Algorithm to find Bayesian Nash Equilibria I am working on a Bayesian game with a finite number of players and discrete types, but the complexity of the equations is not allowing me to find the BNEs by hand.

I read a paper describing algorithms to find approximate BNE in such games but could not understand how to implement it using code.

It would be a great help if someone could inform me about any program for the purpose, or help me with code if possible. Thank you!

A brute-force algorithm might not be the right way to go. Sometimes it is not even feasible for finding Nash equilibria with perfect information. This is because even if players and types are finite, BNE's are a profile of (possibly mixed) strategies that maximize the expected payoff. If the game is sequential, this expectation may depend on the own strategies and the strategies of other players. So the space over which you are looking for best responses is quite large. Moreover, the equilibrium is a fixed point for which, in general, we don't know a lot. For example:

Do you know if the equilibrium exists? is it unique? can you define a contraction operator to update players' strategies that will take you to the equilibrium?

Coding will only work if equilibrium exists, and it will work nicely if your game defines a contraction. In contrast, if it is not unique, you will have to be more careful about the algorithm you use to find/approximate a fixed point.

A more useful approach would be to make assumptions (informed guesses) on how the equilibrium will look like and then verify that such an equilibrium exists. Some common assumptions are: "Symmetry": similar players playing similar strategies in equilibrium, "naive strategies": the equilibrium strategies are relatively simple (for example maximizing instantaneous payoff even though the game is dynamic), etc.

This is no simple task, but often you learn more this way. Keep in mind that often you have a multiplicity of equilibria and BNE must be refined to perfect BNE or sequential BNE or other refinements depending on the application.


Why are population projections so inaccurate? UN in 2015: India's population will surpass that of China in 2022.

Source: https://www.telegraph.co.uk/news/worldnews/asia/india/11770757/Mapped-India-predicted-to-become-worlds-most-populous-country-by-2022.html

UN in 2017: India's population will surpass that of China in 2024.

Source: https://timesofindia.indiatimes.com/india/indias-population-to-surpass-that-of-chinas-around-2024-un/articleshow/59257045.cms

UN in 2019: India's population will surpass that of China in 2027.

Source: https://www.indiatoday.in/india/story/india-population-china-united-nations-report-world-1550962-2019-06-18

No one expects population projections to be 100% accurate but I didn't expect them to be this inaccurate either. What are the possible reasons for the UN getting this wrong so many times and by a margin of several years?

This is because most of these projections are based on extrapolation (in fact almost all forecasting is based on extrapolation) which is inherently extremely inaccurate.

Consider this simple example:

Let’s say that we know that person who gets breast feeding for 3 months will have height 150cm person with 4months 160cm and 5months 170cm. Now based on this it is very easy to estimate that the relationship in this small sample would be:

$$H=120+10M$$

Where $M$ is months of breastfeeding and $H$ height in centimeters. Now based on this relationship we could let’s say expect that someone with 3,5 months of Brest feeding will have 155cm and that would be quite accurate. But see what happens if we start to extrapolate that is to plug there numbers further and further out of our sample.

Let’s start with 6 months that would give us height 180 - reasonable. Let’s try 8 months it would give us 200 still reasonable but let’s try 20 months it would give us height 320 which for human might not even be possible.

The takeaway is that the relationships can change. Between 0-8 months the relationship can be nice and linear but at some point the relationship flattens so extrapolation too far outside the sample will lead to wrong prediction.

The same hold for population growth. If you predict population growth 12 months in advance then that can be easy as the relationship should not change that quickly. However, 10 years ahead it is very likely that the relationship that was estimated based on past birth rates simply changes. This could be due to the fact that the previous estimations were done from past observations at smaller total population (since birth rates can be different at different population levels). Or also because preferences of people changed in unpredictable manner. Or also because many of these projections can use some auxiliary forecasts of for example GDP growth that have their own margins of error.

Hence, it’s not really that surprising the projections were wrong. In fact I could even say given how difficult forecasting and extrapolation is its surprising they are not even more off then they actually are.

Also to really make sure the forecasts were wrong you also have to go to those reports and check their margin of error if one of the sources forecasts that birth rate will be 4% with margin of error of 3% then you can’t say real birth rate 7% was off as it’s covered in margin of error. Statistics is in end only exercise in probability no estimate is certain it’s always just a distribution.


Sources of free European national income and output data? What are good free sources of European National income and output data?

By this I mean, amongst others:
GDP and the variations of this such as; GNP, GNI, NNI and similar.

Preferable in english and with formats that are easy to work with, such as .xls, .csv, .sdv.

The annual macro-economic database of the European Commission (AMECO) provides the data you need.

The data is available for free, in formats that are easy to work with.


Why real wage equals marginal product of labor when return to scale is constant? I can understand that real wage will equal MPL(marginal product of labor) when MPL is diminishing, because firms will employ more labor until MPL falls to real wage.

While, if MPL is constant, implied by constant return to scale, MPL will be predetermined as well as real wage, which won't be affected by firms' behaviors. How can we affirm that MPL equals real wage when they are irrelevant? Not to mention the conclusion of zero economic profit.

Consider that the following production function $Y=F(K,L)$ excibits constant returns to scale ie $F(x K, x L)=x F(K,L)$, for any arbitrary scalar $x$. This means in plain English that eg for $x=2$, doubling the inputs will produce double the output. The intuition behind constant returns to scale is that inputs and outputs are directly proportionate.

In technical terms, an $F$ like that, is called linearly homogeneous. Such functions display the following characteristic, by virtue of their definition: $Y=K\frac{\partial F}{\partial K}+L\frac{\partial F}{\partial L}$. The total value of F can be decomposed into a sum of products; each product is made up of the quantity of the relevant factor and its corresponding marginal product.

Now consider how a firm that is using a constant returns to scale technology and is also a pricetaker in product and labor markets will solve its profit maximization problem; standard treatment proposes that it will find it profitable to employ each production factor up to the point where the value marginal product equals the factor's price or $P_Y MP_X = P_X$, where $X=K,L$.

Therefore, under constant returns to scale and price taking behaviour, linear homogeneity will ensure that (the value) of (optimaly produced) output is exactly offset by payments to production factors hence we are left with zero economic profits.


Identical aggregation Assume the following: all firms are identical, i.e. at each time period $t$,
$\forall i$, $j: F_{t}^j = F_{t}^i = F_t$ and the technology is CRS. All consumers have the same endowment of capital $\forall i$, $j : k_0^i =k_0^j = k_0$. All consumers have the same time endowment in each period t, i.e. $\forall i$, $j : \bar{n}_t^i = \bar{n}_t^j = n$ . All consumers have the same preferences, i.e. $\forall i$, $j : u^i = u^j = u$ with $u$ strictly concave.
The question asks to state clearly and prove a theorem which says that the CE of this economy is the same as one with one firm and one consumer.
Now I was thinking that based on these assumptions: If all firms are identical within and across sectors, and the technology are CRS, all HH have the same $k_0^i$ and $U^i$ , and $U^i$ is strictly concave then, CE of the original economy is the same as one with one firm and one household. By using the First Welfare Theorem we can show that this CE is Pareto Optimal.

Let $x_i(p, w_i)$ be consumer $i$'s (Marshallian) demand and $y_j(p)$ be firm $j$'s profit-maximizing supply at price $p$.
A competitive equilibrium is a price $p$ such that
$$
\sum_{i=1}^I x_i(p, w_i(p, e_i)) = \sum_{j=1}^J y_j(p).
$$

By strict concavity of $u_i$'s, consumer demands are functions, rather than correspondences. Assume also that $y_j(p)$ are functions.
There can be multiple goods---e.g. consumption good/time(labor)/etc.
Agent's wealth $w_i$ may depend on price $p$ and endowment $e_i$---e.g. in an Edgeworth box where demands are Slutsky demands at the endowments---or wealth transfer $w_i$ can be specified as part of equilibrium, subject to
$$
\sum_i w_i = p^T (\sum_j y_j(p) + \sum_i e_i),
$$
i.e. aggregate wealth equals total value of goods.

Aggregating Consumers
Under the assumption that $u_i$'s are strictly concave (and differentiable, say), one can define a representative consumer via a linear social welfare function:
$$
u_{rep}(x) = \max_{\sum_{i} x_i \leq x}\sum_i \frac{1}{I} u_i(x_i).
$$
Then $u_{rep}$ is also strictly concave. Let $u_{rep, l}$ denotes marginal utility with respect to good $l$, then by the Envelope and Lagrange Theorems,
$$
\frac{u_{rep, l}}{u_{rep, k}} = \frac{u_{i, l}}{u_{i, k}}, \;\; \mbox{for all $i$}.
$$
At a competitive equilibrium price $p$, the MRS of $u_{rep}$ at the aggregate
demand $\sum_i x_i(p)$ is the ratio of prices:
$$
\frac{u_{rep, l} (\sum_i x_i(p),w_i)}{u_{rep, k}(\sum_i x_i(p), w_i)} =  \frac{p_l}{p_k}. \quad(*)
$$
By concavity of $u_{rep}$, the FOC $(*)$ implies that the aggregate demand at $p$ is the optimal bundle for the representative consumer $u_{rep}$ at $p$:
$$
x_{rep}(p, \sum_i w_i) = \sum_i x_i(p, w_i).
$$

As you already started to say in the question, this is a general construction of a (local) representative agent under concavity assumption. By the First Welfare Theorem, CE is Pareto. Under concavity of $u_i$'s, Pareto allocations must arise from a linear SWF, which implies existence of a representative consumer.
In this specific instance, consumers receive equal social weights $\alpha_i = \frac{1}{I}$ because equilibrium wealth is equal across agents. In general, $\alpha_i = \frac{1}{\lambda_i}$ where $\lambda_i$ is consumer $i$'s Lagrange multipler. In particular, $\alpha_i$ would be increasing in agent $i$'s share of aggregate wealth.
If $u_i = u$ is homothetic, with possibly different levels of wealth across agents, one can simply take $u_{rep} = u$ trivially. (Concavity assumption not needed.)
Gorman aggregation, alluded to in the comments, is a slightly different context, I believe. Gorman aggregation says that if all wealth expansion curves are parallel at all wealth distributions, then aggregate demand is a function of aggregate wealth and one has a global representative agent. The notion of Gorman aggregation is independent of equilibrium or Pareto efficiency. Here in your question, the local representative agent depends on the initial CE allocation---e.g. different endowments distributions would lead to different social weights.

