How does an increase in the price of "non-wage-goods" increase employment? Keynes (1936, Chapter 2) says that based on the classical theory, "there are only four possible means of increasing employment", the fourth of which is:

  an increase in the price of non-wage-goods compared with, the price of
  wage-goods, associated with a shift in the expenditure of
  non-wage-earners from wage-goods to non-wage-goods.

What does the above quote mean? What are wage-goods and non-wage-goods? And why would an increase in the price of non-wage-goods increase employment?

P.S. Keynes's discussion here is with reference to AC Pigou's Theory of Unemployment (1933), which I can't find online. It seems that Pigou makes a distinction between "wage-goods" and "non-wage-goods". Keynes mentions very briefly that "non-wage-goods" is "Professor Pigou's convenient term for goods upon the price of which the utility of the money-wage depends", but I'm not sure I understand this.

Wage-goods are goods that a worker with wages might buy, perhaps now more commonly called consumption goods

Non-wage-goods are goods that a rentier receiving profits or interest might buy, including what might now be called capital goods or investment goods

As to how to read Keynes's interpretation of Pigou's position (so actually neither Keynes's nor Pigous's), it might be saying that if non-wage-earners shift their demand towards non-wage-goods, this would have the demand-side effect of pushing up the relative price of non-wage-goods and reduce the relative price of wage-goods, with presumably

either the direct effect of increasing both the number of wage-earners employed producing non-wage-goods and their wages,
or the indirect effect of increasing the real wage for all wage-earners (since their wage-goods are now relatively cheaper) above the previous "marginal disutility of labour", and this encourages increased wage-earning employment (what today would be called a substitution effect)


Perfect competition profits question Market is supplied by: 50 competitive companies all of them have relatively low costs given by an equation $C_l(q)=350+2q+q^2$ and by n companies of higher costs given by an equation $C_h(q)=400+2q+q^2$. Market demand is given by $Q=250-10P$. If none of the companies with higher costs will  gain positive profits, how large is n? What is the profit of companies with low costs?

I have no idea how to solve this question, i do not know how to start.

It says

  If none of the companies with higher costs will gain positive profits

I assume this means they're making 0 profits, while strictly speaking it could mean that they make negative profits and leave the market.

So with 0 profits, this means that average costs = price for the high-cost firms.

First, you need to derive the equilibrium price, using that, for the equilibrium price, demand = supply.

$$ \text{total demand} = Q(p) = S(p) = \text{total supply}$$

A firm's supply is the solution to a maximization problem:

$$ q_h(p) = \arg\max_q (p-C_h(q))q \\
 q_l(p) = \arg\max_q (p-C_l(q))q$$

Then, total supply given price $p$ and amount of high-cost firms $n$ is

$$ S(p, n) = 50\cdot q_l(p) + n \cdot q_h(p)$$

Then, our equilibrium condition is simply

$$ S(p, n) = Q(p) $$

This is under defined, as we have one equation and two variables $(p, n)$ to solve for. But wait, we know more! 0 profits for the high-cost firms means

$$ p = C_h(q)$$

To get rid of the additional variable $q$, just use the solution to the firm's problem:

$$ p = C_h(q_h(p))$$

Now we have two equations and two variables, you are all set!

$$ S(p, n) = Q(p) \\
 p = C_h(q_h(p))$$


Can we "prove" that slow growth is due to deficient demand? We hear more and more these days about growth, particularly in the Eurozone and Britain, being beneath its long-term trend due to deficient demand. I can think of a few things which support that idea - such as a drying up of the credit which fuelled pre-crash consumer growth, low inflation and perhaps even deflation, long-term stagnant wages, and all this despite ultra low interest rates and QE. In short, the deficient demand story is one which has an intuitive appeal.

What I don't get is simply this: can we prove that deficient demand is the cause of the problem, and if so how?

This is one of the issues with Macroeconomics - you usually cannot prove these kind of things, you can only find indicators.

That is, because what we observe is always - in the neoclassical language - the general equilibrium, never the "off equilibrium adjustment" (as in the Walrasian Auctioneer). That includes Keynesian logic - these days, the majority of Economists does not think about these traps as off-equilibrium paths, but rather as multiple equilibria [citation needed].

As a comparison, if you only observe the equilibrium outcome, it is hard to say whether a decrease in prices comes from an increase in supply or a decrease in demand. Now, if you could randomize or had a natural experiment at hand (say, randomly shut down half of the firms in the economy), you could actually "prove" the underlying issue with empirical data.

But since this is not feasible within many subjects of macroeconomic interest, disproving ideas using empirical evidence is quite difficult.


Why Nobel prize winners studied economics? Recently I have read a great article about  Olivier Blanchard and I wonder why he has chosen to dedicate his life to study economics? Moreover he managed to do a research in several subfields, which is very impressive.

In the article we can find a quote:

  Also at Nanterre, he developed a fascination with economics and the ways in which it could be used to make the world a better place

Is there any good book or an article which explain why Nobel prize winners chose to study economics? How did they get passionate about economics?

