The Insane Sultan of Slickcrudistan: Calculating Currency Equilibrium I work for a start-up that has encountered an economics problem no one on our team has been able to crack.
A story form and a general form of the problem are below. I believe they are equivalent, but if there is a difference, please defer to the general form.
We understand there is no precise answer to this question and that the value of any currency considers prices in other factors that this question ignores. Still, we figured, or hoped, that there was some general way of approximating this, even if it's under idealized conditions. Thanks!
Story Form

The sultan of Slickcrudistan has gone insane. He has decreed that his country will only accept pre-2015 sand dollars in exchange for oil1. Barrels of oil will be sold to the bidder offering the most sand dollars per barrel. Additionally, the sultan is willing to sell sand dollars back to the public at approximately the current US dollar to sand dollar exchange rate.
His country produces 20,000,000 barrels of oil at a market value of $1,000,000,000 USD/year. Additionally, 100,000,000 pre-2015 sand dollars exist. Assuming liquid and efficient markets, what is the equilibrium price of a sand dollar? How would this change if there were a stable inflation in the quantity of sand dollars?
1 Suppose an extremely cheap process exists for verifying this.

General Form

Currency X has a total circulation of a units and a stable inflation rate of currency units of m percent.
Currency Y has a total circulation of b units and a stable inflation rate of currency units of n percent.
Currency Y is completely debased and of no value in comparison to currency X (at market exchange rates, b << a ).
A market with a value of c units per year in currency X can now only be transacted in a currency Y. c is growing at a stable rate of p percent.
Assuming liquid and efficient market, what is the new equilibrium of exchange?

Using a simple textbook-approach, I will provide one possible answer here, showing that in this approach, the one thing that needs to be specified is "velocity of money" as regards sand dollars.

I will use also the numerical values provided in the question, after cutting out six zeros.
I assume that the Law of One Price holds, so

$$P_s\cdot S_{USD/s} = P_{USD} \tag{1}$$

$P_s$ is "the price level" related to sand dollars, $P_{USD}$ is the price level related to USD, and $S_{USD/s}$ is the exchange rate we wish to find ("how many USD per one sand dollar").

While the price levels are usually price-indexes, here we are looking at a single good, oil, so we can take the $P's$ to mean "price of oil".

The Sultan's oil is the only output that can be bought with sand dollars. And we do know the value of this output in USD

$$P_{USD} \cdot Q_s = P_{USD} \cdot 20 = 1,000 \;\text{USD} \tag{2} $$

Using the Law of One Price, we get

$$P_{USD} \cdot Q_s = P_s\cdot S_{USD/s}\cdot Q_s \implies S_{USD/s} = \frac {P_{USD} \cdot Q_s}{P_s\cdot  Q_s} \tag{3}$$

(don't simplify).

Assuming the Quantity Theory of Money, we have

$$P_s\cdot Q_s = V_s \cdot \bar M_s \tag{4}$$

where $\bar M_s$ is the fixed amount of sand dollars available, and $V_s$ is the "velocity of money" in relation to sand-dollars (we will return to $V_s$). Inserting $(4)$ into $(3)$ and using also $(2)$ and the fixed value of $\bar M_s$ we have

$$(4),(3),(2) \implies S_{USD/s} = \frac {P_{USD} \cdot Q_s}{V_s\bar M_s} = \frac {1,000}{V_s\cdot 100} = \frac {10}{V_s}$$

So, if we can find a value for $V_s$, we have found the exchange rate we are after. The velocity of money can be thought as "how many times that same unit of currency, say the same paper bill, will be used in transactions during a production cycle".

The M1 velocity of money for USD is approximately  $V_{USD} \approx 6$, using this value for the sand-dollars also, we get

$$S_{USD/s} = \frac {10}{6} \approx 1.67$$


Question regarding social welfare in the presence of externalities I am currently learning high school level economics and I do not understand how indirect taxation may increase net social welfare in the presence of negative production externality.

This is because, from analysis of welfare in the market diagram with linear demand and supply curves, I found that the social welfare gain due to a tax correcting a negative production externality is equivalent to the welfare loss to consumers and producers from the taxation itself (resulting in no net change in total welfare).

Theoretically, this can also be explained by the fact that taxation reduces the net satisfaction of consumers, firms, and government, but increases net satisfaction in the 3rd party.

My current understanding is that correcting externalities do not cause net welfare to change, but it allows the socially optimum level of resources to be allocated to production, answering the "what to produce question" and allowing the economy to benefit in the long run, but I'm not at all sure.

Your understanding is close, but not completely correct. Look at the picture below. Blue is the demand curve, Orange the marginal private costs (which in perfect competition is equal to supply). Should there be no taxation or externality the equilibrium price would be P1 and the equilibrium quantity Q1.

If there is a production externality the social costs of production are higher, illustrated by the marginal social costs in grey. The total costs to society (or the 3rd party) of the externality is the area A+B+C.

If the government introduces a tax equal to the external costs of production (the tax rate per unit would be the vertical distance between the orange and grey curve) we would achieve a new equilibrium with a new higher equilibrium price P2 and a lower equilibrium quantity Q2.

The total tax burden for the company is area A. This burden was formerly carried by society and is thus not a net gain, but a transfer. Area B is also a transfer. The upper part above the black line comes from the consumers, the bottom part comes from the producers. There is more re-allocation of surplus going on, on the left hand of the dashed line because prices are higher and quantities are lower, but I haven't illustrated those to keep things simple.

Area C though is a gain. That part of the costs are no transfer from anyone and were borne by society before the externality got corrected (or again the 3rd party)

In conclusion introducing a socially optimal tax level introduces a lot of transfers, but also a net gain in welfare.


Interest Rate Differential and Fisher's Interest Rate Parity The Fisher formula for interest rate parity, as explained here shows that for a given currency pair, the currency with the higher interest rate will depreciate relative to the the currency with the lower interest rate, over a given period of time, for it not then riskless arbitrage is possible. In other words, higher interest, weaker currency.

However, there is another point of view, as given here, that if a country hikes interest rates, then its currency will appreciate, as there will be increased demand for that currency in order to enjoy higher returns, carry-trade style. In other words,higher interest, stronger currency.

The question here is - which is correct? Or are there other assumptions which have not been accounted for here?

I hesitate to mark this question as a duplicate (of this one), but my answer will in part be a replication of part of my answer there.

Let's write the Uncovered Interest Rate Parity expression

$$(1+i_{A,t}) = \frac {S^e_{A|B, t+1}}{S_{A|B, t}} (1+i_{B,t})$$
where $S_{A|B}=$ units of currency A per unit of currency B.
This is the claim.  The numerator is the expected future exchange rate

Assume that $i_{A,t} > i_{B,t}$. Standard economic logic (and a few assumptions on ability to invest over borders), says that then investors would want to invest in country A. To do that they will increase demand for currency A. This should lead to appreciation of currency A. Does the UIRP say something like that?

If $$i_{A,t} > i_{B,t} \implies 1+i_{A,t} > 1+i_{B,t}$$
and so the UIRP asserts that we must have

$$\frac {S^e_{A|B, t+1}}{S_{A|B, t}} > 1 \implies S^e_{A|B, t+1} > S_{A|B, t}$$

Given how $S$ was defined the last inequality means that we expect that the currency will depreciate. Indeed, in the future. Because, what is affected in the first place by the reaction of the investors is $S_{A|B, t}$, not $S^e_{A|B, t+1}$. The reaction of the investors will decrease $S_{A|B, t}$ (which reflects the appreciation of currency A), creating expectations of future depreciation, i.e. leading to $S^e_{A|B, t+1} > S_{A|B, t}$, as the UIRP asserts. Why should we expect depreciation of currency A in the future, compared to the present? Because the inflow of funds in country A will eventually pressure $i_{A,t}$ downwards, investors will stop loving currency A so much, demand for it will eventually fall, hence eventual depreciation.

The UIRP therefore compacts two effects from a discrepancy in interest rates: a first effect of currency appreciation and a second (expected) effect of currency depreciation in the future.

Apart from that explanation, I note that the link discussing the tendnecy to appreciate says also explicitly

  "However, this simple equation is complicated by a host of other
  factors that impact currency value and exchange rates. One of the
  primary complicating factors is the interrelationship that exists
  between higher interest rates and inflation. If a country can manage
  to achieve a successful balance of increased interest rates without an
  accompanying increase in inflation, then the value and exchange rate
  for its currency is more likely to rise."

In other words, the very link that talks about currency appreciation qualifies this to be subject to the fact that higher nominal interest rate does not result in higher expected domestic inflation (this alludes to the Fisher Hypotesis that the difference between the nominal interest rate and the real one is the expected inflation). This qualification essentially says that in order for the initial currency appreciation to persist, we must have differences in the real economy (i.e. that a higher nominal interest rate reflects a higher real interest rate rather than higher expected inflation).


Economic impacts of a declining population In the article “Japan’s population problem” in The Japan Time, Hugh Cortazzi write:

  Japanese leaders and Japanese people generally are well aware of their
  nation’s demographic challenges. The population has begun to decline
  […] The implications for the Japanese economy and for Japan’s position
  in the world should be obvious.

I can see some “intuitive” reason why a decline in population would be an issue for a country, mostly if it comes with a decline in the workforce (roughly decreased labor supply, decreased international competitveness and problems with funding pension system?). But I am interested in more careful and more general analysis.

My questions are:

What are (if any) the economic challenges of a declining population, in the case of Japan (or in general,if not too broad)?
Does there exist modern macroeconomic models (say open economy DSGE) including demographics and studying declining populations ?
Have some paper tried to compare the welfare costs of a declining population with the potential welfare benefits of a declining population (e.g. for a dense country like Japan, decreasing housing prices)?

ad 2.
This phenomenon has been studied a lot. Broadly it is referred to as the demographic transition. A good overview is given by the respective Wikipedia article.

In the field of Long-term macro there are several publications. One of the latest top-journal publications is:
Cervellati M.; Sunde U., Life Expectancy and Economic Growth: The Role of The Demographic Transition, «JOURNAL OF ECONOMIC GROWTH», 2011, 16(2), pp. 99 - 133.

