You might be thinking about Demerit goods. This type of goods have negative externality (cost) that are usually ignored by or unknown to the consumer.
As a result, initial cost of the good is relatively low, when compared to the long term cost for the consumer.

Simple example of a demerit goods are cigarettes, since they have to fulfil two criteria:

be harmful, unhealthy to the individual consumer: smoking is accepted as an unhealthy habit.
have negative externalities, cost to third parties: secondhand smoke.

Finally, it is important to notice that classification of demerit goods is normative contrary to usual positive economic approach when we classify goods based on their price or income elasticity e.g. ordinal, inferior, luxury.


Authoritative Books on Subprime Mortgage Crisis

Trying to think of what's on my bookshelf... this is an incomplete list, but it should get you started.

The Financial Crisis Inquiry Commission Report is the authoritative overview of the housing crisis and its role in the financial crisis. It's unique in that the staff of the FCIC was able to interview essentially all the major players and had access to documents that were (and many of which still are) unavailable to the public. It's also free.

The American Mortgage System: Crisis and Reform by Susan Wachter (editor) is a collection of essays that provide a good overview of many of the main issues.

For a lighter read, All the Devils Are Here: The Hidden History of the Financial Crisis by Bethany McLean and Joe Nocera is good, but flawed.

On Fannie Mae and Freddie Mac, I'd recommend Guaranteed to Fail: Fannie Mae, Freddie Mac, and the Debacle of Mortgage Finance by Acharya, et. al.

House of Debt (Mian and Sufi) isn't bad on some of the causality, but I find that it goes a bit off the rails when it comes to policy prescriptions.


I'm pretty sure that $\mathrm{cl}$ is the set closure operation. I'm less sure about $\mathrm{co}$, but I've seen it being used for the convex hull operation in other contexts.

As a reference, in Fundamentals of Convex Analysis, the same notations are used to refer to the closed convex hull of a set:


Data of Inflation and unemployment for a Panel Data

For unemployment rates, check the ILO. For inflation rates, see the World Bank


How does your dominant strategy change in a second price auction if there are two items?

This question is hard to answer, because it is not clear what the appropriate multi-unit version of the single-unit second-price auction (SPA) actually is and which economic environment you have in mind. There are several possibilities, and I mention some.
There are 4 bidders and two units.

All bidders draw a two values $v_{1i},v_{2i}$ representing the willingness-to-pay for unit $k\in\{1,2\}$, having both units is valued $v_{1i}+v_{2i}$ (only one draw such that $v_{1i}=v_{2i}$ is also possible). There are two separate SPAs and in each one every bidder truthfully bids their value in equilibrium.

All bidders draw  two values $v_{1i}\geq v_{2i}$ representing the willingness-to-pay, where having one unit is valued $v_{1i}$, having both units is valued $v_{1i}+v_{2i}$. There is one uniform price auction, i.e., all bidders submit a bid vector $(b_1,b_2)$, the highest two bids win and the payment per unit is the highest losing bid. It is a dominant strategy to bid truthfully on the first unit $b_1=v_{1i}$, but not necessarily for the second unit, because the second bid could determine the price which a winner of one unit must pay.

All bidders draw  two values $v_{1i}\geq v_{2i}$ representing the willingness-to-pay, where having one unit is valued $v_{1i}$, having both units is valued $v_{1i}+v_{2i}$. There is one Vickrey auction, i.e., all bidders submit a bid vector $(b_1,b_2)$, the highest two bids win and the payments are the highest losing bids of the opponents. It is a dominant strategy to bid truthfully on both units with the same argument as with a single unit.

All bidders have single-unit demand and draw a single value $v_i$. Two SPAs are executed sequentially. The three remaining bidders bid truthfully in the final auction, but none of the four bidders in the first auction do, because there is a positive option value of losing the first auction: participating in the second auction.

All bidders have single-unit demand and draw a single value $v_i$. A generalized second-price auction is executed, i.e., the highest bidder wins and pays the second-highest bid, the second-highest bidder wins and pays the third-highest bid. If two bidders submit high bids and the other two submit low bids, the highest bidder would prefer to bid lower in order to win the second unit instead to then pay the third-highest and lower bid.


A utility function that gives a regressive tax rate

I don't see how the log-log utility function you specify would justify a regressive tax rate. In a simple setup, where government engaged in lump sum spending that had to be financed by a consumption or labor income tax, the log-log utility function would have all the same properties as more typical linear, quadratic, CRRA, and CARA utility functions. quasi-concave, increasing, weakly declining marginal utility, etc.

Usually the motivation for a regressive tax rate isn't the utility function over wealth. It is some other feature of the model, like taxes on wealth discouraging capital formation and therefore harming the productivity of poor households by making them less productive (Judd (1985)). Or some feature of the production function is tied to the income of the rich or high productivity specifically, consider this new paper Jones (2018):

  This paper considers the taxation of top incomes when the following
  conditions apply: (i) new ideas drive economic growth, (ii) the reward
  for creating a successful innovation is a top income, and (iii)
  innovation cannot be perfectly targeted by a separate research subsidy
  — think about the business methods of Walmart, the creation of Uber,
  or the “idea” of Amazon.com. These conditions lead to a new term in
  the Saez (2001) formula for the optimal top tax rate: by slowing the
  creation of the new ideas that drive aggregate GDP, top income
  taxation reduces everyone’s income, not just the income at the top.
  When the creation of ideas is the ultimate source of economic growth,
  this force sharply constrains both revenue-maximizing and
  welfare-maximizing top tax rates. For example, for extreme parameter
  values, maximizing the welfare of the middle class requires a
  negative top tax rate: the higher income that results from the subsidy
  to innovation more than makes up for the lost redistribution. More
  generally, the calibrated model suggests that incorporating ideas and
  economic growth cuts the optimal top marginal tax rate substantially
  relative to the basic Saez calculation

Source: Taxing Top Incomes in a World of Ideas


Influential Theory in the Economics of Poverty

To extend @Majoko's comment, you may be very interested in the book Poor Economics which discusses many of the issues you note. It specifically discusses issues with theory, and of course has a lot of empirical work to back it up.

Perhaps on the other end of the spectrum is general equilibrium theory applied to poverty and the developing world. you should really look into Robert Townsend's work. His "Thai Project" is a massive dive into some of the questions you're asking. A reasonable place to start is probably with his books.

As an aside, I was originally hooked on his work by his fantastic application of microeconomic general equilibrium theory in The Medieval Village Economy, which has sadly gone out of print (although I see there are now some used copies finally selling for less than $70, which is nice). He takes very sparse data and asks what theory might be able to tell us -- then very carefully and purposefully walks the reader from a most basic model through many extensions to explore important possible variations of the medieval experience. It's really an excellent example of applied general equilibrium work, and how theory might still be tested/explored with little data.

This isn't my area of research, but I'm very interested to see other answers appear here.


Research around the free-rider problem when the resource is taken away?

This may not be exactly what you're looking for, but your question reminds me of the work of Elinor Ostrom, who (along with Oliver Williamson) won the Nobel in Economics for her work on what academics in the field call 'the commons'.

Here's a good place to start reading about her work. Check under 'Popular Information' and 'Advanced Information' in particular for details about her work.


Should coefficient on interaction term be positive or negative?

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

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

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


What are some reasons for decline of georgism?

Warren Samuels addresses this issue in his article "Why the Georgist Movement Has Not Succeeded: A Speculative Memorandum."

In summary he argues first that Georgism did not succeed because of the conflation of the ideas of income and productivity, leading people to view a tax on land as a tax on productivity even though the tax is meant to equate income with productivity as referenced in the question. This idea, he says, was reinforced by self-interested beliefs of land owners as well as traders in other markets (he names equities) including preference for passing property through inheritance and viewing the proposed tax system as a threat to income through speculation (such as through the stock market), since it would eliminate speculative gains in land prices. The rise of mortgages and home-ownership increased the number of people with these self-interests.

Second, Samuels addresses the fact that George was viewed by many, including mainstream economists, as a radical and admits that relative to the status quo of changes in tax policy being incremental, the proposed single tax system is radical. The Bolshevik revolution in the 1910's and subsequent red scare caused people to distance themselves from ideas that could be viewed as radical leftist.

Samuels continues on to discuss possible internal reasons, such as lack of leadership amongst George' successors, but notes that he is less confident in discussing these factors.

In addition to this article, four responses and Samuel's response to the respondents can be found in the Jul 2003 issue of American Journal of Economics and Sociology.


The text says domination is "in the game remaining after one stage of elimination".

In stage one, column L can be eliminated. As this is exercise b., I am guessing that was exercise a.


What type of protectionist measure is this?

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.


Has it truly been established that the restaurant industry operates on thin margins?

TLDR: Interesting question, but difficult to answer. The restaurant industry is made up of so many firms and many are small and self-owned. This makes collecting data difficult. The data I did collect shows restaurants operate with margins that are tight, but not as tight as commonly believed.
A potential hypothesis of the reason behind this is restaurants are often small enterprises run by a family. Those businesses may operate on healthy margins in good times but struggle excessively in bad times. Spending at restaurants is highly variable and falls dramatically during recessions. This triggers a wave of failures across smaller restaurants who do operate on tight margins and are unable to secure financing thus causing them to fail. This occurrence might be a large contributing factor to the commonly held notion that restaurants operate on extremely thin margins.

Forbes wrote a piece on restaurant margins in early 2018. The data they complied showed margins to be 6.5% for the most recent year. That is low but certainly not razor thin. However, 2018 was deep into an economic expansion that restaurants were certainly benefiting from. The numbers from earlier years is much tighter. In 2014 it was 2.3%, 2.3% again in 2015, 2.8% in 2016, and 3.3% in 2017. Those numbers paint a different picture which is much gloomier for restaurants.

The dataset posted in the comments does not contain information on profit margins but it does contain information on the proxy measurements return on equity and return on assets. The dataset was published February 26, 2020 and contains a selection of 861 restaurants from across Europe.
For the United Kingdom the average return on equity for a restaurant is 18% and the average return on assets is 4.47%. Spain has an average RoE of 19.3% and RoA of 7.3%. France has an average RoE of 4.45% and RoA of 1.9%. Besides France, these are robust numbers.