The Nobel Prize website is a good source of information. On the economics prize page they have a link to a page for each laureate. From there you can find, in particular, a biography for each prize winner where the laureates often talk about the genesis of their interest in economics.
For example, Eric Maskin writes

I became a math major at Harvard College, where I studied algebra with Pierre Samuel and Richard Brauer and analysis with George Mackey and Lars Ahlfors − all of them inspiring, some of them amusingly eccentric. Almost by accident, I wandered at one point into a course on "information economics" taught by Kenneth Arrow, later my Ph.D. advisor. The course was a hodgepodge of topics from the frontier of economic theory, but a good part of it was devoted to Leonid Hurwicz's work in the nascent field of mechanism design. This work was a revelation to me: it had the precision, rigor, and sometimes the beauty of pure mathematics and also addressed problems of real social importance − an irresistible combination.
In fact, I ended up essentially doing an economics Ph.D. The degree was nominally in applied mathematics. But the applied math program at Harvard in those days was remarkably flexible, and allowed students to study whatever they wanted, as long as they wrote a thesis with "significant mathematical content." I took quite a few economics courses (although none, I regretted later, in macroeconomics or economic history), including Truman Bewley's general equilibrium course, where I first got to work with my classmate and later co-Laureate Roger Myerson (we sometimes tackled the rather demanding problem sets together) and Jerry Green's analytic seminar, whose student participants included Elhanan Helpman, Bob Cooter, and Jean-Jacques Laffont.
As an advisor, Ken Arrow was amazingly generous with his time; and I learned an immense amount from our many one-on-one discussions in his office.


Computing Boston and TTC in Python This is somewhat of a follow up question to Available code for computing solutions to matching algorithms?.

In the above question, I got great answers, but all of them were for R.

I am now programming a lab experiment in otree, which means I am working with Python.

It is fairly easy to find code in python solving matching problems using the Deferred Acceptance mechanism, but I wondered if anyone knew of python code for some of the other common mechanisms in the  literature. Specifically, I am looking for python code for

The Boston mechanism (aka. Immediate acceptance)
The Top-trading cycle algorithm

In the best of the worlds, these codes would

Be compatible with the school choice model (i.e. many-to-one matching problem in which agents in one side of the "market" can be matched to many agents on the other side)
Allow for constrains on the lenght of the preference list agents can report (see http://www.sciencedirect.com/science/article/pii/S002205310900057X)

However, I would already be very happy with python code for Boston and TTC, even if the two last features are not implemented.

I found one implementation of TTC in python at http://www.dreamincode.net/forums/topic/377004-algorithmic-game-theory-top-trading-cycle-procedure/?ref=dzone.

However, it does not seem to include the two additional features I was mentionning.

With of without these two features : I would still love to hear about more implementation of TTC, and about implementations of Boston.


Optimal basket and the maximum utility Given two goods (where more is better), and I am consuming at a point that maximizes my utility (i.e on the budget line, with an indifference curve tangential to the budget line).

When the prices of the two goods change to an unknown, and yet I consume where my utility is the same maximum utility as before, can I conclude that the price of this new basket is the same as before?

Logically, I think it does. But on the other hand, I'm thinking about possibilities where price of good A increases, and price of good B decreases by the same amount, which leaves me stuck.

Given the circumstances and model you describe, consuming the entire budget will give higher utility than consuming less than the entire budget.

You can therefore assume that the optimal basket will have the same total price as before the price change.


Is a 'Brexit' really that bad? There seems to be a lot of fear that a Brexit will have a very bad impact on both the European and the British economy. Why would this be, does a Brexit imply that there will be less trade between EU-countries and Great-Brittain, why is this?

tl;dr: Uncertainty & trade tariffs

detail
The economics have been assessed by a large number of economic specialists, including the very well-respected and independent Institute for Fiscal Studies.
What would Brexit (meaning the UK leaving the EU) mean?
uncertainty
Well, firstly it means years of uncertainty, while replacement trading arrangements are negotiated - typically that takes somewhere in the region of 10 years. The Doha Round of trade talks has been going on since 2001.
Uncertainty requires higher rewards to balance the risks, and that means lower inward investment, and fewer long-term deals.
trade tariffs
Free access to the European market depends on accepting some specific rules that the Brexit campaign consider to be unacceptable, such as the free movement of labour. And it requires membership either of the EU, or of the European Free Trade Area (EFTA). On leaving the EU, UK membership of the EFTA would require EU approval, and the German Finance Minister Schäuble has made it clear that he considers that that would not happen. So one thing that the Brexit campaign and the EU heavyweights should agree on is that the UK would not be a member of the European Economic Area, and that means trade tariffs. A Brexit would be an existential threat to the EU project, so it will be in the interest of its remaining members to make exit as painful as possible, to preserve the unity of the remaining 27. And EU27 trade with the UK is a very small proportion of EU27 total trade, so it's a cheap price to pay.

summary of all effects
The IFS summarises the effects, and the vast majority of specialists predict negative effects at least out to 2030. Here's their summary, from p18 of the report linked above:

It's worth noting that it's not only UK's trade with the EU that would be harmed. The UK has trade deals with much of the world because it is a member of the EU. Without that membership, it would need to negotiate its own bilateral trade deals: such negotiations will also typically take a decade. So the UK's trade with non-EU countries would be reduced too. And there's the reduced economic efficiency of having a much smaller pool of talent to draw on for the workforce. So the numbers in the table above may (depending on the scope of individual studies) include those effects, as well as the EU-trade effect.