Demographic elements can for sure be endogenised into every macro model. But I doubt that it would be very useful for short run DSGE things, since all demographic changes take place with huge time lags. If you want to study those interesting phenomena, you probably have to go more into Long-run Macro / Economic Growth (Unified Growth Theories put emphasis on demographic elements for instance)


Does it ever make sense to underproduce as a firm? The larger the supply, the lower the price. Therefore, the more thneeds you (the firm) produce, the less you'll be able to sell each one for. Traditional sense says that as long as there are people who will buy them, you should always make more thneeds! But given profit is quantity * (selling price - costs), as price drops, you may eventually reach a point where profit decreases the more thneeds you make.
If and when this happens depends on the shape of the supply-demand curve, rather than using the simplified linear ones you learn about in early university economics.
Does this happen? Is there a "supply-induced-price-drop-compensated" ideal quantity to produce to maximize profit?

An interesting case is: should a firm ever produce less than the profit-maximizing output? This could make sense in a dynamic setting: by underproducing in the short run, you might increase future long-run demand. For example, when popular toys like Cabbage Patch Kids and Power Rangers were first released, they were in short supply. Parents went nuts trying to find them, and there was lots of media coverage. Eventually the supply increased; to be honest, I don't know if they raised the price but they could have.


What does trade deficit really mean? I watched a video about how if America imports USD 1m worth of goods but only exports USD 600k worth of goods, there is a USD 400k debt to other countries if the other country allows this deficit.

US importers pay for the value of the goods they import. So why is there debt? Doesn't the US pay in USD the full value based on the transaction? Why would importing have anything to do with exporting, also why would anyone "exchange" goods for credit with somebody that already is USD 18 trillion in debt?

Every country has a trade balance, which is defined as exports minus imports. The United States is a typical observing state, which means their imports are higher than their exports. I do not know the current numbers but USD 1m of imports and USD 600k might be right. In this sense you import USD 400k than you export.
Now as you already pointed out you have to pay you imports in USD. Now the point NickJ mentioned is insofar important  as to understand what you are actually entitled when holding USD. And all you are entitled to is to buy products within the United States. True, you as a single person could change it into another currency, but this does not change the fact that some else is holding USD and is sooner or later going to demand goods in USD.

So it is correct that in some sense running a trade deficit really brings debt to a country.

However, one has to understand that running a trade deficit is not only indebting. In some way it is a credit for future production and consequently employment. The debt you are causing when running a trade deficit can also be seen as in some way storing demand for US products which in some point in the future will be carried out.


Some confusions about instrumental variable (econometrics) As the title says, I have some confusions about instrumental variable.

According to my lecture note (which is supposed to be reliable), instrumental variable has two big properties:

Validity: an instrumental variable and error term are not correlated and it implies that the instrumental variable does not directly lead to changes in dependent variable.
Relevance: an instrumental variable and endogenous variable are correlated.

So here is my confusion. (let's denote z is an instrumental variable)

Endogenous variables are correlated with the error terms and z is correlated with endogenous variable.

Doesn't this imply that z is correlated with error terms? If so, it violates the Validity (mentioned above).

In case my question isn't clear enough. Here is the case where I am stuck: $$
score_i = \beta_0 + \beta_1 course_i + u_i
$$
where $course_i$ is a binary variable of taking a preparatory course and $u_i$ is an error term.

Quite obviously, $course_i$ is correlated with $u_i$ since the parental income is one of the unobserved variables (so in $u_i$) and $course_i$ and parental income are correlated (I think this is also quite obvious).

So far we know that parental income (I think this is an instrumental variable) is correlated with $course_i$. But since parental income was belonged to error term, it violates Validity.

Any help is welcome.

Endogenous variables are correlated with the error terms and z is
  correlated with endogenous variable.

  Doesn't this imply that z is correlated with error terms?

No it doesn't. For mean-centered variables for simplicity, we have for linear models,

ENDOGENEITY: $E(xu) \neq 0$

RELEVANCE : $E(xz) \neq 0$

The above conditions do not necessarily imply non-Validity ($E(zu) \neq 0$).

A very simple example to show that we may have a valid instrument.
Assume $x, u$ are centered on their mean, $E(x) = E(u) = 0$, and that $x$ has a symmetric distribution, $E(x^3) = 0$. Assume that  $E(u \mid x) = ax$.
Then

ENDOGENEITY

$$E(xu) = E\big[E(xu\mid x)\big] =  E\big[xE(u\mid x)\big] = aE(x^2) \neq 0.$$

Consider the candidate instrument $z = x^2 + v$, with $v$ independent from $u$, but $E(xv) \neq 0$. We have

RELEVANCE
$$E(xz) = E(x^3) + E(xv) = 0 + E(xv) \neq 0$$.

VALIDITY

$$E(zu) = E(x^2u) + E(vu) = E\big[E(x^2u\mid x)\big] + E(v)E(u)$$

$$= E\big[x^2E(u\mid x)\big] + 0 = E\big[x^2a x\big] = aE(x^3) = 0.$$


Generating economic growth My background is not in economy, but I know that the indebtedness of the western countries is slowing the growth of the economy.

So my line of thinking is the following. Would it be feasible if a country's central bank (which would be state owned) prints money and then the government by various tenders for small businesses and startups distributes this money?

This created money would be granted for productive purposes only, interest free and not returnable if the company performs well. Also I think that this increase in the money supply would not generate inflation because the money will be backed by future products and services. By this measure the production and consumption would increase in the country. Therefore the state would need not to take foreign loans because the required sum of money for it's purposes would be covered with taxes. Of course small and medium sized companies would be taxed much less than big, multinational companies.

What are your thoughts on this?

Remember that increases in a standard IS-LM model an increase in government expenditure generates an increase in the real interest rate.
As such, private investment decreases. Traditional economic theory would suggest that what you recommend will crowd out private investment. The question can then be modified as follows-  does a 1 Dollar increase in government expenditure decrease private investment by less than 1 Dollar? In other words, is the government multiplier greater than 1? A lot of empirical work has been done on this.


Equity value vs Stockholders Equity Is equity value is the same as stockholders equity? I have been given liabilities and stockholders equity total also and I need to calculate the leverage ratio, but I not sure what numbers should I use and whether I need to calculate the equity value using asset value and etc. or I could just plug in the number.

"Stockholder's equity" is how we label Equity in corporations, so it should be identical to the general concept of "Equity", except if, by a confusing misuse of words, by "Stockholder's equity" the authors meant "Shareholder Capital", which sometimes it is used to mean only a part of Equity (the nominal (par) value of shares issued), the other main parts of Equity being "Paid up capital" (amounts paid "above par"), various "Reserves", Retained Earnings.


Why do stricter emission limits cost jobs? I live in Germany and as most people know the car industry is very important in our country. Currently, there is a discussion about stricter emission limits for cars in the European Union. The car industries main criticism of stricter limits is that they supposedly lead to lots of jobs being lost. I don't quite understand why this should be the case.

Why do (don't) stricter emission limits lead to job loss?
What theoretical mechanism is at work here? Is there any empirical evidence that this is actually the case (stricter limits lead to job loss)?

Why do (don't) stricter emission limits lead to job loss?

I am not knowledgeable of the mechanism and exact details of the emissions paraphernalia, but the sector's worry makes perfect sense. Stricter regulations lead to or contribute to
job losses.

Stricter emission regulation entails a greater probability and/or magnitude of fines and sanctions to non-compliant companies. To avoid those sanctions, a company will be forced to spend additional resources to (1) replace technologies that are otherwise perfectly operational, (2) focus on expertise that distracts that industry from its core business, and (3) fund expenses that result from the increased overhead. The question is where those resources will come from.

Car makers may opt to pass that cost to consumers. However, that decision predictably will push sales down, thereby leading to overcapacity of labor and consequently layoffs.

Alternatively, car makers may decide to absorb the new compliance costs and leave the price of cars unchanged. But the prospect of reduced profits would prompt stockholders to sell their stock, thereby weakening the car maker's ability to meet its financial obligations. To cope with (or avoid exacerbating) this imbalance, the car maker has to reduce costs; and the readily available alternatives to that effect are layoffs and a freeze of new hires.

Furthermore, for car makers with significant reliance on exports, compliance with stricter regulations tends to hinder their competitiveness especially with respect to non-EU car makers which are not subject to akin regulatory constraints. Thus, EU car makers will lose [international] market share, most likely impacting its ability and interest to keep that much of its labor force.


How do I apply the distance-weighting matrix in a spatial autoregressive model Can someone explain how to solve the following problem in a spatial auoregressive model.
The form is:

where p is the SAR coefficient and W is a distance-weighting matrix with a 0-diagonal.

The world only consists of Poland, Germany, and Austria. The weighting matrix is such that a country with a land border receives a w=1 and 0 otherwise. So the Matrix looks as follows:

p = 0.5 and there is a shock to FDI in Poland of size 10. How much would FDI increase in Germany? I cannot make a hold how to make use of W. Thanks!

The weight matrix that you have illustrated needs to be row-normalized, i.e. the row-sum must be one in order for the rho parameter to have the proper parameter bounds, i.e. between (-1/lambda,1), where lambda is the smallest real eigenvalue of the W matrix.

When the weight matrix is row normalized and there is a change in the dependent variable, the shock in that other country will be an average of the surrounding values.

I'm not sure if this helps but a good resource is the LeSage and Pace text, Introduction to Spatial Econometrics, CRC Press 2009.

You can also visit www.spatial-econometrics.com to download free PDF books on spatial econometrics as well.


Uses of simple interest Recently I started to read again Brealey & Myers's "Principles of Corporate Finance" (an older edition I hold it since I attended to the university course on Economics and Corporate Finance as a part of the curriculum in Electronics Enginering at the University of Bologna), since I need to evaluate the profitability performance of some projects I am involved with. The two authors use the NPV method which assumes (more or less explicitly) the use of compound interest, perhaps familiar to all of us, and, en passant, mention the existence of the simple interest. Inspired by curiosity, I searched for applications where the interest rate is required to be simple, but I was not able to find anything outside examples in textbooks and lecture notes, so my question is: what are the uses of simple interests in current economy?
Edit on behalf of the comments. I am asking this question because I am curious to see some examples and understand the reason why, in these cases, the simple interest is used. In my understanding, the use of compound interest is extremely natural since it corresponds to the intuitive concept that the invested money (continuously) produces a cash flow that is implicitly reinvested (at least up to the moment when the intial investment + the interest has to be payed back), thus it implicitly generates a (continuous time) conpound interest rate: for the simple interest I am not able to imagine such an intuitive explanation.