Aggregating Firms
As pointed out in the comments, to aggregate firms one just uses the CRS assumption and take $F_{rep} = F$. For a CRS firm, doubling the input means output also doubles, with the same marginal products. In equilibrium, the firm still makes zero profit. For any one of the $J$ firms, aggregate production $\sum_j y_j(p)$ would also be optimal at the same equilibrium price $p$.
At the given equilibrium price $p$, $p = \nabla F(y_j(p))$, the gradient vector of marginal products of firm $j$ for all $j$. By the CRS/homogeneous-of-degree-one property,
$$
\nabla F_{rep}(\sum_j y_j(p)) = \nabla F(y_1(p)) = p,
$$
which tells you $y_{rep}(p) = \sum_j y_j(p)$.
Putting it together, given CE with allocation
$\{(x_i(p))_i, (y_j(p))_j \}$ and price $p$,
the allocation $\{\sum_i x_i(p), \sum_j y_j(p) \}$ and price $p$
is a CE for the economy with one agent $u_{rep}$ and one firm $F_{rep}$.


Returns to Scale Microeconomics Are there any production function $f(x_1,\ldots,x_n)$ that is having decreasing returns to scale, given that the marginal product in every input $i$ in the function $f$ is constant?

Seems like the only function $f$ that fits your description
$$
\forall i: \frac{\partial f(\mathbf{x})}{\partial x_i} = c_i
$$
is
$$
f(\mathbf{x}) = A + \sum x_i c_i.
$$
(Frequently $f(\mathbf{0}) = 0$ is assumed. The assumption is referred to as "no free lunch".)
Then you can apply the definition of returns to scale.


Why are second price auctions preferred if they don't maximize expected revenue? The reasoning usually given for why you would use a second price auction (SPA) as opposed to a first price auction (FPA) is that FPA encourage underbidding while SPA encourage truthful bidding. That is, bidding your true value is a weakly dominant strategy in SPA, whereas in FPA, bidding below your true value is the dominant strategy. See this question.

My question is: why does it matter to the seller whether people bid truthfully or not? Initially, I thought that since SPA induce truthful bidding, they also maximize expected revenue for the seller, which is why a seller would use SPA.  But, according to the revenue equivalence theorem, FPA and SPA generate the same expected revenue. So, shouldn't it not matter to the seller what auction they choose? Why would a seller prefer SPA -- which are generally harder to explain -- if it doesn't generate higher expected revenue?

I can think of three possible explanations:

There's a mismatch between theory and the real world. Maybe in theory SPA and FPA should generate the same revenue, but in practice they don't. If so, is there any empirical research that shows this?
The seller's goal is to collect information rather than to maximize revenue. Maybe the seller has a product and they don't know how much to sell it for. In that case, an SPA could help them generate an accurate demand curve.
To benefit the buyer. If there's no cost to the seller in terms of revenue, but a benefit to the buyer, a seller might want to use SPA. But this leads to the question: why does the seller care about helping the buyer? Maybe in order to encourage more buyers to participate in the auction? And, possibly encouraging more buyers to enter the auction would raise the expected revenue from the auction, if those new buyers were higher bidders.

Since SPA are so common in online advertising (google adwords) and eBay, they might be the most widely used auction there is today. So, I'm wondering why sellers prefer them to FPA. Is any of these explanations on the right track?

I don't think sellers would prefer SPA over FPA. In fact, the SPA is riskier than the FPA, if we look at it from a seller's perspective. The reason is because the distribution of prices in case of the SPA is a mean preserving spread of the distribution of prices in FPA(you can refer to Vijay Krishna's Auction Theory for the proof).

However, the VCG mechanism finds a lot of applications in real life scenarios(like in case of network routing algorithms). It just so happens that the VCG mechanism can turn out to be the second price auction, given that certain conditions are met.

The Generalized SPA is another such example, that draws its basis from the standard SPA. Please see https://en.wikipedia.org/wiki/Generalized_second-price_auction .

As far as the English Auction is considered, it is equivalent to the SPA only in the case of independent bidders. If the values realized by the bidders depend upon the the values realized by others(meaning the valuations are now interdependent), the English Auction no longer remains equivalent to the SPA(interdependence is something that on can expect to be more prevalent in real life cases).

Another thing, the RET states that the 'expected revenue' is same for standard auctions with symmetric bidders. The payment received by the seller is just the highest bid. Thus, receiving a higher payment in either auction(FPA or SPA) depends on the values realized by the bidders(and the bidding strategy).


Interest Rate and Foreign / Domestic Investment I read that increased interest rate attracts foreign investment but discourages domestic investment.

Why does interest rate have different effects on foreign and domestic investments?

Great question! I know it gets little confusing.

Let's take an example of US and India. I am in the US. India's interest rate (return on investment) is 10%. The US has 8%. Then, I will invest in India -- more ROI. Hence, high-interest rate means more foreign investment.

However, my brother in India wanted to build a building there. Since the interest rate is high, taking loans is more expensive, and hence he will decide not to invest -- not to make that building. So, because of high-interest rate, domestic investment decreases.


How does an increase in domestic interest rate increase capital inflow? What I have typed in the title is all I want to know.

There is no domestic interest rate; there is a world interest rate.

What you presumably mean to ask is:  How is that a change in the world interest rate, caused by a change in domestic supply or demand, increases capital inflow?

Answer:  Because the foreign supply and demand for output are being held constant, an increase in the interest rate leads foreigners to produce more and consume less.  The excess has to go somewhere, i.e. it has to be lent to a non-foreigner, i.e. to a domestic citizen.


what does historical volatility explain? Let's assume we have close prices of one stock of period one year. As far as I understand historical volatility is standard deviation of log return, however I do not understand what this actually mean.

Let's assume last traded price was $120 and HV is 0.29.

What does this really mean? That we can assume next price will be within the range of 29,58 (which is 29 percent of 120) above or bellow $120?

No. Volatility by itself is a meaningless number.

Volatility becomes relevant when used in a context, such as when comparing between assets, or to identify how much the stability of a financial instrument has changed over time. In these two examples, dividing volatility by the mean rate of return gives a more useful, dimensionless number known as coefficient of variation.

Historical volatility may also serve as input parameter for simulation of an asset price, provided that the analyst already has in mind a probabilistic model. The example you outline is akin to estimating a confidence interval. Your example reflects an assumption that the asset's behavior is modeled with a probability density function which is symmetrical with respect to the latest price.

There are other uses of historical volatility, but the ones above are among the most typical applications of that concept.


Very elastic supply + very inelastic demand Suppose we have a very elastic supply curve and a very inelastic demand curve. Further suppose there is a decrease in input prices which shifts the supply curve outward. By taking an extreme representation (vertical demand curve and horizontal supply curve), I can see that it will be mainly price that is affected: the equilibrium price decreases while equilibrium quantity hardly changes.

How can I show this more intuitively or mathematically?

Edit: Just thought about this. I don't think the elasticity of the supply curve matters. Only the elasticity of the curve that isn't shifting does. Is this the answer?

Consider the inverse functions

$$Q^d = A-bP$$

$$Q^s = C + dP$$

to have the situation described by the OP, we will have that $b$ is "very small" while $d$ is "very large".

Equilibrium price and quantity are

$$P^* = \frac {A-C}{d+b} = \frac {A}{d+b}-\frac {C}{d+b}$$

$$Q^* = A- b\frac {A-C}{d+b} = A- b\frac {A}{d+b}+b\frac {C}{d+b}$$

The change described by the OP amounts to $\Delta C > 0$. Then

$$\Delta P^*|_{\Delta C} = -\frac {1}{d+b}\Delta C $$

while

$$\Delta Q^*|_{\Delta C} = \frac {b}{d+b}\Delta C$$

Comparing the two in absolute terms, we get

$$\frac {|\Delta P^*|}{\Delta Q^*} = \frac 1 b$$

... from which we conclude:

1) To have equilibrium price be relatively more affected than equilibrium quantity when the supply curve shifts outwards, we need the marginal effect of price on quantity demanded ($b$) to be smaller than unity

2) The above does not depend on how elastic or inelastic is the supply curve.


Can the stock market show indefinite exponential growth? In a comments on a question on money.SE, the following dialog took place:

  Eventually there will not be enough matter to represent all the money, so we know for certain that the answer is "No" for a long enough term.

--yters

  What do you mean by "represent?" Do you mean that we won't be able to build computer chips that can store a digital representation of someone's stock income? Do you mean that we will no longer be able to cash out our stock portfolio into a fixed commodity like gold, at a fixed dollar price? The former seems wrong to me, and the latter irrelevant.

-- BenCrowell

  @BenCrowell: the stock market is not abstract, it depends on investors expectations on the real economy. Its obvious that the economy cannot grow forever, as the planet (and its resources) are finite.

-- Martin Argerami

I'm not convinced by the argument that Martin Argerami claims is obvious. It seems to me to rest on a false assumption that value is measured by resources, e.g., that a dollar's "true" value is measured by how many milligrams of gold it can buy. But I'm not an economist. Would anyone like to take a shot at explaining who is right?

May I rephrase your question into the broader question "Can economic growth continue indefinitely?"

(In response to objections that eventually the sun will burn out or the universe will suffer heat death, I take indefinite to mean "lasting for an unknown or unstated length of time" (OED). So I am thinking of 100s, 1000s, or even 10000s of years ahead. But I am not thinking of billions of years ahead or the "infinite future".)

Non-economists commonly believe the answer to be "no", giving some reason along the lines of "resources are finite!"

But the economist's answer to this is "Yes, of course economic growth can continue indefinitely." And so to answer also your narrower question, "Yes, of course the stock market can show indefinite exponential growth." (By "can", I mean that this is at least conceivable. Whether it will is a different matter altogether. After all the world might end tomorrow in a nuclear apocalypse.)

I think we can distinguish between two common fallacies at work here.