Are lotteries auctions? I heard one professor of my university say that "lottery is a kind of auction. So we can predict it! Then we could get a lot of money!"

Since he is in the mathematics department, and I know little about that matter, I couldn't answer to my gut feeling which told me that he was wrong.

So, from the Economist's perspective, is it true? Is a lottery some kind of an auction?

Generally, and surprisingly, yes, lotteries are similar to auctions. What do I mean by that?

In an auction, you increase the likelihood of winning by increasing your bid. In many auctions, if you increase the bid sufficiently much, that probability will go to one.

A similar thing is true for lotteries: the more tickets you buy, the higher is the likelihood of success. It is not a one-for-one correspondence, but it holds. And again, by predicting other people's actions (are they more likely to bid/gamble on week days or week ends), you can increase your chances of winning the lottery.

However, this means that you can increase your chances of winning, not that you will make a net surplus ("get a lot of money"). In the same way as sometimes, you can bid "too high" and make a net loss in an auction, you can pay a too high price for the (expected) win. In a lottery, this is quite often the case.


Profit maximization question Two firms are in a market together. They produce a product.

Total revenue from sales is $y=K+L$

K is the amount of capital

L is the amount of labor

These two firms each specialized in supplying one of inputs and the cost of the input supplied is incurred by the person providing it.

For capital, the cost is $K^2/2$ and for  labor, the cost is $L^2/2$

And they share revenue from their business equally.

I need to find firstly that if eac is interested in maximizing his own profit, then how much of each input will they use, and how much profit will each make. And secondly, I need to find the profit maximizing level of inputs for whole business.

As a result, I need to compare what I have found in both parts.

———-

my solution

For firm 1,

$$max [1/2(K+L)-K^2/2]$$

FOCs:

$1/2-K=0$

So $K=1/2$. He use 1/2 unit of capital.

And his profit is $\pi= 1/2*(1/2+L)-1/4=1/2*L\ge 0$ for $L>0$

Similarly,

For firm 2,

$$max [1/2(K+L)-L^2/2]$$

FOCs:

$1/2-L=0$

So $L=1/2$. He use 1/2 unit of labor.

And his profit is $\pi= 1/2*(1/2+K)-1/4\ge 0$ for $L\ge 0$

=======

And I have tried to find the profit maximization for entire business

$$max[(K+L)- K^2/2-L^2/2]$$

FOCs;

$1-K=0$ so K=1

and

$1-L=0$ so L=1

And profit $= (1+1)-(1/2+1/2)=1>0$

Now, all parts of my solution are correct?

You make a mistake in setting up your individual profit functions. Given that the total revenues from sales are $y=K+L$ and they share revenues equally their revenues are $1/2*(K+L)$


Why isn't the cost of shoes affected by their size? I have noticed that many shoe selling shops I have visited have the same price tag regardless of the shoe size.

Intuitively I'd think the bigger the shoe the more material and consequently capital invested in producing it. That being the case why would a manufacturer equally price dissimilar shoe sizes?

Most of the price of creating a shoe is the cost of labour to make it and the cost to ship it to the store. The cost of the materials needed to make the shoe is negligible. So, they can ignore the difference in material costs without losing too much money.

But why would they want to lose any money at all? Logistics. Keeping track of the different prices per shoe, printing the different labels, making sure the shoes are sold at the right price, paying people to determine how much of a price difference the company should charge are all things that cost money.

So the company is looking at creating a giant logistical nightmare for themselves, costing them who knows how much money, all for a penny difference between a size 8 and a size 13.

Trying to charge a different price would be a case of being 'penny smart; dollar stupid'.


Why is a high government debt/GDP bad? Why is a high government debt/GDP bad? It is frequently mentioned as something bad. Today here, for example.

I get that when the government spends, real resources like workers or raw materials are used, which is a real cost to society.

I also get that the government needs to tax, because otherwise the increase in money supply in the private sector would be too great. Perhaps the government also need to tax in order to ensure a demand for currency, I don’t know.

But why focus on the debt/GDP ratio? In Sweden, most of the government debt is to the central bank. Why does that matter?

Isn’t it more important to focus on how much the government should increase (or decrease) the money supply? Are these two things equivalent?