Interest payments are contractual payments. They need to be specified with an exact formula. For a given set of cash flows, one could come up with a multitude of formulae that end up giving the same values. In order to make interest rates comparable, laws, regulations, and market conventions specify that different conventions be used.
Of these conventions, simple and compound interest are possible choices. For simple interest, the interest payment is just the interest rate times the principle times a time factor. Compound interest takes into account increases in principal.
If a loan has associated interest payments that must be paid immediately, the loan resembles a generic bond: principal amount does not change. Bonds have a wide variety of conventions to convert the price of a bond to a yield, including a “simple interest rate” convention. However, changing the convention does not change the contractually defined price or cash flows. Since generic bonds do not roll interest payments into the principal, “compound interest” does not make sense.
For loans, interest is often rolled into the principal. We can then use simple interest or compound interest conventions.
Assume a monthly frequency, with no calendar date irregularities, for a loan agreement.

The interest rate could be specified as a simple interest rate of 1% a month.
The interest rate could be specified as an annual compound interest of $1.01^{12}-1$ or 12.68% (approx).

Regardless of the convention used, if the borrower makes no payments for a year, the principal will grow by (roughly) 12.68% since the lender will roll the interest into the balance at the end of the month, and then make the simple interest calculation based on the new balance. That is, lenders will still charge interest on interest in practice.
Which one to use is purely a cosmetic decision - is it easier to work with 1% a month, or 12.68% a year?


Which market category does this sustainable product belong to? I'm currently working on an assignment, which is making an export plan for a product aimed at Asia. However I can't define the market of my product.

My product is basically an artificial riverbank; a mat made of coconut fibers with pre-grown plants in it, which can be easily placed on riverbanks to add more green and biodiversity to the place. It's completely sustainable and meant for urban areas.

To export it, I need to find market info. I can't find the import value or any solid statistics to describe the market of this niche product. I basically want the definition of a market where there is a lot of info and statistics, which I can "relate" to this product.

Like for example: it's easy to find the import value for 'fruit' in Japan. To which category could my product belong to? (or is the closest to? outdoor plants,.. any ideas?)

not even sure if this is the right forum to ask this stuff, but thank you very much anyway!

I'm from Canada and I work on policies supporting "clean technology" development, but its a very nascent sector from a statistical standpoint.  Statistics Canada only recently formalized a (very imperfect) definition, and our federal export development branch politely puts your problem this way: "For most Canadian cleantech exporters, the ASEAN markets are remote and not well known. Companies who feel that these countries may provide export opportunities should consult with Export Development Canada and the Canadian Trade Commissioner Service."

If you want to do some tough research, I would use search terms like "clean technology", "environmental goods and services", "water management", "land reclamation", etc. But in short, you're coming up dry because there's very little out there.


What are the limitations that a country faces in increasing its Forex Reserve? The Forex Reserve of a country remains in the locker of its central bank and does not earn any interest for that country. What are the measures that the central bank of a country can take to overcome this and other related demerits. Further due to this demerit,does a country really have a saturation/limitation level beyond which it is uneconomical to pile up its Forex Reserve?

The foreign exchange reserves of a country are normally invested in short-term government bonds in countries with liquid currencies (or trade partners). It is a portfolio of assets, and so the reserves may be diversified. On average, it should earn the risk-free short-term rate of the reserve currencies.

The cost to the country holding reserves is that they have to issue currency/bank reserves as the flip side of holding the forex reserves. These excess reserves will need to be drained, and so in some cases needs to issue bonds or bills to do so. In other words, the country needs to pay the domestic interest rate in order to hold the forex reserves; you can think of them borrowing to finance the position. (They could raise reserve requirements, forcing local banks to effectively loan money to the central bank to finance the reserve. This pushes the interest cost onto the domestic banking industry.)

Since a central bank can create its own currency costlessly, it appears that this might be a good deal. But creating a very large reserve position is effectively a huge bet, and any losses are effectively a cost to the taxpayer. (The Swiss attempt to limit Franc strength versus the euro ultimately failed as the position was not politically viable.)

Furthermore, the countries where you hold the reserves may not be amused with the country holding its exchange rate at too low a level. The country may become the target for corrective trade policies if reserves are "too large."

Finally, the reserves are lent to another government. If relations with that country deteriorate, those reserves are at risk of being seized.


Clarification on the definition of Bayes Correlated Equilibrium I would like your help to understand the definition of Bayes Correlated Equilibrium (BCE) in an incomplete information game at p.7 of this paper.

Let me summarise the definition provided in the paper.

There are $N\in \mathbb{N}$ players, with $i$ denoting a generic player.

There is a finite set of states $\Theta$, with $\theta$ denoting a generic state.

A basic game $G$ consists of

for each player $i$, a finite set of actions $A_i$, where we write $A\equiv A_1\times A_2\times ... \times A_N$, and a utility function $u_i: A\times \Theta \rightarrow \mathbb{R}$.
a full support prior $\psi\in \Delta(\Theta)$.

An information structure $S$ consists of

for each player $i$, a finite set of signals $T_i$, where we write $T\equiv T_1\times T_2\times ... \times T_N$.
a signal distribution $\pi: \Theta \rightarrow \Delta(T)$.

A decision rule of the incomplete information game $(G,S)$ is a mapping
$$
\sigma: T\times \Theta\rightarrow \Delta(A)
$$

Definition of BCE: The decision rule $\sigma$ is a BCE for the game $(G,S)$ if, for each $i=1,...,N$, $t_i\in T_i$, and $a_i\in A_i$, we have
$$
\sum_{a_{-i}, t_{-i}, \theta} \psi(\theta) \pi(t_{-i}|t_i, \theta) \sigma(a_{-i}| a_i,t_i, t_{-i}, \theta) u_i(a_i, a_{-i},\theta)
$$
$$
\geq
\sum_{a_{-i}, t_{-i}, \theta} \psi(\theta) \pi(t_{-i}|t_i, \theta) \sigma(a_{-i}| a_i,t_i, t_{-i}, \theta) u_i(\tilde{a}_i, a_{-i},\theta)
$$
$\forall \tilde{a}_i\in A_i$.

Question:

1) I don't follow how the conditional expectation is computed in the definition. Consider for example the left hand side (LHS) and let me go through each step by using the notation $Pr(\cdot)$ to generically denote any probability distribution.

The LHS is the expected payoff of player $i$ where the expectation is computed wrto anything that is unknown to him conditional on what he knows. Hence,
$$
\sum_{a_{-i}, \theta, t_{-i}} u_i(a_{-i},a_i, \theta) \times Pr(a_{-i}, \theta, t_{-i}| t_i, a_i)=
$$
$$
\sum_{a_{-i}, \theta, t_{-i}} u_i(a_{-i},a_i, \theta) \times Pr(a_{-i}| \theta, t_{-i}, t_i, a_i)\times Pr(\theta, t_{-i}| t_i, a_i)=
$$
$$
\sum_{a_{-i}, \theta, t_{-i}} u_i(a_{-i},a_i, \theta) \times \underbrace{Pr(a_{-i}| \theta, t_{-i}, t_i, a_i)}_{\equiv \sigma(a_{-i}| a_i,t_i, t_{-i}, \theta) \text{ [OK!]}}\times \underbrace{Pr(t_{-i}|\theta, t_i, a_i)}_{\equiv \pi(t_{-i}|t_i, \theta)? \text{ Where is $a_i$?} }\times \underbrace{Pr(\theta| t_i, a_i)}_{\equiv \psi(\theta)?\text{ Where are $t_i, a_i$?}}=
$$

Are we assuming

1) $t_{-i}\perp a_i $, conditional on $\theta, t_i$

2) $\theta \perp t_i, a_i$

?

2) How does the definition of BCE simplify to when $N=1$?

From reading at p.25 of the linked paper, it seems that a BCE is still intended as mapping from state and signal to a probability distribution over actions. From reading at p.26 of the linked paper, the authors then say "[...] In that case, the set of BCE correspond to joint distribution of actions and states [...]". I'm confused.

Also, when $N=1$, how does the definition of BCE differ from the definition of Bayesian Nash Equilibrium?

3) Just as a curiosity, what it is the reason of including the adjective "correlated"?

I think the reason you're having difficulty is that your definition is actually not equivalent to Bergemann and Morris' definition of BCE, except under specific assumptions which include the ones you state regarding independence. However, in general, we do not wish to make these assumptions. (For example, assuming that $t_{-i}$ is independent of $a_i$ conditional on $\theta$ and $t_i$ means that the mediator cannot reveal any additional information about other players' types once they have revealed the state to a player. This seems unnecessarily restrictive.)

In the paper, a BCE induces a probability distribution $\Pr$ that satisfies

$$ \sum_{a_{-i},t_{-i},\theta}\Pr(a_i,a_{-i},t_i,t_{-i},\theta) u_i(a_i,a_{-i},\theta) \ge \sum_{a_{-i},t_{-i},\theta} \Pr(a_i,a_{-i},t_i,t_{-i},\theta) u_i(a^\prime_i,a_{-i},\theta) $$

for all $a_i^\prime \in A_i$. If we wish to express this inequality in terms of player $i$'s expected utility given their information, then we divide both sides by $\Pr(a_i,t_i)$. Similarly, from the inequality

$$ \sum_{a_{-i},t_{-i},\theta}\Pr(a_{-i},t_{-i},\theta \vert a_i,t_i) u_i(a_i,a_{-i},\theta) \ge \sum_{a_{-i},t_{-i},\theta} \Pr(a_{-i},t_{-i},\theta \vert a_i, t_i) u_i(a^\prime_i,a_{-i},\theta), $$

we can multiply both sides by $\Pr(a_i,t_i)$ to recover the first expression above. To see how this squares with your calculation, notice that

$$ \begin{align*} \Pr(a_{-i}\vert a_i,t_i,t_{-i},\theta) \Pr(t_{-i}\vert a_i,t_i,\theta)\Pr(\theta\vert a_i,t_i) \Pr(a_i,t_i) &= \Pr(a_{-i},t_{-i},\theta \vert a_i, t_i) \Pr(a_i,t_i) \\
&= \Pr(a_i,a_{-i},t_i,t_{-i},\theta) \\
&= \Pr(a_i,a_{-i}\vert t_i,t_{-i},\theta) \Pr(t_i,t_{-i} \vert \theta) \Pr(\theta)\\
&= \sigma(a_i,a_{-i}\vert t_i,t_{-i},\theta) \pi(t_i,t_{-i} \vert \theta) \psi(\theta).
\end{align*} $$

In particular, we have that $$ \Pr(a_{-i}\vert a_i,t_i,t_{-i},\theta) \Pr(t_{-i}\vert a_i,t_i,\theta)\Pr(\theta\vert a_i,t_i) = \frac{\sigma(a_i,a_{-i}\vert t_i,t_{-i},\theta) \pi(t_i,t_{-i} \vert \theta) \psi(\theta)}{\Pr(a_i,t_i)}. $$ This makes it difficult to get the decomposition you want without making needlessly strong independence assumptions.