The Australian Taxation Office collects data on many industries including the restaurant industry. Average total expense for a small restaurant is 85% (65,000-500,000) and for a large restaurant (2,000,000+) 92%.

There is an interesting comparison of margins at McDonalds and high-end restaurants over on Quora.


Does anyone know of any resources that discuss the differences between Hicksian and Marshallian remanding in depth and in an organized way?

Technically they are related but are not the same Marshallian (or Walrasian henceforth) demand is the result of $x(p,w)\in argmax_{y\in\mathbb{R}^{L}_{+}}u(y)$ subject to $p'y(p,w)\leq w$. The Hicksian demand is the result of the dual problem $h(p,u)\in argmin_{y\in\mathbb{R}^{L}_{+}}p'y$ subject to $u(y)\geq u$.
The formal relationship is established trough the value functions of both problems, for the walrasian demand we have the value function or indirect utility $v(p,w)=u(x(p,w))$ and the value function of the second problem (hicksian demand) is the expenditure function $e(p,u)=p'h(p,u)$.
Now, the indirect utility and the expenditure are inverses of each other in the following sense:

$e(p,v(p,w))=w$
$v(p,e(p,u))=u$

And to answer your question $x(p,e(p,u))=h(p,u)$ and $h(p,v(p,w))=x(p,w).$
This means that this demands have different properties but can be made equal by adjusting the wealth in the case of the walrasian demand such that I maintain the consumer in a fixed utility level u, thus obtaining the hickisan demand and vice-verse changing the utility level with changes in wealth using to go from the hicksian to the the walrasian.
The properties of each demand comes from the properties of the value functions and are a consequence of the theorem of the maximum. Like continuity of the objective.
A good source is Nolan Miller notes http://business.illinois.edu/nmiller/documents/notes/notes4.pdf.
But every micro theory books covers this material.


Does the Independence Axiom Require Statistical Independence?

First Question:

Yes, you can obtain $P \succsim P' \Rightarrow P \succsim a P' + (1-a)P \forall a\in (0,1)$ from setting $P''=P$ in the axiom. Thus, your new condition is a special case of the independence axiom as stated.

Second Question:

Statistical independence of $P,P',P''$ is not assumed in the independence axiom. The notion of statistical independence of lotteries is not even meaningful since you can only choose one lottery. Only when you would choose multiple lotteries at the same time their dependence would matter since you may be able to reduce/increase risk by combining lotteries which are not independent.


Revealed preferance: elementary question

Yes, your reasoning and your conclusion are correct.


Econometrics - Why does adding a dummy varaible improve my Ramsey RESET test result?

As I understand, the Ramsey RESET test ... is not actually a general test for omitted variable bias. Rather, it is a test for misspecification. Specifically, if the model is properly specified, "no nonlinear functions of the independent variables should be significant when added to the estimated equation"

This is completely correct, the idea of the RESET test is that if you have following some model:

$$ y = \beta_0 + \beta_1 x_1 + ... \beta_k x_k + e_i$$

The RESET test will test for correct functional specification by estimating auxiliary regression:

$$ y = \beta_0 + \beta_1 x_1 + ... \beta_k x_k + \gamma_1 \hat{y}^2 + \gamma_2 \hat{y}^3 +  e_i$$

and then testing with an $F$ test whether $\gamma_1$ or $\gamma_2$ are statistically significant. Hence, what the test actually does under the hood is to check whether the squared predicted values and cubed$^1$ predicted values can still explain some variation in $y$ after accounting for all the independent variables.

This can only be the case if the original model did not already explained $y$ fully as the original model is still included in the RESET test and hence the RESET test tells you there is some functional miss-specification. The intuition is that if non-linear combinations of the explanatory variables (through $\hat{y}^2$ and $\hat{y}^3$) have any power in explaining the response variable, the model is misspecified in the sense that the data generating process might be better approximated some non-linear function.

However, the RESET test does not tell you what kind of miss-specification it is. It can be an omitted variable, it can simply be the case that data are highly nonlinear, it can be there is some multiplicative relationship between the variables so log-log regression where everything is log linearized would be more appropriate and so on.

This being said it is fully possible that the miss-specification was the fact that you omitted a dummy variable. Dummies actually help to solve certain kind of non linearity. Having a dummy variable allows regression to have not just 1 intercept but two separate intercepts. For example, if you are examining the regression of wages on education and dummy is female, it allows for all females in the sample to have different intercept than Males (see the picture below I took from Wikipedia). In essence the dummies allow you to control for a non-linearity in data as you can imagine there being two data clusters one around the line with female dummy set to 1 and one around the line where female dummy is set to 0 (i.e. the male line). In fact data where you need to control for some qualitative state like female and male can sometimes even look in a way look like there is quadratic or cubic relationship if you plot them on scatter-plot.

Consequently adding the dummy might have genuinely solved the problem. An important caveat is that a lot of other things can get wrong in statistics so there could be other problems to see that one would have to examine the whole estimation. For example, there might be some outliers in your data that RESET test confuses for nonlinearity. This being said it is entirely possible the dummy variable solved the problem.

Also It is possible to also include higher orders of $\hat{y}$ but often it is often argued that quadratic and cubic are sufficient in most applications (see Wooldridge Introductory Econometrics: A Modern Approach, Fifth Edition).


How does a central bank create the money used for quantitative easing or lowering the value of their currency?

Short Answer

  Can a central bank simply by fiat change its holdings of its own currency, and then use this new money in any way they please?

Theoretically it can, if you don't mind destroying credibility and the economy in the process. In modern economies there are regulations in place that make this impossible. So no.

  Do they later have to "pay back" this money to balance the books, or can they simply forget about it?

If they keep "printing" new money and keep paying back old money in perpetual, the net effect is not having to pay back. So the US government can afford US\$19T of debt. But technically they have to pay back. See long answer below.

  Or more concretely: if the ECB buys bonds with newly created electronic money, and these bonds later default, would that be a problem for the ECB or could they laugh it off?

ECB can laugh it off, but Draghi can't, and certainly Eurozone can't either.

Long Answer

First you have to look into the process of money creation. Let's say you provide an ounce of gold bar (asset) to the Fed, in exchange the Fed will pay you an equivalent sum for your gold,  the current market price, say US\$35. The gold is now in the Fed's reserve (it is called Federal Reserve for a reason). Archaically, you can redeem your gold bar with US\$35.

However, note that debt instruments (i.e. bonds) are also assets. Therefore the government can issue short-term bonds to the Fed that the Fed will put in its reserve, and hand the cash to the government. The book is still balanced because the bonds in reserve are now "disabled", just like you cannot use your gold bar anymore when it's in reserve. But there will be more liquid cash in the market, cash that can be used to do other things, such as investment. When the bonds mature, the process is reversed. Furthermore, the interest (profit) earned from the government bonds will also be remitted back to the government, so the book is still balanced even when interest is taken into consideration.

Quantitative easing is similar. In addition to government bonds, the central bank is now allowed to buy a set quantity of financial instruments that it normally wouldn't have access to, in the same exchange mechanism as stated above. QE allows central banks to (directly) influence interest yield of other instruments, in addition to the usual interbank interest rate which is already close to zero. A lower interest rate makes investment more attractive, which drives the economy. Now that there is more cash in circulation, exchange rate falls, which makes foreign direct investment attractive because US assets cost less in foreign currencies's perspective.

Now, what if the bonds default? Let's suppose there are US\$100 out in circulation, backed by US\$100-equivalent of reserves. If US\$20 of the bonds default, the value of the US currency in circulation will drop in value accordingly in terms of exchange rate. i.e. nominally the dollar notes still say US\$100, but the actual purchasing power will drop to only US\$80.

Suppose that initially US\$20 of reserve is in bond and US\$80 is in gold. When you reason further, had it been a fixed exchange rate system, once the bonds default, if the owners of the US\$40 of gold rush to redeem their gold at a fixed rate, the reserve will now be worth US\$40. The remaining US\$60 in circulation will now have only \$40/\$60 (= 2/3) of its initial purchasing power (compare with 80% purchasing power right after the default). If all US\$80 of gold reserves is redeemed, the remaining US\$20 in the market will worth US\$0. This is one of the reasons why fixed exchange rate won't work: Once there has been a default and people rush to redeem the reserves, hyperinflation follows.)


How to theoretically explain an exponential income distribution?

...find economic theories that support the exponential hypothesis, but, as I've said, I haven't found any.

I don't think you will. For purposes of economic argument, the characteristic of the Exponential distribution that stands out and must be defended, is that it has its maximum at zero.

Then, arguing that an Income distribution follows the Exponential, means that we accept that the most probable situation to be observed is zero income. Is it? I don't think so.

As regards the study you link to, the main piece of evidence for the fit of the Exponential to the data is Fig 1 page 2. The authors write that they consider it a very good fit. I most certainly don't: the histogram in Fig 1. has clearly a mode at strictly positive values and not at zero. Βut this is the most critical piece of evidence as to whether the data follows an Exponential or not.

At page 4, the authors try to deal with this critical deviation of the data from the Exponential graph, by mentioning that there may be under-reporting at low values, but that's a very vague argument, unsupported and unsubstantiated.

a) From a theoretical perspective, it is not realistic to argue that the most probable income observed is zero
b) The data support this by providing a strictly positive mode for the frequency.

Therefore I don't see a case for the Exponential.


The $k+1$ parameters are $k+1$ unknowns. In general, you need at least $k+1$ equations (which are observations in the context of OLS estimation) to uniquely pin down those $k+1$ unknowns.


Do I make correct conclusions about international trade (and ways to increase GDP) from the expedenture approach formula for GDP?