Firstly, the use of debt/GDP as the ratio is somewhat arbitrary. One could easily look at debt/government revenue, and it may be a more useful metric. However, the convention to use GDP for scaling these series. (One can argue that GDP represents the full income capacity of the economy for debt service.)

For countries that borrow in a foreign currency (or in a currency where they do not directly control the central bank), a high debt ratio indicates a greater risk of default. There is no gurantee that they can their hands on the foreign currency to repay debt. You need to look at other things as well, but it's one common metric.

If the country controls the currency it borrows in, it should be able to arrange its affairs to avoid default. (There is no guarantee, however.)

However, even if we ignore default risk, the greater the debt level, the greater the interest expense for the government. The exact mechanisms are debated by various schools of thought, but it is reasonably safe to argue that greater interest payments will squeeze out other spending if we want to keep inflation around a target level. There are two ways in which a greater debt load increases interest payments.

Even if the rate of interest is unchanged, a greater amount of debt implies more interest to pay. This effect holds by definition.
A greater debt-to-GDP ratio might increase interest rates. The magnitude of this effect is controversial. The example of Japan in recent decades (high debt ratios, low nominal yields) demonstrates that the effect is not very large, even if it exists.

There is a school of thought that argues that we need to "pay back" debt in some sense; this is often referred to as the governmental budget constraint. This view can be summarised as: greater debt now means greater future taxes, and people do not like taxes. (This is sometimes called Ricardian Equivalence.) The exact mechanism is controversial. (I have severe doubts about the mathematics behind it, for what that's worth.)

In the case where the central bank has bought a lot of government debt (quantitative easing), the expectation is that the central bank will eventually reverse that policy. In any event, the central bank needs to pay interest on resserves if it wishes to raise market interest rates to control inflation, and the consolidated government will face a similar interest cost as the case of bill issuance.

Finally, the money supply is related to debt levels; both are forms of government liabilities. In most modelling traditions, people only target a certain anount of money holdings (that earn no interest), and the rest is invested in bonds/bills. Therefore, we only expect money to grow in line with transaction needs, and this level may have little resemblance to total debt levels.


Why do currencies cover orders of magnitude? Using 1 USD as a reference, most currencies are within an order of 5 away from the USD: that is, one unit of most currencies is worth between 0.2 USD and 5 USD. (Source.) In fact, most European currencies (Pound, Euro, Franc) are almost exactly 1 USD (0.75, 0.90, 0.98, respectively).

However, there are some currencies that are orders of magnitude away from the USD: 100 Yen constitutes a USD, and 1000 Won constitutes a USD.

Why are these currencies so far from the value of 1 USD? What happened during the development of these countries (in this case, Japan and South Korea) that caused their currency unit to be astronomically different from the USD?

No matter where you live in the world, there is sort of a minimum value that your currency needs to practically be able to represent somehow.  If your standard unit of currency is more than that minimum value, you need to subdivide your currency to be able to represent smaller values.  In the U.S., we subdivide our U.S. Dollar into 100 cents, meaning that the smallest value that you can spend is $0.01.  (My parents talk about being able to go to the store when they were kids and buy candy for 1 cent, but that is no longer the case.)

If your standard unit of currency is small enough, you don't need to subdivide it any further.  This is the case with Japanese yen; 1 yen is roughly equivalent in value to 1 U.S. cent, and you won't find anything for sale in Japan for a fraction of a yen.

I visited the Czech Republic last summer.  One Czech koruna is roughly equal to 4 U.S. cents, and I didn't see anything for sale there for fractions of a koruna.

There really isn't anything more to it than that.  If we, in the U.S., decided that we didn't like the decimal point anymore and valued everything in cents, nothing would change, except that what we know today as the one-dollar bill would have the number 100 on it, and a price tag that had $4.95 on it today would look like 495¢ instead.

Currencies change in value with respect to each other from time to time.  You can read about some of the events in the past that affected the value of the Japanese yen on the yen Wikipedia article, but none of that history is really relevant if you are concerned about the value today.  If a currency goes up in value, it will just have to be subdivided more so that the smallest values can still be represented.  If on the other hand, the value of the currency goes down (much more common), some of the smallest subdivisions will be eliminated.  Canada has already stopped production of their penny, and there is discussion in the U.S. about doing the same here.

When the Euro was created (about 20 years ago), they had to pick some value to begin with, and they chose to make the Euro equal in value to the U.S. dollar at the time.  It has since changed in value with respect to the dollar, and today 1 euro = $1.11 USD.


Understanding the elasticity of demand for a monopoly Question: Your are working for a firm that is a monopoly. It is producing using technology that exhibits obvious decreasing returns to scale. After working with them for a while, a co-worker makes a mistake and accidentally increases the price per unit from \$10 to $11 for a week. You notice that the quantity sold drops by 5%. Management asks you to think about whether any strategic implications can be drawn from this episode. What do you write in your memo in response?

Answer: Quantity decreases by 5% while price increased by 10%, so total revenue increases. Since there are no economies of scale, cost decreases as you sell less and does total profit rises. Management should then raise the price.

