the hospital for a few months) the card would not accept new deposits until there was "room" for more.

http://www.fns.usda.gov/pd/supplemental-nutrition-assistance-program-snap - Participation and Costs is the first file in the list

Under the current rules, one problem with stopping activity reports is that all of the statistics you see there would be gone. Another more serious problem is that SNAP recipients are restricted from purchasing certain goods; it's not just that the SNAP card is only accepted at certain merchants.


Is it easier to borrow money during a recession or high inflation period? During a recession the FED applies expansionary monetary policies while during high inflation periods it contracts the money supply which respectively lowers and raises interests rates.
Given that someone is willing to pay a fixed interest on their loan are they more likely to get it during the recession or during the high inflation period?

The question wording is somewhat vague, so I am interpreting it as follows: assuming an entity wants to borrow at some fixed interest rate, is it more likely to be able to do so in a recession or in a high inflation period?
The following factors matter.

The willingness of lenders to lend depends up on the state of the cycle. As noted by Henry in a comment, lenders were largely unwilling to extend new loans during the Financial Crisis of 2008. Since defaults generally rise in recessions, lending generally tightens up even under less extreme conditions.
The risk-free curve generally falls in a recession (for countries that control their currency, like the United States). This would make it easier to get a loan versus a fixed rate. However, credit spreads tend to widen (due to greater default risk), so depending on the credit quality of the borrower, the borrowing rate might go up.
Risk-free rates tend to rise in an inflationary period, which might partially be offset by tighter credit spreads.

These factors pull in different directions, so there is not enough information to answer the question as stated.


Does aggregate demand increase investments? I just read that increase in aggregate demand increases investment for a given interest rate. How is it possible because when aggregate demand increases, this shifts the demand for money to the right leading to higher interest rates. Higher interest rates should reduce investment. Am I correct in with my argument?
And help will be appreciated.

Once again, the fixed thing is interest rates. There are numerous ways in which a government can control an interest rates: one of which is to control the money supply. I feel that in your case, you are assuming that the amount of money in the economy and the speed of money flow is fixed. However, we can control the interest rates by controlling the money supply. When we want to make an interest rates at a fixed term, we want to pump more money into the economy and thus increasing the supply of money and keeping the interest rates as low as it used to be. Thus it is possible for that to happen. Please note that I have also assume that the interest rates dixed and the economy is not running at the intermediate or full capacity


Alternative inflation metrics I am looking for the most famous alternative inflation metrics  used by some acknowledged economists other then CPI and PCE.  In my opinion energy, food, education, healthcare, housing and transport is much more important then say a cellphone or a new tv, if anyone knows of any index weighting in this manner and have a similar idea around why to weight like this, please let me know.

The PPI (Producer Price Index) measures the domestic output of raw goods and services.

The GDP deflator measures the changes in all goods and services produced in an economy.

For your purpose the US Bureau does release indexes that drill down further into the PPI in the form of industry level classifications and commodity classifications.


What does Yanis Varoufakis mean by "surplus recycling mechanism"? Yanis Varoufakis, the current finance minister of Greece, talks about a "surplus recycling mechanism", a term he coined and uses to describe (as I understand it) a relief valve for economies running a surplus.

While I haven't read his book, I watched some of his talks and read his blog posts. I couldn't quite figure out what he means by this. Could someone please explain what he means by "SRM", and why he considers it important, crucial even, to prevent major recessions?

Here's what I've figured out so far. The surplus being talked about is the trade surplus. That is, countries which export more goods than they import run a surplus, and get a net influx of cash (or, in the past, gold). This cash can either be hoarded, or reinvested. Internal expenditure is ignored as irrelevant, as only the interactions between countries are being looked at. If hoarded beyond a certain breaking point, bad things happen. A surplus recycling mechanism compels a country to reinvest the cash overseas.

Or so it seems. Is my understanding of what "SRM" means correct? Also, if so, according to Varoufakis (or Keynes, who apparently had the exact same realisation around WW2 time), how exactly does hoarding without bound cause bad things / recession?

It would also help to know whether Varoufakis' ideas / interpretations are widely accepted by mainstream economists, currently being debated, or are a fringe/minority view.

"Surplus recycling" is a term coined (to my knowledge) by Varoufakis to describe the fact that a country that enjoys a trade surplus should reinvest the surplus in the domestic economies of its trading partners. Such a policy was conduced with success by the United States in the years following WW2, where the Marshall plan and similar policies in Asia took place, mainly for political reasons.

As Varoufakis states it, there is no reason for the market to proceed to such a transfer, yet it does sound reasonable to keep trade partners in good shape.

In Europe, Germany's trade surplus is notable for being the only important European surplus. Surplus recycling is one way the Greek government is trying to get Germans to feel right about handing out money to European countries that are struggling with their economy, another infamous attempt being WW2 reparations.

I believe you're somewhat wrong in your interpretation because the question here is not whether to reinvest or not (this is a problem which is well treated by "classic" macroeconomics), but where to reinvest the money. The alternative is hence between domestic and foreign investments, and there is no known economic mechanism that supports foreign investments unconditionally. Varoufakis work aims at fostering foreign investment from Germany to southern Europe. I don't see anything controversial in his definition, but he is defining a policy, not a model.

The problem with solely-domestic investments is that, on the long term, it weakens trade partners, which weakens domestic economy in turn. I don't think there is much debate among the fact that trade balance is not a self-correcting problem. The real debate (and it's political for the moment, an open field for economic research) is on what end the policies to solve the problem has to be carried: the one for which it is easier to solve (Germany), or the one for which the problem is worse (Greece).

The amount of money we're talking about is sizable to say the least, and can be viewed here as suggested in a comment.


Limit of this sequence // broadness of inputs Let there be a unit measure of inputs. Define by $C_i = \left[\int_0^i c(i)^{1-\alpha}\right]^\frac{1}{1-\alpha}$ a cost index of using up to $i$ as input.

I discretize $c(i)$ by $c_0, \dots c_i, \dots c_I$. Let for example $c_i = 1 \,\forall i$, and $\alpha = 0.5$. Let $I = 5$. To approximate the integral, I simply sum up terms and divide by $I$.

Then we have $C_1 = (\frac{2}{5}\sqrt 1)^2$, $C_2 = (\frac{3}{5}\sqrt 1)^2$ etc. So this is an increasing sequence, and $C_1 = 4/25=0.16$.

Now I need the corner case, $C_0$. $C_0$ only uses $c(0)$ as input, so I'd think that

$$ C_0 = (c(0)^{1-\alpha})^\frac{1}{1-\alpha} = 1$$

But that clearly can't be the limit of the discretized sequence, since $\lim\limits_{i\to 0} C_i \to 0$.

So, as the variety of inputs decreases, the cost index decreases - until you only have one variety, and then it explodes? Could someone please shed some light on this?

I think the appropriate discretisation should be something like
$$C_i=\left[\int_0^i\!c(i)^{1-\alpha}\,di\right]^{\frac{1}{1-\alpha}}=\lim_{I\rightarrow\infty}\left[\sum_{j=0}^{(I-1)i}\frac{1}{I}c\left(\frac{j}{I}\right)^{1-\alpha}\right]^{\frac{1}{1-\alpha}}$$

The below figure illustrates where each term of the sum comes from (for the case of $I=5$)

(The reason the sum goes up to $(I-1)i$ is that we start counting from $j=0$ and want to have $I$ bins in total.)

In your example with $c(i)=1$ and $\alpha=1/2$, this would yield
$$\left[\sum_{j=0}^{(I-1) i}\frac{1}{I}\sqrt{1}\right]^2=\left[I i\frac{1}{I}\sqrt{1}\right]^2=i^2.$$
We can compare this to the true value of $C$: $(\int_0^i\!\sqrt{1}di)^2=i^2$. Thus, this particular example is special because the discrete approximation gives an exact expression for the integral even without taking the limit. The reason for this is that $c(i)=1$ is a constant function so a rectangular approximation of the areas beneath it is perfect for any number/size of Rieman rectangles.

But suppose we take $c(i)=i^2$. We then have $(\int_0^i\!\sqrt{i^2}di)^2=i^4/4$ and $$\left[\sum_{j=0}^{(I-1) i}\frac{1}{I}\sqrt{\frac{j^2}{I^2}}\right]^2=\frac{(I-1)^2 i^2 (1-i+I i)^2}{4 I^4}.$$
In the limit this approximation converges on the true value: $$\lim_{I\rightarrow\infty}\frac{(I-1)^2 i^2 (1-i+I i)^2}{4 I^4}=\frac{i^4}{4},$$
but for finite $I$ the approximation is imperfect.


Is it enough to prove that $x \not \succsim^* y$? I'm trying to negate that: $\exists B \in \mathcal{B}$ such that $x,y \in B$ and $x \in C(B)$.
Looks that the negation is equivalent to: $\forall B \in \mathcal{B}(x,y \in B \implies x \not \in C(B))$. Is it right?