Fallacy #1. "Economic growth is about making ever more "stuff", digging ever more gold and other natural resources out of the ground, burning ever more energy, etc." (This caricature is perhaps why many non-economists and especially environmentalists are averse to economists and the idea of economic growth.) The fallacy typically continues, "Resources/the universe is finite. Therefore economic growth must also be finite."

But this is wrong. Economic growth is about improving human well-being, broadly conceived.

It is true that for a long time (the past few centuries), improvements in human well-being were largely through improvements in material well-being and highly-correlated with making ever more stuff and burning ever more energy. After all, it was not two centuries ago that the vast majority of mankind lived at bare subsistence level. (Indeed, even today, many people still do.)

But going forward, it is perfectly conceivable that we make ever less "stuff", dig ever less "stuff" out of the ground, and burn ever less energy, and yet still become ever more well-off. This is actually already happening today in the rich countries (see e.g. falling energy use, briefly analyzed below).

Since the 1930s and 1940s, we've measured economic growth mostly by GDP growth. But economists have always recognized that GDP is a very flawed measure of well-being. Economists are working on alternatives that better capture the notion of improvements in human well-being or equivalently, economic welfare. I do not expect that in 100 years, the current concept of GDP without fundamental modifications will still be used to as the primary measure of economic well-being.

(Footnote: Perhaps in the future, we will also include non-human well-being in our conception of economic growth. But for now, we still restrict attention mostly to human well-being.)

Fallacy #2. "Bad things (like the consumption of food or resources) will grow rapidly or even exponentially. In contrast, offsetting good things (like technology) can at best grow arithmetically. Therefore, there are necessarily limits to growth."

This fallacy is not new. Here's an example of doom-and-gloom predictions from each of the past three centuries, all of which proved to be wrong.

Malthus (1798): An Essay on the Principle of Population.

2010 commentary:

  Malthus began with two “fixed laws of our nature.” First, men and
  women cannot exist without food. Second, the “passion between the
  sexes” drives them to reproduce.

  He explained that, if unchecked, people breed “geometrically” (1, 2,
  4, 8, 16, etc.). But, he continued, the production of food can only
  increase “arithmetically” (1, 2, 3, 4, 5, etc.). “The natural
  inequality of the two powers of population and of [food] production in
  the earth,” he declared, “form the great difficulty that to me appears
  insurmountable [impossible to overcome].”

  Malthus concluded: “I see no way by which man can escape from the
  weight of this law.” In other words, if people keep reproducing in an
  uncontrolled geometric manner, they will eventually be unable to
  produce enough food for themselves. The future, Malthus argued,
  pointed not to endless improvement for humanity, but to famine and
  starvation.

The Great Horse Manure Crisis of 1894:

  Writing in the Times of London in 1894, one writer estimated that in 50 years every street in London would be buried under nine feet of manure. Moreover, all these horses had to be stabled, which used up ever-larger areas of increasingly valuable land. And as the number of horses grew, ever-more land had to be devoted to producing hay to feed them (rather than producing food for people), and this had to be brought into cities and distributed—by horse-drawn vehicles. It seemed that urban civilization was doomed.

In 1972, exactly such a book title was published: The Limits to Growth:

  Our attempts to use even the most optimistic estimates of the benefits of technology in the model did not prevent the ultimate decline of population and industry, and in fact did not in any case postpone the collapse beyond the year 2100 (p. 145.).

This was a highly-influential best-seller that has sold over 16M copies in over 30 languages.

Take their example of gold. On p. 56, they calculate that if gold use continued growing exponentially AND there was 5 times as much gold available as there were known gold reserves (they thought this was a very optimistic assumption), gold would be depleted in 29 years, or in 2001.

Surprisingly, 2001 came and went and gold continued to be mined. Indeed, more than ever. Gold mining graph (source):

Roughly every 5 years since 1972, The Limits to Growth folks (AKA the Club of Rome) have released a new update to their 1972 book, each time explaining why they had been correct all along (of course) and sometimes pushing back their predictions about when the eventual collapse will set in. In their 30-Year Update, they make no mention whatsoever of gold.

The following is the response by two critics to The Limits to Growth, also quoted by Robert Solow in a Newsweek article:

  The authors load their case by letting some things grow exponentially
  and others not. Population, capital and pollution grow exponentially
  in all models, but technologies for expanding resources and
  controlling pollution are permitted to grow, if at all, only in
  discrete increments.

(Footnote: Doomsday-mongering was especially fashionable in the West around the 1970s. See also the famous Simon-Ehrlich wager at around the same time.

Predictions at the polar extremes capture the public's attention. Ray Kurzweil comes to mind as someone who makes similar predictions, but at the polar opposite.

In contrast, the median economist is cautiously optimistic, believing merely that slow but steady, sustained growth is possible. No doomsday, no stagnation, but no impending Singularity either. Not exactly a position that sells many books.)

In 2012, a physics professor wrote a somewhat-influential blogpost: Exponential Economist Meets Finite Physicist, exhibiting both of the above fallacies. That someone as intelligent as a physics professor could commit both fallacies shows that economists must do a far better job at educating the public.

There is plenty that is wrong in that blogpost and perhaps I will do a sentence-by-sentence dissection elsewhere, but this is probably not the proper avenue. Here I'll merely point out one obvious factual error that's of particular relevance. He claims as fact that

  energy growth has far outstripped population growth, so that
  per-capita energy use has surged dramatically over time—our energy
  lives today are far richer than those of our great-great-grandparents
  a century ago [economist nods]. So even if population stabilizes, we
  are accustomed to per-capita energy growth: total energy would have to
  continue growing to maintain such a trend [another nod].

As Tim Harford points out, this is FALSE. In recent decades, energy growth per person in many countries has actually been falling, even as GDP per capita has risen. Graph (data from World Bank, June 1st 2017 update):

In every rich country, per-capita energy use peaked years ago and has been falling ever since. In fact, in some countries, it peaked DECADES ago (peaked in 1978 in the US, in 1979 in Germany, and in 1973 in the UK).

(One would've hoped that a physics professor backed up his factual claims with something more than a fictitious and bumbling economist who repeatedly nods.)

See also falling energy intensity (energy use per unit of GDP) (source):

The highest per-capita energy use ever attained was the US in 1978. My prediction is that global average human well-being will keep improving, but global per-capita energy use will never hit the US 1978 peak (at least not until we start populating other planets and stars).


Phillips curve and flexible prices I am working in a New Keynesian context so that the Phillips curve is usually specified as follows
\begin{gather}
\pi_t=\beta E_t\pi_{t+1}+\kappa x_t
\end{gather}
where $\beta$ is the discount factor, $\kappa$ is the slope of the curve depending negatively on the degree of price stickiness in the economy and $x_t=y_t-y^N_t$, with $y^N_t$ is the natural (potential) level of output

What is driving me crazy is if this curve, specified as above, still make sense when we assume prices are fully flexible.

I would say no, because in a flexible price context, the output gap would be zero and the firms would optimize in a static fashion (no need of taking into account expectations of future inflation). But, I have no idea about how to "transform" the model in this direction.

The New Keynesian Philips Curve (NKPC) may be derived using price settings frictions introduced by Guillermo Calvo. The NKPC can under such conditions be written as you write it, i.e. $$\pi_t=\beta E_t\pi_{t+1}+\kappa x_t,$$ and where $\kappa=0$ if no firm change their prices, and $\kappa=\infty$ if all firms change their prices.  (Technical note: Here I allow myself to work with the extended real line, viewing $\pm\infty$ as entities and not concepts.)

The background given above, then, does not seem to say anything about the output gap $x_t$. If $\kappa=0$, then inflation follow its trend, i.e. $$\pi_t=\beta E_t\pi_{t+1},$$ and if $\kappa=\infty$ then $\pi_t=\infty$ (given that the expected inflation is bounded below).

This, at least, answer your first question: If fully flexible price setting is interpreted as the case when all firms change their prices, then $\pi_t=\infty$, which is understandable, but not realistic. What we may say, though, is the more firms there are who change their prices, the closer to hyperinflation we are.

To me it seems that we can not from the NKPC alone say whether the output gap will be zero if $\kappa=\infty$. Often we have to supplement the NKPC with the DIS $$x_t=E_tx_{t+1}-\frac{1}{\sigma}(r_t-r^n_t),$$ where $r_t$ is the real interest rate and $r^n_t$ is its natural level, and add some additional information on whether we have random shocks in e.g. the output gap.


Bertrand-equilibrium with discrete price set Consider a market for a homogenous product with three producers, firms A, B and
C. The firms have constant marginal costs which are equal to $c = 20$ for each firm. Consumers always buy from the firrm with the lowest price. If the lowest price is set by two (three) firms, half (one third) of the consumers go to each of those firms.

Consumer demand is given by $D(p) = 50 - p$. Each firm can only choose prices from the set $\{10, 20, 30, 40, 50, 60\}$.

Determine all Bertrand-Nash equilibria.

Attempt: First, we observe that the monopoly price is 35 (this is easy to determine). Also, profit is zero when the price of any firm is 20, and profit is negative for $p = 10$. I thought that this means that any price-set of the form $\{20, p_B, p_C\}$ would do (and similarly $\{p_A, 20, p_C\}$ and $\{p_A, p_B, 20\}$), as long as all other prices are at least 20. This is not the case, however, since $\{20, 30, 30\}$ will cause all customers to go to firm $A$, resulting in 0 profits for everyone, but if firm $A$ increases price to 30, all firms will make a positive profit, hence $\{20, 30, 30\}$ is not Pareto-efficient. Hence, the only Pareto-efficient price-sets are those where two firms have price 20, and the remaining firm has any price that is 20 or higher.

My mistake was that I missed the $\{30, 30, 30\}$ equilibrium. But how could I have seen this? I always thought that if all companies have constant and identical marginal costs (in this case 20), the only Nash-equilibrium is the one in which all companies have their price equal to the marginal costs. Apparently, this is not the case here.

What am I missing? What is the general approach to problems of this type? Any help is greatly appreciated.

The key is the definition of the Nash equilibrium solution concept that you are applying to solve your game. In non-formal terms, a Nash equilibrium is a set of strategies such that no player can increase his or her payoff by deviating to some alternative strategy.