I would like to clarify certain things about this answer. Intuitively I understand that if the percent increase in price is greater than the percent decrease in quantity then the firm is making profit. This, however, is not parallel with my understanding of elasticity. We know that a monopolist operates on the elastic portion of demand curve i.e. $|e|>1$ since this is where revenue is positive. Using this methodology for the question above, we should observe an $|e| > 1$. However this is not what we see, rather it is $|e|=|\frac{.05}{.10}|=|0.5|<1$. How come these two explanations are not parallel?

From the sounds of the question, the firm isn't operating at optimal efficiency. As you note, this firm is not on the elastic portion of the demand curve because $|e|=|\frac{.05}{.10}|=|0.5|<1$.

As an employee of this firm, you should suggest that they continue to adjust the price until they transition to the elastic portion of the demand curve. Once they do this, the firm should notice that their marginal revenue becomes positive.

I think your confusion stems from (1) your ability to think critically and (2) a misunderstanding that its the marginal revenue which monopolies want to be positive. Questions such as these are usually designed to capture a person's basic understanding of a concept, you pulled together multiple concepts..."too smart for the question." As for marginal revenue, this can be negative, but a firm that wants to maximize profit should adjust their business practices if marginal revenue is negative.


what alternatives can possibly back a new currency A currency can be backed by a trusted issuing authority, by a scarce resource or by the scarcity of its money base (eg bitcoin). Are there any other known working alternatives.

The value of money is derived entirely from others' willingness to accept it in exchange for things of value.

Money has in fact emerged— Rai stones on Yap is the classic example— without the existence of either a "trusted authority" mandating its use (I assume that by "trusted authority" you mean a government-mandated fiat currency) or any recourse to a scare resource (e.g., notes redeemable for silver or gold).

While the Yap stones themselves (the monetary base) were in fact scarce, and some degree of scarcity is a necessary condition for money to act as an effective store of value, it's not a sufficient condition, as FooBar noted in his comment. Even if a monetary base is finite, what matters is that people are willing to accept that form of money as payment, which is in turn generally determined by whether other people will be willing to accept that form of money as payment. It's collective agreement that money has value that makes it valuable. If people some day find no reason to continue using the Rai stones as money (they've been replaced by US dollars for day-to-day use, and they're only used for certain traditional exchanges now), they will lose their value as currency, despite their continued scarcity.

Specifically regarding Bitcoin, there has been significant skepticism in the economics community about whether it is actually a currency, with Yermack (2013) noting that it functions poorly as a store of value and unit of account, and that its transaction volumes have been quite low.


Help interpreting standard deviation I am looking at the 1979 cohort of the National Longitudinal Survey of Youth from the BLS. See here : https://www.bls.gov/nls/nlsy79.htm
I am just having some trouble interpreting the values for standard deviation.
Suppose I am looking at log of wages (natural log of wages).
Suppose my mean is 2.5, and standard deviation is 0.5.
How can I interpret my SD? Do I need to assume that the population distribution for log wages is normally distributed with zero mean and standard deviation 1?
I am just getting a bit confused here because standard deviation is a relational measure. We need to relate it to something, perhaps some standardized values, in order to conclude whether it is relatively high or low. Is it possible to do this without assuming anything about the population distribution? (such as zero mean or standard deviation 1)
Thanks.

First, there are substantial reasons to believe the data is not log-normal so it would be improper to assume log-normality.  So, no you should not do that.
You can research the literature on youth wages, it may have information on distributions.  However, that is probably more than is necessary.
There are two primary ways to estimate the standard deviation in economics.  There are more than two ways.
Both of those ways understand the idea of an estimator as being "good" by finding an optimal procedure by integrating the product of a utility function and a probability distribution to create a risk function.  The method with the "best" risk function for a given utility function "wins."
And you probably just thought it was a formula.  There is more than one formula.
The two methods have a slightly different interpretation.  If the method of maximum likelihood was used, then the mean and the standard deviation are the most likely values for the observed data.  All other methods are methods of mediocre likelihood after all.  If the Frequentist method was used, which is the most likely case, then it is an unbiased estimator, so that if you were to repeatedly make measurements, then the value it gives you will be correct, on average, though not necessarily even close for a specific case.
Since you do not know the distribution, you probably used the Frequentist method.
Now as to how to interpret it, you don't really.  It is an estimator.  Without more information, it just sits as is.  Of course, you do have more information.  You have the sample mean and you have Chebyshev's inequality.  You know that 75% of the values must be within two standard deviations and 88.88% must be within three standard deviations.  You can choose any arbitrary set of valuations that you like.  You can look at 2.5 standard deviations, or you can reverse it and solve for a fixed percent.
That will give you a feel for how wide wages really are, in logarithms.
It is here that the two interpretations become important.  If you decide to reverse the logarithmic transformation, the Frequentist estimator is no longer an unbiased estimator.  That is because the logarithm is concave.  You just cannot plug the values in and then reverse the process.  Nonetheless, at this scale, unless you are actually doing scientific work, they are probably not that far off.
The Maximum Likelihood Estimator is invariant to transformation, so you can plug it into the exponent of the base of natural logarithms and get a correct estimate.
Even doing that, however, is more informational rather than interpretational.
Interpretation must always be within the framework of an economic theory.  It has no meaning otherwise.  For example, imagine you were baking a cake and you accidentally added one egg too many.
If you were baking a six-inch diameter cake for a child's birthday then that could have an outsized effect.  If you were baking a cake that is ten feet tall and twenty-five feet wide in a pyramid shape for the winning Super Bowl team, then it's not going to matter.
It also depends on what area of economics you are looking at the data for.  You can use the same data to look at many different types of real-world problems.  In some problems, a wide or narrow spread of wages could be good, while others bad.