Yes, it is. Step by step:
$\lnot \exists B \in A (x,y \in A \land x \in C(B))$ is equivalent to
$\forall B \in A \lnot(x,y \in B \land x \in C(B))$ is equivalent to
$\forall B \in A (x,y \notin B \vee x \notin C(B))$ is equivalent to
$\forall B \in A (x,y \in B \implies x \notin C(B))$.
Reference: How to prove it, by Velleman


Economics in nature? Unsure if this is off topic but have there been any attempts to look at the "economics of nature"? I mean this in the sense of measuring the "economic activities" of the animal kingdom.

From wikipedia

  An economy (From Greek οίκος – "household" and νέμoμαι – "manage") is an area of the production, distribution, or trade, and consumption of goods and services by different agents in a given geographical location.

we can see all of these activities in a bee hive (other than trade I guess). It seems like it can work very well with alot of the inter-temporal models we see in intermediate macroeconomics.

Practical questions for analysis include:

How is "income" or food distributed in a colony
what is the Lorenz curve in a colony
what is the MRS between present and future consumption in a colony

It would be interesting for the sake of real world policy application, much like engineers design from nature can we create economic policy from it?

You may want to take a look at Evolutionary Game Theory. Instead of using the regular equilibrium concept developed by Nash, it uses the concept of an Evolutionarily Stable Strategy (ESS).
The idea isn't that players are rational and are choosing strategies given what others are doing to maximize payoff. The idea is: each mutation of that species is "programed" to adopt a particular action (instinct), and when different mutations of the gene interact, it will generate probabilities of survival. Thus, an equilibrium strategy is an ESS, which are the types of actions instinctive to a certain gene type, which will tend to survive and procreate, passing forth the gene.
Game Theory is a field that has had intensive collaboration between Biology and Economics. I am sure you will find some interesting stuff.


What are the differences between the older gold standard and the current fiat money standard? My current limited understanding is that the gold standard was a system in which there was a fixed currency amount per unit of gold. For example, 1 ounce of gold might be 100 USD. Another country like UK might peg their currency to be 1 ounce of gold for 50 GBP.

This means that GBP and USD would also be fixed at 1 GBP for 2 USD?
What would be an example of how trade would occur between these two countries? Say that the US had oil that the UK wanted to buy. Would the UK give the US GBP in exchange for the oil? Then in return, the US would use this GBP and return it to the UK government in exchange for some predetermined amount of gold? So in the end US gold reserves would increase and UK gold reserves would decrease? But doesn't this then mean that the US would have to print more money to keep the gold/USD exchange rate fixed?
In today's fiat currency, how does trade occur? I understand that different factors like interest rates and inflation can affect exchange rates.
But why do countries hold currencies of other countries in "reserve"? Why is this necessary?

The gold standard in the US was actually kind of complicated.

You had the government issuing notes off of gold, and private banks issuing bank notes off of gold...but also banks issuing notes/deposits off governments notes as well.  A pyramid on a pyramid.

Neither was 100% backed and both were vulnerable to runs.

In 1933, FDR no longer let the public redeem gold for dollars.  A default of sorts...but we were never on a true gold standard!  We always had more promises than gold.  The same with the banks.  Given that gold used to be equivalent to dollars (as the Fed used to exchange the two), banks would use dollars as reserves for convenience...but soon they became the monetary base.

Now the US still maintained an international gold standard.  But this too was fractional and had more promises than assets.  Countries (most notably) the French did not like how "overbooked" the dollar was to gold and started redeeming their gold in mass.  There was a run by international central banks on the dollar and Nixon had no choice but to take us off the international gold standard as well.

So it is confusing, but we went off the gold standard twice.  Once to the public (FDR) and once to international central banks (Nixon).

So how did this work before 1972?  Gold was the international reserve currency, but on top of this the dollar was the means by which gold would be commonly traded between countries.  It was much more difficult to clear transactions in gold than paper (or accounting) dollars, which led to its popularity as a reserve currency.  On occasion of course individuals would demand gold for dollars and you would have physical transfers take place (as in load the gold onto the ship and send it over the high seas).

If you are interested in the history of the American gold standard, I highly recommend the book A History of Money and Banking in the United States:
The Colonial Era to World War II by Murray N. Rothbard:

mises.org

So what is the difference between the old system and the current system?  Not much as we were never on a true gold standard.  But in a nutshell, banks used to be able to redeem dollar bills or central bank deposits for gold.  Now dollars are not redeemdable for anything.  You can see on the Fed balance sheet a holdover for this as gold is still considered an asset and dollars (paper and electronic) as liabilities.

en.wikipedia.org

So how would trade occur pre-Bretton Woods?  Mostly through banks.  The receiver bank would obtain credit for gold, or a national currency that was convertible to gold (dollars or say pounds).  If one party wanted to convert currencies they could but it mostly took place as a transfer from say "pound deposits" to "dollar deposits".  If the new party demanded their payment in gold they could obtain this but it rarely happened.

After Bretton Woods, international trade was mostly facilitated by dollar deposits with the promise of gold redemption of a foreign central bank demanded it (which Nixon ended).

Now when gold reserves were physically demanded, did this cause problems?  Yes!  Remember, all countries and banks issued more notes/deposits for dollars than they had (somewhat dishonest but that is another matter).  Say the pound (during the standard) lost a bunch of reserves...so they go from a ratio of say 1000 central bank deposits to 200 gold to 900 central bank deposits and 100 gold.  A serious blow to credibility which could lead to a run on the currency. Do they have to print or destroy more notes/deposits...no because they do not 100% back gold.

So why do countries hold reserve currencies today?  They kind of don't need to, but there is a reason.  Basically private banks operate by maturity mismatching (balancing short term debt against long term assets).  When a currency is not stable (like from a small nation) short term interest rates are too volatile for banking and in fact bank runs can be initiated from clever predator foreign inverters (like George Soros).  Politicians like banks...and for some reason they think they are important to the economy, so go to great ends to prop them up.  For a small nation this means their currency must be somewhat stable for their banking system to survive...and the nation achieves this by maintaining a peg.  You can only maintain a peg if you can manipulate the market, so countries hoard foreign assets like dollars so they can buy and sell their home currency (like say the Peso) so it achieve its peg rate.

As for clearing of international transactions this is mostly done with bank money, but dollars are a common facilitating base for these transactions (although certainly many other currencies are being used now).


Monopoly firm's block pricing strategy making max. profit I have question about max. profit condition for monopolist block pricing.

I learned that to maximize profit in block pricing, given a linear demand curve function and constant MC, calculate $Q_2(Q_1)$, and $P_S(Q_1)$ then find $Q_1$ maximizing profit and then find $P_1$ and $Q_2$ the $P_2$.

This is what I read from the textbook (Microeconomic, Besanko).

But I heard somewhere that when in following case,

with right-downward sloping $MC$ and $AC$,

Profit maximizing first block price and quantity is $P_1$ and $Q_1$ where $AC=MR$
and second block price and quantity should be $P_2$ and $Q_2$ where $AC=D$

I've thought about this for 1 day and still couldn't get why maximizing condition is like that.

The reason why the profit maximising condition is like that is because the monopoly is Price Discriminating between those who are willing to pay at  $P_1$ and $P_2$ for $Q_1$ and $Q_2$ respectively.

This increases the area of producer surplus to an area greater than what it would be by charging $P_1$ and $P_2$ alone.


Interpretation of sub-unity money velocity I've read through questions like: Implications of declining money velocity and noticed this trend has intensified since, with velocity printing the lowest readings in history in the past few months. Currently, velocity stands at 1.13.
https://fred.stlouisfed.org/series/M2V
From what I gather, the mainstream interpretation is that the low velocity levels are a result of monetary stimulus making its way into M2. The expanded balance sheet of the Fed was mainly aimed at stabilizing financial markets rather than the real economy. With interest rates near/at zero, cash replaces short-dated bonds as the preferred risk-free liquid asset. In this sense, velocity reflects growing demand to hold cash versus use it for transactions in the real economy.
I haven't found any literature on sub-unity velocity, so I'm left wondering if there is some sort of singularity that cannot be crossed without violating a sacred economic theorem. However, given that:
$$ V = GDP/M2 $$
It would seem that there is nothing in the laws of physics (indeed, nor economics) that would serve as a fool -proof guarantee that GDP must exceed money supply. Surely with Weimar Germany and other hyperinflationary episodes, the ratio slipped into sub-unity territory. I concede it may be an extreme scenario for much of the developed world, but in the face of supply chain disruption and quarantine measures, it merits a thought experiment.
Question
Hypothetically, if the US was to fall into sub-unity velocity, would there be a clear interpretation and how much significance would the act of crossing below one have? Optionally, what if V was negative?
(I realize not everything can be taken to the extreme in econ. As an example, take negative prices. Instead of customers paying firms for goods, they would pay firms not to produce. Or whatever the case, the interpretation of negative prices isn't clear.)