Let's consider $\{30,30,30\}$. In this 'putative' equilibrium, firm A's profit is

$$\frac{D(p)}{3}(p-c)=\frac{20}{3}(30-20)=\frac{200}{3}>0.$$

Could A do better with a lower price? A price of $p=10$ is less than his cost, so this obviously can't be better. Likewise, a price of $p=20$ yields profit

$$D(20)(p-c)=0,$$

which is less than the profit (200/3) in the putative equilibrium. So, again, a deviation to $p_A=20$ is not profitable.

Can A do better by deviating to $p_A>30$? The answer is clearly no because any $p_A>p_B,p_c=30$ implies that A attracts no demand and therefore earns zero profit.

We thus observe that A cannot find a profitable way to deviate from the putative equilibrium $\{30,30,30\}$, so this is indeed a Nash equilibrium.

To address your final question: there are two general approaches to problems of this type.

For each player in the game, compute their best response (i.e. profit-maximising strategy) to each possible combination of strategies by the other players. Then look for all situations in which every player is playing a best response; that is a Nash equilibrium.
Guess a set of strategies that you think might be an equilibrium. Then verify that is is indeed an equilibrium by checking that no player could do better by changing their strategy.


Effect on monopoly price Suppose a monopolist adopts a technology that allows him to produce his product at lower cost. What is the likely effect on the monopoly price ?

$P=\frac{\epsilon}{\epsilon +1} MC$

This is the markup rule for price-setting firms.

Now, it is clear that a firm with monopoly power will never set $P=MC$. However, we can assume for now that the term involving epsilon is fixed for our firm with monopoly power.

If this firm adopts technology that reduces costs, what do you think will happen to the marginal cost curve (in what direction does the marginal cost term move in the above equation)?

Given the expected change in marginal cost, in what direction should price change?


In auction theory, why is my own valuation a random variable? Auction theory typically (always?) begins by assuming that each bidder's valuation is a random variable. Now, it might seem reasonable (at least from a Bayesian perspective) for you to treat other people's valuations as random variables. After all, you don't know their valuations! However, what justification can there be for treating your own valuation as a random variable when deciding on how to bid? And are there any approaches which do not begin with this assumption?

Edit: Here's another way of posing the question. In the context of auction theory, people normally seem to define a strategy as a function mapping from my (random) valuation to my bid. But assuming that I know my valuation, why not simply define my strategy as my bid?

In most of the literature I have read on private value auctions you do actually know your own valuation in the auction, it is your private information. It has a distribution from the point of view of others, who can only guess at your valuation.

Another interpretation would be that your valuation is actually random before getting detailed information on the object you are bidding on. How much would you pay for this bottle of wine that I have here on my shelf? Oh, it depends on the wine? Then without knowing the exact type of wine and assuming it has some random distribution your valuation is also a random variable. Once you learn the exact type of the wine you learn your own 'type', which is modeled as getting a private signal about your valuation.

In case of noisy observation your valuation can actually be random. E.g. I tell you the type of wine but you have never had it before. Or in case of gas companies, they have an inexact estimate about the yield of a gas field. Their 'real' valuation depends on the 'real' yield, without knowing that they can only bid based on some expected values.


What does it mean, 'Higher interest rates attract FIIs and FPIs'? What would interest rates have anything to do with shares? When we say a higher interest rate attracts FII/FPI, does it not mean it is investing in shares of a company? For example, how does it help a foreign company, if it is investing in the shares of an Indian company because rates are high in India? It isn't some 'Fixed Deposit' or Mutual Fund, returns out of investment in stocks would be purely based on fluctuations of share price, nothing to do with interest rates; so how would a high interest rate deter the returns out of investment in shares?

Foreign Institutional Investors (FII) and Foreign Portfolio Investors (FPI) can and do invest in government securities as well. There may be restrictions of course leading to imperfect capital mobility. For example in India, FIIs/FPIs cannot hold more than 6% of outstanding stocks of securities.
As interest rate increases (usually because of an external shock - such as a policy shock by the Central Bank), there is (increased) room for arbitrage. This attracts investors looking to make quick money.
You are right that interests may not impact share prices, but there is some relation of course. This comes, among other things, from risk management. Portfolio managers balance risk by dividing investment in risk free government securities and equity. When return on g-secs go up, this balance goes into disequilibrium. New investors can invest more in equity as some additional risk is balanced by increased returns in g-secs (you can think of the two assets as imperfect substitutes). So this increases prospects for more investment in equity and so it makes sense to quickly invest in them as well for short term gains.
All this logic will, however, go into disarray as we bring in expectations of future interest rates. This is why FIIs/FPIs are also referred to as hot capital flows. These investments are short term and the flow can quickly reverse with slight changes in market sentiments and expectations.


A doubt on the Regression of Mankiw, Romer, Weil 1992 paper I'm trying to replicate the regression of the MRW 1992 paper.
(Here's the data, if you're interested)

In the same page where the data set is available, there's this handout explaining how to replicate the results. In page 2 of this handout, we can see two simple stata commands:

li_y=ln(i_y/100)
 g lpop=ln(0.05+popgrowth/100)

My question is why the variables i_y (this is Investment over GDP), and popgrowth(this is an averaged population growth rate between 1960-1985) are divided by 100?

Nowhere in the MRW 1992 paper, do I read something telling me that it's necessary to divide it by 100, or do I?

Any help would be appreciated

I had a look at the data, and it is like @denesp says in his comment: e.g. a $2.60\%=0.0261$ population growth rate is written as $2.60$, a $24\%=0.24$ investment-to-output ratio is written like $24.0$, etc.
So they must be divided by $100$.


Can be the duality theorem applied to not locally non-satiated utility functions? I have the following not locally non-satiated utility function:

$$U(x,y)=-(x-1)^2-(y-2)^2$$

where $U(x,y): \, \!R^n_+ \rightarrow \!R $

The 3D plot of this function is an infinite paraboloid; therefore, $U(x,y)$ can be considered as a not locally non-satiated utility function.

After I've found the Marshallian demand and the indirect utility functions, I'd like to determine the Hicksian demand curve and the expenditure functions using the duality theorem. Can be the duality theorem applied to this type of not locally non-satiated utility functions?

This system doesn´t have solution, because the consumer want to maximize their utility, so there is not a possible solution because is better consume x=0 that any other bundle


What is the "gross national saving" for? I don't understand what the term Gross National Saving is for. According to the world factbook, it represents the following:

  Gross national saving is derived by deducting final consumption expenditure from Gross national disposable income, and consists of personal saving, plus business saving, plus government saving, but excludes foreign saving. The figures are presented as a percent of GDP. A negative number indicates that the economy as a whole is spending more income than it produces, thus drawing down national wealth (dissaving).

This represents the sum of savings by person, company, and government. But what is this beneficial to? Is a country that has high GNS more stable in finance? When should one look at this statistics to gauge what? In financial stability, is this a better indication than national debt as a percent of GDP, the dependency rate on government bond, or something others?

The first point is that this is a flow statistic: it is the annual excess of income over consumption, in contrast to level statistics such as gross national debt which are largely accumulations of past flows.

As what gross national saving is for: it funds investment, which affects future income and thus future consumption.  Indeed, one of the tautologies of macroeconomics is that Savings = Investment.

A low savings/GDP figure may indicate excessive consumption or insufficient  income.  It may lead to either inadequate domestic investment or the need to borrow from foreigners to fund domestic investment.

A high savings/GDP figure may indicate insufficient consumption or excessive income.  It may lead to either unproductive domestic investment or the need to lend to foreigners to recycle the funds.

There is no optimal figure for savings. Comparative figures for different countries and global trends over time are published, for example from the World Bank.


How infinite Nash equilibria are possible in a game? I was studying games when one of the players seems to be indifferent between two or more pure strategies because he gets the same payoff with each strategy. We say that there are infinite Nash equillibria in the game but I am unable to calculate it and get an intuitive idea of how is it happening.
For example in the following game
$$\begin{array}{c|a|c} & L_2 & R_2& \\ \hline L_1 & (3,1) & (0,1) \\ \hline R_1 & (0,1) & (4,1) \\ \hline \end{array}$$

Seemingly, P2 should not even bother about anything even if he is playing pure strategy or randomizing. But here if we assume that P2 plays L with probability q and P1 plays L with probability p then making them indifferent we see that we cannot calculate p but q comes out to be 4/7. How is it possible or what is the interpretation ? If I am doing it wrong then what is the correct way to determine equilibria in this case ?

Another example is

$$\begin{array}{c|a|c} & L_2 & R_2& \\ \hline L_1 & (1,1) & (0,0) \\ \hline R_1 & (0,0) & (0,0) \\ \hline \end{array}$$

How many Nash's equilibria are possible in this ?

Well the intuition is quite straightforward: as you have mentioned yourself, player 2 is indifferent between playing any action in pure strategies, or randomizing in any possible way. So, for a mixed strategy equilibrium to exist, player 2 needs to play L w/ probability 4/7. If this is the case, it is irrelevant what Player 1 player---player 2's outcome is the same. As a result, in pure strategies the Equilibria are L,L and R,R and, in Mixed strategies, q=4/7 and p can take any value between 0 and 1. Hence, there exist infinite possible Nash Equilibria (p just has to obey the fundamental laws of probability).


Difference between Opportunity cost and marginal cost I understand that the marginal cost is the cost of producing one additional unit of a good or service.

Is it correct to say that the opportunity cost is part of the marginal cost (I'm trying to figure out what is meant by this picture below)?

And secondly, is this statement correct "whatever a producer receive aboves its opportunity cost of providing the good/service is its producer surplus?" I read this online. Isn't it suggesting that the opportunity cost is the marginal benefit (because price received minus the points on the supply curve is producer surplus)?

Opportunity cost is the price of doing something in terms of something else. For example, cost of taking trip to Prague may be giving up new bike. In this broad sense marginal cost of producing one unit of q would be also it’s opportunity cost because you could use the same resources to produce something else. Opportunity cost of producing 1 widget at 5€ might be giving up possibility to produce 2 pins at 2,5€ each.