How popular are alternative standard of living measures amongst economists? GDP as a measure of the well being of an economy has been criticised as not being an accurate measure of the quality of an economy, as it excludes non-commericial interactions (such as housework or volunteer work) and includes negative events (such as graffiti and cleaning up after it) as economic activity.

However, at the same time, GDP is a good predictor of a society's wellbeing.

Some people have suggested instead of relying on GDP as the primary measure of an economy's performance, we should use something like the Genuine Progress Indicator (warning: PDF).

The question is, how much traction does this idea have, in economic circles?

This question is somewhat subjective but I'll attempt to provide an answer.

Real GDP is a very useful concept in economics. It provides a very good indicator on the size of an economy. It does have its limitations, some of which you have described.

Many economists are interested in measuring populations in different ways. At the moment, social mobility and inequality are getting a lot of attention. In analysing these issues, there is not as much value in observing the real GDP figure. Further treatment needs to be done.

Essentially, on a macroeconomic scale, GDP is very useful. When the analysis looks at individuals and concepts like welfare, it takes a far less prominent role in the analysis and other indicators are more commonly used.


Domestic Demand, Private Consumption, Public Consumption, Gross Fixed Investment Relationship I'm reading the IMF's January 2016 Report on Sweden's Economic Indicators, and the top section has the following:

Domestic Demand (2012) Percent Change: -0.6

Indented below are:

Private Consumption (2012) Percent Change: 0.8
Public Consumption " ": 1.1
Gross Fixed Investment " ": -0.2

I think the final one, Gross Fixed Investment, is the same thing as Gross Fixed Capital Formation? Although if someone could clarify, that would be useful.
My main question is, should Private Consumption, Public Consumption, and GFI all equal to Domestic Demand? My thinking was that domestic demand constituted these three elements (hence why they were indented), and some sort of weighted combination of them should give the -0.6% change drop in domestic demand?

I assume your numbers come from the 2012 numbers on page 4 or 5 of this document, which are rather different to the 2012 domestic demand numbers the IMF published a year earlier on page 28 or 29 of this document (the earlier version had domestic demand increasing in 2012 by 0.3% rather than decreasing by 0.6%)

They do look curious, for the reason you give.

Digging into Statistics Sweden's website, there are figures for various selected components of the expenditure measure of GDP.  It is particularly noticeable that in 2012, gross fixed capital formation fell by 0.2% while gross capital formation fell by 5.0%.

So an explanation could be a dramatic in the difference between gross capital formation and gross fixed capital formation.  This difference could include changes in inventories and changes in valuables: there seems to have been a fall in inventories in Sweden in 2012 after a large rise in 2011 and it is the combination of these two which leads to the sharp fall in gross capital formation in 2012 and so the fall in domestic demand.


Fixed effects in treatment model Hello in a simple treatment model

$$y=\beta_0+\beta_1w+e$$

where $w$ is unity for treatment by group.  Should you add dummies for the groups to control for differences. I read somewhere that you should never but I cannot remember where or why.

This sounds like the standard "drop one dummy" requirement when binary characteristics are included in linear regression - because otherwise, we will get perfect mutlicollinearity and no-solution.

Assume you have three subgroups, separated by age: Y(oung), A(dult), O(ld). You have reasons to believe that the effect of the treatment correlates with age-group, and you want to control for this association. If you include three dummies in the regression to that effect, you will create perfect mutlicollinearity - because if you sum these three columns of the regresor matrix row-by-row, you will get a series of Ones, which is already present in the matrix, since there exists already a constant term and so a regressor that consists of a series of Ones.

In such cases, we exclude from the regressor matrix any one of the three control dummies (for many reasons it is not a good idea to drop the constant term instead of one of the dummies).
This has the effect that the interpretation of the results becomes conditional on the group whose dummy we excluded: if say we specify

$$y=\beta_0+\beta_1w + \gamma_1A + \gamma_2O+e$$

then $\gamma_1$ measures how much more (or less, if negative) being Adult affects the outcome, compared to being Young, and $\gamma_2$ analogously for Old.