Your conclusion would be correct in pure endowment economy where there is no production $Y(L) =0$ (assuming only labor as factor of production) and everyone has the same endowments. In an endowment economy where there is no production and GDP is just dropped on both home and foreign country trade is indeed a zero sum game as $M$ subtracts from your endowment since $Y=C+I+G+X-M$ (Although its worth noting that in the long run trade must balance $X-M=0$ for reasons relating to exchange rate, savings, investments and movements of factors of production - but since it is not directly related to your question I wont go in depth into that)

However, real life economies are not pure endowment economies. Production and output $Y$ depend on how efficiently we can produce output. In real life trade allows countries to produce more i.e. have higher $Y$ and thus GDP than without trade.

Consider simple Ricardian model where you have 2 countries utopia and neutopia. Both have 100 labor $L$ avaiable. Assume there are two products wine $w$ and cloth $c$. Utopia can produce 1 unit of $w$ for 2 units of labor and 1 unit of $c$ for 1 unit of labor and neutopia $1w$ for $1L$ and $1c$ for 2$L$. Now if they dont trade with each other and if they both split their labor supply equally between wine and cloth Utopia gets to consume $25w$ and $50c$ and neutopia $50w$ and $25c$. Now if instead of autarky they decide to trade and Utopia will specialize only in cloth it can produce $100c$ and Neutopia if it specializes in wine can produce $100w$. Now both countries can trade lets say 50 units of wine for 50 units of cloth and now both countries have $50w$ and $50c$. Both countries expand their production possibility frontiers by engaging in trade and trade is not zero sum as both countries are better off.

Hence, as a result of comparative advantage $Y$(trade) > $Y(autarky)$. So once you allow in the identity $Y=C+I+G+X-M$ the output $Y$ to be increasing function of country's  PPF its not correct to say that trade is zero sum game.

Of course, in a classroom setting its fine to apply national identity just to some pure endowment economy where your zero-sum conclusion about trade is correct. Or you could even allow for some production function but assume all countries have exactly same production function and exactly same resources endowments and there can be no economies of scale etc. where there is no reason for trade. But you are making a mistake by using a simple identity that ignores comparative advantage, factor endowments etc. and just making conclusions about international trade in real world.


Here are a couple hints for the two that you haven't answered:

The prisoner's dilemma is characterized by the inability to sustain the Pareto optimal payoff as a Nash Equilibrium due to the existence of a profitable deviation for both players. Each player has a dominant strategy to "Defect" and so the unique Nash Equilibrium is one where both players "Defect". Does that hold here?

A (possibly mixed) strategy $a$ (weakly) dominates another strategy $b$ for a given player $i$ if player $i$ (weakly) prefers playing $a$ to $b$ for any strategy vector of the other players. In your case, there is just one other player, $j$, and so $i$ simply has to prefer $a$ to $b$ for any strategy played by player $j$.

You just need to see if that holds for your two players.


Including (demand) price elasticity in a price regression model

The incorporation of a price elasticity in your regression requires that your dependent variable, quantity,  be logged as well.

Take an example of a basic demand side equation including two independent variables

$$Q_d=\beta_0+\beta_1 P+\beta_2 S+\mu$$

where $Q_d$ is quantity demanded, $P$ is the price of the good in question and $S$ is the price of a substitute.

To incorporate price elasticity in this regression you have to log your dependent $Q_d$ and then log price $P$ as well.

$$\ln(Q_d)=\beta_0+\beta_1 \ln(P)+\beta_2 S+\mu$$

Only via this framework can we calculate elasticity, given by $\beta_1$.

In terms of calculating equilibrium we would require the use of simultaneous equations where supply $Q_s$ is logged.

However this calculation of percentage change in $Q$ can be transformed easily by specific equilibrium quantity by using basic algebra such as:

1.$$Q_d=Q_s=Q^*$$
2.$$\ln(Q_d)=\ln(Q_s)=\ln(Q^*)$$
3.$$\mathrm e^{\ln(Q_d)}=\mathrm e^{\ln(Q_s)}=\mathrm e^{\ln(Q^*)}$$
4.$$Q_d=Q_s=Q^*$$

The same steps can be followed when calculating $P^*$.

Hope this helps.


How does reverse repo rate affect money supply?

Reverse Repo Rate (RRR) is the rate at which the central bank "borrows" money from commercial banks. (In practical terms it refers to the surplus funds that these commercial banks park with the central bank.)

This leads to a FALL in the total money supply as it soaks liquidity from the market.

This reduction in total cash flow in economy (which is now lying stagnant at the central bank) implies a weakened monetary base and reduced capability of banks to "create" more money as they are left with little real cash to extend loans upon given the cash reserve ratio requirements.


How do companies with shareholders close up shop?

We need to distinguish between private corporations, and public. Private corporations are largely free in what they do, public corporations listed on stock exchanges have to follow various procedures.

For any corporation, there’s no guarantee that you make a profit, so what price you bought it at makes no difference.

If a company wound up its affairs, it would make a final cash distribution to shareholders, and that would be it. The cash would either be a dividend or a return of capital, depending upon the equity levels of the company.

The problem is that do this, the company would have to sell all assets simultaneously. That is normally difficult to do, and so it is much more usual for the entire firm to bought out (after selling some assets).

Furthermore, having a listing on the stock exchange is itself valuable. It would be far more common for a company to pursue a “reverse takeover”: the listed company appears to take over a private firm, but the private firm actually buys out the existing shareholders. This way, the private firm saves the expenses of seeking a listing on the stock exchange. Just shutting the firm down would probably be viewed as a suboptimal course of action, and might expose the directors to lawsuits.

What is more likely is that companies largely fail, and end up having to shut down most of their operations. After awhile, they will not meet listing requirements to remain on the stock exchange, and the shares are delisted. The shares still exist, but it is very hard to find buyers.

If you want to find examples, you could just do a web search looking for the terms “delisted companies” and the name of a stock exchange that you are interested in. The following link is an example:
TSX Venture Exchange listing changes


Why does the Balance of Payments have to (more or less) equal zero

It was also really strange for me at first. I asked from many people who might happen to know the answer. However, they were all not 100% satisfactory. I think, Kenny LJ's answer is 99.5% correct but i feel that it's still missing something. My explanation is to add to his/her answer something i think very very subtle, but hopefully important, one.

Think you have an organization and record the purchase in your balance sheet. You will purchase the good as an asset with an debit entry. Also, you will credit your cash with the same amount.

When these two entries come to the BOP, the asset will be in CA and the cash will be in FA. Why the money should be recorded in FA? When a country starts to hold a foreign currency /it was well before and independently of your purchase/, it's recorded in BOP as an investment to the foreign country. Now when you pay with the money of the foreign, you stop your investment and make it a physical good. So your stake with the other country doesn't change, but its form. So the balance is not affected in the end.

If you work with other examples, it'll become clearer and clearer. Let me give some.

Imagine you export something to a foreign country. How will it be 0 in BOP? An export debits your goods and increases the CA. If you get a foreign currency from your foreign partner for the payment, it'll be credited as investment to the other country as you hold its currency which will credit or decrease the FA.

Imagine you borrow from a foreign country, it'll be an increase in FA as it's a foreign investment to your country. But in which currency will you hold your investment proceedings? You may start holding that country's currency. This will be recorded as your country's other investment to the other country which will be decrease in FA.

If you sell above investment money into your country's central bank and your central bank holds it as cash, your country's other investment's increase will be undone which will result in positive FA from the investment /it'll look like the foreign country invested positive amount in net/. But the official reserve account of the country will increase with the same amount which will also make the BOP 0.

I hope it helps.


How to verify Value Function in nonzero sum two player Differential Game?

The first panel shows the final value function after iterating 80k (!). Should probably try an implicit method. The second panel shows the evolution from frist guess to final result $v^0\to v^j$, $j=80k$. Third panel is the distance between the value functions and fourth shows the error.

Note that the value function is convex-concave. This is due to the fact that for the limit case the law of motion tends to infinty $\lim_{k\to 0} \dot{k} = \infty$.

By the maximum principle optimality requires that the Hamiltonian
\begin{align}
H_1(k,\tau_1,\tau_2^*,\lambda_1) := F(k,\tau_1,\tau_2^*) + \lambda_1 f(k,\tau_1,\tau_2^*)
\end{align}
is concave in $(k,\tau_1,\tau_2)$ (sufficient condition). Now we have
\begin{align}
\rho v(k) = \max_{\tau_1} H_1(k,\tau_1,\tau_2^*,\lambda_1).
\end{align}

I was wondering if the value function must be (strictly) concave to ensure optimality?

Any reference is appreciated.


Statistical distribution of wages and wealth

Globally, there is Lakner and Milanovik (2015)'s elephant graph:

Hellebrandt and Mauro (2015)

Thus, the two previous distributions look like bimodal log-normal distributions.

or CDFs, as in MacAskill's book Doing Good Better

Did not find something strictly related to wages. For most of people, income may be a good proxy of wages.


Why obligation acceleration triggers Credit-Default Swaps (CDS)?

There is an example of its use at definedterm.com from a Cemex 2006 Note saying

  "Obligation Acceleration" means one or more Obligations in an aggregate amount of not less that the Default Requirement have become due and payable before they would otherwise have been due and payable as a result of, or on the basis of, the occurrence of a default, event of default or other similar condition or event (however described), other than a failure to make any required payment, in respect of a Reference Entity under one or more Obligations.

What this seems to mean (IANAL so this is not legal advice) is that a default or similar event (perhaps of a coupon) may lead to some or all of the amount borrowed becoming repayable earlier than originally planned, i.e. accelerating the obligation


Does savings always equal investment? Are there any cases where savings could be removed from the economic system altogether and break the balance?

Does savings always equal investment?

If we are talking about national accounts then yes. Output of closed economy is given by:
$$Y = C+I+G \tag{1} $$
Private saving $S_p$ is by definition is disposable that is not consumed (see further explanation in Blanchard et al. Macroeconomics an European Perspective pp 55) so:
$$S_p= Y- T-C \tag{2}$$
Public saving $S_g$ is by definition equal to difference between taxes $T$ and  gov spending $G$ (see ibid) so we have:
$$S_g= T-G \tag{3}$$
Substituting 3 into 2 (by solving for T) and then into 1 (by solving for Y) gives us:
$$S_p+S_g + G + C= C+I+G \tag{4} $$
Now just by simple algebra we can see $G$ and $C$ are eliminated so we are left with:
$$S_p+S_g =I$$
So total saving (public and private), must be at all times equal to investment. The above is pure accounting identity, it simply must hold the same way as it is not possible that in some company assets are not equal to liabilities and equity.