What the quote says is not that only time has opportunity cost but that you should not forget to add the opportunity cost of the persons time to the costs.

Also opportunity cost is not producer surplus. You don’t need to give up producer surplus to produce the particular good or service you are producing. You could include that in opportunity costs if you would be looking at it from a point of view of person deciding to leave the market to go to do some other business or retiring


Country specific economic recession/financial crisis data? Many financial crises are at the global level, yet some of them can be country-specific, especially the ones connected with political instability.

For example, the 1990 recession of Russia, the 1958 recession in China, and the recent Brazil currency crisis is kind of independent of the global economic situation. The Eurozone crisis also only applies to a limit number of nations. Examples also include the Iceland bankruptcy.

So my question is, how could we identify those country-specific crises? Are there any established methods/datasets? Any references or ideas or suggests or guidelines will help!

Several articles use data sets on this issue but I am not sure that all the data sets are freely available.

Valencia & Laeven (2012) use the IMF country reports to create their data set. It covers all IMF member countries since 1970.
EDIT: it is available here, as pointed out by @dismalscience.
Reinhart and Rogoff (2009) have 70 countries since roughly 1900 based on a wide set of sources.
Romer & Romer (2017) construct financial distress index at semi-annual frequency for 24 countries based on the OECD Economic Outlook. It is available since 1967. This data set is freely available and also contains a measure for the depth of the crisis.


How come debts is higher than assets? Investopedia has a definition about Debt ratio, I do not understand how come Debt ratio can be higher than 1. Because it means that equity is negative (because Total Assets=Debt+Equity).

Equity can be negative when a firm accumulates losses and liabilities exceed the number of assets. In that case debt ratio can be bigger than 1.


Why is market absorption of issued US Treasury Bonds (with the Fed purchase plan) a problem? Financial market reports suggest that there are uncertainties about the Federal Reserve's ability to absorb new US Treasury Bonds issued in larger quantities to support the US government's growing budgetary requirements (i.e. the pandemic support of the economy).
This hypothesis is bolstered by the example of 2018:

...real yields rose and stocks and corporate bonds got clobbered until
the FED reversed its tapering exercise and started buying USTs in
size.

Questions:

Why can't the Treasury and the Federal Reserve agree upon a
controlled issuance and instant procurement of UST bonds "straight
from the printing press"?
Why subject the market to the ambiguity of
being able to partake in this exercise, which is specifically aimed at funding
the budget through the Fed's resources?

Why can't the Treasury and the Federal Reserve agree upon a controlled issuance and instant procurement of UST bonds "straight from the printing press"?

Treasury bonds are not “printed” at a “printing press,” the only “printing press” is run by the U.S. Mint, where they print Federal Reserve Notes (e.g., dollar bills). Treasury Bonds/Notes/Bills are sold at auction.
Not sure of the exact statute that forces this, but the Federal Reserve does not bid at auction, they buy in the secondary market. This answers your question.
Update: a FAQ on the Fed website: link.

Why subject the market to the ambiguity ...

Because there is no legal alternative, other than changing Fed operating procedures to having them cap bond yields. (One can search for discussions of “yield curve control” for more details.)
As for financial market commentary, it is not always reliable, so statements made there need to be taken with a large grain of salt.


Do large public companies ever "quit while they're ahead"? Large public companies (e.g. S&P 500) seem to end their lives in one of two ways: either they're acquired (or taken private), or they go bankrupt.

Theoretically it seems like there should be a third option: to wind up the company and return assets to shareholders (as Michael Dell famously suggested Apple should do). A company that realises its industry is in decline and it's about to become unprofitable as a business surely ought to do this; it would give the shareholders at least some cash, rather than the nothing they'll get in bankruptcy. But I can't remember this ever happening, at least in my lifetime (alternately, maybe it's common enough to simply not be news?). A struggling company like HP or Nokia or Blackberry seems to always keep going to a buyout or the bitter end, even when "everyone" can see they're doomed.

Are large public companies ever simply wound up? If not, why?

Assume a company decides to "wind up". What would happen? Its competitors would want to get hold of its tangible and intangible assets (like customer base, patents etc). How is this different from "fighting to a buyout"? In this second scenario, the company has always available the option/threat of continuing competition (possibly harmful to the competitors), while in the "wind-up" scenario it does not -it has committed to leave the business. So "fighting to a buyout" gives the company better position in negotiations, and so chances to increase its selling price compared to the "wind up" scenario.

You could spice this with theories about management, and how "management will not let go" etc, but the above provides an interpretation that appears more widely applicable.

Compared to smaller companies, large companies have more market power and so the "threat" of continuing competition weighs more heavily with competitors.


Homework Question - Price Floor / Elasticity of Demand I'm currently taking undergrad microeconomics and came across the following question:
The current price floor in the agricultural lettuce market makes it such that price of lettuce is 25% higher than equilibrium price and 100 heads of lettuce are demanded. Assuming that the elasticity of demand for lettuce is -0.50, what would be the equilibrium price and quantity of lettuce if the government removed the current price floor?
Here's how I've tried to solve the question: https://imgur.com/gallery/blUjgcu .
The answer is

 Price = $0.75, Quantity = 112.5.

but I don't know how to solve that.
Thanks

Price elasticity of demand of $-0.5$ means that if price increases by $1\%$ demand decreases by $0.5\%$ (and vice versa in case of decrease).
Consequently, if the equilibrium quantity with floor is $100$ and the price of lettuce is $25\%$ that means that eliminating the price flow - which will offset the $25\%$ will increase the quantity demanded by:
$$0.5\cdot25\% = 12.5\%$$
$12.5\%$ increase from $100$ is $112.5$ so that will be new quantity.
Regarding the price you don't mention what the price at the price floor originally was but it should decrease by $25\%$ from its original value.


Why are there fewer high schools than elementary schools? In nearly every public school district in the U.S., one can observe the following pattern: There are fewer middle schools than elementary schools. And there are fewer high schools than middle schools. (And the count of students per school goes inversely as the count of schools.)

But why is this the case? Is there any explanation for this based on economic principles?

For example, why is the reverse not the case? Why are there not fewer elementary schools than high schools, let's say?

Two relevant economic principles are:
Economies of scale: These are a more significant issue for middle and especially high schools which have a greater need for specialist teachers, as others have pointed out, and also for specialist facilities such as science labs with supporting technicians.  Such teachers and facilities would tend to be under-utilised in small schools, resulting in higher costs of provision per child. Elementary schools, on the other hand, rely more on generalist teachers so can operate efficiently on a smaller scale.
Based on a survey of literature on scale economies in education, Andrews, Duncombe & Yinger (2002) found “some evidence” that the optimal size of elementary schools was 300-500 pupils while that of high schools was 600-900 students.  The reason for identifying an optimal size (rather than concluding that larger is always better) was that large schools can also have disadvantages, such as more bureaucracy leading to lower student and staff motivation and less parental involvement.  Note that these optimal ranges were based on studies focusing on the US: different ranges might be optimal elsewhere given different school curricula and different staff salary levels.
Travel costs: Older children are more likely to make their own way to school, while younger children are more likely to be accompanied by a parent. Hence the costs of travel to school, for a given journey, and including not only fares and/or fuel costs (if any) but also and especially the opportunity cost of a parent's time, tend to be greater for younger children.
More formally, family behaviour can usefully be considered within the framework of a household production model in which households derive utility $U$ from commodities $Z_i$ which they “produce” using inputs consisting of market goods $x_i$ and/or time periods $T_i$.  Becker (1965) writes this as (p 495):
$$U = U(Z_1,…,Z_m) ≡ U(f_1,…,f_m) ≡ U(x_1,…,x_m; T_1,…,T_m)$$
The $f_i$ are the “production” functions, although the term production is used here in a somewhat specialised sense: Becker gives the example of the commodity sleep being “produced” via input of a home, a bed and time. Households aim to maximise utility subject to constraints on both income and time (albeit there may be scope to trade off income against time by adjusting hours spent in paid work).  Within this framework a child’s education can be regarded as a commodity produced using time spent in school, doing homework and travelling to and from school, and perhaps market goods (school fees if applicable, fares or fuel costs if required for travel).  A longer journey to school will imply a greater input of time, with a consequent lesser availability of time for other commodities and therefore less overall utility.  Crucially, this effect will tend to be larger for younger children who are more likely to be accompanied by a parent, whose time should also be counted as an input.  Moreover in some cases a parent’s time on a twice-daily school trip will reduce their hours of availability for paid work, again resulting in lower overall family utility.  Hence families, seeking to maximise their utility, will have a strong incentive to try to ensure (via voting or campaigning) that public schools for younger children are small and numerous so that travel times to school are generally short, and less incentive to do so for schools for older children.


Estimating Equilibrium Price for Advertising using Simultaneous Equations Model I am attempting to build a simultaneous equations model that estimates the equilibrium price of display advertisement, but I have only seen textbook examples with Quantity being the dependent variable - this question is similar: Equilibrium Price - OLS Regression. However, I assume that quantity is also endogenous, and I think I should use two stage least squares to produce unbiased estimates. Display advertisement is bought/sold in online marketplaces, and that led me to believe this model would provide a good fit.

$P_{Dt} = \beta _{0} + \beta _{1} Q_{t} + \beta_{2} Visits + u_{t}$

$P_{St} = \alpha _{0} + \alpha _{1} Q_{t} + \alpha_{2} Print_{t} + \alpha_{3} Prod_{t} + u_{t}$

$P_{Dt, St}$ = Inverse Demand and Inverse Supply
$Q_{t}$ = Quantity of Display Advertisement
$Visits$ = Index of web traffic/visits (akin to income effect)
$Print$ = Price of print advertisement (substitution effect)
$Prod$ = Creative production costs (factor of production)

If anyone has experience modeling structural equations with price as the dependent variable I would really appreciate hearing your thoughts on how I should create a predicted value for Quantity and finalize a reduced form equation. Thanks!

You're definately on the right track. What you are doing is estimating the inverse demand and inverse supply in your market. The variables Visits Print and Prod can be used as "shifters" i.e. instruments for the quantity in the equation in which they are not present. Visits can be used as an instrument for quantity, when estimating the inverse supply equation and Print and Prod can be used as instruments for quantity when estimationg the inverse demand equation.