Hypothetically, if the US was to fall into sub-unity velocity, would there be a clear interpretation

$V$ is by definition the average number of times 1 unit of currency is used (See Fed explainer on that). A clear interpretation of $V<1$ is that there are some units of currency that were never used during the measurement period. If an hypothetical economy consists of 2 1\$ bills, 1 will be buried  in the garden and never used and the second one only used once to buy goods and services worth of 1\$ the velocity of money would 0.5 (you could either calculate this directly as $V=\frac{1+0}{2}$, or indirectly in this scenario $M=2$ and $PY=1$ so you will have $V=\frac{1}{2}$.
Furthermore, note the equation for velocity actually calls for nominal output not GDP. That is the equation is given by $V=\frac{PY}{M}$, nominal GDP is just gross nominal output (in fact even this is a derivation the relationship actually is $V=PT/M$ where $T$ is number of transactions (see Mankiw Macroeconomics 8ed pp 108) but under very light assumptions one can derive that $PT=PY$ so we can run with it). This does not mean you can't use gross nominal output as a proxy, gross nominal output tries to capture $PY$, but you should be aware that there will be measurement error and GDP excludes gray/black market activity and so forth.

how much significance would the act of crossing below one have?

There would be no special significance to that per se. This would be like asking what would be special significance of CPI index crossing some arbitrary threshold like 1.05.

Optionally, what if V was negative?

$V$ proper cannot be negative because the smallest amount of times you can use unit of currency is 0 times. Its like asking if number of pies that you eat can be negative. That is simply impossible. This being said you could probably measure negative $V$ if you use $GDP/M$ to measure it but then you are running into a problems that arise from a fact that GDP is not exactly the same as nominal output.
For example, consider some state that completely disintegrated into Hobbesian anarchy, where all activity is done in grey/black markets with exception of 1 importing company, yet for some reason there are still statisticians going around and recording output in formal sector. Now let us assume that people get 1000 nominal income earned at grey and black markets, use half of that to import goods and services. Since GDP only tracks legal activity and since imports count negatively toward $GDP=c+i+g+(x-m)$ one would record negative nominal GDP and then $V$ will be negative as well, but that's rather due to limitations of measurement technique that you use not because $V$ as a concept can be negative.


Exercise about Monopoly price charging In a two-period lived economy, one consumer wishes to buy a TV set in period 1. The consumer
  lives for two periods, and is willing to pay a maximum price of $100 per period of TV usage. In
  period 2, two consumers (who live in period 2 only) are born. Each of the newly born consumers is
  willing to pay a maximum of fifty dollars for using a TV in period 2. Suppose that in this market
  there is only one firm producing TV sets, that TV sets are durable, and that production is costless.

  (a) Calculate the prices the monopoly charges for TV sets in periods 1 and 2.

  (b) Answer the previous question assuming that in the first period, a consumer who lives two
  periods is willing to pay no more than twenty dollars per period for TV usage.

My attempt

For this I consider cases whether person 1 buys tv in period one or not.
If he not buys then monopolist sell tv to other person for 50 yielding profit of 100 but also he can charge 100 for person 1 so total profit is 200. So my question is whether he charge 50 or 100 from person 1 as there is not given about price discrimination.
Also if he buys tv in period 1 then 100 for second period person is same but then how to calculate it for period 1 price is it 150 or 100 as person 1 not want to give more than 100 for period.

I do not understand your attempt very well.

Assuming that the monopolist cannot directly price discriminate (i.e. charge different prices to old and new consumers in the same period), then in the second period it is optimal to offer a price of 50 and sell to everyone, regardless of whether the old guy bought or not.

Knowing this, the old guy would buy in the first period iff the price gives him a total surplus of 50 (which he can get by waiting). Hence, the initial price should be 150.

If, on the other hand, the old guy has a value of only 20, then in the second period the monopoly price would still be 50. Hence, the old guy has no surplus from waiting and the monopolist should charge 40 to him in the first period.


Very basic question about confidence intervals Suppose that I estimate a (frequentist) confidence interval for the sample mean of a variable $X$, say at the 95% level. Suppose I also estimate a 95% confidence for the sample mean of a variable $Y$.

Claim: we cannot reject the hypothesis that $X$ and $Y$ have the same
mean at the 5% level if and only if these confidence intervals
overlap.

Is this true? I have a vague recollection that the answer is 'no'.

Yes your vague recollection is correct. You can verify it with a trivial example.
Lets take $\bar{X}=10$, with $\sigma(X)=2$ and $n=30$. So the $95\%$ confidence interval (using student's t distribution) is approximately given by  $10 ± 0.75$.
Now suppose $\bar{Y}=11$ with $\sigma(Y)=1$ and $n=30$ so the $95\%$ confidence interval is given by approximately $11 ± 0.37$.
Confidence intervals above clearly overlap since for $\bar{X}$ the upper bound is 10.75, but for $\bar{Y}$ the lower bound is $10.63$ but when we actually do the t-test for difference in their means we get:
$$ t=\frac{10-11}{\sqrt{\left(\frac{2^2}{30}+\frac{1^2}{30}\right)}} \\
 \approx -2.5 $$
Hence in this case we clearly can reject the null hypothesis that the means are same even at $5\%$ (in fact the $t$-stat is very close to being rejected at $1\%$ even) despite that their confidence levels happen to overlap.


Can I use calculated data for regression Can I use calculated data for regression analysis.

case 1: first run OLS $y = \alpha+\beta x$, and get $\hat\beta$, then calculate $z = h^\hat\beta$, at last run $m = \gamma + \mu z$.

case 2: follow the same settings as case 1, run $z = \zeta + \rho p$.

case 3: use matlab solve equation $k_i = \sum_j d_{ij} k_j$ for $k_i$, then run $w = \theta + \pi k$.

where $\alpha$,$\beta$,$\gamma$,$\mu$,$\zeta$,$\rho$,$\theta$,and $\pi$are coefficients, the other letters denote the variables.I have the variables y,x,h,m,p,$d_{ij}$,w. All the relationships between variables are from the models.

They are independent cases that I ran into.

I am going to estimate the coefficients $\mu$,$\rho$,and $\pi$.

I'm afraid the accepted answer is not precise enough, and can be deeply misleading.

This issue is formally called the Generated Regression problem which arises when we use "generated" regressors in a regression. This is a very common feature of estimations like Heckman Selection Model, where we use the predicted Inverse Mills Ratio from the selection equation in the structural equation. We need to divide the issue in two:

Consistency: there is usually no problem of consistency when using generated regressors in an estimation. A formal proof can be found in Wooldridge (2010), page 123.
Statistical inference: here there might be problems. Under the null that generated regressors are zero, then standard errors and all tests are valid (you might still need to correct for heteroscedasticity and serial correlation as usual, using robust standard errors). However, if the generated regressor is statistically significant, then the standard errors and in consequence any test are invalid. What you need is a correct estimation of the asymptotic variance. The formulas depend on each case (more information in Newey and McFadden [1994]). However, a general solution to calculate the consistent standard errors is to use bootstrapping. As an aside, for example, if you use Stata, just run your normal command with the following code before:

bootstrap, reps(400) seed(10101): regres ...

reps is the number of repetitions and seed is for reproducibility.

TL;DR

If your generated regressor is statistically significant in your regression, then you need to estimate the standard errors using boostrapping because they are invalid. If they are insignificant, you are safe.


Debt accumulation equation derivation: valid given that it rests on calculus and the time period is a year? (nowhere near infinitesimal?) Above is an image of what I’m referring to. The top ‘rule of thumb’ is derived using calculus, and hence is only valid for infinitesimal changes in t. However, this equation is considered over the period of a year, which is a large unit of time. How can this equation be justified?

I've put a derivation of the 'rule of thumb' below (in case you weren't sure how it was derived). I've derived the product case, but it can be used to show the quotient case, which is what I put at the very bottom. Please excuse my naff handwriting!!

$$\frac {\Delta d_{t+1}}{d_t} = \frac {\frac {D_{t+1}}{Y_{t+1}}-\frac {D_{t}}{Y_{t}}}{\frac  {D_{t}}{Y_{t}}} = \frac {D_{t+1}Y_{t}-D_{t}Y_{t+1}}{D_{t}Y_{t+1}}$$

$$=\frac {D_{t+1}Y_{t}}{{D_{t}Y_{t+1}}}-1 = \frac{Y_{t}}{Y_{t+1}}\cdot \left[{\frac {D_{t+1}}{D_{t}}   -\frac {Y_{t+1}}{{Y_{t}}}}\right]$$

$$=\frac{Y_{t}}{Y_{t+1}}\cdot \left[{\frac {\Delta D_{t+1}}{D_{t}}   -\frac {\Delta Y_{t+1}}{{Y_{t}}}}\right]$$

So the "rule of thumb" deviates from the above exact expression by (multiplicatively) $Y_{t}/Y_{t+1}$.

Now, we are talking about the growth rate of the Debt/GDP ratio. Say the ratio was $120\text{%}$ and it went to what? in one year? Say it went to $D_{t+1} /Y_{t+1} =  130\text{%}$. Then its exact growth rate is $130/120 -1 = 8.33\text{%}$ Assume also that GDP grew at 5% yearly rate, so $Y_{t}/Y_{t+1} = 0.95238$.

In this numerical example, the "rule of thumb will give as Debt/GDP ratio growth rate $8.33\text{%} \times 0.95238 = 7.933 \text{%}$, or less than half percentage point underestimation. This is considered a small inaccuracy in the real world, when one discusses broadly these magnitudes. And in general the above numerical example exaggerates, in most cases the growth rate of the GDP and of the Debt/GDP ratio are smaller than above, so the inaccuracy will be even smaller. Hence, the "rule of thumb" becomes acceptable in general also in theoretical models.