However, if the resource is subsequently destroyed, it is then removed from the economy. In that case, the savings have increased but the investment hasn’t?

No. You need to realize that $C, I, G, Y  $ or $S$ must be defined over some time period like a day, month, year, decade and so on. Let us assume that we are talking about yearly period for a simplicity sake. For example suppose that in 2010 goods worth of 1000e were produced, people wanted to save 200e but in the same 2010 100e  were destroyed (gov is assumed away). Well the GDP gets calculated at the end of the time period so if we would look inside the time period before destruction GDP would look like $Y=1000$, $Y-C=800$ $S=I=200$ but after destruction it would look like  $Y=900$, $Y-C=800$ and $S=I=100$. You see that it would all perfectly balance and overall what is reported at the end of the year is  $Y=900$, $Y-C=800$ and $S=I=100$.

Does destroying a resource count towards investment?

No, but it will no longer count toward output as well. Investment will be lower but output for the same period will be lower by equal amount making it all equal.
To give you an intuition, you should realize that $Y$ output/income must always be equal all spending $C+I+G$ (for closed economy), if you lower spending on  $I$ (because part of it is destroyed and thus no longer counts), $Y$ has to drop as well.  What you are saving in real terms is not money but output -that is what matters, you are consuming output, investing output (which is equivalent to saving output as proven above) or government is consuming output - it is all just breakdown of what happens with output Y, saving part of it does not make it no longer output.

Is this any different from the way investment takes resources away from an individual and puts it into an economy?

Yes of course. Investment is basis for capital formation which in turn expands the societies production possibility frontier (see discussion of this in ibid ch 14).
Destruction of those resources will lower the total investment, hence ceteris paribus negatively affect future output (however, note here everything is expressed in real terms not nominal terms i.e. destroying money would not have the same effect as that would just change nominal value). However, as explained above it also lowers present income so national accounts perfectly balance each other.


Due to the linearity of the utility function the utility maximization problem for individual $i$ has either one of the two corner solutions, or it is indeterminate.

The individual $i$ has to solve the following problem

$$\max_{x_{1i},x_{2i}}[ x_{1i} + \beta_i x_{2i}]$$

$$s.t. x_{2i} = 1-(1+r)x_{1i}, \;\;x_{1i} \geq 0,\;\;x_{2i} \geq 0 $$
Solvency is also imposed -i.e. the individual cannot borrow in the first period more than what he can repay in the second period (including interest).

One can deduce that

$$\text {"flatter" budget constraint:}\;\; -(1+r) > -\beta_i^{-1}   \implies \{x_{1i}^* = (1+r)^{-1},\;\;x_{2i}^* = 0\} $$

$$\text {"steeper" budget constraint:}\;\; -(1+r) < -\beta_i^{-1}  \implies  \{x_{1i}^* = 0,\;\;x_{2i}^* = 1\}$$

.."steeper" and "flatter" with respect to the utility (linear) indiference map, and with $x_{2i}$ in the vertical axis.

Working the implied inequalities we re-write the solution as

$$\beta_i < \frac 1{1+r} \implies \{x_{1i}^* = (1+r)^{-1},\;\;x_{2i}^* = 0\}$$

$$\beta_i > \frac 1{1+r} \implies \{x_{1i}^* = 0,\;\;x_{2i}^* = 1\}$$

In the $N$-identical individuals case, and with $\beta_i, i=1,...,N$ being a random variable we can only talk about expected demand in the first period, denote it $E(d_{1i})$ for the individual and $E(D_1) = N\cdot E(d_{1i})$ on aggregate.

We have

$$E(d_{1i}) = \frac 1{1+r} \cdot \Pr\left[\beta_i < \frac 1{1+r}\right] + 0 \cdot \Pr\left[\beta_i > \frac 1{1+r}\right] $$

The second term vanishes.

Given the assumptions on the distribution of the $\beta$'s its density function over the domain is $f(\beta_i) =2$ and so the remaining probability is (as long as $r \leq 1$)

$$\Pr\left[\beta_i \leq \frac 1{1+r}\right] = \int_{1/2}^{(1+r)^{-1}}2{\rm d}\beta_i = 2\left(\frac 1{1+r}-\frac 12\right) = \frac {1-r}{1+r}$$

and so we have

$$E(D_1) = \frac N{1+r}\cdot \frac {1-r}{1+r} = \frac {1-r}{(1+r)^2}N$$

which is decreasing in $r$.

If $r$ hits unity, expected demand will be zero -because
a) It would place a solvency ceiling to loan demand to be not higher than $1/2$ so that with interest rate $100\%$ all production of the second period would then be needed to repay the loans. This means that with $r=1$, maximum consumption (and utility) in the first period will not exceed $1/2$.
b) the discount factor being greater or equal than $1/2$, implies that by taking zero loan in the first period, one would enjoy the full unitary production of the second period, with utility higher than $1/2$. So for non-zero demand for loans in the first period, it must be the case that this demand can exceed $1/2$. When $r\geq 1$ it cannot, hence the zero expected demand.

Note: if instead of a "stochastic distribution" of the $\beta$'s we think of a "uniform allocation" of them in the $[1/2,1]$ interval, then we can think of expected demand as deterministic demand.


Which economist suggested solely printing money to borrow and not have bonds?

I think that Stephanie Kelton is an economist who has mentioned this before. From my research, it is based on the MMT. Some practitioners of the MMT believe that the government should not issue bonds, but can instead print money. I think that I may have heard Kelton mention this a few years ago, but I am not that into the MMT. I would do some research on the MMT however, and Kelton, and that can likely lead you to the answer you're looking for.


Piracy/File sharing - Why aren't songs, movies or ebooks given for free (+ads) like TV?

It's called a Principal-Agent Conflict.
The RIAA/MPAA act as agents on behalf of the people who actually produce content (and consequently end-consumer value).
To maintain relevance to their principals', the RIAA/MPAA must signal value to them (i.e. claim loudly and repeatedly that they do something good for them [regardless of the validity of that claim]).
Firstly, this signaling is demonstrably an example of the Principal-Agent problem, in that it diverts resources away from actually advancing the principals' interests, but more so in that it creates a perverse incentive for lobbying groups to fight imaginary fires.
The impact of piracy on the broad economy is believed to be near zero, so IP laws are effectively just rent-seeking $^{[2]}$ anyway.
Whether or not that particular type of rent-seeking is always a drain on the broad economy (in that it distorts markets producing deadweight loss in excess of the externalities corrected) is up for discussion, though it is known to be possible (insofar as the existence of an optimal tax [or government induced market distortion] is necessarilyy proof of the existence of an excessive tax).


How to approach such question of two periods and asymmetric information game?

You want to solve these types of games using the logic of backward induction and when beliefs become necessary, assume a pooling or separating equilibrium.

For example, start with the final nodes. It is clear that player 1 will choose C if no one has contributed before, and he is of the low type. He will choose N if someone has contributed before or if he is of the high type.

Knowing this, when player 2 makes her decision it is also easy to see that she will never contribute if player one contributed in the first period. If player 1 did not contribute in the first period, payer 2's decision depends on whether she thinks that player 1 is of the high type or of the low type. She would want to contribute if the belief that player 1 is of the high type is high enough otherwise she would prefer to choose N.

This is were assuming a separating or pooling equilibrium comes in handy. For a separating equilibrium, player 2 will learn player 1's type by the moment she has to make a decision, so she would choose C if player 1 is of the high type and choose N if it is of the low type (this is because she anticipates perfectly what player 1 will do in the second period since she knows his type).

Giving player 2's strategy, player one in the first period will choose to not contribute if he is of the high type (it is not profitable for him and he anticipates that 2 will realize he is of the high type and pay the public good), and player 1 will choose to contribute if he is of the low type (since he anticipates that player 2 will know he is of the low type and not contribute, so he would end up paying for the public good in the second period, but for him, it is better to get $b_1-\underline{c}$ rather than $\delta(b_1-\underline{c})$).

We conclude that this is indeed an equilibrium because each type of player one ends up choosing a different action in the first period (separating) and every player is best responding to the other player's strategy, there is no profitable deviation. In this case, player 2 assigns a probability of 1 to player one being
of the high type if he does not contribute in the first period and 0 if he does.

Let's now assume a pooling equilibrium. In this case when player 2 makes a decision she doesn't know what's player 1 type. She only knows that with probability $p$ he is of the low type and $1-p$ he is of the high type. Regardless of this uncertainty, if player one already paid for the public good, player 2's best response is N, if player one did not pay for the public good, player 2 can pay for it and get $b_2-c_2$ or not pay for it and get $b_2$ with probability $p$ or zero with probability $1-p$. Therefore, she chooses C if and only if $b_2-c_2\geq pb_2$. That is if $b_2\geq \frac{c_2}{1-p}$ (i.e. if she values the public good enough).

Suppose the last inequality does not hold, in that case, player 2 does not pay for the public good. Given this strategy player one of the low types would prefer to choose C while player 1 of thee high type would prefer to choose N. This contradicts the assumption of a pooling equilibrium. In contrast, if the inequality above holds, a pooling equilibrium exists only if $b_1-\underline{c}\leq \delta b_1$. That is if $b_1\leq\frac{\underline{c}}{1-\delta}$ (if he doesn't value the public good to much so as to not be willing to wait).

I gave less detail for the pooling equilibrium, but hopefully, you can follow were the inequality comes from.