A well known example of how this works is Grady's article on Fulton fish market. You can find STATA code that replicates that article here: https://www.stata.com/data/s4poe/chap11.do .

The data sets for the stata code are here: http://www.principlesofeconometrics.com/poe4/data/stata/ .

Of course you should test the validity of the assumptions behind the use of IV in your SEM with the Hausman, Sargan-Wu and Stock-Yogo tests.


Second order partial derivative and cross second-order partial derivative I'm following a paper (Full text available here!) where at some point (pag.17 and 20) the author get the following derivative:

$$\frac{\partial V}{\partial L}=Y-X\frac{dY}{dX}=\alpha X^{-\frac{c}{b}}Y^{\frac{1}{b}}$$

where: $Y=\frac{V}{L}$ and $X=\frac{K}{L}$

Then, starting from this he calculates the partial derivative with respect
to L and the cross second-order partial derivative (the partial derivative with respect to K), whose results are shown below:

$$\frac{\partial^2 V}{L^{2}}=-\frac{\alpha }{bL} X^{-\frac{c}{b}}Y^{\frac{1}{b}-1}\left ( X\frac{dY}{dX}-cY \right )$$

$$\frac{\partial^2 V}{dKdL}=\frac{\alpha }{bL} X^{-\frac{c}{b}-1}Y^{\frac{1}{b}-1}\left ( X\frac{dY}{dX}-cY \right )$$

I was stuck trying to derive these latter derivatives. Is there anyone who can help me with this? Thank you so much!

Is there anyone who can help me with this?

Here it is. Equations 1-3, and 5-6 are obtained in preparation for the 2nd derivatives of V with respect to L and K.

Let me know if you have any questions.


why doesn't every country scale up the prices to the international level? I live in an Asian country in which the average monthly salary is maybe 300-400 dollars but things (apart from exported goods like laptops or smartphones) are reasonably cheap compared to their price in the US for instance.
One pizza is around 3 dollars, you can rent a decent hotel room with less than 20 dollars and average monthly rent for apartments in our capital city is around 150 dollars.
my question is why doesn't our government scale up everything like 5 times so the pizza would cost 15$ but at the same time salary is 2000 dollars?
That wouldn't make any difference for us but now our country seems to be a heaven for foreign tourists and I think this can make things better.
I know I'm not the first person that this idea has crossed his mind but can't figure it out what are the technical issues which prevent this idea from happening.

For simplicity suppose the local currency exchange rate is 1 LOC = 1 USD.

Suppose that the central bank simply print out 5 times the paper money in circulation, creating inflation. Pizza would then cost 15 LOC instead of 3 LOC. But then if the exchange rate regime is floating (majority of countries now use this), then the inflated money would be worth less, causing the exchange rate to fall to 5 LOC = 1 USD. That is, you need less USDs to exchange for 1 LOC. In essence, tourists would be paying the same (3 USD, which is now equal to 15 LOC).

So the next question is, why don't the central bank make their local currency appreciate (make 1 LOC = 5 USD, so that the pizza that cost 3 LOC would now be equal to 15 USD.)

Well, the demand and supply for money is what determines the exchange rate. If you want to know more about this I'd suggest you read more on exchange rate intervention here.


Difference between capital and current account Why is an increase in foreign assets in a country different from us just selling foreigners our goods? As in why is one (inc. in assets) in capital account and the other (exports) in current account?

You can think of the capital account as "exports of liabilities" - a capital account surplus means that a country is exporting liabilities (borrowing) from abroad to pay for imports of goods and services and/or for income transfers abroad (a current account deficit). An increase in foreign assets owned by the US is an import of liabilities: the US is buying liabilities from rest of the world by sending them goods and services (or reinvesting the returns from the assets they already own). The increase in foreign asset holdings corresponds to a current account surplus (as it must), but they are not the same thing.

The capital account and the current account of the balance of payments measure the same thing: the absolute change in the external debt stock (defined generally to include all liabilities, equity is in here as well) of a country. They just go about the measurement in different ways: the capital account measures the change in the external debt stock directly by looking at financial asset holdings, whereas the current account notes that an increase in the external liability stock of a country has to come from either a net import of goods and services or income transfers (interest payments, dividends, etc), so it measures these instead. In practice, measurement errors mean that the two come out to be different, but as a matter of accounting they have to be equal.

The reason increases in holdings of foreign assets is in the capital account is simply because that's what the capital account measures, and it's not in the current account because that's not what the current account measures. The question is a bit like asking "Why is rental income not in the expenditure method for calculating GDP?" Rental income is in there, but due to the way the expenditure method measures GDP, it is measured implicitly as part of expenditures.


Simplest model of an economy exhibiting (hyper)inflation I would like to find a minimal mathematical model for describing financial crises of the type that produces hyperinflation.

Here's a naive attempt, just to give the idea of what I'm thinking of.

There are n actors, each initially has 1 dollar. There are two operations:

actor i can transfer x (potentially a fraction) dollars to actor j
actor i can make promises to actor j (maybe of the type: if you transfer 1 dollar to me today I will transfer 2 dollars to you tomorrow).

One can then define the quantity of money in various ways: the first way is that it is always n. Then there is no inflation of course. Or one could define it to be the sum of money that people owe to you. Et.c. I don't know what is the most reasonable defintion.

The model ignores commodities (one can suppose that transfers of dollars involve transfers of commodities, but the latter are ignore). I would the following to happen: I postulate some rational behavior and preferences on the actors, and the result is that the quantity of money has dramatic behavior as a function of time.

I suppose many people have attempted to do this, but I don't know how to find it in the literature (I'm not an economist).

I agree with Guy that your model is simplistic. My own position is that hyper-inflation is first and foremost a political phenomenon. It results out of specific political policies and choices.

In other words, hyperinflation is a political process, not a financial process which proceeds with some sort of inevitability once a tipping point has been reached.

Although you also hear about when the dollar will fall off the cliff or that kind of talk, its inaccurate. Destroying a currency is not like falling off a cliff, where gravity takes hold all the way to its demise.

Destroying a currency is deliberate and requires a lot of manhandling and pushing up the steep incline and eventually shoving it off the cliff.

At any point up to the final shove into oblivion, the political winds could change and the policy pressure that is destroying the currency would cease.

Currencies are destroyed as an unintended consequence of saving the status quo from losing power. Rather than risk a decline in power, an upheaval in the fiefdom, elites in the status quo choose to debauch the currency as a short-cut to their unsustainable financial woes.

We have a great example with what is going on in Venezuela right now.

But lets imagine an example here in the States. Let's say tomorrow the Federal government says that all Social Security recipients who were receiving 2,000 a month will now receive 200 dollars a month. Rather than risk the firestorm that would ignite and get rid of some very powerful people, the government chooses to debauch the currency so that the 2,000 dollars will soon only provide 200 dollars in purchasing power. The government has de facto reduced the payment by 90% via destruction of its currency. But due to the stealth of this process, the citizenry are blind to the erosion.

If you take 10% of their money away every year via debauching the currency, then in nine years they have lost 90%, no fuss no muss, and the status quo stays intact.

If the populace goes on for several decades like this, no worries, but if it starts to lose trust in the currency, thats how hyperinflation starts to set in. Again, its a political act, not a financial one and its not an inevitable conclusion of anything, it can be stopped in its tracks.

So what I am saying that unlike how in our economics courses, we may be given a model to measure classic inflation, hyperinflation or the debauchery of the currency cannot be viewed in that same manner. No real model to measure when its going to happen, it all depends on the politics of the day and there is no inevitability, it can start to go in that direction and then be stopped in its tracks, because its a political phenomenon not a financial one.


When does gambling reduce risk? Suppose that you face risk. It is obvious that taking gambles whose outcomes are negatively correlated with the outcomes of your other gambles can reduce your overall risk ('hedging'). My question, however, concerns uncorrelated gambles - can these reduce your overall risk, and if so when?

Edit: to be clear, I am asking about when you can reducing your risk by taking additional uncorrelated gambles, not simply by replacing some gambles in your portfolio with others.

In standard cases, you cannot generally reduce risk by gambling with uncorrelated gambles.  With that said, a lot of your question depends entirely upon how you start defining terms.

Let me begin by defining risk as being exposed to uncertainty.  If you are not exposed to any uncertainty at the moment, then adding uncorrelated gambles to any outcome present in your life merely adds risk.  This definition is important because it often generates a completely opposite result from defining risk in terms of exposure to a chance of loss.

Imagine you went out today to play the Mega Millions Lotto with once chance in forty-five million of winning.  There is almost no risk in that transaction as there is almost no uncertainty.  You are going to lose.  It is not risky at all.  It is nearly a risk-free asset.  It is a risk-free asset whose expected value is less than a penny, but it is nearly risk-free.  This is why states love offering lotteries.

Now let us change our definition to risk as being exposed to a chance of loss.  In that case, a lottery ticket is very risky.  Indeed, the exposure is nearly the full dollar and the chance of an upside looks pretty grim.  With that definition of risk, voluntary exposure makes little sense.

It is the word voluntary that is the key.  Now let us make this game a little more extreme and involuntary.  To set this up consider the film, Phone Booth.  In the film, the lead character has been using the last phone booth in New York to contact his mistress behind his wife's back.  A sniper takes up a location where he can call the lead character through the phone booth and control him.  If he fails to do what he is told, he will be killed.  He has to confess his betrayal.  There is risk present in that the killer may kill him anyway.

Consider any circumstance where an involuntary outcome will happen in the future unless a gamble is taken.  The gamble is uncorrelated with the outcome but will prevent the outcome.  An example of this is any consumption deferral to avoid starving in the future, such as saving or investing.

The firm's outcomes are uncorrelated with your life expectancy unless you happen to run the company.  If you take the gamble, then your life is correlated with the firm's well-being, but theirs is not correlated with yours.  This is known as asymmetric association.  One of the best measures of this is Somers' D.  If you take no gambles then you will run out of resources when you can no longer work.  If you take gambles, uncorrelated with your long-run well-being, then you may live to be very old.