When $N=1$, there is only one player, so the equilibrium is (in some sense) degenerate. However, the difference between one-player BCE and one-player BNE is that the BCE set is larger, and includes any BNE. (Indeed, this is true even when $N>1$.)

For your second question:

  a BCE is still intended as mapping from state and signal to a probability distribution over actions. From reading at p.26 of the linked paper, the authors then say "[...] In that case, the set of BCE correspond to joint distribution of actions and states [...]". I'm confused.

Formally, a BCE is a probability distribution of actions for each realisation of the state and signals. This probability distribution induces a joint distribution over actions and states. Just integrate out $(t_i,t_{-i})$ in $\Pr(a_i,a_{-i},t_i,t_{-i},\theta)$ to get that joint distribution.

Finally, this equilibrium concept is called Bayes Correlated Equilibirum because it extends our definition of correlated equilibrium (defined by Aumann for complete information games) to games of incomplete information, in the same way that Bayes-Nash equilibrium extends Nash equilibrium.


Can the US dollar collapse and what are steps that I should take in the event that this happens? A friend of mines says that the US dollar is so "heavily intertwined" in other nations that if the US Dollar was to become worthless then that would have a major impact on the world.

However with the little to no backing in gold and division of the US dollar by digital currency as well as referring to history, isn't the US headed down hill?

There is the argument that the US dollar was able to buy more in the past however it seems to be proportional; the dollar bought more however we made less as a normal wage eg. cents versus dollars.

For example, other countries buying our food producing land, concrete factories being owned by other nations when our highway infrastructure needs repair, small factories closing and machinery being auctioned at little to no cost.

So... I was thinking about starting to save in Euros and perhaps looking into Bitcoin which I understand is volatile but it is rare and capped...

Any thoughts on this?

Further I am not heavily into economics (that's probably pretty obvious) so if you can fill in any additional gaps I missed, I would appreciate that.

The reason the US dollar is not destined to collapse anytime soon is that the United States has the most powerful military in the world, and one of the strongest economies.

To put it simply, we produce sufficient food and clean water to feed our people, and we have sufficient housing and infrastructure to ensure that basic needs are met for the vast majority of our citizens. That isn't likely to change in the near future. This means that our currency in a way (though not directly) is backed by those resources (food, water, shelter, electricity, etc.) despite not being tied directly to an indicator like gold. This being the case the only other possible downfall of our currency would be theft or extortion by foreign powers that would deprive us of those resources. As I first noted, our military ensures that this will not happen.

Often, a point of concern for many people is our debt. We have $20 Trillion in debt at the moment. However, just like you wouldn't go try to collect the debt owed to you by "El Chapo," Al Capone, John Gotti, or other violent groups with more guns than you, other countries are deterred from attempts at aggressive collections on the US debt. This is where the intertwining of our economies becomes important. With those economic relationships in place, these countries ultimately get things of value from the United States. Why would they cede those things to the detriment of both the US and that country unless they had an extraordinary reason? This paradox helps to ensure the stability of the currency as well.

That said, if it's still something you're worried about gold and bitcoin are both good investments, as are foreign currencies. A fundamental principle in investments is diversification. The more you spread your money into reasonable investments the less likely it becomes that all of your investments will fail. Thus you will always have something to fall back on.


What does the area defined by two different values for quantity under a supply curve represent? Assume that a and b (b is greater than a) indicate the quantity of supply on a linearly increasing supply curve. How can be the area formed by those two points under the supply curve interpreted? The interpretation should be made independent of a demand curve. That means no equilibrium price and producer surplus to account for. Could that be the difference between production costs for the given range of quantity?

Your intuition is right, but you are not accounting for fixed costs.

The supply curve is the part of the marginal cost curve above its intersection with the average variable cost curve. Marginal costs are defined as the derivative of the cost function (or the variable cost function as the derivative of fixed cost is zero).

To get the area you integrate. That is, you get back the variable cost.
So the area below the supply curve between $a$ and $b$ is the difference of the variable costs.


Why marginal revenue must equal marginal cost? Price  Quantity   TR      TC   Profit   MR    MC
6         0       0       3     -3     -     -
6         1       6       5      1     6     2
6         2       12      8      4     6     3
6         3       18      12     6     6     4
6         4       24      17     7     6     5
6         5       30      23     7     6     6

Consider table above. If my understanding is correct, optimal quantity equals 5, because at this point MR = MC.
But after producing 5th widget, profit does not increase.
Then why is producing 5 widgets considered to be profit maximizing quantity, but not 4?

Literally from the definition of Marginal Cost; it is the cost of producing one additional unit.

As your marginal revenue remains constant, pretty clear that you are going to make the maximum profits as the curves intersect at MC = MR. In the specific case that you consider, YES, you can choose either of 4 units or 5 units to be produced but, as Maarten said, your profits will definitely rise if you consider Optimal Production -2 units VS -1 unit in a general scenario.

This is the simple the reason why we say that MC = MR equilibrium is the optimal point to maximize profits. Doesn't mean you can't reach a similar state of profits before it can happen, just that MC = MR will for sure give you a maximal profit.

Also, emphasis on the point Discrete Quantities. Under a continuous distribution, your profits will keep increasing as long as the next extra unit produced will sell for more than it's production cost; i.e. till MC tends to the value of MR.


How is an interest swap collateralized I am trying to understand what it means for an interest swap to be collateralized.
If for example, I am paying fixed to a bank and receive floating in return. Who is giving collateral to whom? and how is the amount of collateral calculated?
I read that: "swaps are collateralized at the onset and then collateral is called up or down depending of changes in the market value of the swap". Don't really understand what this means and I would appreciate an example.

I am out of touch with the movement towards centralised counterparties, but I assume that the basic principles are similar to when I looked at it.
All derivatives have a risk measure like a daily Value-at-Risk (VaR) associated with them, as well as a net present value (NPV). The fact that it is a swap does not matter; all derivatives will be covered by the same collateral agreement.
The VaR/NPV is calculated using an accepted methodology by both parties. The counter-parties then post accepted collateral in an amount that covers the worst case of the NPV moving against them by the risk measure. (In the case of central clearing, both sides post collateral to the central clearer.) E.g., if the NPV of the counterparty is +\$2 million, but the daily risk is \$10 million, they need to have at least \$8 million in collareral.
This way, if one side fails, the other side can seize collateral to make up for the value of the derivatives position.
In the pre-central clearing days, in the case that a dealer is dealing with an entity that is hedging interest rates, but does not otherwise trade derivatives,  the dealer typically sets the terms on how collateral works unilaterally (e.g., the dealer does not post collateral). Banks are in the business of assessing and managing credit risk, so they can handle the credit risks associated with swaps relatively easily. I do not know whether this pattern of behaviour is still allowed under central clearing.


Transforming an indirect utility function into an expenditure function in preparation for our upcoming exam, our tutor has uploaded sample questions. One of them is the following:

This is my solution:

Which differs from the solution, which gives the ordinary square root of the same parameters, not the 4th-one. I can't find my mistake, does anyone have any ideas?

There is no error in your calculations. The problem is with the indirect utility function that you were given.

An indirect utility function should satisfy $v(\alpha p_1,\alpha p_2,\alpha y)=v(p_1,p_2,y)$. In other words, if income goes up and prices go up by the same factor then everyone is as well off as they were before.

Unfortunately, in this case $v(\alpha p_1, \alpha p_2, \alpha y)= \frac{1}2\alpha^2\frac{y^4}{p_1p_2}$


Mortgage loans from foreign banks at lower interest rates I had a thought - what if I live in a relatively poor country like let's say Russia and I would like to buy a house. In order to do that, I need to take a mortgage loan. In Russia however, interest rates are pretty high, lets say the best offer from a bank is 15 % annually. That's a lot but due to high interest rates, unlike in rich EU countries, the housing prices relative to income are not that high.

What does stop me from taking a loan from a bank in a rich EU-country to build or buy a house in a poor country like Russia, while having EU-level interest rates below 3% instead of the Russian 15%?

The low interest rate will be in a different currency. If your domestic currency falls in value, the value of the mortgage in terms of the domestic currency goes up.

Entities borrowing in a foreign currency and then running into difficulties is a standard features of financial crises over history.


Understanding the Components of Optimization What are policy function, objective function, constraint function, choice variables and parameters within the context of a utility maximization problem?

I don't understand which each of these are and I was not able to find out from resources online. Your help will be much appreciated.

I will give a general answer (for the specification of utility maximization), and I will give a more specific example of Cobb-Douglas utility:
$$U(x_i,y_i)=x_i^{\alpha_i}y_i^{1-\alpha_i}$$

$\textbf{Objective function:}$ In the utility maximization problem, the objective function is going to be the utility function. This is the function which you are trying to maximize. Therefore the objective function for agent $i$ in our example is:
$$U(x_i,y_i)=x_i^{\alpha_i}y_i^{1-\alpha_i}$$

$\textbf{Constraint function:}$ The constraint function is the function that limits the agent's ability to consume. If these functions were not in place, any agent with a strictly increasing utility function would choose to consume infinite goods. The two most common types of constraints are resource constraints and budget constraints. Resource constraints are just a maximum amount of a resource available (which makes sense because we know that resources are finite). A budget constraint is basically a constraint that says that you cannot consume more goods than you can buy. Examples of the two are below:

Resource constraint:
$$\sum_{i=1}^nx_i=A,\quad \sum_{i=1}^ny_i=B$$
where $A,B<\infty$

Budget constraint:
$$P_xx_i+P_yy_i= Z_i$$
where $Z_i$ is income of agent $i$ and $Z_i<\infty$

$\textbf{Choice variables:}$ These are the variables that each agent chooses to maximize utility. In our example the choice variables for agent $i$ are $x_i$ and $y_i$.