Lastly, for the last type of equilibrium you just have to realize that for player 2 if player 1 has not contributed to the public good yet if could be because he is of the high type (mass $=(1-p)$) or because he is of the low type and did not contribute (mass $=p(1-\alpha)$). Therefore, it is of the high type with probability $\frac{1-p}{1-\alpha p}$ and of the low type with complementary probability. So for player two to want to randomize she should bee indifferent between contributing or not. Therefore $b_2-c_2=\frac{p(1-\alpha)}{1-\alpha p}$. This equation gives you the equilibrium value of alpha. Similarly, player 1 of the low type should be indifferent between paying in the first period or with probability $\beta$ get the good for free, and probability $1-\beta$ pay for the good in the second period. Therefore $b_1-\underline{c}=\beta c_1+(1-\beta)\delta(b_1-\underline{c})$. Which will give you the equilibrium value of $\beta$.


What is the correct way to calculate a selling price from margin and a cost?

The "margin" is a portion of the selling price. It is defined as

$$\text {margin} \equiv \frac {P-C}{P}$$

From the above definition, we see that the margin cannot exceed $100\%$.

If one has the cost and he wants to calculate the price in order to have a specific margin, one must calculate

$$P(\text {margin}^*) = \frac {C}{1-\text {margin}^*}$$

The first formula written in the question is wrong, because it uses "margin", but it would become correct if instead one used the concept of "markup".

The "markup" is defined as the percentage increase of cost in order to determine the selling price:

$$\text {markup} \equiv \frac {P-C}{C}$$

It is easy to obtain that the relation between them is

$$\text {margin} = \frac {\text {markup}}{1+\text {markup}}$$


TFP estimation as residual and normality of errors

TFP is not simply a residual value in a regression as you have assumed, it is called residual because it is observed rather than measured. That is what probably causes your confusion.

It is what is left after the Labour and Capital inputs have been accounted for. Normally you can break TFP down further into components of technological progress, scale effect and technical efficiency.

There is plenty of literature and sometimes conflicting views on the measurement of TFP and growth accounting on the web. Perhaps the below links can serve as a starting point.

Measuring TFP growth and TFP overview


Macroeconomics Textbook on New-Keynesian models

Michael Woodford's book Interest and Prices, while it may not be explicitly New Keynesian, may have some of the rigor you're looking for applied to this class of models.

A more direct alternative would be New Keynesian Economics edited by Mankiw and Romer. While it's a collection of papers not a textbook, if you're looking for underpinnings of New Keynesian models this'd be a good place to start. Also "The Science of Monetary Policy: A New Keynesian Perspective" by Clarida, Gali and Gertler.


Can a complement good be free or have a fixed cost?

Air is a complement good for a lot of things. If you get no air at all then food, gold and iPhones give you no utility either. And air is free! Except in Spaceballs...


How does one graph indifference curves for a set of Lexicographic preferences?

You can draw discontinuous functions in a standard $R^2$ space. For example when you draw a floor functions (a discontinuous function), the standard coordinates are still appropriate. Just make clear what to what part the discontinuous point belongs to.
Usually, for lex. preferences, one draws only the preferred set. Here you can find a graph of this kind (page 2).
Yes, each point is an "indifferent singleton" (if we may say so, as your set has only one element, and of course you're indifferent between the same thing).
The infinity number of points is not a problem. When you draw a preference map (for standard preferences), there are an infinite number of possible indifference curves. The idea is just to know how many you need to make your point. If you're using a software, you can plot with colors instead of a huge number of lines...


Long-term interest rate and stock market correlation

Many organisations borrow money to purchase shares (trading on margin). Their enthusiasm for doing this will depend on the interest rate. So lower interest rates means more borrowing for purchasing shares, which means prices rise.

A similar thing happens with other stuff that people tend to buy with borrowed money - like housing.


How many major economic systems are there?

Wikipedia has a comprehensive list of  economic systems.
If you want to start thinking about number major economic systems that exist I recomend looking at the section on an economy's  allocation mechanism.
In particular, Wikipedia lists the following kinds of system:

The basic and general economic systems segmented by allocation are:

Market economy ("hands off" systems, such as laissez-faire capitalism)
Mixed economy (a hybrid that blends some aspects of both market and planned economies)
Planned economy ("hands on" systems, such as state socialism, also known as "command economy" when referring to the Soviet model)
Traditional economy (a generic term for older economic systems)
Participatory economics (a system where the production and distribution of goods is guided by public participation)
Gift economy (where an exchange is made without any explicit agreement for immediate or future rewards)
Barter economy (where goods and services are directly exchanged for other goods or services)
Post-scarcity economy (a hypothetical form where resources aren't scarce, such as Marx's concept of a Communist society)


If we estimated the value of all the assets in the world and compared it with the estimated total wealth of individuals, would the results be similar?

As currently written, the question asks whether the value of all assets equals the wealth of individuals. This is trivially not the case, since assets can be liabilities of another entity.

As an example, imagine an economy in which one individual owns both an industrial firm and a bank. The bank can make a loan to the firm, and both entities’ balance sheets grow - the bank gets a loan asset, the firm gets a new deposit at the bank. This means that the total value of all assets increases by double the amount of the loan. However, the act of taking out a loan and not spending it does not increase the value of a corporation, and so individual owning the two banks has no increase in wealth.


How do I use a monopsony (product market) graph to show that a firm has more buying power over a supplier?

I am not sure what you mean by a monopsony graph. If you mean a graph wherein you show that Marginal Factor cost is not equal to the inverse input supply curve, then you do not need the graph at all. The fact that $MFC(x) \neq w_x$ shows that the buyer has market power.

Not sure what you mean by having "more buying power".


It refers to the reserves that banks have to hold in fractional reserve system. A fractional reserve system is a monetary arrangement where bank is allowed to use depositors money for loans as long as they keep a fraction of it as a reserve. For example, if reserve requirement is set to 10% if you deposit 100\$ in your bank they must keep 10\$ and they can lend the rest 90\$.

Portion of the reserve requirements in US is hold by the Federal Reserve (Fed). Also, as a central bank Fed can create new bank reserves (money) for the domestic banks in times of need. Hence this is where the name comes from - from the fact that central bank can hold reserves or create new ones.

However, I would not read too much into the names of banks, note virtually all banks around the world operate in similar fashion like Fed but they are not called reserve banks. For example, Bank of England, Bank of Japan, ECB they all have similar functions.


If you take the vector $\mathbf{x}$ as the center and an $\epsilon > 0$ sufficiently small as the radius, then the open ball (local neighborhood of the vector $\mathbf{x}$) is the set of all vectors $\mathbf{y} \in \mathbb{R}^{n}$ whose distance to the center $\mathbf{x}$ is less than $\epsilon$ measured w.r.t. the metric $\Arrowvert \cdot \Arrowvert $, i.e., more formally as

$$\mathbf{B}(\mathbf{x},\epsilon) := \big\{\mathbf{y} \in \mathbb{R}^{n}\,\Big\arrowvert\, \Arrowvert \mathbf{y} - \mathbf{x} \Arrowvert < \epsilon \big\}.$$

Notice that measuring a distance by a metric is only possible within a metric space or normed space like Hausdorff or Banach. Topological spaces do not have in general a metric, in this case the above concept must be generalized. Fortunately, all finite dimensional spaces have a canonical norm, i.e., the Euclidean norm.


Are Investments positively or negatively correlated with interest rate

History is plenty of different situations, but usually it works like this:

Low interest rates will increase demand of borrowing money and will decrease the interest of investors in lending (they will probably try to find another place with higher interest rates to invest in).

As a consequence, there will be less people offering money, so the interest rate will increase and the demand of borrowing money will decrease (because it will be more expensive). Maybe it will reach a kind of balance or maybe it will attract imvestors again (it depends on both local and international situation).


To answer the specific question, I believe the largest hf in the world is Bridgewater (assets under management of around 120bn USD). Assets of around 500m USD would be considered average and north of 1bn usd large. Bridgewater is an outlier. I do not know if one larger has ever existed but I doubt it.

As to what effects they have on the economy well, funds can serve as catalysts for economic events (e.g. Soros' fund and others catalysing the UK exit from the ERM). They serve as vehicles for pooling and allocating capital and so act as intermediaries between those who wish to lend (investors in the hedge fund) and those who wish to borrow (firms issuing bonds etc. which the hf buys). This function only applies when the hedge fund is making a primary investment though - when it is buying something in the secondary market rather than a first issuance funds do not have this role. They largely determine things like commodity prices, exchange rates through the bulk of money they control together, although no hedge fund is large enough to control these markets directly.


Annual Fraud Recovery Over Time: Should I adjust for inflation?

You should definitely adjust for inflation, as you should with all monetary variables. I wouldn't worry using the CPI, you could use an alternative indicator as a robustness check to see whether the choice of indicator affects your main conclusions.


Why debt/equity ratio is limited to between 0 and 9

When a company is in near-bankrupt state, it's equity $\rightarrow0$, meaning that D/E goes $\rightarrow\infty$. Including such observations would make the resulting mean D/E meaningless. This is why boundaries are needed


In what country outside of the EU is the public sector the highest percentage of GDP?

The answer seems to be Kiribati, with a whooping 92%.

https://en.wikipedia.org/wiki/Government_spending#As_a_Percentage_of_GDP


Articles about the economics of non-compete contracts

Ghosh and Shankar (2017) "Optimal Enforcement of Noncompete Covenants", Economic Inquiry

  Noncompete covenants or covenant not to compete (CNC) are clauses in employment contracts in which the employee agrees not to gain employment with a competitor firm. In this article, we study the efficiency aspects of such contracts by incorporating the effect of labor mobility restrictions on knowledge transfer across firms, investment decisions by firms, and investment by workers. Following research that shows state‐wise variations in the degree of CNC enforcement, we allow the strength of CNC enforcement to vary as a matter of regulatory policy and derive the optimal strength of enforcement. We also look at how regulations around CNCs should be optimally designed when employers can use collusive agreements, such as “no poaching” agreements, as an alternative to noncompete clauses. Given recent allegations of employer collusion among large Silicon Valley firms, we argue for a cautious approach in designing policies on CNC enforcement.