Now imagine that you must gamble involuntarily, then you can improve your rate of return and reduce your risk by using the Kelly Criterion.  The Kelly Criterion would increase your utility provided that the return was anticipated to be positive on every gamble.  Otherwise, if all gambles yield a negative return, then you should only gamble if the probability of loss from gambling is less than the probability of loss from fire or theft of cash.


Why Is Cointegration Important In Practice? In one of my econometrics classes. I'm nearly finished a problem set and assigned readings on an introduction to cointegration. I've essentially finished the assignment, run dickey fuller tests on some data, estimated cointegration relationships, and estimated an error correction model. But I'm often surprised at how textbooks in econometrics tend to drive right away into the details without first explaining the big picture and how various concepts are applied in practice. I was wondering:

Could anyone offer an intuitive explanation on how cointegration is important in practice. For example, if you are building models for policy analysis, or finance, or macroeconomic analysis, could you talk about some practical instances where cointegration comes into play and why it is important in these instances?

Thanks very much everyone for the help!

I think it is a very classical economic teaching problem - showing how something is relevant in the real world.

First, it solved a problem where linear regressions could lead to spurious results: https://en.wikipedia.org/wiki/Cointegration

  ...Before the 1980s many economists used linear regressions on
  (de-trended[citation needed]) non-stationary time series data, which
  Nobel laureate Clive Granger and Paul Newbold showed to be a dangerous
  approach that could produce spurious correlation, since standard
  detrending techniques can result in data that are still
  non-stationary. Granger's 1987 paper with Robert Engle formalized the
  cointegrating vector approach, and coined the term.

  For integrated I(1) processes, Granger and Newbold showed that
  de-trending does not work to eliminate the problem of spurious
  correlation, and that the superior alternative is to check for
  co-integration. Two series with I(1) trends can be co-integrated only
  if there is a genuine relationship between the two. Thus the standard
  current methodology for time series regressions is to check all-time
  series involved for integration. If there are I(1) series on both
  sides of the regression relationship, then it's possible for
  regressions to give misleading results...

Second, our "Sister site" actually does a nice job explaning the intuition behind, which can explain why it is important in the real world - are two different time series related? And can we test for this?:

https://quant.stackexchange.com/questions/219/what-is-the-intuition-behind-cointegration

I really like this one:

  "Think of a man walking his dog. He will go along and his dog will
  stroll along running back and forth. Man and dog are mathematically
  "cointegrated".

  As an investor you bet that the dog is coming back to his master or
  that the leash has only a certain length.


Music Streaming Impact on Producers I am currently writing a news commentary on music streaming services. My commentary is focused on demand and supply, consumer and producer surplus, externalities, and public goods. And there are a few things that I am kind of confused in some parts:

Are music streaming services considered public goods?  My teacher said they are public goods as it is non-rivalry in consumption. But don't users need to pay for the service and therefore excludable in consumption?
Does music streaming create a negative externality to the producers? The producers are supposed to earn money through creating music but with music streaming they earn less than they should.
Finally, why do artists still decide to put their music on the music streaming services even they earn less than they should?

Thank you all very much for helping me. I just started learning about externalities so the questions may seem dumb. Thanks a lot!

Remember that rivalrous goods mean that someone else consuming it takes some benefit from other people using it--obviously not true for music unless you are a very spiteful consumer. Excludability means you can prevent others from listening to it. Once one person buys it and they start blaring the music, they can't stop others from listening to it, unless they have headphones or something. So it could be considered excludable, but music streaming is often used for parties and such. There is also the issue of torrenting and sharing music online, which makes you the music streamer. So the question to consider is whether music is turning into a public good, and what that means for music streaming.
In any industry, there is always loss from resale transactions. Someone who buys a book from someone else isn't buying it from the publisher or the author. It's just that with music people really like to resale music for zero price (free), which seems odd in a way. Nevertheless, we still see people buy music from musicians because they can be assured of higher quality (so there is product differentiation between a ripped song and the original) and there is probably some weird intrinsic value we get from being a patron of the arts (think Kickstarter or GoFundMe). Is there a negative externality from music streaming services? Probably.
Artists put music on streaming because some see it as better than the traditional way nowadays, just putting your CDs in stores or whatnot. If you get even "less than deserved" from doing that, well...

That's just skimming the surface of this issue probably, so hopefully others will be elaborate better than me.


Does the political claim "will create X jobs" have an economic definition? I often see claims that new (generally government) projects will "create n jobs".

For example, this 2013 claim from the Economic Development Blog about the 2020 Olympic Games:

  The Olympic Games are expected to create 152,000 jobs nationwide across Japan. This includes 84,000 new jobs in Tokyo and 68,000 in the rest of the country.

I have always found such claims to be vapid, because it doesn't say how long the jobs last.

Sticking to the example: One of those new positions might be to be a security guard for a month during the games. One of those new positions might be to work on the planning for the event for seven years. One of those new positions might be to be a groundskeeper at a new Olympic facility for decades.

Lumping these together seems like it is a misleading metric. Perhaps saying "250,000 job-months" would be a better measure?

But I am economically naive. Perhaps economists have already considered this and have a standard definition I don't know about to allow them to properly compare.

Are these figures mostly meaningless, just being used to hype a project by its proponents? Are they accepted estimates of real economic boost a project might bring?

There is no standard, internationally agreed definition of what should count as "a job" when conducting economic impact assessments.  However, it is an important question that is often (not always) taken seriously when constructing such estimates.

Sometimes it is very important that jobs estimates are comparable.  This is particularly the case when politicians have to decide between competing investments.  If project A creates 1000 jobs and B creates 1200 jobs, then you should be sure that those estimates used the same methodology (and that it was sane) before deciding between the two.  For this reason governments often have official (though maybe internal) guidance on how to calculate the number of jobs created.  This is particularly true in the international development sector, where it is now quite common for government interventions to be aimed primarily at job creation.

On the other hand, it is not necessarily the case that we would want to use the same definition in all contexts, even if it's the same government creating estimates.  For instance, the UK government may want to use different criteria for assessing a community regeneration project in northern England than it would for an aid project in Afghanistan.  It would hopefully be transparent in both cases.

Each case is complicated for lots of reasons, including those you mention and many others.  How many hours a week must you work to have a job?  Does that change depending on what local working patterns are?  What if your job is seasonal?  Does it make a difference if you left another job to take the new one?  Does it matter if your previous job was in the informal sector, or part time, or not as well paid?  Does it matter if your job conforms with the ILO core conventions?  What about the new jobs that would have been created anyway?  And what about indirect jobs created as a result of increased spending of newly employed people (the multiplier), or because people copy you (spillovers)?

EDIT: There is a comparison of some common job creation definitions for development in a DCED working paper on pp12-13.


International shipping services count as exports? A Greek ship owner transports mouse traps from Albania to Japan, making every year ten million Euro in revenue and one million Euro in profits.

The total value of the mouse traps he transports every year is one hundred million Euro. So Albania is exporting one hundred million Euro every year. The ship owner charges 10% of the value of the goods, making a revenue of 10 million Euro (Albanians are paying him that money for transporting the goods to Japan). After paying his expenses: fuel, food, ship repair, taxes, etc., he gets one million Euro in profits.

The question is: does his revenue count as a Greek export? One can argue that Greece is exporting a transporting service so it should count as Greek export.
Also the revenue should count as Albanian imports since they pay an external company for the service.

It's complicated, and it is supposed to depend on where the ships are generally operating from, rather than the country of the firm that owns the ships or the flag under which they are flown. Under the 2008 System of National Accounts (the international standard for calculating GDP), overseas shipping is generally to be allocated on the basis of the ports out of which the fleet is serviced. See 4.13, on page 62. The document to which it refers is the Sixth Edition of the IMF's Balance of Payments and International Investment Position Manual. You'll want to look specifically at Chapter 4, 4.131-4.136.

So if we assume that the ship owner is actually operating out of Greece, in your example he would be considered to be exporting the service for which he is paid 10 million in revenue.


Estimating national intangible wealth I seem to recall reading about the following research regarding "national intangible wealth" (IIRC):

For each country, compute the GDP.
Convert the GDP to "total national capital" using an interest rate (e.g., assuming 5% interest, the total national capital of a country with GDP=\$5B will be \$100B), the same(?) interest for all countries.
Subtract from the above total national capital all the tangible capital: industry, farms, infrastructure, education of the population - everything you can put a price tag on.
The result is the "intangible national capital" - stable non-corrupt government, courts that enforce contracts, work ethics...

I tried to google things like "national intangible wealth" &c, but found nothing reminiscent of the above approach.

Could you please provide a reference? Criticism of the methodology?

The reference is World Bank (2006). You can see the detail of the methodology in Appendix 1, and their estimates of intangible wealth in Appendix 2.

There are other methodologies to measure intangible wealth (e.g. here and here). Alternatively, there are many ways to compute natural and physical capital, which will give different results to the one given by the WB, even if using the same formula to compute intangible capital. For example, see here. If you search in google or here things like "measuring capital stock", you get tons of hits too.

I think that because this is a relatively new research area, there is no "official" guideline about how to measure intangible wealth. Maybe in the future some sort of standard will be produces, pretty much like the standard for GDP came to be (which is still subject to criticism anyway).


How successful will OPEC's predatory dumping strategy be? Since the fracking industry in the US has started to grow rapidly, I have heard increasing reports that OPEC is attempting some form of predatory dumping in the hopes of making the fracking industry in the US unprofitable.
How successful do economists predict that OPEC's dumping strategy will be?  For example, does OPEC have a large profit margin and the fracking industries a small profit margin (making fracking an unprofitable enterprise quite easily under some form of predatory dumping) or are the profit margins close enough to make any predatory dumping infeasible in the short-run?

This is the cost curve of oil production (North American shale at $65):

Source

And this is the cost curve of major American projects:

Source

While "Citi's Ed Morse highlighted this chart, showing that for most US shale plays, costs are below $80 a barrel."

And clearly, many of these new projects would lead to losses with oil prices at $60:

Source

The problem with predatory pricing (if it's purposeful) is that OPEC itself depends on high oil prices to ensure balanced budgets in their (mostly dictatorial) regimes. Their sovereign funds are large enough to survive a brief (2-3 years) period of low oil prices, but in the long run, dumping endangers their rulers' positions:

Source

You can't kill American oil production this way—it would return after these two-three years anyway.