Definition of a 'Competitive Firm' and a 'Perfectly Competitive Firm' In many of my intermediate microeconomics quiz and test questions I encounter the term "competitive firm" and/or "perfectly competitive firm", e.g.: In the short run, a perfectly competitive firm earning positive economic profit is...

My textbook has no explicit definition for either of the terms.  What assumptions should I make about:

The firm
The market the firm is operating in

Without seeing a particular context, it is hard to be 100% sure. But typically the term "competitive" is used as shorthand for "perfectly competitive".

  A market is perfectly competitive if everyone in that market takes the price as given. That means a seller in a perfectly competitive market can sell as much or as little as he likes (and a buyer can purchase as much or as little as he likes) at the prevailing market price. Nobody has any power to influence the market price.

Contrast this with something like a monopolist, which can set whatever price it likes and therefore obviously does not take the price as given.

A firm in a perfectly competitive market would be said to be a "competitive firm".


Rationale and Methodology for Discounting the Investment in an NPV Calculation It is clear to me why the benefits accruing from an investment should be discounted. What I wish to understand is what the correct way discount the investment itself is.
Assuming zero inflation, consider that at a personal discount rate of $\rho$, the net present value of an investment $K$ can be computed as
$$
 \frac{R}{\rho - \mu} - K\ ,
$$
where $R$ is the expected revenue flow with trend $\mu$. If this quantity is positive, the investment is a good one. But suppose I pose the question of how much I stand to gain by delaying the investment to some later time $t$, say. The return term above is modified to $R_0 e^{\mu t}/(\rho - \mu)$, and if I leave $K$ as is, this new NPV will be strictly greater than the old value: a speculative bubble. I hence have two questions.

Should $K$ be discounted when computing the NPV of the investment at some future time? If so, what would the rationale be? I can understand the time value of money applied to the return, but why should a future investment (i.e. a future cost) be discounted?
If the answer to (i) is in the affirmative, would it make sense to use a different discount rate for $K$ than $\rho$? It seems to me that costs should be discounted differently (more gently) than returns.

To be clear, we are assuming that the nominal investment value is a constant $K$. As such, if we calculate the NPV in the future, that future NPV will rise.
Of course, we do not work with future NPV’s, we are making a decision now, and so we need to discount that future NPV by the discount rate, to get an apples-to-apples comparison.
I will now look at the sub-questions.

An investment $K$ in the future is not the same thing as an investment $K$ now. We can buy a zero coupon bond with maturity $t$, and meet the future outflow of size $K$ with an bond that costs $Ke^{-r_bt}$, where $r_b$ is the mathematical discount rate on the bond. (Quoted yields follow different conventions, so you need to adjust quoted yields for the calculation.)
The reason I would discount future outflows at the bond rate is because that is the mechanism to translate current cash to future cash flows in a “guaranteed” fashion. You could use the project discount rate, but you are assuming reinvestment at the project discount rate, which is awkward if the project is only implemented in the future. The exact answer will depend on conventions for the NPV calculation, but there are pros and cons of each definition.

Which bond to use? If one is cautious, one sticks to “risk-free” sovereign bonds. (Disclaimer: all bonds have risks.) If one feels lucky, one can take credit risk with the investment, raising the bond yield. However, default risk then needs to be taken into account in the NPV analysis.
Since one might not find a zero coupon bond, one needs to calculate a zero coupon curve from observed bond yields. This is non-trivial, but descriptions would be found in most textbooks of fixed income analysis.


What type of protectionist measure is this? I am currently studying an economics case study on protectionist measures but came across a measure which I have not heard off before, one which research has not shed any light on. The case study gives examples of protectionist measures from a range of countries, the one I am confused about reads:

  Fuel for official cars in Argentina can only be bought from state-owned oil companies

The protectionist measures such as tariffs and quotas do not seem to apply here. Further research gives this list of protectionist measures, but this doesn't appear to fit in one of those categories either.

Several Google searches have turned up no results either.

My Question: What type of protectionist measure is the example above?

Within the WTO framework, this would fall under the government procurement agreement, as it is a restriction on who the government can buy from that limits opportunities for foreign firms.


Rent dissipation meaning? What is Rent dissipation? Please explain with an example.
I tried to search it on the internet about it. And I couldn't find anything in simple language. It was the esoteric language and was unclear. I wish there might have been a simple paragraph out there that could explain its meaning.

You may find this article useful Licensing and Rent Dissipation.

In simple terms you might think of it as the devaluation of an 'asset' of some sort.


Isn't it the case that figures on employment should equal the sum of employees plus the self-employed? This is a question about data consistency. I'm using the AMECO database and I'm interested in employment data for Greece.

My current understanding is that the series about Employment (NETD) should in principle be equal to the sum of the series on Self-employed persons (NSTD) plus the series on Wage earners (NWTD).

In fact, this is what the information on the Employment series says.

Now, if one plots the employment series along with the sum of the series on wage earners and the self-employed-or inspects their relationship otherwise- it will become evident that the expected equality is verified only for a part of the sample (after the '90s).

What is the reason for this discrepancy?

update: In the following plot the blue series depicts Employment proper (NETD) while the red series is the one I constructed by adding NSTD (self-employed) and NWTD (employees). It's the later one that falls short of the former.

This becomes more evident in the next plot. It depicts the annual percentage difference between the constructed employment series (the red line above) and the AMECO series for employment (blue), which I consider as a baseline.

Casual inspection of the plots demonstrates the fact that for almost the first half of the sample the constructed series falls short of the baseline. In plain English, up until the 90's employment in Greece is not exhausted by the sum of the self-employed and employees.

Such a discrepancy is not detailed in the data description for employment (see link in the question above) and it begs the question which series provides the correct answer to the question "What is the level of employment in Greece up to and including the nineties?".

Also, the motivation for this question is not simply the level of employment. Please note that if the constructed series is off, that means that eg when trying to retrieve the adjusted wage share for Greece, one ends up with a lower figure for the period relevant to the observed discrepancy.

While you didn't share in which direction the equality is off, I would imagine that there is a double-counting issue. If someone is a self-employed person AND a wage earner (e.g. perhaps they have a salaried position but also do freelancing on the side as a registered independent contractor), this may lead to the sum of self-employed workers + wage earners to be higher than Total Employed. That's my thought.


Strictly increasing but not convex preferences Is it possible to have preferences that is strictly increasing but not convex?
Will perfect substitutes indifference curves show strictly increasing but not convex preferences? I am confused, as won't perfect substitutes be considered as convex?

Take $u(x,y)=x^2+y^2$ on $\mathbb R_+^2$. The function is strictly increasing in both $x$ and $y$, but the indifference curves are concave to the origin. Hence the preference it represents cannot be convex. For example, $u(1,0)=u(0,1)=1$, but the average of the two bundles is less preferred:
\begin{equation}
u\left(\frac12,\frac12\right)=\frac12<1=\frac12u(1,0)+\frac12u(0,1).
\end{equation}
The indifference curves for perfect substitutes are straight lines. They still represent a convex preference, although not a strictly convex one.


CobbDouglas: Constant marginal costs and constant returns to scale A company has a production function:
$$y=x_1^{\alpha}x_2^{1-\alpha}$$
where $0<\alpha<1$. Factor input 1 costs $w_1> 0$ and factor input 2 costs $w_2> 0$. The company wants to minimize its production costs when it produces y> 0 units of the output.
I have in a problem found that MC:
$$MC=\frac{\partial c}{\partial y}=w_1((\frac{w_2\alpha}{w_1(1-\alpha)})^{1-\alpha})+w_2((\frac{w_1(1-\alpha)}{w_2 \alpha})^\alpha)$$
We see that marginal costs only depending on $w_1$ and $w_2$ and thus not on y. So we have that the marginal costs are constant. But why is that the case?
What is the economic interpretation?
I think maybe I should use returns to scale?

Since the exponents add to one the production function has constant returns to scale, which means that, given factor prices, total cost is linear, which means that it's derivative (= marginal cost) is contant.  If you change the exponent 1-alpha to beta where alpha+beta < 1, there will be decreasing returns to scale (but still homotheticity) and you will get increasing marginal cost.


Where are bank loans in balance sheet? I am looking at the balance sheet of Coca-Cola (https://www.marketwatch.com/investing/stock/coke/financials/balance-sheet), but I cannot guess where loans with banks are. These liabilities accounts are:

ST Debt & Current Portion LT Debt   25.23M  25.94M  6.45M   7.06M   7.53M
Short Term Debt     -   -   -   -   -
Current Portion of Long Term Debt   25.23M  25.94M  6.45M   7.06M   7.53M
Accounts Payable    79.48M  69.45M  109.87M 162M    251.98M
Income Tax Payable  -   2.52M   -   -   -
Other Current Liabilities   111.6M  110.91M 111.11M 157.49M 198.4M
Dividends Payable   -   -   -   -   -
Accrued Payroll     49.42M  49.4M   51.19M  68.99M  84.74M
Miscellaneous Current Liabilities   62.19M  61.52M  59.91M  88.49M  113.67M

But debt is bonds, accounts payable refer to money owed to suppliers (https://en.wikipedia.org/wiki/Accounts_payable). Is it under "Other Current Liabilities"?. How can I know? Anyone has experience looking at balance sheets? I'm learning this.