Garmaise (2011) "Ties that Truly Bind: Noncompetition Agreements, Executive Compensation, and Firm Investment", Journal of Law, Economics, & Organization

  We study the effects of non-competition agreements by analyzing time-series and cross-sectional
  variation in the enforceability of these contracts across U.S. states. We find that tougher noncompetition
  enforcement promotes executive stability. Increased enforceability also results in reduced
  executive compensation and shifts its form towards greater use of salary. We further show
  that stricter enforcement reduces research and development spending and capital expenditures per
  employee. These results are consistent with a model in which enforceable non-competition contracts
  encourage firms to invest in their managers’ human capital. On the other hand, our findings
  suggest that these contracts also discourage managers from investing in their own human capital
  and that this second effect is empirically dominant.

Two other recent empirical papers may also be of interest:

Jeffers (2018) "The Impact of Restricting Labor Mobility on Corporate Investment and Entrepreneurship"
Starr (2018) "Consider This: Training, Wages, and the Enforceability of Covenants Not to Compete"


Introductory book for asset pricing and financial economics

If you are looking for something simpler before jumping to Black-Scholes, consider the textbook "Investments" from Bodie, Kane, and Marcus.

You can look at the table of contents. The book assumes that the reader does not know stochastic calculus and continuous time finance, but it still gets to the Black-Scholes formula.


Macro regressions, especially annual ones, have in general two flaws:

They have small sample problems and
They have no proper identification

In order to circumvent problem #1, people often assume that the DGP process behind different countries are the same, increasing observations from perhaps 60 to 600.

In order to attack #2, many people add timing assumptions. However, this is still no clear identification, these are still assumptions.

To see the issue: Imagine high inflation at $t-5$, and low growth at $t$. Using a standard timing assumption, the former caused the latter. However, we like to think about agents as forward looking. Can we be certain that expectations w.r.t. the latter didn't influence the former?

Especially because of #2, this type of regressions have lost popularity. Also, there is not really much more to do.

tl;dr: No important new results that I know of.


Effect of changing Non Labor Income on Consumption-Leisure problem

This has to do with the form of the utility function. Assume instead that,say, we had

$$U(c,l) = c^{1/2} - \frac{1}{2}l^2$$

Does now $R$ affect the labor-supplied decision?

Solve it and explore. Check also the link offered in a comment to your question.


Have countries ever tested economical measures at city level?

Yes, there are lots of examples of countries piloting new economic measures before they are rolled out nationwide.  A couple of recent examples are of Finland piloting universal basic income and the UK piloting universal credit in 12 local authorities, which was then extended nationwide in a number of stages.


Producer Econometrics: Univariate modelling with missing data

Alternatively, you can use the mean of the period, or fit a linear trend and interpolate. These methods use more information than just two years, which has the benefit of accounting for possible idiosyncratic factors in 2012 or 2014, with the cost of perhaps adding idiosyncratic factors from years as far as 2017.

Here is the R code with the three methods (including Alecos's):

# Interpolate between 2012 and 2014
df = data.frame(year = 2010:2017, y = c(22306000,22420000,23010000,NA,25430000,25601000,25267000,23895400))
df$y[is.na(df$y)] = mean(df$y[df$year==2012 | df$year==2014], na.rm=TRUE)

# Replace with mean of period
df = data.frame(year = 2010:2017, y = c(22306000,22420000,23010000,NA,25430000,25601000,25267000,23895400))
df$y[is.na(df$y)] = mean(df$y, na.rm=TRUE)

# Regression interpolation
df = data.frame(year = 2010:2017, y = c(22306000,22420000,23010000,NA,25430000,25601000,25267000,23895400))
fit <- lm(y ~ year, data=df)
df$y[df$year==2013] <- predict(fit, newdata = data.frame(year = 2013))

The results with each method are 24220000, 23989914, and 23753107 respectively. They are different because the series does not follows a linear trend:

# Plot
df = data.frame(year = 2010:2017, y = c(22306000,22420000,23010000,NA,25430000,25601000,25267000,23895400))
plot(x=df$year,df$y, type="l",lwd = 2)

Thus, it seems Aleco's method might be the most appropriate in this case. (It is also possible to fit non-linear trends)


Academic paper which justifies why companies are run better privately

I think this is what you are looking for.

It is a quite interesting paper. I hope it helps.


What does it mean for a firm to have a 0.95% dividend?

As of the market close on 2/14/2020, Apple's stock price was \$324.95 per share. The forward looking dividend (based on announced dividend policy over the next year) is \$3.08 per share. The forward looking dividend yield is therefore $\frac{3.08}{324.95} = 0.00948$ or 0.95%. This means that for every share, the firm is planning to pay out \$3.08 over the next year, so the effective yield is that payout over the current stock price. Essentially, every \$100 invested in Apple will throw off 95 cents of cash over the next year.

Source: Yahoo Finance


Why does Ricardian Equivalence not hold when there are different borrowing and lending rates on the market?

Barro helped define Ricardian equivalence, wherein one of the assumptions was that the capital market is perfect(can lend and borrow at a single rate).
so it can be easily inferred that Ricardian equivalence does not hold true when borrowing and lending rates are different.
and while it is assumed under Ricardian equivalence that consumers are able to save/ spend according to tax regimes, it is debatable, as was mentioned by Ricardo himself, that people may have a myopic approach towards tax regimes.
although it holds credibility in some specific examples, the discounting of one of its basic assumptions can be the reason for it not holding true when borrowing and lending rates are different.

it would be more helpful if you could elaborate on the type of examples/statements you want to support your answer.


What are the arguments against the rational expectations hypothesis?

The Rational Expectations Hypothesis (REH) is an hypothesis about aggregate expectations. I believe it is illuminating to post here a lengthy quote (part 2) from Muth (1961) paper where REH originated (bold letters are our emphasis):

  2. THE "RATIONAL EXPECTATIONS" HYPOTHESIS
   Two major conclusions from studies of expectations data are the following:
  1. Averages of expectations in an industry are more accurate than naive models and as accurate as elaborate equation systems, although
  there are considerable cross-sectional differences of opinion.
  2. Reported expectations generally underestimate the extent of changes that actually take place.

  In order to explain these phenomena, I
  should like to suggest that expectations, since they are informed
  predictions of future events, are essentially the same as the
  predictions of the relevant economic theory (We show in Section 5 that
  the hypothesis is consistent with these two phenomena). At the risk of
  confusing this purely descriptive hypothesis with a pronouncement as
  to what firms ought to do, we call such expectations "rational." It is
  sometimes argued that the assumption of rationality in economics leads
  to theories inconsistent with, or inadequate to explain, observed
  phenomena, especially changes over time (e.g., Simon 1959). Our
  hypothesis is based on exactly the opposite point of view: that
  dynamic economic models do not assume enough rationality.

  The hypothesis can be rephrased a little more precisely as follows: that
  expectations of firms (or, more generally, the subjective probability
  distribution of outcomes) tend to be distributed, for the same
  information set, about the prediction of the theory (or the
  "objective" probability distributions of outcomes).

  The hypothesis asserts three things: (1) Information is scarce, and the economic
  system generally does not waste it. (2) The way expectations are
  formed depends specifically on the structure of the relevant system
  describing the economy. (3) A "public prediction," in the sense of
  Grunberg and Modigliani (1954), will have no substantial effect on the
  operation of the economic system (unless it is based on inside
  information). This is not quite the same thing as stating that the
  marginal revenue product of economics is zero, because expectations of
  a single firm may still be subject to greater error than the theory.

  It does not assert that the scratch work of entrepreneurs resembles
  the system of equations in any way; nor does it state that predictions
  of entrepreneurs are perfect or that their expectations are all the
  same. ...

I believe that it should be clear from the above that:
1) REH  is not an assertion about each separate individual, but about the properties of the "prevailing" expectation produced by the black-box combination of individual expectations.  In other words the REH is assumed, without really making any assumptions about individual rationality.

2) It has as much to do with  the "internal consistency" of the economic model itself, because by construction and without any economic assumptions, $E(X\mid I) = X+ e,\; E(e\mid I) =0 $.

The fact that the predominant economic model framework has been that of the "representative" (identical) consumer, nevertheless blurred the distinction between the aggregate expectation, and individual expectations on aggregate variables. This provided shallow "micro-foundations" to the REH, (shallow because it is not really micro-founded, that which essentially assumes away the need to aggregate), but also, it moved the debate into the arena of individual expectations formation and whether individuals use information efficiently or not, which raised valid objections as those mentioned in the answer by @EnergyNumbers.

But really, at the individual level, the hypothesis that individuals use the mathematical expected value comes essentially from Expected Utility theory, that predates the Rational Expectations, and has a debate on its own (also here in Economics.SE)

Another set of "arguments against" the REH (which gave very interesting literature), was collected early on in the book "Individual forecasting and aggregate outcomes - Rational Expectations examined" 1983 R. Frydman and E. Phelps (ed). Of which I mention two:

1) Being an equilibrium concept, REH requires co-ordination of expectations formation (which is really not that realistic) or properties of Nash-equilibrium: this last insight gave us "Eductive Expectations" and some really thoughtful works by Roger Guesnerie.

2) The second one, which became rather more widely spread than Eductive Expectations, is "Adaptive Learning" (see "Learning and Expectations in Macroeconomics" By Evans and Honkapohja, 2001).
Adaptive Learning pointed out that REH assumes that economic agents know the structure of their environment perfectly. So in Adaptive Learning models we have the first systematic approach to model uncertainty : as economists, so economic agents do not know the environment perfectly, and they have to estimate it and learn it gradually (hence "adaptive learning"). In this strand of literature, "learning" is done through econometric methods, mainly least-squares (which is a very intuitive least-distance mathematical approximation method). Roughly speaking, here agents' expectations are not the expected values, but the estimated expected values. This creates much more interesting and realistic dynamics, that some times may converge (someday) to an REH equilibrium (which makes Adaptive Learning a "selection mechanism" for the sometimes multiple REH equilibira), or to some other point, not predicted by REH.

Research into the issue of aggregate expectations formation and modeling is currently exploding, see for example another Frydman & Phelps (ed.) book, "Rethinking Expectations" (2012), in parallel with the emerging "Post-Walrasian" direction in Macroeconomics (see D. Colander (ed). Post-Walrasian Macroeconomics 2006).