The \$60-80 band leaves space for most American projects, while oil below \$60 kills too many OPEC members. So, it does not seem to be a good dumping strategy.


Need help identifying this cognitive bias or fallacy pointed out by Kahneman in Thinking Fast and Slow This was in Thinking Fast and Slow by Kahneman.
He described a situation where someone might prefer A to B, and B to C, but then might prefer C to A (when A and C are directly compared to each other).
I can't seem to remember the name of this bias or fallacy, and I looked in the book but wasn't able to find the passage.
Anybody remember what it was?
(The last time I posted a behavioral economics question on here, some people protested that it didn't belong here. For your information, Kahneman has a Nobel in Economics, so please take your objections to the Nobel Committee. Thank you and good day.)

Update: the term is: "Preference Reversal"

When this event occurs it is known as a failure of "transitivity" of preferences.

Transitive preferences are such that for every  X,Y,Z, if X is preferred to Y and Y is preferred to Z then X must be preferred to Z.

Economists define rational preferences as binary relations that are complete and transitive, meaning that we can compare everything and the comparisons are consistent.


Austrian business cycle This video on the Austrian business cycle seems to state that when rates are low this signlas to investors that there is plenty of money to borrow and plenty of resourses to deploy. However I dont understand to 100% how resources and available cash are linked tho, whats the idea? Why must low rates mean plenty of resourses?
video

As a disclaimer, I think the Austrian business cycle is incorrect. I will try to explain in a sympathetic fashion. Mises.org has a great deal of resources on Austrian economics, much of it free.
From a quick watch of the beginning of the video, the distinction is between a market rate of interest, and the “artificial” interest rate set by the central bank.
In the case of a market rate of interest, the belief is that prices for everything will set to some balanced arrangement: the demand for investment goods will balance the supply, and there will be a matching balance in lending activity (with the interest rate on loans being the price that clears the market). In classical economics, this balance would be described as an equilibrium. However, different Austrians disagree on how to describe this, but they generally reject using “equilibrium.” You would need to find another source to explain their terminology.
Getting to your question, Classical authors can explain why the balance in lending markets coincides with the balance in physical resource markets in equilibrium. Roughly speaking, if any market is unbalanced, this would unbalance other markets, so all of them have to end up in equilibrium. The Austrians somehow end up with the same conclusion, but different authors appear to explain it differently.
(The issue with “artificial” interest rates is that Austrians argue that central banks invariably set interest rates too low, and thus there is excessive investment - “mal-investment.”)


Proof of Concavity of Cobb-Douglas Function Given the function $F(\mathbf{x})=x^{a_1}_1x^{a_2}_2 \ldots x^{a_n}_n$ defined on the set $S=\{\mathbf{x}=(x_1, \ldots, x_n) \in \mathbb{R}^n: x_1>0, \ldots ,x_n>0\}$ with $a_1,a_2,\ldots,a_n > 0$ and $a_1+a_2+\ldots+a_n=3$, I want to:
(i) Show that $\mathbf{x} \cdot \nabla F(\mathbf{x}) = 3F(\mathbf{x})$ at every $\mathbf{x}$, where $\nabla F(\mathbf{x}) = (\frac{\delta F(\mathbf{x})}{\delta x_1},\ldots,\frac{\delta F(\mathbf{x})}{\delta x_n})$.
I was able to work out that $\mathbf{x} \cdot \nabla F(\mathbf{x}) = a_1x^{a_1}_1 + \ldots + a_nx^{a_n}_n$ but got no further. Need help with this part!
(ii) Determine whether $F(\mathbf{x})$ is concave in $\mathbf{x}$ on the set $\mathbf{x}$.
My first thought was to use a Hessian matrix but that would be too tedious for this function. Is there a better method?

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


Industrial Economics I am currently struggling trying to find the short-run equilibrium price, output per firm, and profit per firm if $190$ firms supply the market. I am given $p=102-1/2Q$ and $C(q)=5q-6q^2+3q^3$.

First I started off with $P=MC$.
So $P=9q^2-12q+5$, thus $9q^2-12q+(5-P)=0$.

Then, I Used the quadratic equation and came out with $q=2/3+1/3\sqrt{p-1}$.

Then I did $Q=nq=190\left(2/3+1/3\sqrt{p-1}\right)$.

Equating demand and supply I obtained $P\approx 2.32$ and then plugged back into $q\approx2/3+1/3\sqrt{2.32-1}$ to get $q\approx1.05$

Finally, I plugged $q$ and $P$ into $\pi=q\cdot P-C(q)$ and came up with $\pi\approx 0.33$. This just seems crazy to me! I have tried for the past few days over and over again to understand, but I am completely lost.

Any help would be greatly appreciated!

I went over your calculations and they seem to be right. In principle, this is a valid answer, but I understand that the numbers seem suspicious. Are you sure this is the right problem?

Update: everything checks. I think your answer is correct, although it looks "weird" for a textbook problem.


Income Elasticity and Convexity of Demand in Income What needs to be true about the demand function $z(y)$, where $y$ is income, for the income elasticity $\varepsilon = \frac{dz(y)}{dy}/\frac{z(y)}{y}$ to be always greater than one (so that the good is always a luxury)? In particular, does the demand function have to be convex in income? Would that be a sufficient condition?

This may not be the answer you are looking for.

What you want may be technically feasible, but just barely. What I mean is that for any $\delta > 0$, you cannot have the income elasticity always be larger than $1 + \delta$. The simple reason is that it would mean that the amount spent on the good always increases faster than the income. Then eventually the amount spent on the good would just overtake the income, but this is, of course, a contradiction.

Income elasticity being exactly equal to one would be easy, e.g. demand derived from Cobb-Douglas.

You should also be able to construct a function $z(y)$ for which
$$
\epsilon(y) = 1 + \frac{1}{y},
$$
so that $\epsilon(y) > 1$, although
$$
\lim_{y\to \infty} \epsilon(y) = 1.
$$
You would need to solve a differential equation:
\begin{align*}
1 + \frac{1}{y} & = \frac{dz(y)}{dy}/\frac{z(y)}{y} \\
\\
z(y) \left(\frac{1}{y} + \frac{1}{y^2}\right) & = \frac{dz(y)}{dy}.
\end{align*}
Unfortunately I am not good at these, so I don't know what $z$ yields a solution, but I don't think this is what you had in mind anyway.


What is a what is meant by a "workhorse" macroeconomic model A number of times ive seen the Neoclassical Growth Model and Overlapping Generation Model setups referred to as a "workhorse of modern macroeconomics". What does this mean exactly?

It is meant in a way that these models are highly influential and many papers are based on them.

From my own experience it is impossible to attend macroeconomic conference without having couple of papers that are based on models of overlapping generations or on neoclassical growth model.

The reason for that is that the models are quite useful and easily to adapt in lot of different settings. You can use overlapping generations model to examine anything from simple household savings decision to topics that are even outside the realm of macroeconomics such as optimal wealth taxation or environmental policy.

When it comes to the Neoclasical growth theory, for better or worse most of the research in the literature on economic growth in past few decades heavily focused on Solow-Swan model. In mainstream the only competition to Solow-Swan is the endogenous growth model (for which Romer got his Nobel Prize), but due to difficulties in verifying it empirically Solow-Swan is still dominant growth model.

Both of the above mentioned models can be adapted to so many settings that it would not be completely incorrect to think of them more of as a mathematical tools like for example Lagrangian optimization and hence many call them workhorse models since they do most of the work in the mainstream macroeconomics. Essentially, with a little bit of demagoguery you could say that for a decent academic career in macro it is enough to learn how to solve and play with one of the above mentioned models.

For an illustration consider this: In quite popular macro handbook - Advanced Macroeconomics from David Romer, first two chapters are about Solow-Swan and overlapping generations model. By word count almost 1/6 of the handbook is devoted to them, and beside these two models, only other models that have separate chapters devoted to them are the endogenous growth, real business cycle and dynamic stochastic general equilibrium model, other chapters usually squeeze multiple different models in themselves showcasing how important the above mentioned are.


What made The Wörgl Experiment successful? Background:

  In 1932, in the midst of the Great Depression, the small town of Wörgl in Austria successfully experimented with its own local currency (in the form of a stamp scrip) ...  They not only re-paved the streets and rebuilt the water system and all of the other projects on Mayor Unterguggenberger’s long list, they even built new houses, a ski jump and a bridge ... every one of the schillings in stamp scrip created between 12 and 14 times more employment than the normal schillings circulating in parallel. (Source)

I would like to understand better what made the currency successful. The article offers this short explanation:

  Because a stamp needed to be applied each month (at 1% of face value), everybody who was paid with the stamp scrip made sure he or she was spending it quickly, automatically providing work for others.

What does it mean to "apply a stamp each month"? Does the scrip lose 1% of its face value every month? Is that the incentive for spending? Isn't that economically the equivalent of a normal currency with high inflation? Why was this experiment so successful, and if it truely was, why haven't we seen more experiments like it?

It was successful because it combined three things at the same time.

Firstly, it increased available currency at a time when currency was scarce for any but the rich - so everyone was more solvent.

Secondly, it had a negative interest rate, so the encouragement was to spend quickly.

And thirdly, it was a local initiative, and belonged to the town, at a time that was particularly introspective - isolationist, even.


Utility function for introductory microeconomics What are the utility functions standardly used in introductory microeconomics courses. My own list would include

Perfect substitutes: $U(x,y) = ax+by$
Perfect complements: $U(x,y) = \min(ax,by)$
Cobb Douglas: $x^\alpha y^{1-\alpha}$
Quasi-linear: $x + y^\alpha$
CES: $U(x,y) = (x^\rho+y^\rho)^{1/\rho}$

Anyone else that would be typically included?
EDIT:
To be more specific I am primarily interested in different types of preferences not positive monotone transformations of the above specifications.

One that was not mentioned in question is the quadratic utility (aka preference for extremes):
$$U(x,y) = x^2+ y^2$$
This one is less common but still used in micro courses.