$\textbf{Parameters:}$ Parameters are also called state variables. These are the variables which the agent has no control over. In our example the parameters are $\alpha_i,B,A,Z_i, P_y,P_x$.

$\textbf{Policy function:}$ The policy function is also called the decision rule. This is what you get from solving the maximization problem. In the context of utility maximization problem, the policy function is the Marshallian demand (how much you want of each good). The policy function gives you your choice variables as functions of your state variables/parameters.


What does Adam Smith mean when he says wages are determined by: "advancing, stationary, or declining state of the society." I'm reading the Wealth of Nations. Smith explains in Book One that wages for labor are determined not by how wealthy a nation is but rather by its rate of growth. At the end of chapter seven he introduces the topic with this:

  First, I shall endeavour to explain what are the circumstances which
  naturally determine the rate of wages, and in what manner those
  circumstances are affected by the riches or poverty, by the advancing,
  stationary, or declining state of the society.

  Smith, Adam. The Wealth of Nations (p. 24). Neeland Media LLC. Kindle
  Edition.

In chapter 8 he goes into detail on this. Introducing an extensive section of examples of advancing, stagnating, and declining societies and the relative hight, mediocrity, and poverty of wages (respectively), he says:

  It is not the actual greatness of national wealth, but its continual
  increase, which occasions a rise in the wages of labour. It is not,
  accordingly, in the richest countries, but in the most thriving, or in
  those which are growing rich the fastest, that the wages of labour are
  highest.

  Smith, Adam. The Wealth of Nations (pp. 26-27). Neeland Media LLC.
  Kindle Edition.

His picture of the stagnating society looks grim enough, with the average laborer having barely enough to feed his family:

  If by digging the ground a whole day he can get what will purchase a
  small quantity of rice in the evening, he is contented. The condition
  of artificers is, if possible, still worse. Instead of waiting
  indolently in their work-houses for the calls of their customers, as
  in Europe, they are continually running about the streets with the
  tools of their respective trades, offering their services, and, as it
  were, begging employment.

  Smith, Adam. The Wealth of Nations (p. 27). Neeland Media LLC. Kindle
  Edition.

His picture of a declining society is hard for a sympathetic person to read:

  The lowest class being not only overstocked with its own workmen, but
  with the overflowings of all the other classes, the competition for
  employment would be so great in it, as to reduce the wages of labour
  to the most miserable and scanty subsistence of the labourer. Many
  would not be able to find employment even upon these hard terms, but
  would either starve, or be driven to seek a subsistence, either by
  begging, or by the perpetration perhaps, of the greatest enormities.
  Want, famine, and mortality, would immediately prevail in that class,
  and from thence extend themselves to all the superior classes, till
  the number of inhabitants in the country was reduced to what could
  easily be maintained by the revenue and stock which remained in it,
  and which had escaped either the tyranny or calamity which had
  destroyed the rest.

  Smith, Adam. The Wealth of Nations (p. 28). Neeland Media LLC. Kindle
  Edition.

I am a layman to economics. My question to the community is: is this still generally accepted economic theory? Can a "static" society not expect high wages for labor but rather expect generally decreasing wages for labor until they fall to barely subsistence levels? Can we only expect high wages for labor in countries with every increasing productivity? I know this is science, so you kind of have to take it as it is, but I admit this seems grim to me.

Taken literary the passages do not hold up, but the passages also have to be read in the context they were written. An important caveat is that Adam Smith actually did not propose any explicit theory of wage growth rather the above quotes are observations he made at the time of the writing (at least I think that the passages when read in the context of the chapter should be interpreted as empirical observations). Take the first quote:

  It is not the actual greatness of national wealth, but its continual increase, which occasions a rise in the wages of labour. It is not, accordingly, in the richest countries, but in the most thriving, or in those which are growing rich the fastest, that the wages of labour are highest.

This observation was made on the basis of him comparing England which was traditionally a backwater - a poor country, with stagnant but 'rich' countries such as Qing dynasty China.  But the observation itself was incorrect. At the time no published real GDP statistics existed and so Smith just thought that China is richer due to the fact that in the West China was often mystified and its wealth was exaggerated.

As the Maddison's estimates show (see graph at the bottom), at the time of publishing of the Wealth of Nations the Britain was already much richer than China.  However, even at that time it was well known China was stagnant and UK was growing rapidly due to its early industrialization and so Smith conflated those.

Moreover, also in recent history we can see that Euro-area (comprised of mostly Rich developed countries) in last decade experienced very slow growth - that although technically not stagnation comes close to it - has higher real wages than China which  experiences rapid growth (between 2011 and 2019 it was always higher than $6\%$), yet real wages are higher in the Euro-zone than in China.

However,  wages tend to raise with economic growth. In fact from macroeconomic perspective there is no meaningful distinction between output and income. Moreover, until very recently average wages tracked productivity very closely and even though in US it is no longer true that they do in many places they still continue to do so. Over long periods of time eventually the output and wages will be higher in countries which are 'thriving' in sense they experience economic growth. This can be shown in the same estimates from the Maddison which shows that although all of the countries in the graph were roughly equally poor in 1500, the countries that experienced high economic growth, are the ones that now have relatively high average wages and standards of living.

So to sum up Adam Smith was not wrong in observing that wages tend to be higher in the 'most thriving' countries, but he was not correct when he said the wealth of the country - at least understood as the output of the country or GDP is not accompanied with high wages.

Of course, converse applies as well. A country which experiences negative economic growth will see its real wages and standards of living falling, and stagnant countries will experience stagnation also with respect to real wages.


We see stocks outperforming things like bonds in the long run (past 100 years), but could this be an artifact of that particular 100 year timeline? When looking at historical return patterns for investments, one can clearly see the stellar performance of equities over the long haul. That being said, we know that we can center in on certain 20-25 year time spans throughout that century where the return characteristics look drastically different.

If this is the case, then couldn't the entire 100 year period demonstrating the attractive returns for stocks be an aberration over hundreds or thousands of years, especially considering how global growth has changed since pre-history? And how could we hope to know? Is there a statistical/probabilistic way to be understand whether our "long-run" returns are in fact indicative of some sort of deep principle regarding average returns in a market economy?

Yes. The relative performance of stocks and bonds depends on monetary policy. Stocks benefit from low interest rates and inflation while bonds benefit from high interest rates. Over the 19th century for example, stocks deflated along with the overall economy while bonds yielded a small positive return.


Books and resources on how policies/regulations are made on exchanges like NYSE, NASDAQ, LSE, etc? Different stock exchanges (for example, NYSE vs KRX) have similar but different regulations overall. Each exchange has different concerns and each exchange has a different approach to handle problems like volatility, etc.

How can I learn more about the thought process that goes into making policies/regulations to handle such problems?

Is there a specific discipline that studies financial exchanges and their regulations? Market Economics? I think that's too broad a term.

Bonus question: How do governments decide when to intervene on bad regulations/policies made by financial exchange marketplaces (? by this I mean: stock markets, foreign exchange markets, etc)

Maybe I don't have a clear question. In that case, can you provide some relevant introductory references or keywords to research?

If my question is not appropriate here, can you suggest where else I can get answers?

This document, published by the International Organization of Securities Commissions, states three objectives and describes thirty-eight principles of securities regulation:
https://www.iosco.org/library/pubdocs/pdf/IOSCOPD561.pdf
Objectives

Protect investors

ensuring that markets are fair, efficient and transparent;

reducing systemic risk.

The Securities and Exchange Commission (SEC) is the official federal regulator in the United States. Administrative law regulations are made in a context of procedures relating to the Federal Register and/or Code of Federal Regulations. This is a Guide to the Rule Making Process:
https://www.federalregister.gov/uploads/2011/01/the_rulemaking_process.pdf
North American Securities Administrators Association (NASAA) has much information about its efforts to solve problems under the objectives published on this site:
https://www.nasaa.org/
Rules established by government authority or customs with commercial authority are efforts to solve a particular social problem, procedures to solve those types of problems, and procedures to monitor behavior and enforce rules. Your research would be based on comparisons of these elements in unique case studies or contexts regardless of the information sources which should be available to the public.


Can inflation occur in a positive-sum game currency system such as the Stack Exchange reputation system? As most active users of this site know, the way the reputation system works is that everyone starts out with 1 reputation and a user can earn more reputation by asking good questions and writing exceptional answers (as well as other methods), and a user can lose reputation by writing bad questions and answers.  This way, users can make a profit or take a loss without taking/giving currency from/to another user.  Can inflation happen with a system like this?  As more reputation is gained, does it mean less?

In the Stack Exchange reputation "economy", we can think of the reputation points as "money". And the "goods" are:

Downvotes — cost 1 point each.
Various privileges — zero cost, but unlocked only when the user reaches various thresholds.

To my knowledge, these prices (1-point cost of each downvote and privilege thresholds) have never changed. And so, there has never been inflation. What has merely happened is that "wealth" (the total stock of reputation points) has kept increasing.

Response to Pere, who writes:

  Newer sites have lower thresholds for several privileges - for practical reasons - and those thresholds rise as the site expands. For example, being able to create tags "costs" 150 reputation in Economics SE, 300 reputation in Cross Validated SE and 1500 reputation in StackOverflow. Therefore, privilege prices are subject to inflation as sites grow.

Each individual SE site is its own individual "economy" that is sealed off from all other SE sites.¹

And so, whether "prices" differ across SE sites does not matter. What matters is whether "prices" have changed over time, within each SE site.

To my knowledge, the privilege threshold "prices" on Economics SE have never changed.

And it also seems that for the original, flagship site (Stack Overflow), "prices" have also not changed for many years. We can, for example, compare today's "prices" with those from 2013:

As you can see, all prices have remain unchanged since 2013. There has therefore been zero inflation since (at least) 2013. The only change is the introduction of a "new good", namely "Access to site analytics", which is priced at 25,000 points.