I will try to answer to your last question. I did not read the paper but in models with higher dimensions, it is always difficult to find an analytical solution.
If there exists an analytical solution (for a very basic model with a one-state variable), it is possible to derive the initial conditions for your control and state variable from your differential equations.

However, in systems where there does not exist an analytical solution, you are supposed to solve it numerically, in which case you must give a numerical value for one of your variables (or more until you find steady state values for all your variables.)

After, you can find the steady-state values of your variables in which case, your initial conditions should not be so far from the steady state level (otherwise, there would be some convergence problems in your model if you don't choose the appropriate initial values, close to steady state. It is another issue.)


The Billion Price Project offers what you want:

  Daily price indices, monthly, and annual inflation rates for Argentina
  and the US. Monthly data with annual inflation rates for Argentina,
  Brazil, China, Germany, Japan, South Africa, UK, US, 3 US sectors, and
  global aggregates (including Eurozone). Daily PPP series for Argentina
  and Australia.

However, these data, which come mostly from online transaction data, are imperfect because they end in 2015. However, I've put together some code so you can see that there is not very much high frequency price level variation for the basket of goods:

import delimited pricestats_bpp_arg_usa.csv
drop if country=="ARGENTINA"
gen date2 = date(date, "DMY")
format date2 %d
tsset date2
twoway (tsline indexps)

tssmooth ma indexps_ma30  = indexps, window(30)
twoway (tsline indexps) (tsline indexps_ma30)
gen monthly_diff = indexps - l30.indexps
gen monthly_diff_ma = indexps_ma30 - l30.indexps_ma30
gen abs_double_diff =  abs(monthly_diff -  monthly_diff_ma)

sum indexps indexps_ma30 monthly_diff monthly_diff_ma abs_double_diff, detail
twoway (tsline monthly_diff) (tsline monthly_diff_ma)\

This generates a figure comparing the 30 day moving average price level and actual price level you can see below that there is very little difference between the smoothed and actual price level. The price level of a broad basket of prices doesn't fluctuate enough for daily inflation to be very different from assuming a constant inflation (which is roughly equivalent to using the average).

I estimate, using the calculations above, that monthly inflation is about 11 basis point per month. Using a measure of inflation rather than the price level shows that the smoothed and raw inflation estimates are very similar. This variation could be because there is measurement error and bias from the high frequency calculation approach.

Bottom line, I would just stick with converting monthly series to an implied daily rate. Depending on if you care about business days or calendar days and how you feel about using real time data, this could be as simple as: $$ \hat{r}_{daily\ implied, t} = ( 1 + r_{monthly\ observed, t})^{1/30} -1 +\epsilon$$


Why doesn't the supply curve shift to the left in the following situation? Why do producers respond to the surplus by cutting their prices?

Why doesn't the supply curve shift to the left in the following situation?

Because in order for a demand curve to shift demand has to change at any price. For example, let us suppose that the demand function is given by:
$$D_1 = 100 -P$$
If a firm changes price it chargers it does change quantity demanded  $D_1$ but does not shift the whole demand function $D = 100 -P$. If quantity demanded changes just because price varies, we call this movement along demand curve.
However, suppose now that there is some change in preferences of people so that demand function $D_1$ shifts and we will have new demand function $D_2$:
$$D_2 = 50 -P$$
Can you see the difference? Now at any price demand will be smaller compared to $D_1$. If price is $5$ the demand in $D_1$ will be $95$ but in $D_2$ only $45$, if price is $10$ then $D_1 = 90$ and $D_2 = 40$ and so on.  This is what we would call shift in demand (in fact if you would plot $D_2$ an $D_1$ you would see that $D_2$ is just $D_1$ shifted to the left.

Why do producers respond to the surplus by cutting their prices?

Because, within the bounds of a simple supply-demand model,  if there is a surplus of goods producers have two options:
A) throw the goods away and get nothing.
B) sell them at lower price.
selling them at lower price if you can is more rational then just throwing the goods away (at least it would be in a simple models, there might be some complex strategic interactions where it might be other way around, but you won't encounter such more nuanced and complex models in econ 101 textbook).


Bidder Count Impact on Uniform Price Economics

It is a known result in Mechanism Design that both first-price as well as second-price auctions yield the same expected revenue, under certain conditions (like independence of valuations, private information, etc). Consult   Jehle, G. A., & Reny, P. J. (2011). Advanced Microeconomic Theory (3d ed.), ch.9 on Auctions and Mechanism Design, for a very accessible exposition of the basics, as well as for the full set of conditions that must hold.

The answer to your question is bound to be distribution-specific. Assume as an example, that, from the point of view of the seller, all (unknown to him) valuations of the bidders for the object for sale, come from a Uniform $U(0,1)$ distribution: this implies that we have normalized the value of the object for sale and that we express the possible valuations of it as a percentage of its possible maximum value, which is assumed common for all bidders. I.e. What we say here is :"we don't know how much each bidder actually values the object, but we do know that the maximum possible valuation by a bidder will be some $V>0$, and this $V$ is common to all bidders". We do not assert that there exists some bidder that actually values the object at $V$.

In such a setup, the Expected Revenue of the Seller is

$$ER(N) = \frac {N-1}{N+1} \tag {1}$$

where $N$ is the number of bidders. Again, this essentially expresses expected revenue as a fraction of the object (unidentified) maximum value.

Now you can play around with $N$ to see how the expected revenue changes, in absolute, relative and percentage terms. It sure isn't changing linearly, but it is everywhere increasing in $N$, approaching unity (i.e. the object maximum valuation).

This should be intuitive in the framework adopted: the more the bidders are, the more probable becomes to obtain higher and higher valuations of the object, and so also to sell it at a higher value.


Sum of residuals and Matrix calculus (step by step)

Let $\mathbf A,\mathbf B$ be $m\times n$ matrices (or vectors is either $m$ or $n$ is $1$),
\begin{align}
(\mathbf A+\mathbf B)^T&=\mathbf A^T+\mathbf B^T \tag{1}\\
(\mathbf A\mathbf B)^T&=\mathbf B^T\mathbf A^T \tag{2}
\end{align}

Thus,
\begin{align}
(\mathbf y-\mathbf X\beta)^T(\mathbf y-\mathbf X\beta)&=(\mathbf y^T-(\mathbf X\beta)^T)(\mathbf y-\mathbf X\beta)\\
&=(\mathbf y^T-\beta^T\mathbf X^T)(\mathbf y-\mathbf X\beta)\\
&=\mathbf y^T(\mathbf y-\mathbf X\beta)-\beta^T\mathbf X^T(\mathbf y-\mathbf X\beta)\\
&=\mathbf y^T\mathbf y-\mathbf y^T\mathbf X\beta-\beta^T\mathbf X^T\mathbf y+\beta^T\mathbf X^T\mathbf X\beta \\
&=\mathbf y^T\mathbf y-2\mathbf y^T\mathbf X\beta+\beta^T\mathbf X^T\mathbf X\beta \tag{3}
\end{align}
where line 1 uses $(1)$, line 2 uses $(2)$, and the last line follows from the fact that $\mathbf y^T\mathbf X\beta$ and $\beta^T\mathbf X^T\mathbf y$ are both $1\times1$ scalars.

Let $\mathbf a,\mathbf x$ be $n\times 1$ vectors and $\mathbf A$ a symmetric $n\times n$ matrix. Matrix calculus has the following rules:
\begin{align}
\frac{\mathrm d\ \mathbf a^T\mathbf z}{\mathrm d\ \mathbf z}&=\mathbf a \tag{4} \\
\frac{\mathrm d\ \mathbf z^T\mathbf A\mathbf z}{\mathrm d\ \mathbf z}&=2\mathbf A\mathbf z \tag{5}
\end{align}

Applying these to differentiating $(3)$ with respect to $\mathbf\beta$, we get the first order condition:
\begin{equation}
-2\mathbf X^T\mathbf y+2\mathbf X^T\mathbf X\beta=0
\end{equation}
Solving for $\beta$, we get the usual OLS formula.


Can people lack a comparative advantage and a comparative disadvantage?

Comparative advantage doesn't work like that.

If person A's CA is cooking, person C has a comparative advantage in foraging. With B, C has a comparative advantage in cooking.

It's not possible to have a comparative advantage or comparative disadvantage in everything: If you were better at everything than someone else, you would have an absolute advantage. As soon as two people have different skills for anything, they have a comparative advantage of some kind.

It is possible for two people to have no comparative advantage/disadvantages whatsoever: If both people are exactly equal at everything they can do, then there is no comparative advantage or disadvantage between them at all.


Good data sources from China are hard to come by. For official data, you can find nearly all available data series through the company called CEIC, although this is somewhat expensive. In general, the history of many of these series doesn't go very far back either, since it is only in the last decade or two that China has really become serious about collecting economic data. If you want something that goes back to before 1990 or so, there are perhaps academic sources that do this (I don't know them), though this data will probably be based on very rough estimates in that case.


How does a country get so far in debt, and who is it in debt to?

Mostly because of government-issued bonds. These can be held by other governments, private entities or even the various government agencies: In the US, starting with the last category:

  Intragovernmental Holdings. This is the portion of the federal debt owed to 230 other federal agencies. Intragovernmental holdings total $5.6 trillion, almost 30 percent of the debt. Why would the government owe money to itself? Some agencies, like the Social Security Trust Fund, take in more revenue from taxes than they need. Rather than stick this cash under a giant mattress, these agencies buy U.S. Treasurys with it.

  Debt Held by the Public. The public holds the rest of the national debt of $14.7 trillion. Foreign governments and investors hold almost half of it.

Since I see you're from the UK... over there bonds are called gilts. And here's a breakdown of their ownership from 2009 (since that's what I could easily find):

  The biggest owners of gilts are insurance companies and pension funds. For them, gilts are predictable investments, which are particularly useful when a low-risk product is needed. Pension funds, for example, will usually switch an individual's holdings from higher risk investments, such as shares in companies, and put them in gilts as the person gets closer to retirement.