In the link one can very clearly see that the company has no contractually short term debt, and in the short-term (i.e. in the next 12 months) has to pay part of its long term debt. Also, that the debt amounts are not included in the line "Accounts payable"

Also, one can see its long term debts

And no, debt is not only bonds.


What's the next largest company after Facebook of which the majority of the votes is controlled by a single person? Mark Zuckerberg controls 57.9% of all votes among Facebook shareholders [1]. Currently, Facebook's market capitalization is more than $650B. It has been among the global top 10 public corporations by this measure for a long time.
Which company is currently the next largest by means of market capitalization in which a single person controls the majority of the shareholder votes? Also of interest: in which a single entity (possibly institutional) takes that position.
PS: please help me out with the tags

This question is likely to go stale pretty fast, for two reasons. First, ownership and control of companies is always subject to change; and second, market capitalization can also show substantial swings from quarter to quarter (see Apple's valuation at \$835 billion in Q1 2019 vs \$1,305 billion in Q4 2019 for just one example). I'm writing this in June 2020 and will try to indicate dates on my sources, but it won't be constant.
However, I do think there is value to answering this, to the extent that it explains not-commonly-understood aspects of how corporations work in practice.
The crucial distinction being made in this question is between voting rights and share ownership. You have to go pretty far down on the list to find a company for which stock constituting majority ownership is still in the hands of a single individual; however, it is not uncommon for companies to have dual voting structures which allocate more votes to the share types owned by insiders--a control structure which is considered harmful by knowledgeable commentators. In the example given, Zuckerberg does not own 58% of Facebook; he just has a majority of the insider shares, which get 10 votes each (as opposed to 1 vote for the publicly traded shares).
So ultimately the question is about control of the companies' decision-making--leadership and policies--and the extent to which outside investors can direct that. To answer that we have to look in quite some detail at their voting structures.
The following list is companies by largest market capitalization as of March 31, 2020:

Microsoft: no dual structure

Apple, Inc: one-share one-vote, no absolute majority shareholder. Has made moves to allow large investors more of a say in nominating board members.

Amazon.com: one-share one-vote, no absolute majority shareholder (Bezos remains plurality controller with roughly 16% of the vote)

Alphabet has majority control in the hands of two people (Larry Page and Sergey Brin)

Alibaba Group: Up until late last year, when founder Jack Ma stepped down and relinquished a lot of control, this would probably have been the winner. It's tough to say, because due to restrictions on foreign ownership, Chinese business structures are very complicated--lots of shell corporations. The company was originally listed in the US because its dual-share structure was illegal in China. Also, Alibaba is worth more than Facebook, so it wouldn't be the next one after Facebook...

Facebook, Inc -- already discussed

Tencent -- fuzzy. I haven't gone to the Chinese sources on this, and there's a lot of chaff in the search results; news about Tencent's control of online gaming and music sales is drowning out information about who controls Tencent. This is a possible candidate.

Berkshire Hathaway -- Warren Buffett controls about a third of the votes as of 2018

Visa -- charter appears to prevent anyone from owning more than 15% of the vote

Johnson & Johnson -- does not appear to have dual voting structure

I suspect it's going to be tough to find a similarly high-placed firm with sole-individual voting control, because even among firms with dual-class stock structures, most of the time those shares are split among cofounders, as with Page & Brin, or the cofounders of Lyft (who share something like 49% of the voting rights). Also, I'm having trouble finding a good summary of firms by current market capitalization; the easily-structured lists I'm seeing are for end 2019 (e.g.) or are from dodgy-looking sites.
However, even looking at majority vote control doesn't resolve the issue; you still really have to dig into the details on a company-by-company basis. For instance, Elon Musk effectively controls Tesla, despite having only around a fifth of the vote, because the charter requires nigh-impossible supermajorities for investors to challenge management decisions.
We can at least set a floor on the query: EchoStar Communications, market cap as of this writing \$3 billion, has a "substantial majority" of votes controlled by the founder. So any other candidate would have to have a market capitalization between \$3 billion and \$265 billion.
The short answer is it's difficult to find any single individual who has the level of influence and direct control that Zuckerberg has, but there are plenty of firms--especially in the tech sector--with structures that give founders a long-term controlling interest. Facebook is unique in having one founder and being so blatant, but the trend is quite common.


Do machines reduce labor... or so they redistribute, alter, and globally increase labor? John Stuart Mill famously remarked that labor-saving machines have not saved one minute of labor. More seriously, Marx argued, roughly, that machines can gain temporary market advantage, but cannot produced "surplus value," which come only from increasing attachment of labor. (Though Marx's value theory is complex and slightly ambiguous.)

Nonetheless, observers, neoliberal and socialist alike, seem to agree that machines are "productive" and "labor-saving" overall. For neoliberals this is productive "innovation" and for leftists "technological unemployment." The idea of a future where "most work is done by robots" seems remarkably widespread. This strikes me as a fallacy for three reasons.

First, in a rough adaptation of Say's Law, someone must obviously make, fuel, and maintain the machines. Someone else must, for example, mine the additional metals, feed the miners who mine the metals, raise the farmers who feed the miners who....etc.

Second, the rise of "labor-saving technology" since the 19th century has come with a huge, five-fold increase in the  global laboring population. The "local" increases in per-laborer productivity appear more than offset by the attachment and utilization of increased, lower-cost labor worldwide.

Third, the idea of "robots doing all the work" would seem to violate the Second Law of Thermodynamics. Machines cannot run or reproduce themselves. The only "perpetual motion machine" is life itself. Without humans all machines succumb to entropy almost immediately. This would apply to any level of technology.

I am not arguing that machines make no difference. But is this difference primarily local and conditional? Is the local "productivity" of machines primarily and irreducibly a way of displacing labor globally... and redirecting labor through "machines" from lower-cost to higher-cost zones?

Above all, is it logically possible for machines to produce more "work" in total than goes into them? Again, even apart from issues about "quality of work," I am always surprised at how many people seem to assume this "robot replacement scenario" is plausible.

P.S. Though I would like to respond to answers and comments, the "comment" function is not working for me at the moment, I have asked "Help" about it. My argument from thermodynamics appears to be misunderstood, I will address as soon as possible.

The only "perpetual motion machine" is life itself.

No it is not. We also convert energy to heat as we go through life. We are certainly not immune to the second law of thermodynamics, we increase entropy all the time.

  Machines cannot run or reproduce themselves.

Why not? There is already factory robots making other robots. But of course, they run on fuel. But again, humans also run on fuel, we just call it food.

  [...] someone must obviously make, fuel, and maintain the machines. Someone else must [...] mine the additional metals, feed the miners who mine the metals, [...]

Yes, there is a kind of dependency graph, and for now there are many spots for humans, there are many things the machines just cant do. But there are no fundamental reason why a machine can't fix another machine, and there is no reason why there can't be a "universal repair machine" which also repairs copies of itself.


UBI - Raising the Poverty line Imagine if a country starts to pay $1000/month to all citizens.
Then my landlord knows that I can afford to pay a bit more rent from next month.
So will my favorite ice-cream place, my barber and in general the entire market around me raises it's price because of the theory of tragedy of commons and everyone would want a bigger piece of pie from my income.
Some of the proponents of UBI argue that we would effectively remove poverty with UBI, but with the logic above, it seems like a snowball effect will make everything more expensive and nullify the effect  of UBI to remove poverty by causing inflation.

When everything becomes more expensive, wouldn't it just raise the poverty line keeping the poor still in need of support?
Is there any research done on this subject?

P.S: I realize this is home-cooked economics, I have never studied economics academically so excuse me if the solution is fairly obvious but I can't see it and Googling it isn't helping as I don't think I know the right terms that I should lookup.

No, this question is based on fundamentally flawed premises.  There is a plenty that you can criticize about UBI and generally literature does not consider UBI efficient redistribution policy, but none of what is mentioned in the question holds for UBI.
Addressing UBI

Lets start by correcting misconceptions:

Theory of tragedy of commons has nothing to do with what you describe. The theory of tragedy of commons is:
a) A theory about situation where private property rights are non-existent. Unless you want to make claim that property rights are missing in the market for ice cream, barber services or entire market generally suffers from lack of property rights - which is empirically absurd assertion outside few specific markets or countries like North Korea - tragedy of the commons simply does not apply here as for tragedy of the commons you first have to have some commons to begin with.
b) the tragedy of the commons is not about increases in prices. In fact, under tragedy of the commons prices will tend to be lower, or in some cases even impossible to exist without further government intervention (e.g. clean air is an example of resource suffering from tragedy of commons) than they would be in presence of property rights. Furthermore, the tragedy of the commons will generally cause prices to be undesirably low (from societal perspective) which will result in overexploitation of common resource.