Response to @kbelder, who writes:

  What about bounties? I bet those have historically trended upwards in value

The "prices" of bounties have likewise been fixed. Bounties may be offered at "prices" of 50, 100, 150, ..., and up to 500 points. I believe these prices have been fixed since the inception of Economics SE and at least since 2013 for all SE sites.

Moreover, bounties are pure transfers from one user to another.² It may be true that thanks to increased overall "wealth", the average value of a bounty has risen (i.e. in the past, most bounties were offered at close to the minimum price of 50; whereas today higher prices are offered). However, we do not consider this "inflation". Instead, we consider this to be real wealth effects.

Analogy: Say that in 1919, the New Yorker on the street might on average give \$0.20 (in 2019 dollars) to a homeless person. In 2019, this might instead be \$1 (in 2019 dollars). The average real transfer from a New Yorker to a homeless person has risen five-fold in real terms. This is not inflation. Instead, it is a consequence of increased overall wealth.

Footnotes.

To my knowledge, there is one thing that links reputation points across the various SE sites. This is the automatic +100 points for established user accounts that are "trusted" on the SE network. I'm not sure how this works. But I would say that these +100 points are relatively inconsequential and may be safely ignored. They would perhaps be the real-world equivalent of an immigrations officer giving a "trusted" visitor \$1 the first time that visitor arrived in that country.
There are actually three things that can happen to a bounty. First, the full bounty is awarded (I believe this is the most common case). Second, half the bounty is awarded to the highest score (provided that answer has a score of at least +2 — see Economics.SE bounty rules here). Third, no bounty is awarded. In the latter two cases, we do not quite have a pure transfer; instead, we have a leaky bucket where either half or all of the points are "lost to society".


Moral Hazard or Adverse Selection? I pay the doctor before he conducts the surgery.

Can anyone explain to me whether this statement shows moral hazard or adverse selection?

The problem you are facing has probably both: Moral Hazard and Adverse Selection.

We have hidden action by the doctor (you can't really observe his level of effort during the surgery), therefore we have Moral Hazard.

Additionally, you (probably) can not know beforehand of the doctor is a good or bad doctor, so his type (good or bad) is unknown. So, there is hidden information and therefore possibly Adverse Selection.
One example could be that a good doctor would never work for the amount you pay, so the doctor you hire is of the bad type.

Remark: I did not define good/bad doctor here, as it could be many different things; a bad doctor could just be a lazy doctor or a badly trained doctor.


Isn’t a zero-coupon perpetual bond not worthless if the relevant government has some probability of buying them back? A government issues perpetual bonds with no interest payments, no coupons: Most economists that are not hyper-dovish would argue such a bond is intrinsically worthless. However, if a government were desperate for some form of credit in regard to these instruments, wouldn’t there be some probability of the government buying these instruments back and thus granting them value?

If I understand you correctly, the bond pays out nothing whatsoever. Such a bond must be worthless. The value of the bond is equal to the net present value, i.e. the sum of the discounted value of all future cash flows, which are zero in your case. If the government would buy it back, it would necessarily buy it back at a price of zero. Therefore, the bond will remain worthless in any case.


How does inflation work in real life? So when the government prints more money, then it is said the people will have more money in general and as a result the prices of goods and services will also increase. So in the end, we will end up buying the same amount of goods, but by paying more. So its the concept that the more the things is available the less value it has.
I do not understand how this works in real life.
When the government prints more money, how does this extra money end up in the hands of the people, they still are being paid the same amount of salary annually by their employers. The income of people is fixed.
Secondly, why does the price of the goods increase? If rice is worth 1$ per kilo, then just because people are richer why does the cost of rice increase ?

I have recently started studying economics.

When the government prints more money, then how does this extra money end up in the hands of the people, they still are being paid the same amount of salary annually by their employers.

This is really two questions:

How does the money get into the economy? The US government increases the money supply by having the Fed buy things with dollars that did not previously exist.  Typically they buy financial assets, pushing their price up and putting new money into the hands of the previous owners of those securities (often the US treasury, which means it is injected into the economy in the form of government spending).

How do individuals get this money if their incomes are fixed?  For a given individual, their income may be fixed in the short run.  However, across the economy there are many people whose incomes fluctuate with sales or who are up for raises that depend on sales or profit.  Or who get a higher wage when they change jobs.  As the money supply increases, consumers have more money in hand and spend more money, raising wages for those whose wages can go up using these mechanisms. Your intuition is right about people with truly fixed wages, though: in the short run, they do not participate in the money supply increase.  This is why people on a fixed income (like elderly people living on a pension) hate inflation.

Overall inflation shifts wealth from lenders to debtors and from those with fixed incomes to those with adjustable incomes.

  why does the price of the goods increase?

The price of a good is the equilibrium between the people buying and the people selling.  A change in the money supply does not change how many goods there are to sell but it does change how many dollars the people buying them have.  If people have more money, they will be willing to pay more, so the price goes up.


What are the (immediate) effects of changing a good's price on consumer and producer surplus? Basically, I'm trying to understand why the total surplus is maximized at the equilibrium and what happens if the price isn't at the equilibrium.

Say the price of a good is the equilibrium price. Now make it more expensive. I know that after a while the price will adjust to the equilibrium again, but what will happen before that? I'm trying to use an example but there are things I can't fill in:

The equilibrium price of the good is \$20 and the equilibrium quantity is 20. Given a straight demand and supply curve and a maximum buyer's imposed value of \$40, the consumer surplus is $\frac{1}{2}(40-20)\cdot20=200$ and the producer surplus is $\frac{1}{2}(20-0)\cdot20=200$.

Now make the good \$30. The quantity demanded falls to 15 and the quantity supplied rises to 25. Now, the consumer's surplus is the triangle I marked in blue, $\frac{1}{2}(40-30)\cdot15=75$ (because only 15 items will be sold), but what about the producer's surplus? Is this the triangle I marked in red? I think not, because that seems to imply that the price is only \$10. But if not, what is the producer's surplus, and why?

Thanks in advance and my apologies for the possibly confusing phrasing.

What is CS and PS out-of-equilibrium at $P=30$:
I think that answer to this question lies in misunderstanding the definition's of consumer and producer surplus.
The consumer and producer surplus are actually (following Mankiw Principles of Economics, 8th  ed, pp 135 and 140

consumer surplus:
the amount a buyer is
willing to pay for a good
minus the amount the
buyer actually pays for it

producer surplus
the amount a seller is
paid for a good minus the
seller’s cost of providing it [where Mankiw later in chapter explicitly states cost is here to be interpreted broadly as "the value of everything
a seller must give up to
produce a good", including the opportunity cost (or more broadly s wilingness to sell)].

You will note that the definitions above talk about price people pay (i.e. actual market price) not 'equilibrium price'. Some lecture notes or textbooks will include the word equilibrium in the definitions but that is only because virtually all analysis using Supply-Demand is an analysis of some equilibrium.
More rigorously, since the maximum willingness to buy is bounded by the demand curve and willingness to sell by supply curve we can define consumer surplus as the area below the demand curve and above price paid by consumers and
$$CS =  \int^{q_m}_0 D(q) dq − p_mq_m $$
where $D(q)$ is arbitrary demand curve, $p_m$ is price consumers have to pay in the market, and $q_m$ quantity sold at the market.
$$PS =  p_mq_m - \int^{q_m}_0 S(q) dq $$
wher $S(q)$ is some arbitrary supply curve (also if we would want to be even more general we could allow $p$ to be different for suppliers and consumers e.g. situations with taxation where there would be wedge between price consumers pay and price per quantity suppliers get due to the tax wedge).
Yes, in some chapters or lecture notes the above formula will be defined in terms of equilibrium price but that is only because the market price/quantity is the equilibrium price/quantity in any equilibrium analysis (i.e. in equilibrium $p_e = p_m, q_m=q_e$).
However, in an out-of-equilibrium analysis you have to use actual market prices (this would be equivalent of analyzing price floor or price celling (e.g. see Mankiw Principles of Microeconomics, 8th  ed, pp. 116).
Consequently, in your case the consumer and producer surplus can be properly visualized as shown on the tikz graph below I made:

where the area of consumer surplus (out-of-equilibrium) at price $P_m=30$ is the blue shaded region below demand and above market price bounded by market quantity, and the producer surplus (out-of-equilibrium) at price $P_m=30$ is the red trapezoid (area under the market price and above supply bounded by market quantity).
We can also calculate the area of that trapezoid, although to do that we need to know what is the price at which $Q_S=0$ (or explicitly know what the supply and demand equations are). In your question you don't state what the  price at which supply is equals zero is but if you would provide it we could calculate it (also you seem to have made some mistake when copying down the problem as your demand does not lie on a line since it is given by points $(0,40);(15,30);(20,20)$ - which simply mathematically cannot lie on a single line - I originally planned to go all the way deriving the linear demand and supply equations based on the points but this mistake in problem set up makes it impossible ).
Why is total welfare maximized in equilibrium?
Well the reason for this is that under all the background assumptions of the stylized partial equilibrium model (e.g. no market failures and other 'shenanigans' that would affect PS and CS in way not shown in the partial equilibrium analysis here), the total combined area of PS and CS is maximized at the equilibrium price and quantity.
I won't be providing a rigorous proof of this as that would require a lot of calculus and this problem is long as it is, but I encourage you to take a look at proofs provided in MWG, Microeconomic analysis pp 328 or Varian, Microeconomic Analysis pp 224 if interested.
However, the reason why the welfare  be easily seen graphically by the following thought experiment: would the total surplus be larger if $P>P_e$ or if $P<P_e$? The answer is no as you can see visualized in the two figures below. As in both figures below the total surplus area will always fit within the big triangle given by area below demand and above supply clearly the total welfare is in both situations lower than the total welfare in a situation where $P_m=P_e$.

PS: An important caveat to note is that the above applies when you want to analyze what would be the total welfare outside equilibrium vs the welfare in equilibrium. If you want to compare two situations which are both equilibrium e.g. supply shifts to the right due to technological progress, you have to compare the total welfare in the market in the old equilibrium vs the new one. You should not confuse such situations with market not being in equilibrium.


How much influence does the president really have on US economy? We hear a lot about how the economy changed under a certain president, but how much does the incumbent actually affect the economy? Are the fluctuations we see in economic growth due to natural market fluctuations or can they be attributed to policy changes?