  Next on the list comes investors overseas. Unfortunately, nobody keeps records showing in which countries these gilts are held. This is in contrast to, for example, the US, which regularly publishes lists of the countries that own its Treasury Bills. So we know that at the end of 2009, $302.5bn (£196bn) of US government debt was held in the UK, making the UK the third-biggest investor behind Japan and China.

  The next biggest category holding UK government debt is banks, which includes the Bank of England. Since March 2009, as part of its quantitative easing programme, the Bank of England has bought just short of £200bn of gilts, making it the third-biggest holder of UK government debt.

And a more recent (2017) article (although lacking a pretty graph) roughly paints the same picture for UK's debt:

  Traditionally, around 40% of UK public debt was held by pension funds and insurance companies, which form a captive market because of their need for predictable and safe long-term investment returns. Around a quarter was held by other UK financial institutions and households, and the rest by overseas investors.

  QE [quantitative easing] has disrupted this pattern. Now, around a quarter of issued gilts are held by the Bank of England under its Asset Purchase Facility. Official data still show overseas holdings at around 27%, with insurance and pension funds’ share down to 28%, and other UK financial institutions holding around 40%. But once the store of gilts sequestered on the Bank of England’s balance sheet is excluded, overseas buyers account for 35% of gilt holdings and other central banks another 11%.

  Uniquely, more than 10% of the UK’s debt cannot be traced to either domestic or overseas buyers due to the paucity of data from the regular auctions. Lack of clarity on who’s holding the debt makes it harder to judge the risks of buyers selling-off or staying away. That fuzziness that may have helped to keep the markets calm.

How can countries of the world operate owing such vast amounts of money?

It depends on the country. Countries whose currency is attractive enough, e.g. the US dollar can "get away with it" by "printing" more money (see quantitative easing), although they can't do that too fast because that can cause inflation. The bonds of the big countries have had somewhat of "miraculous" negative real interest rate in the short run recently (although lacking a pretty graph):

  UK national debt is currently issued at a yield of less than 1% – far below the rate of inflation (2.6% in July). And this means Britain can effectively raise money free of charge in real terms. [...]

  So why are UK bonds still flying off the shelves, allowing the government to plug the gap in its spending plans with virtually “free” money? It is possible that investors are snapping-up new gilts simply through a lack of alternatives. If (as some fear) overpriced stock markets and property are about to crash and once-buoyant emerging markets are in trouble then the public debt of stable rich countries becomes the least worst option. US and German debt issues are proving similarly popular at rock-bottom yields.

Although this year the bond rates are expected to tighten, they are still mostly negative in real terms (for the big boys, but not so much for the smaller fish with weaker economies; the exception being the US which slighly above zero):

  Negative real borrowing costs add fuel to markets that are already on fire, limiting the downward pressure on bonds, keeping corporate spreads on the tight side and pushing stocks to new high after new high. [...]

  For investors, it’s a chicken and egg scenario. They’re crying out for policy “normalization” - higher rates and less central bank “interference” in markets - but are enjoying the asset price boom that’s in large part a direct consequence of central bank largesse.

Countries whose debt is denominated in a foreign currency, or a currency they can't print for some other reason, e.g. being in monetary union (ahem, Greece) can be in a world of hurt if they suddenly are threatened by default (inability to pay back on schedule). Typically the IMF steps in but it also imposes conditions in terms of structural reforms etc. for their bailouts.

E.g. news from July this year:

  Greece is scheduled to end nearly a decade of external help this August, after implementing more than 400 policy measures demanded by creditors. The yield on the 10-year government bond has fallen about 30 basis points in the wake of the recent debt deal. It moved from standing at about 4.2 percent to 3.9 percent. In contrast, Italy’s 10-year yield currently stands at 2.668 percent and the U.S.’ at 2.85 percent.


Is there any academic paper documenting the importance of the Operating Cycle?

I typed "Operating Cycle" into Google Scholar, and got some hits like
The Operating Cycle: Risk, Return and Opportunities by John C. Groth
Abstract:

Highlights the operating cycle, its importance, and reviews basic relationships related to the cycle. In particular, it focuses on capital “flow through”, invested capital, capital at risk, and economic returns generated relative to capital employed. Reveals an amplification effect that results from improvements in the management of the cycle, that benefit traceable to a reduction in operating risk allowing incremental benefits from financial leverage. Suggests specific actions to take with respect to the cycle that will improve the value of your firm. Shows that small improvements in operating factors within the cycle yield amplified benefits to the firm. The discussion ignores taxes except in instances when tax effects are important. This does not detract from the discourse or conclusions. Reveals that increases in firm value that result from improved management of the operating cycle stem from several sources: greater levels of economic returns from operations; a reduction in operating risk; less capital invested and at lower risk; lower cost of capital; and increased tax benefit.


Which areas of mathematical knowledge are required for understanding different genres of theoretical economics literature (and at which level)?

For microeconomic theory, a starting point would be

Basic multivariate calculus,
topology/set theory
real analysis,
probability theory,
a basic knowledge of linear algebra.

For 'applied' micro theory (theoretical industrial organisation, applications in information economics, etc.), or for reading of a graduate-level microeconomics text (such as Mas-Colell, Whinston, and Green's "Microeconomic Thoery"), a good understanding of the basics of these areas will suffice. Most material will be set in something like a Euclidean space and will draw on a fairly restricted set of methods and results from the above domains. You can already get a long way with a good understanding of the basic continuity properties of the reals ($\epsilon$-$\delta$ proofs, open and closed intervals, intermediate value theorem, basic fixed-point theorems, etc.), the ability to do partial differentiation, integration, and to calculate conditional probabilities and expectations.

As one turns to the journal literature and looks more towards pure (rather than applied) economic theory, the level of mathematical sophistication increases somewhat and it becomes more likely that you will encounter more exotic (from the point of view of economics) mathematical methods and results.


Which countries have the comparative advantage in Ricardo's example?

The mistake that you are doing is that you are treating the numbers in the table below that I assume you took from wikipedia as quantities that can be produced but they are not

          Cloth Wine
England     100 120
Portugal    90  80

Wikipedia states that in the problem they present these are "hours of work necessary to produce one unit" of given goods. So its not that England can produce $100$ cloth and $120$ wine. It takes $100h$ of labor to produce $1$ cloth and $120$ hour to produce $1$ unit of wine. Same for Portugal. This is the original table from wikipedia from which I assume you took the numbers:

So in this example if England had access to only $100$ hours of labor it would be able to produce exactly $1$ cloth and only $5/6$ units of wine.  Hence actually the opprotunity cost of $1$ cloth is $0.833$ wine and for $1$ wine the opportunity cost is $1.2$ cloth- the exact opposite in terms of OC.

The same holds for the Portugal - you will find exact opposite result namely in Portugal the opportunity cost of $1$ cloth is $0.888$ wine and opportunity cost of $1$ wine is $1.125$ cloth.

Since the opportunity cost of producing cloth is lower in England it has comparative advantage in cloth production and since the opportunity cost of producing wine is lower in Portugal it has comparative advantage in wine making. Hence, also the final result will be opposite.

Consequently, in this case wikipedia is correct in stating that "England has a comparative advantage in producing cloth due to lower opportunity cost" given the numbers they assume. So England should produce cloth after all. You have to read problem very carefully - dont just assume that you know what the table presents.


Is there a way to trade currencies several times and end up with more money than one starts with?

You might be interested in triangular arbitrage. In efficient markets this should not be possible, I don’t think...


Sample weights in Stata: fweight vs. pweight

mean command with pweight gives you mean and sd estimates, which in turn gives you estimate of the coefficient of variation.

pctile also takes pweight. It will generate percentiles.

kdensity only gives point estimates, not confidence intervals of the density estimates, so I think using fweight instead of pweight is fine. But I'm not certain about this.

Alternatively, svy: commands may make your life easier when working with survey data. See here for a quick intro.

Also, think through whether you want to describe your sample, or to make inference about the population. See here for an example. An relevant quote from the link:

  It was intentional that summarize does not allow pweights. summarize’s purpose, as I see it, is to provide descriptive statistics for the sample, not to provide inferential statistics for the population. By this criterion, I argue that pweights do not belong here since pweights are used to provide estimates of the population parameter mu.


Term for when using a single number is used instead of a function?

A cost function can be constant (in $q$), but this term is not particular to economics.


Is technical analysis somehow a valid method for investment?

The Lo, Mamaysky and Wang paper Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation is probably the best investigation of this question. He found there were some patterns that seemed to be useful, notably the Head and Shoulders pattern.


Year Fixed Effects in a Dynamic OLS Regression with Cointegrated Variables

No in pure time series we generally don't use fixed effects. If you have data on lets say monthly frequency you could include dummies for months in general, e.g. having February, March, April ... dummies but you would include them as a general dummies where all Februaries are part of the February dummy rather having a separate dummy for each time period.
You can also include dummies for time periods where you think that the period was special in some way. For example, you could include a special dummy for all crisis years. Similarly, you could include some dummies for structural breaks and so on.
Furthermore, dynamic OLS model is more of an umbrella term. For example, the above would hold for ARDL/Pesaran error correction model. There might be dynamic models that have further issues, it is always best to survey literature on the particular model you are actually using then just generalizing.
PS:

I know that one should control for year fixed effects when you have panel data.

This is actually not generally valid statement. Yes more often than not you want to control for year  fixed effects in panel data but not always.


Effect on Large Company on Redistributing Profit from Shareholder to Employees

What other economic impacts would be expected if Disney reduced it's
  net profit margin by 10% purely by increasing low wage employee
  remuneration?

The reduction of net profit margin might exceed the percentage of wage increase if benefits, insurance premiums, and any [Disney's] other obligations are tied to wages.

Likewise, a reduction of net profit margins might prompt shareholders to dump Disney stocks and invest in other companies they consider more profitable and/or unlikelier to act to the detriment of shareholders.

Companies with significant levels of debt might experience an increase in financial costs (higher interest rates) if --for instance-- the reduction of profit margin prompts a rating agency to lower the company's grade a notch.

This answer is neither an exhaustive list of possible impacts nor an assessment of whether or not wages at large corporations currently are at fair levels.