UBI Should not Cause Significant Inflation:

First, it is important to understand that profit maximizing firms can't just set prices in arbitrary fashion. They are limited by the parameters of the market such as the level of competition or market structure we are talking about. Inflation, is generally unaffected by redistribution.
Inflation is macroeconomic phenomenon and depends on the equilibrium price level set on the money market. The money market equilibrium can be in it's simples form described by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY$$
Where M is the money supply, V velocity of money, P price level and Y output.
Solving for price level and log-linearizing we get:
$$\ln P=\ln M+\ln V−\ln Y$$
Thanks to everything being in logs we can directly interpret any change in $P$ (i.e. inflation if change is positive or deflation if negative) in response to right hand side variables as percentage changes. So if money supply would expand by $1\%$ we would expect inflation to increase by $1\%$ ceteris paribus.
However, UBI does not directly affect the right hand side variables.
a) Provided that UBI is funded by taxes not high powered money it does not affect money stock of economy at all. So it does not affect $M$ at all.
b) Velocity of money is quite constant in a long-run, in short-run it depends mainly on the business cycle and interest rates. There is no reason to suspect UBI would have any effect.
c) UBI is a redistribution measure so it transfers output from one part of economy into another. To the extent this is funded by distortionary taxation it reduces economic efficiency and output in an economy which has no market imperfections. However, real life economies contain externalities, missing markets and other issues that can create efficiency cause for redistribution (see discussion of this in Atkinson (2015) Inequality). Generally, empirical literature shows that too large levels of redistribution can lead to lower growth of output, but modest redistribution seems to have little to none impact on it (see Jonathan, Ostry and Berg: Redistribution, Inequality, and Growth). Consequently, unless the UBI would be set to some extremely large value it should have no significant effect on $Y$ and thus again no effect on inflation.
UBI could distort relative prices because while everyone receives the UBI only some people pay for it. To the extent that the spending patterns of people who receive net transfer and those who on net pay into the system relative prices could change in a way that would hurt poor even if inflation remains overall constant. This would happen because it would lead to increase in demand for goods that low-income people consume while simultaneously decreasing demand for items that high income people consume. However, this effect would happen with any redistributive measure, and in addition there is no reason to believe this effect would be large enough to offset real increase in welfare of the poor thanks to the redistribution.
Literature on UBI
For overview of literature on this you can see Hoynes and Rothstein (2019) or Martinelli (2017) and sources cited therein. As mentioned, at the beginning, literature is generally negative towards UBI but that is because research shows it is less efficient and more wasteful than traditional redistribution systems, not because it would lead to inflation.


Historical GDP of world economies back to 1945: What are the most complete and reliable data sets? I need the historical GDP of all modern countries (or at least the vast majority) from 1945 to now. It seems the world bank data only starts in 1960 or later. I found Angus Maddison's data, but I don't know how reliable it is. Can anyone tell me if it is reliable? Are there other good data sets for my needs?

As far as I know Angus Madison's GDP figures are one of the most reliable sources of historical data, even if data construction is as always diputable. The Review of Income and Wealth published a rigorous debate between Angus Maddisson and Carsten A. Holz regarding Maddison's estimates on China's growth.

You may also find useful the  Historical Bilateral Trade and Gravity Data set (TRADHIST) provided by the CEPII, which partly uses Maddison's data. TRADHIST gathers more than 1.9 million bilateral trade observations for the 188 years from 1827 to 2014. TRADHIST also provides about 42,000 observations on aggregate trade, and about 14,000 observations on GDPs and exchange rates respectively. This data set is publicly available.


What happens to the stock market if no one wants to buy? When the stock market crashes, if everyone wants to sell, who will buy? Is it possible that  no one could sell his shares because no one wants to buy them?  If so, what would happen? Would share price decrease? Would it drop to zero?
I was told that the company will buy if everyone wants to sell. I don't think that is true.

Yes, price will decrease. If nobody wants to buy at lower prices, sell  orders will push stock prices toward zero.
This is possible in periods of financial turbulence, especially for companies that are very exposed to uncertainty and have do not have positive financial results to show to investors.
If you are interested in exploring this topic, I suggest that you start by reading  about the stock market crash of October 1987.


How much is someone willing to pay to own a monopoly? I'm currently working on a problem from Intermediate Microeconomics Workouts by Varian and I've become stuck on a particular question to do with monopolies.

We are given the demand curve for a monopolist:

$$ q = 160-2p $$

and the total daily costs:

$$C = 2000 + 10q$$

From this, I've found the profit-maximising price, quantity and daily profit which are as follows:

$$p* = 45$$
$$q* = 70$$
$$\pi* = 450 \text{ per day}$$

Now, the question I'm stuck on is: If the interest rate is 10% per year, how much will someone be willing to pay to own the monopoly?

My first approach was to simply multiply the total profits per day times 365 days times 1.1 to get the yearly profits with interest, but apparently that's incorrect.

I'm not super clear about the policy here regarding self study questions. I'll give a hint for now.

You can translate the question into: finding the present value of a perpetuity, which is the present value of a constant and infinite sequence: (450*365, 450*365, ...)


Causes of recent UK Deficit In 2008 the UK deficit was around £10Bn - in 2010 it had reached around £100Bn.

I realise this was due to the "global recession" but exactly why did the deficit grow so much?

My understanding is the deficit is the UK Treasury income less expenditure, so did income drop (and why) or did expenditure increase and again, why?

I imagine the recession would show a reduction in tax receipts but £100Bn seems excessive and also there may be some increased borrowing leading to increased debt payments but again the figures seem huge.

Was it the bank bail-outs to blame?

My data is from here.

Finally is austerity likely to return the UK treasury to surplus given that there is a finite amount of spending that can realistically be cut?

The chart you are looking at is off by a year: it should have shown about £10 billion in 2007 and almost £100 billion in 2009.  See the ONS figures for the "Public sector current budget deficit, excluding public sector banks" and click on "table" and "year"

It is more common to look at "Public sector net borrowing, excluding public sector banks" but the story is similar: about £37 billion in 2007 and about £153 billion in 2009

There was a reduction of about £25 billion in central government current receipts  and an increase of about £60 billion in central government current expenditure  plus some other things happening.  Falling receipts included lower corporation and income taxes and part of a 12 month cut in VAT, while increasing expenditure included support for banks and increased numbers of people claiming unemployment and other benefits.  Interest payments (part of expenditure) actually fell by about £4 billion due to lower interest rates, though they rose the following year due to the increased debt

You can find more data in the ONS Public Sector Finances time series dataset spreadsheet


Resolution - Ramsey growth model with per capita variables Let's say that we have the sum of the utility of a social planner
$$\int_{0}^{\infty}U\left(C\right)e^{-\rho t}dt$$
where $C$ is the total consumption. If we want to write this by a per capita variable $c=\frac{C}{L}$ where $L=e^{nt}$ is the total number of population that grows exogenously at rate $n$. We can reformulate this such as
$$\int_{0}^{\infty}U\left(c\right)e^{nt}e^{-\rho t}dt$$
Until now, everything is straightforward. However, if we have started by a specified functional form such as a CRRA utility
$$\int_{0}^{\infty}\frac{C^{1-\sigma}}{1-\sigma}e^{-\rho t}dt$$
We would not have reached the result above and should have some exponent term with $\sigma$.  What is the  logic behind? There is something I miss.

The reason why the $e^{nt}$ term is there is because you want to multiply the whole utility by the number of people. You are actually not substituting consumption into the utility but multiplying the utility of an individual by the number of individuals. So the problem would look like:
$$\int_{0}^{\infty}\frac{c^{1-\sigma}}{1-\sigma}e^{nt} e^{-\rho t}dt$$
At least this is how it is explained by Barro & Sala-i-Martin in their textbook Economic Growth 2nd ed. pp 87 where they say [emphasis mine]:

The multiplication of $u(c)$ in equation ...  by family size, $L = e^{nt}$, represents the adding up of utils for all family members alive at time $t$.

So the way how I understand it you are multiplying all the individual utilities by the population.
In fact I am quite sure of it since in Romer Advanced Economics 4th ed in chapter 2 pp 54 there is Ramsey model where the objective function is given as:
$$\int_{t=0}^{\infty} e^{-\rho t}\frac{c^{1-\sigma}}{1-\sigma} \frac{L(t)}{H} dt$$
which is essentially exactly the case you are looking for where the only difference is that Romer also adds the $H$ parameter which is the number of households so $L(t)/H$ would be population per household. Romer also later substitutes $L(t)=L(0)e^{nt}$ which for $L(0)$ normalized to 1 gives almost the same function (with that extra $H$ parameter - but for $H=1$ it would give you exactly the same result).


To use seasonally adjusted data or not seasonally adjust data? Im currently doing research using some macroeconomic data.

I just want to know what are the pros and cons of using seasonally adjusted/non-seasonally adjusted data in terms of forecasting.

There is a theoretical objection to using seasonally adjusted data, which I saw in an essay by Kalman (developer of the Kalman filter); sorry, I cannot find the reference. The argument is that seasonal adjustment is a filter, that has its own dynamics. You are then embedding these filter dynamics within the system that you are modelling. This would be a bad idea in engineering systems, but I am not entirely convinced it matters for economic systems. (My academic background is in engineering control systems.) However, if the variables you are forecasting exhibit roughly the same seasonal pattern, separately seasonally adjusting them might be problematic.