Situations of perfect (or near) multicollinearity may nevertheless occur even in this approach, depending also on the nature and distribution of values of the dependent variable. If the dependent variable is also binary, such possibilities increase, since we may have phenomena of "complete separation/perfect prediction" and the like.

In general, including controls in treatment regressions is a standard approach, and very reasonable. Including dummies as controls, may have the above mentioned complications.


The decline in the number of domestic servants does it mean that the market mechanism does not work—that the offer
of the going rate of wages does not secure a servant because servants
do not move to the highest bidder? This complaint—which would
be far from unanimous—would have economic significance because
it would imply that wages do not allocate servants: there is, however,
little empirical support for it.

From "Domestic Servants in the United States, 1900-1940" by George Stigler.
Did the number of domestic servants decline during the second half of the 20th century, and if so, what are the possible explanations for this decline?
Please post answers with academic references only.

I think that what Stigler called 'domestic servant' would be nowadays considered 'domestic worker'. For example, according to the Luebker, Oelz, & Simonovsky (2013). Domestic workers across the world: Global and regional statistics and the extent of legal protection (a technically semi-academic source as it is a technical report but based on comments I believe this would be acceptable to you), implicitly equates domestic workers with servants (and provides statistics on domestic work). According to the report:

With respect to North America, national sources also show a relatively low share
of domestic workers in total employment – 0.5 per cent in the United States (2010)
... For the United States, the 2010 Current Population
Survey put the number of domestic workers at 667,000 men and women. This represented a substantial decrease, of roughly 140,000 workers, following the onset of the
economic crisis; the same survey counted more than 800,000 in the pre-crisis years
2005 to 2008. Job losses among domestic workers were therefore quite substantial –
an aspect that is not commonly highlighted in discussions of the employment impact
of the global economic and financial crisis. ...
Historical sources indicate that the number of domestic workers was substantially
higher at the time of industrialization in the United States. The censuses of 1870 and
1900 counted 975,000 and 1,455,000 “servants”, respectively (see Rubinow, 1906). [emphasis mine]

Note that the number reported above by Rubinow roughly match statistics reported by Stigler.
According to the report indeed the number of domestic worker ('servants') declined in the second half of 20th century as in 2005-2008 the number of these workers was roughly half of what it was in 1900.
The data sources for US are listed as:

U.S. Bureau of Labor Statistics, Current Population Survey 2010 (Labor Force Statistics: tables 17 and 18 at www.bls.gov).

Additionally they frequently reference data from published papers/reports/books like the Rubinow in the excerpt above.
As to the reason what is the explanation of this decline - the authors do not mention specifically reasons for the historic decline in the U.S. (although for U.K. they cite changes to immigration policy which in past allowed servants to get settled status after 5 years), but the authors and also sources they cite argue that historically most domestic work was done by; a) women, b)  immigrants.

There is a peculiar historical continuity with respect to the overrepresentation
of international migrants among domestic workers. Based on United States Census
data from the late nineteenth century, Rubinow observed (1906, p. 508) that “[a]s
most means of employment are closed to the foreign-born (even English- speaking)
women, almost every second woman is forced to become a servant”. At the time, the
largest numbers of migrant domestic workers in the United States came from Ireland
(195,000), Germany (161,000) and Sweden (45,800).

In the report they also argue that most of domestic work is still performed by migrants or people who face barriers into entry to other occupations. Hence, my first guess would be that the number of domestic servants declined because nowadays especially women but migrants as well face less restrictions when entering into other occupations (although to be clear this is my conjecture).


Applying real growth rate to nominal value What happens if one applies a real GDP growth rate to a nominal GDP value? The result can't be a GDP figure in constant prices, since that would imply applying a real GDP growth rate to constant GDP figure.

Any thoughts?

This will provide you with a GDP in constant prices of the previous year. "Real GDP" only make sense if you mention which is you basis year. It is not an absolute figure.

Indeed, it would not make sense (beside research purposes) to display a real GDP in terms of the first year in which GDP was recorded. Accumulating 50 years on inflation in your figure would produce a tremendous discrepancy between your real GDP and your nominal GDP, resulting in confusion.


Is there a model for how much a philosopher produce in his lifespan? Is there a model for how much a philosopher produce in his lifespan?

If not, state the economical reason for why we pay the philosopher.

Here is a somewhat creative (and very imprecise) answer:

Let's assume that Philosophy creates no direct value for society (which seems implicit in your question). However, Mathematics and various other scientific disciplines to some extent originated from Philosophy. Most recently, Linguistics originated as a field of Philosophy. Based on this we can estimate the marginal product of a philosopher. You will need two numbers:

A: Take the marginal value of each invention generated by these fields. For example, speech recognition on your cell phone would not have been possible without Linguistics and thus Philosophy. You can estimate the marginal value of speech recognition by your willingness to pay for a phone with or without speech recognition. Do this for all products and services of an economy. (You can also take market prices and make some strong assumptions about the economy, such as competitive markets, etc.). Using time discounting, you can estimate the value of having a product one year earlier.