Here is one paper that may be of interest:

  Analyses of the effects of election outcomes on the economy have been
  hampered by the problem that economic outcomes also influence
  elections. We sidestep these problems by analyzing movements in
  economic indicators caused by clearly exogenous changes in
  expectations about the likely winner during Election Day. Analyzing
  high frequency financial fluctuations following the release of flawed
  exit poll data on Election Day 2004, and then during the vote count,
  we find that markets anticipated higher equity prices, interest rates
  and oil prices and a stronger dollar under a Bush presidency than
  under Kerry. A similar Republican-Democrat differential was also
  observed for the 2000 Bush-Gore contest. Prediction market based
  analyses of all Presidential elections since 1880 also reveal a
  similar pattern of partisan impacts, suggesting that electing a
  Republican President raises equity valuations by 2-3 percent, and that
  since Reagan, Republican Presidents have tended to raise bond yields.

Partisan Impacts on the Economy: Evidence from Prediction Markets and Close Elections Snowberg, Wolfers, and Zitzewitz (2006)

This might give some indication of an upper bound on these effects since only some of the increase in stock market wealth is from an increase in aggregate wealth. The rest comes from a change in transfers and so not really an effect on the economy.

Here's a similar paper from Germany:

  Rational partisan theory suggests that firms perform better under
  right- than left-leaning governments. In the pre-election time,
  investors should anticipate these effects of government partisanship.
  This is the first study to investigate such anticipated partisan
  effects in Germany. Applying conditional volatility models we analyze
  the impact of expected government partisanship on stock market
  performance in the 2002 German federal election. Our results show that
  small-firm stock returns were positively (negatively) linked to the
  probability of a right- (left-) leaning coalition winning the
  election. Moreover, we find that volatility increased as the electoral
  prospects of right-leaning parties improved, while greater electoral
  uncertainty had a volatility-reducing effect.

Partisan politics and stock market performance: The effect of expected government partisanship on stock returns in the 2002 German federal election   (Füss, Bechtel (2002))

It also depends on the baseline way of measuring impact. A really terrible president might be able to wreck serious damage on the economy while the other branches and electorate would take time to undo that damage and remove him. Should presidential performance be measured against the very worst that an incompetent or malicious person could deliver? Or are they best compared with other likely serious contenders? These papers above are much more measures of the latter than the former.


The Effects of Demonetisation I do not wish to get into the details of the Demonetisation implemented by the Indian Government on 8th November, 2016. Endless political debates have already been conducted advocating or berating this step. As an Economics student, I would like to get some technical insight into this action and the economic effects of demonetization in general.

I am not an expert in biology but let me give you some intuition through it.

For instance if you have some impurities in your blood. There are two ways to remove that impure blood from your body.

1) To give you some medicine that enters your system to cure you. This is a slow procedure and may not guarantee concrete results.

2) To artificially suck entire blood out of your body and make attempts to purify it and then refill it into your body. This is a fast procedure and will produce certain concrete results which can either be positive or negative.

Now, if the second method seems lucrative to you, make sure you think of what will happen to you in that time interval when your body is without blood.

Noe let us come to Economics.

Money is a medium of exchange and store of value.

Let me write a simple equation of money.

$MV = PY$

$M$ ~ Amount of money in circulation.

$V$ ~  Velocity of Money. Velocity of money is nothing but number of times the nominal money is changing hands

$P$ ~ Price level

$Y$ ~ Output in the economy

$PY$ hence is the value of output or GDP.

You can make an intuitive sense of this equation that is the GDP of the country is how fast a given quantity of money circulates in the economy. Suppose the GDP (aggregate expenditure) of a country is \$1,000. The amount of money in circulation is \$500. So money should change hands two times for expenditure worth \$1000 to occur which makes velocity of money = 2.

Now once you have digested this relationship.  Demonetisation in the Republic of India was not an attack on the quantity of money but on the velocity of money in circulation.

It did not make the existing money worthless since the old cash could be exchanged for new cash but it choked off the flow of money that is the velocity of money in the economy since old cash which made for 86% of the entire money supply ceased to be a legal tender. Now coming back to our equation:

$MV = PY$

There was an artificial decrease in velocity(V) so the right hand side of the equation $PY$ must fall to maintain the equilibrium. That is GDP must fall temporarily which is the stagnation of the economy.

Understand it this way, you temporarily decrease the purchasing power of the people by pulling all the money out of the system. People stop buying stuff and sellers cannot sell their stuff. Producers will stop producing and people will lose jobs. Hence this is an artificially created recession.

This was perfectly evident in the growth rate of the country that slumped by about 2% in the beggining of 2017. The 2% of India's GDP is a phenomenal multi billions of dollars which India lost and which is the actual monetary cost of this decision.

Now the fundamental question at the heart of economic decisions - Does the benefits justify the costs? Which is a debatable topic as you mentioned so I am not going into that.

But what I personally believe is, Indians should have thought it out more rigorously and thoroughly before making such an unconventional move.


Tax revenue formula maximization- whats the name of this formula? I have been teaching intermediate microeconomics and have come across a formula a number of times relating the tax rate at which revenue is maximized if elasticities are constant. This formula is defined as follows:
$$T_{max}=\frac{\varepsilon}{\varepsilon-1}\left(\frac{1}{\eta}+\frac{1}{\varepsilon}\right)$$
where $\varepsilon$ is our price elasticity of demand and $\eta$ is our price elasticity of supply.

This seems to be just a spin on Ramsey's rule. By Ramsey's rule (derived through Lagrangian method assuming zero cross-elasticities) the optimal tax for a market where supply is not explicitly  modeled is given by:
$$\frac{t}{1+t}=\frac{1}{\epsilon}$$
Well technically it is $\frac{t}{1+t}=\frac{1-b}{\epsilon}$ but $b$ which is parameter that depends on marginal cost of public funds is often omitted/assumed to be zero in introductory problems for students.
The Ramsey rule above can be solved for $t$ as:
$$t = \frac{\epsilon}{\epsilon-1} \left( \frac{1}{\epsilon}\right)$$
The version you showcase is just derived with also explicitly taking into account supply as opposed to just from consumer problem where supply is not explicitly modeled showed above.
Given that I think it would still be called 'optimal Ramsey taxation'. To my best knowledge this kind of tweaking of the model would not have it's own special name, but I also tried  to do literature search on Ramsey models with supply elasticity which did not yielded any results, but absence of evidence is not necessarily evidence of absence.


How do penny auctions make money? What are penny auctions? Given the great discounts they claim (up to 95%), how do they make money?

In a penny auction, each bid raises the going price of an object by just one penny. However, placing such a bid is costly whether or not you win. Usually it costs one dollar to place a bid -- sometimes this is obfuscated by making you purchase bids (or bidding credits) before you participate. In any case, if the opening bid of an auction for something is 0.01, and the auction ends with the price at just 10, then one thousand bids have been placed and therefore the site has made 1,000 on top of what the item actually sells for (10). So if the item has a value of 500, then they would represent that as 98% discount even though they actually made a profit of 510, simply because they ignore the bidding costs (their primary source of profit).

Now, if you happen to be the person who makes the winning bid, and you have not bid previously, then obviously you would be getting a very good deal -- in the example above, you would be paying 11 for an item that might be worth 100 or more. However, it is difficult (and out of your control) to be the winning bidder. After every bid, time is allowed for other bidders to outbid you, in which case you lose the money you spent on the bid.

With all of this in mind, participating in penny auctions is essentially gambling. Sites that market these discounts and obfuscate the cost of bidding are highly misleading. I personally believe they should be banned. Note that these penny auction sites should not be confused with standard auction sites like Ebay. In standard auction sites, you pay only if you win -- you do not pay simply to make a bid.


Slope of a production function Let $F(K,L)$ be a production function with variables $K$ for capital and $L$ for labor.

The slope of the $F(\overline K,L)$ ($K$ taken constant) is defined as the marginal product of labor ($MPL$) such that:

$$MPL=F(K,L+1)-F(K,L)$$

Most production functions have a positive decreasing slope due to diminishing marginal product and therefore are not straight lines. How is the $MPL$ formula still valid? Isn't that the same formula to find a gradient $m$ of a line (i.e. $\frac{y_{2}-y_{1}}{x_{2}-x{1}}$)? If we take any function whose representation isn't a line, its slope at a certain point is equal to the slope of the tangent at the point and not the formula for the gradient $m$.

Also, supposing the given formula for $MPL$ is true, shouldn't we also have $MPL=\frac{\partial F}{\partial L}$?

The (partial) derivative of a continuous function is defined as
\begin{align}
\frac{\partial F(\overline K, L)}{\partial L} := \lim_{\Delta L \to 0}\frac{F(\overline K, L + \Delta L) - F(\overline K, L)}{\Delta L}.
\end{align}
Now if $L \in \mathbb{N}$, then you have a lower bound for the increment $\mathbb{N} \ni \Delta L \geq 1$. Otherwise the definition above is not well defined for $\Delta L = 0$.
Such that we finally arrive at the approximation
 \begin{align}
\frac{\partial F(\overline K, L)}{\partial L} \approx \frac{F(\overline K, L + 1) - F(\overline K, L)}{1}.
\end{align}


During an economic expansion, how do the ratios of Return on Equity and Return on Asset are affected? From my perspective, during an economic expansion, industrial production, employment, personal incomes and sales are increased excluding the inflation rate. To be more specific, companies buy new machines or build new factories to increase the production in this period and to expand the business, the company should finance the expansion either through debt or equity.

Therefore I thought Return on Equity (ROE) would be increased because companies borrow more debts, which leads the denominator of ROE formula, shareholders' equity, to be decreased and it results ROE to be increased.

However if the company finance their expansion by the equity, not through debt financing, then denominator of ROE formula, shareholders' equity would be increased therefore the ROE will be decreased.

Then during an economic expansion, how does the ROE will going to be changed, decreased or increased?

If all else were equal, then using more equity financing would reduce return on equity. (This is assuming a normal situation where the return on assets is greater than the cost of interest. If the interest cost is greater than the return on assets, using debt for financing reduces profits. In this case, there are less profits, and a smaller equity base. The net effect on the return on equity depends upon the exact numbers.)