Most economic forecasting exercises involve variables with different seasonal patterns, and it is probably easier to work with seasonally adjusted data. You would have to embed the deseasonalisation within your model, which raises model complexity, and probably introduces extra errors that we know that we can explain.

If your objective is to forecast the non-seasonally adjusted variable, the usual practice in finanicial market economics is to come up with an estimate of the non-seasonally adjusted variable, then apply the existing seasonal pattern. The main example I have in mind is the forecasting of the CPI index in the inflation-linked markets, where the instruments are linked to the non-adjusted index. These forecasts were short-term (few month horizon), and were expected to be fairly accurate. Even long-term forecasts had a seasonal pattern built into them, since it mattered for relative value even for instruments with longer maturities.

Academics may prefer other techniques, but I am unaware of their use in short-term inflation forecasting.

If you are attemptng to forecast an aggregate index by forecasting its components, you might need to forecast each component, and then aggregate and seasonally adjust using the same algorithms used by the statistical agency. However, it’s rare that you can get the level of accuracy needed for this to matter.


Opportunity profits vs. opportunity costs Having learned that

Opportunity costs = the costs for avoided profits

are a well established and quite useful economic concept, I wonder how its counterpart is officially called and investigated:

Opportunity profits = the profit by avoided costs

Costs can be avoided in many different ways:

by paying unfair wages
by not providing good working conditions
by paying too low taxes
by exploiting the environment without paying for avoidance or reparation of damages and pollutions.

My question is for

the official name of "profit by avoiding costs"
some standard references on this topic
esp. in comparison with opportunity costs

A useful article on opportunity costs is this one:

  Do Economists Recognize an Opportunity Cost When They See One?

One may as well ask:

  Do Economists Recognize an Opportunity Profit When They See One?

Side question (the other way around): Would

paying higher wages than normal or necessary
providing better working conditions than normal or necessary
paying higher taxes than normal or necessary
paying more for avoidance and reparation of environmental damages and pollutions than normal or necessary

count as opportunity costs?

Opportunity cost is simply the value not obtained of the highest value alternative. It can be positive or negative; meaning it doesn't really make sense to define the opposite as opportunity profit. There is only two ways to go about it rationally, either you are profiting from doing something, or you are not profiting by not doing something, which is defined as opportunity cost. Opportunity profit would just equate to opportunity cost because you are not doing whatever the opportunity is. (Also, I'm not the down voter).


Dynamic programming with housing consumption and labor I try to solve the following maximization problem of a representative household with dynamic programming. However, my last result is not similar to the solution. Could any one help me?

$$\max\limits_{C_{t},H_t,N_t} E_0 \sum_{t=0}^{\infty} \beta^t\Bigg[logC_t+jlogH_t-\dfrac{(N_t)^\eta}{\eta}\Bigg]$$
$C_t,H_t,N_t$ represent consumption at time t, housing stock and working hours, respectively.
Household budget constraint:

$C_t + b_t +q_t(H_t-H_{t-1})=\dfrac{R_{t-1} b_{t-1}}{\pi_t}+w_t N_t+F_t$

$b_t$ denotes bank deposits, $R_t$ is the return from deposit, $q_t$ is the price of housing, $\pi_t$ is the inflation rate and $w_t$ is the real wage rate. $F_t$ denotes profits received from firms.
To sole this problem, I use dynamic programming with these steps:
Step 1: Bellman equation:

I identify $b_{t-1}$ as the state variable, since the household must know the deposit in the previous period. The budget constraint can be rewrite as:
$b_t=f(C_t,b_{t-1},H_t,H_{t-1},N_t,F_t,q_t,R_{t-1},\pi_t)$

Step 1: Setting up the Bellman equation:

$V(b_{t-1})=\max\limits_{C_{t},H_t,N_t} \Bigg\{logC_t+jlogH_t-\dfrac{(N_t)^\eta}{\eta} +\beta E_tV(b_t) \Bigg\}$

Evolution of the costate variable $b_t$, using envelope theorem:

$$\dfrac{\partial V(b_{t-1})}{\partial b_{t-1}} =\beta E_t \dfrac{\partial V(b_{t})}{\partial b_{t}} \dfrac{\partial b_t}{\partial b_{t-1}} = \beta E_t V'(b_t) \dfrac{R_{t-1}}{\pi_t}$$ (1)

Step 2: FOC

First order condition (FOC1)
$$\dfrac{\partial V(b_{t-1})}{\partial C_t}=\frac{1}{C_t}+\beta E_t V'(b_t)\dfrac{\partial b_t}{\partial C_t}=0$$
$\dfrac{\partial b_t}{\partial C_t}=-1$

$\dfrac{1}{C_t}=\beta E_t V'(b_t)$ (2)

Inserting (2) into (1) twice to get the Euler equation, we have:

$$\dfrac{1}{C_t}=\beta E_t \Bigg(\dfrac{R_t}{\pi_{t+1 C_{t+1}}}\Bigg)$$

This result is similar to the solution

FOC2:
$$\dfrac{\partial V(b_{t-1})}{\partial N_t}=-(N_t)^{\eta-1}+\beta E_t V'(b_t)w_t=0$$
Inserting (2), we have:
$\dfrac{1}{C_t} w_t = -(N_t)^{\eta-1}$, This result is similar to the solution

FOC3: The third FOC involves taking the partial derivative of $V(b_{t-1})$ with $H_t$, but I cannot get the same result with the solution:
The solution is:
$$\dfrac{j}{H_t}=\dfrac{1}{C_t}q_t-\beta E_t \dfrac{1}{C_{t+1}}q_{t+1}$$

I only end up with:

$$\dfrac{\partial V(b_{t-1})}{\partial H_t}=\dfrac{j}{H_t}+\dfrac{1}{C_t}(-q_t)=0$$
Did I miss something?
Did I correctly identify the state variable? I suspect that it has something to do with $H_t$ and $H_{t-1}$, but I cannot figure it out

$$V(b_{t-1})=\max\limits_{C_{t},H_t,N_t} \Bigg\{\ln C_t+j\ln H_t-\dfrac{(N_t)^\eta}{\eta} +\beta E_tV(b_t) \Bigg\}$$

so

$$\beta E_tV(b_{t})=\beta E_t\left[\max\limits_{C_{t+1},H_{t+1},N_{t+1}} \Bigg\{\ln C_{t+1}+j\ln H_{t+1}-\dfrac{(N_{t+1})^\eta}{\eta} +\beta E_{t+1}V(b_{t+1}) \Bigg\}\right]$$

But forwarding the budget constraint

$$C_t + b_t +q_t(H_t-H_{t-1})=\dfrac{R_{t-1} b_{t-1}}{\pi_t}+w_t N_t+F_t$$

we get after re-arranging,

$$C_{t+1} =- b_{t+1} -q_{t+1}(H_{t+1}-H_{t})+\dfrac{R_{t} b_{t}}{\pi_{t+1}}+w_{t+1} N_{t+1}+F_{t+1}$$

So $\beta E_tV(b_{t})$ is also a function of $H_t$ through $C_{t+1}$.


Federal Reserve vs National Bank The US had a national bank during the first few decades after its birth before it was abolished.  Today, we have the Federal Reserve.
What are the differences between the Federal Reserve and a National Bank (specifically, with regard to their intervention policies and powers for acting within the economy)?

The two Banks of the United States (the First and Second) were nothing like the modern Federal Reserve system.  For example, the First was prohibited from buying government bonds (one of the main roles of the Federal Reserve system is to buy and sell government bonds).  Further, neither of the national banks had any role in regulating the banking system.  They were simply the only interstate banks allowed.  All other banks had to be confined to one state.  The national banks primary impact on the money supply was to require smaller banks to pay them in silver and gold to redeem checks deposited in the national banks.

By contrast, the Federal Reserve system actively regulates banks, requiring them to maintain a percentage of their deposits as reserves.  It actively sets two rates:  the rate at which it loans money to banks to cover reserve shortages (called the discount rate) and the rate it pays on excess reserves.  The latter power is relatively new.  Previously the Federal Reserve did not pay interest on excess reserves.  The Federal Reserve also sets a target for the funds rate, which is the average rate at which banks loan money to each other.  The funds rate target is what most people mean when they refer to the Federal Reserve setting interest rates.

The Federal Reserve has two main ways to affect the funds rate.  First, it publishes a target rate for the average.  Second, it buys and sells government bonds in what are called open market operations.  When it buys bonds, it adds money to the system, reducing the number of banks that need to borrow and increasing the number of those with money to lend.  This pushes the average rate to fall, as there are more lenders and fewer borrowers.  When it sells bonds, it pulls money from the system, reducing the number of banks with money to lend.

The Federal Reserve can also compete with lenders by loaning money to banks at the discount rate.  This decreases the number of banks looking to borrow from other banks, which would push rates down.  It rarely does this however.  Most banks prefer to borrow from other banks, as there are fewer restrictions.

The Federal Reserve also has two ways to influence how much banks keep in reserve.  First, it sets an explicit reserve requirement.  Every bank must keep that much in reserve.  Second, it can pay interest on excess reserves.  The higher that rate, the more likely banks are to keep excess reserves instead of loaning them to individuals, companies, or other banks.  This would push up the funds rate average, as fewer banks loan.

Again, the two Banks of the United States were not central banks the way that the Federal Reserve is.  Yes, they could print banknotes, but so could other banks of the time.  They had no special banking privileges.  They were simply the only interstate banks allowed during their charter.


What trick can be used to calculate mixed-equilibria? In continuous games, the probability distributions over the players' strategy spaces are infinite. How then is it even possible to then derive a mixed-strategy nash equilibrium?

One would have to show that the mixed-strategy of one player is the best possible mixed-strategy response to the strategy of another player. In the continuous case, how is this even possible? How do you maximize over "all possible probability distributions".

Can anybody provide a clue?

The "trick" is to identify an equilibrium action where you know (or can pin-down) the payoff. You can then impose indifference between this action's known payoff and the payoffs from other actions (which will depend on the mixing probabilities) to determine those equilibrium mixing probabilities.
A nice example can be found in a Varian's "A Model of Sales". Let me describe a simple version of that model before discussing what it teaches us about finding continuous mixed equilibria.

Set up
Two firms each set a price, $p_i$, for a homogeneous product they product at zero cost. There is a continuum of consumers, each willing to pay up to $v$ for the product.
A fraction $a$ of the consumers (call them "shoppers") will buy from whichever firm sets the lowest price (breaking ties randomly). A fraction $\frac{1-a}{2}$ of the consumers (call them "1's captives") always buy from firm $1$ (as long as $p_1<v$). The final  $\frac{1-a}{2}$ of the consumers (call them "2's captives") always buy from firm $2$ (as long as $p_2<v$).
You should be able to quickly check that this game has no pure strategy equilibrium (think about why we can't have an equilibrium with $0<p_1<p_2$, $0<p_1=p_2$, or $0=p_1=p_2$).
Thus, we look for a mixed strategy equilibrium where prices are drawn from the distribution $F$. Let the support of $F$ (i.e., the range of prices over which firms mix) be $[\underline{p},\overline{p}]$.
No firm will ever choose $p_i>v$ because it then serves no consumers, but could earn a profit of $v(1-a)/2$ by serving its captives at a price of $v$. Thus, $\overline{p}\leq v$.
A firm's profit if it sets price $p$ is
$$\frac{1-a}{2}p+ap[1-F(p)].$$
The first term is the profit from captives (who the firm serves for sure). The second term is the profit from shoppers, who are served only if the rival firm sets a higher prices (which happens with probability $1-F(p)$).
Finding the mixed-strategy equilibrium
We know that if the firm is to mix over prices $p$ and $\overline{p}$ then it must be indifferent:
$$\frac{1-a}{2}p+ap[1-F(p)]=\frac{1-a}{2}\overline{p}+a\overline{p}[1-F(\overline{p})].$$
Notice that if we could eliminate the $\overline{p}$ terms from the right-hand side then we would have an equation that could be solved for the equilibrium strategy, $F$.

The next part is the key to being able to find the equilibrium, so I'll put it in a box:
Let's think about what happens when a firm sets $p_i=\overline{p}$. Because $\overline{p}$ is the highest price ever charged in equilibrium, we know that the firm never serves the shoppers at that price (i.e., $F(\overline{p})=1$). Moreover, since the firm serves only its captives who will buy at any price below $v$, it must be the case that $\overline{p}=v$.

We therefore know that:

$\overline{p}$ is in the support of $F$, meaning firms must be indifferent between $\overline{p}$ and any other price
$\overline{p}$ results in profit $\frac{1-a}{2}\overline{p}$
$\overline{p}=v.$

Putting these facts together with the indifference condition, we have
$$\frac{1-a}{2}p+ap[1-F(p)]=\frac{1-a}{2}v,$$
which implies
$$F(p)=1-\frac{\frac{1-a}{2}(v-p)}{ap},$$
which is our mixed strategy equilibrium. The only part of the equilibrium we haven't solved is the value of $\underline{p}$. But this is easily found by solving $F(\underline{p})=0$ for  $\underline{p}$ now that we know $F(\cdot)$.

Final remarks
The trick used in the above example is pretty useful more generally.
Unless the equilibrium strategy, $F$, has an atom, we know by definition that $F(\underline{p})=0$ and $F(\overline{p})=1$. Thus, if we can use economic reasoning to determine the value of either $\overline{p}$ or $\underline{p}$ (as in the box above) then we can eliminate all of the terms that depend on $\overline{p}$ (or $\underline{p}$) on the right hand side of our indifference equation and then solve for $F$.


What is "industrial capitalism"? What's the difference between "industrial capitalism" and "agrarian capitalism" and "mercantilism" and the "industrial revolution" and the 20th century ideas of "Keynesianism"?

Is agrarian capitalism- plantations, industrial capitalism- the exploitation of women working in clothing factories?

Industrial capitalism, characterized by its use of heavy machinery and a much more pronounced division of labor.  It is a system  whereby industry and resources are owned by few for profit. In this capitalist system means of production were privately owned.  Its is marked by the rise of monopolies and trusts dominating industry and other aspects of society. Often used to describe the economy of the late 19th and early 20th century.

Agrarian capitalism refers to the description of agricultural economy. It is centered upon the production, consumption, trade, and sale of agricultural commodities, including plants and livestock, is rural rather than urban-based.

mercantilism was based on the idea that a nation's wealth and power were best served by increasing exports and limit imports.

The Industrial Revolution began in the 18th century, when agricultural societies became more industrialized and urban.  During this period society moved form primary Agrarian capitalism  to Industrial capitalism.

An agrarian society Wealth comes from the land. Industrial society refers to a society driven by the use of technology to enable mass production, supporting a large population with a high capacity for division of labor. Industrial society is characterized by the use of external energy sources, such as fossil fuels, to increase the rate and scale of production.

Mercantilism developing during 16th century came about  as governments created incentives to only buy its own countries goods especially among colonies.   However, these views changed with the introduction of capitalistic beliefs and value to the late 1700s.    The industrial revolution came about because industrialization required significant work and investment from individuals and not necessarily the government.

Keynesianism - the theory made an argument for active government intervention during recessions, leveraging tools of monetary and fiscal policy to restore confidence, boost output, and smooth the ups-and-downs of the business cycle.

To answer your question agrarian capitalism does include the use of plantations.

During the industrial revolution women entered the workforce in textile mills and coal mines in large numbers.  Women and children often worked in the factories and mines in order to help pay for the families cost of living.   Women were not valued the same as men in the workplace, and were often paid much less than men.  However, during this time the early feminist movements started as women began to organize and protest for more equality in society.

https://www.historycrunch.com/role-of-women-in-the-industrial-revolution.html#/


WAPM and CRS across all production plans In Hal Varian's Book "Microeconomic analysis" on page 35 he gives the following description of a profit maximising firm.

  ...If the firm is maximising profits, then the
  observed net output choice at price pt must have a level of profit at least as
  great as the profit at any other net output the firm could have chosen. We
  don't know all the other choices that are feasible in this situation, but we
  do know some of them-namely, the other choices $y^s$ for $s = 1,. . . , T$ that
  we have observed. Hence, a necessary condition for profit maximisation is
  that
  $$p^ty^t\ge p^ty^s$$
  for all $t$ and $s=1,...,T$

  We will refer to this condition as the Weak Axiom of Profit Maximisation
  (WAPM).

In the case of a firm which has a production function with one input and one output where $p=w$, such that $p$ is the price the output is sold and $w$ is the price of the input across all production possibilities sets. Can such a firm be called profit maximising at any level of output?

Sure it can, because the maximal profit is 0, and that level is attained at all output levels.

A similar problem is a profit maximizing firm with constant returns to scale. If such a firm has a maximal profit it can attain then that profit level is 0. If the maximal profit level was something else, it could be increased by doubling or halving production.


What are the Economic reasons and explanations to make a referendum? Australia is now conducting a survey on same sex marriage, to decide if they take the vote to the parliament or not. Although it is called a survey, the population is treating it as a referendum. The government could decide on its own to legalize the same-sex marriage, the same way it decides on topics such as immigration laws.

Are there any economic arguments that help a government to decide which topics are polled from the population and which are not?

Polling is expensive so only issues that a lot of people feel strongly about will get polled.

You can imagine that every citizen $i$ would pay $r_i$ monetary units to have a certain policy changed. This number may also be negative to reflect that some people like the current policy better than the proposed change.
Ideally the government would like to know $\sum r_i$, if its positive or negative. But I am sure there are also a lot of practical political considerations. However polling itself has a significant cost. Let us denote this by $C$. The government probably has some vague idea about $\sum r_i$. E.g. most people don't care about the color of chewing gum wraps, so the $\sum r_i$ for banning silver coloring is likely negligable. In this case a poll to determine the exact value would be wasteful as
$$
\sum r_i - C < 0.
$$
So when you pick something to poll it is probably a salient issue, something that a lot of people know about and have strong opinions about. As I said, I am sure that these considerations are usually secondary to political ones.