However, this tells us nothing about observed data during an expansion, it just tells us about the difference between two hypothetical scenarios (the scenarios being defined by the level of equity financing).

Aggregate profits are determined by many factors. The effects of those factors change every cycle, and may be unrelated to businesses' financing decisions.

For example, if the wage cost per unit of output (unit labour cost) is rising faster than selling prices, business profit margins will tend to fall (wages will represent a greater share of total income). Conversely, the profit share will generally rise if unit labour costs increase slower than selling prices. There is no law of economics that says which outcome will occur, and so we cannot be sure what is happening to profit margins.

Therefore, we have no way of answering the question of what happens to ROE during expansion, without pinning down what else is happening at the same time.


Do US 501(c)(3) non-profits have to divulge their investments? Do US non-profit organizations with tax exemption under Section 501(c)(3) of its Internal Revenue Code which have investments (such as university endowment funds) have to divulge these investments in any sort of filings? If so, are these required to be available to the public?

Form 990 and associated schedules:

  The Form 990 provides the public with financial information about a
  nonprofit organization, and is often the only source of such
  information. It is also used by government agencies to prevent
  organizations from abusing their tax-exempt status. In June 2007, the
  IRS released a new Form 990 that requires significant disclosures on
  corporate governance and boards of directors. These new disclosures
  are required for all nonprofit filers for the 2009 tax year, with more
  significant reporting requirements for nonprofits with over \$1 million
  in revenues or \$2.5 million in assets. In addition, certain nonprofits
  have more comprehensive reporting requirements, such as hospitals and
  other health care organizations (Schedule H). The Form 990 may be
  filed with the IRS by mail or electronically with an Authorized IRS
  e-file Provider.

  The Form 990 disclosures do not require but strongly encourage
  nonprofit boards to adopt a variety of board policies regarding
  governance practices. These suggestions go beyond Sarbanes-Oxley
  requirements for nonprofits to adopt whistleblower and document
  retention policies. The IRS has indicated they will use the Form 990
  as an enforcement tool, particularly regarding executive compensation.
  For example, nonprofits that adopt specific procedures regarding
  executive compensation are offered safe harbor from excessive
  compensation rules under section 4958 of the Internal Revenue Code and
  Treasury Regulation section 53.4958-6.

Wikipedia on Form 990

In particular, SCHEDULE D. The level of detail is not rich but the information is public enough for Charity Navigator to make use of these filings in their evaluations. You can search for a charity's form 990 here.


How to estimate if goods are complementary or substitutes when one good is always offered for free? Usually  whether two goods are complementary or substitutes can be measured by estimating cross-price elasticity of demand. If cross-price elasticity of demand is negative the two goods are complements and if the cross-elasticity of demand is positive they are substitutes. However, how would we determine if goods are complements or substitutes when one is provided for free (e.g. are free e-books on Bayesian analysis and coffee complements or substitutes?).
Now, as far as I understand, theoretically this does not pose any issue because even though price of one good is always set to 0 there will be some theoretical demand for the e-book that will depend on price (even if we can't observe any price other than 0).  But from a practical perspective would it be possible to estimate cross-price elasticity empirically in such case?
Normally, we would estimate cross-price elasticity in some sort of regression like (or more sophisticated analogues):
$$\ln q_x = \beta_0 + \beta_1 \ln p_x + \beta_2 \ln p_y +...+ \epsilon$$
but $\beta_2$ can only be identified if $VAR(p_y) \neq 0$ since $\beta_2= \frac{COV(q_x,p_y)}{VAR(p_y)}$.
Are there any models that could allow us to estimate cross-elasticity even in such cases or is it simply impossible? Are there other empirical methods of determining if goods are complementary/substitutes aside from estimating cross-price elasticity?
I tried to do due diligence search on google scholar but even though there are plenty of papers discussing estimation of cross-price elasticities (such as Deaton 1987), I was not able to find paper discussing this issue. This being said estimating such elasticities is not area of my specialty so I am not sure if I am missing some important keywords. I ask this question because I TA undergraduate microeconomics class and one of the students raised this, in my opinion very interesting, question.

One answer is to try to find variation in the non-pecuniary price of the free good. Here is a famous example from estimating demand for public parks:

In 1949, Harold Hotelling wrote a letter to the National Park Service,
outlining a method where the park visitor’s round trip distance could
be used to proxy the recreation trip price, so that consumer’s surplus
estimates might be recovered. The idea was to obtain the net benefit
for outdoor recreation for a particular geographic area. The CVM
method was suggested in the same year in an article by
Ciriacy-Wantrup, although the first actual application of the method
(to deer hunting in Maine) was by Robert Davis in his Harvard PhD
dissertation, in 1963.

The new economics of outdoor recreation
Hanley, N. ;  Shaw, W. S ;  Wright, R. E. (2003)
Chapter free here
It seems like something very similar is possible here. For example, say you were asking about complementaries between the radio (which is free) and cars (which are not). You could look at hard of hearing people, and how demand changed for the radio as more and more expensive equipment is required to listen to the radio.
Or consider evaluating if public schools and Disney World are complements or substitutes. Using distance from school as a proxy for the variation in the cost of "consuming" school, you could use that variation to trace out the cross-price elasticity of Disney with respect to school.


Is any aspect of the cryptocurrency adoption violating a widely held economic tenet? This is not a homework question.  I am merely interested.

As an academic discipline, Economics refers to various laws and widely held beliefs including, but not exclusive to;

Production precedes consumption
Value is subjective
Production has cost
Money is not wealth
Supply and demand

Etc etc.

Is the rise of cryptocurrency refuting or violating any typically held economic beliefs?  Or, inversely, are cryptocurrencies/society acting exactly as Economics would logically predict?

There is quite a bit of research on it and a good argument as to why central banks should not issue cryptocurrencies, but should issue electronic money.  I would recommend reading https://research.stlouisfed.org/publications/review/2018/02/13/the-case-for-central-bank-electronic-money-and-the-non-case-for-central-bank-cryptocurrencies/

and

https://research.stlouisfed.org/publications/review/2018/02/13/blockchain-what-it-is-what-it-does-and-why-you-probably-dont-need-one/

https://research.stlouisfed.org/publications/review/2018/02/13/is-bitcoin-a-waste-of-resources/

Nothing about cryptocurrencies is surprising to me.  Indeed, the separate parts have been in use, in some cases, for hundreds of years.  Bitcoin is a clever combination of things that have long existed.  The other cryptocurrencies, such as Etherium, also offer self-executing contracts.  Those are also very old.  The simplest that you may physically see are sight drafts, which are common in the southeastern United States.  It is a draft printed on an envelope and is payable only when the envelope contains a properly executed document.

There is nothing surprising to me about how cryptocurrencies are behaving, but they cannot continue like this and they won't.  You should read "Good Money," by George Selgin, who writes about the creation of private money in Britain by button makers to meet an unfilled demand.

What you are seeing is a process by which people learn.  If you think this whole process through, you will find that you will not want to participate in this little revolution until supply and demand intersect.  By limiting the number of coins the various firms have created artificial scarcity.  However, we now have 759 cryptocurrencies and growing.  Each one makes the others just a little less valuable.  Although there is an argument against a central bank entering the market, if one did, the private money would vanish if the official money could be exchanged at a 1 to 1 rate.

Imagine the impact on Bitcoin prices if the Chinese or British central bank allowed people to walk in the door and exchange their cyptocurrency directly for cash?  No trading costs?  Think about how easy it would be to pop this bubble.  What if Bank of America were to offer one instead of an unknown, small, private company?  What if they allowed direct deposits and withdrawals?  What if they paid the mining costs to their own computers?

You are looking at the modern version of the South Sea Bubble or the Tulip Bubble.  When people are learning and making money, they do funny things.


What defines a data generating process Let’s say we have a certain DGP $y=c+ax+bz+ error$. I take this to mean that conditional on the values of $x$ and $z$ in a certain instance (and no additional information )the expected value of $y$ can be inferred by plugging the values into the above equation. Now let’s say $x$ and $z$ are correlated. A different DGP may now be $y=d+mx+error$ where m may be higher(or lower) than $a$ due to the correlation of $x$ and $z$. Now wouldn’t $y=d+mx+error$ also be a valid DGP given that the expected value of $y$ conditional on $x$ (and no other information) is given correctly?

There seem to be (at least) two ways of interpreting the concept of a 'data generating process':

The data generating process is a correct description of the causal process
that generates the values of the dependent variable $Y$.
The data generating process specifies the expected value of the dependent variable $Y$ given the values taken the independent variables.

Now the answer to your question seems to depend on which interpretation we take:

If we follow interpretation 1, then these cannot be both data generating processes: either variable $Z$ causally determines $Y$ or it does not.
If we follow interpretation 2, then these can both be valid data generating processes. As you point out, there is no reason to suppose that $\mathbb{E}[Y|X = x]$ is the same as $\mathbb{E}[Y|X = x, Z = z]$.


Help understanding expression for continuous discounting In footnote 3 of their paper "Patent Breadth, Patent Life, and the Pace of Technological Progress", O'Donoghue Scotchmer and Thisse take a discount rate of $r$ and write

  If the flow of profit $\Delta$ lasts for length $t$, the discounted profit is $\Delta(1 − e^{−rt})/r$.

Can someone explain where the expression $\Delta(1 − e^{−rt})/r$ comes from?

Whilst I am familiar with continuous time discounting, I have never seen it formulated in this way before. I would usually expect the expression for discounted profit to be $\Delta e^{-rt}$.

From time $0$ to time $t$ the profit flow is constant $\Delta$. The discounted value of the profit flow of any instance $s$ is $\Delta \cdot e^{-r s}$. To get the total discounted profit we will need the integral of this from $0$ to $t$:
$$
\int_0^t \Delta \cdot e^{-r s} \ ds = \left. \frac{\Delta \cdot e^{-r s}}{-r} \right]_0^t = \frac{\Delta \cdot e^{-r t}}{-r} - \frac{\Delta \cdot e^{-r \cdot 0}}{-r}
$$
And as $e^{-r \cdot 0} = e^0 = 1$, this is
$$
- \frac{\Delta \cdot e^{-r t}}{r} + \frac{\Delta \cdot 1}{r} = \Delta \cdot \frac{1 -e^{-r t}}{r}.
$$