B: You must now assign the marginal contribution of a philosopher to the invention of linguistics to the speech recognition software. The marginal contribution seems to be infinite, since without linguistics there would be no speech recognition. However, you may simply assume that each additional Philosopher speeds up the process of the invention of linguistics by an equal amount. Thus, if you would have hired one more philosopher, the time needed to invent Linguistics would have been N/(N+1) the time N philosophers needed to actually invent linguistics.

Combining the information from A and B for all products gives you the marginal product of each philosopher. Note that this is only a rough answer and one would still need to carefully formulate the assumptions. However, it gives you a rough idea of how you could go about finding the marginal product of an otherwise unproductive philosopher.


Increasing prevalence of price discrimination It seems to me that the variation of prices for similar or identical products has grown over the last decade. A few examples:

On major air routes, price differences between low-cost and traditional carriers are extreme.
Retail sales appear more frequent and significant than ever.
At a grocery store, on any given day, it seems like some 30% of products are discounted. And I have received up to seven non-negligible coupons (for future use) even when making negligible purchases (under $5).
"Deal sites" like Groupon (and a thousand others) have become prevalent.
Single consumer electronics items are released as many different versions (with many different prices) with only slightly differing specifications.

All in all, it just seems like companies are getting more sophisticated (and more aggressive) about extracting as much of each consumer's willingness-to-pay as possible. This begs the question:

  Can you think of any data that could be used to quantify the increase
  of price discrimination across time?

Note on edit: I originally asked about welfare considerations also, but found a fantastic answer to that question here.

For current data, you could use a scraping program to collect data from firms' websites. This was the approach taken by a recent paper for airline pricing, so it would definitely work for your first example. In general, it should work for any market that has a significant online presence with universal price quoting. Retail sales should more or less satisfy that description. Grocery stores too nowadays, at least the big ones. See the paper cited for more info on its methods.

But, as your question pertains to the evolution over time, you'd need past data as well. Have a look at The Billion Prices Project at MIT and Harvard. http://www.thebillionpricesproject.com/datasets/

Williams, K. R. (2017). Dynamic Airline Pricing and Seat Availability (Cowles Foundation Discussion Papers No. 2103). Cowles Foundation for Research in Economics, Yale University. Retrieved from https://ideas.repec.org/p/cwl/cwldpp/2103.html


How to determine price per unit and quantity sold of product from financial statement Situation

I hope I'm asking in the right place. I'm writing a paper on the application of quadratic functions in economics and intend to use the Total Revenue function as well as the Profit function for a specific product in order to derive conclusions and whatnot. For the moment, all that I require is the price (or demand) function of a given product in order to find the rest out. For the price function:

  p(Q) = m - nQ

in order to find out what m (the slope) is, I would require coordinates (Q, p). Q being the quantity demanded (or sold apparently according to this link) and p being the price per unit sold.

I require the price function in order to make the TR (Total Revenue function).

Attempted Solutions

I have looked online for methods to derive the number of units sold from financial statements made by the company but I find that:

I need the price per unit for this (that that I do not have)
financial statements pertain to all products sold by the company and
as such are an inaccurate representation of the price function for
that particular product

For the profit function which requires the cost function, I have managed to find the solution from the financial statement but once again point 2 still stands. I think that if I find a business that exclusively sells one product, I will manage to derive the second cost function from the financial statements but once again, I do not have a solution for the first one.

Question

I am really lost in regards to what I should do in order to obtain data that I can use to analyze and ultimately demonstrate the application of mathematics in economics (specifically two sets of price per unit and number of units sold). I really hope that someone can help me with these questions and provide not necessarily the aforementioned solution that I desire but any solution to the situation I am in.

What you are trying to do here is estimate the demand curve of a firm. Broadly speaking, even if you got data on price and quantity, you would not be able to estimate this because your right-hand-side variable (quantity) is also determined by the supply curve. This is what people call the 'simultaneity' form of the problem of endogeneity.

The way to resolve this is to find a credible instrument that allows you to model movements in quantity that arise from changes in supply. For example if you found data on changes in the oil price, and found that they affect the quantity of goods purchased in the market you are estimating the equation for, you would essentially be able to 'trace out' the demand curve.

However, reading between the lines of your query, I suspect you are not particularly familiar with econometrics so the above may not be useful to you. If this is a school project (as opposed to university or other higher level of education), I think you could take the approach you are suggesting and then get additional points if you can explain what I just did above.

Company annual reports should contain the information you need, so long as you focus on companies that sell 'real goods' as opposed to services (think automobile manufacturers rather than tech companies or law firms). For example, page 71 of the Daimler annual report (see here) contains data on number of cars sold, and page 228 contains total revenues. If you want to break this down by type of vehicle sold, see page 253 for revenue by type of vehicle.

In general (i.e. when you look at other annual reports) you will find that:

You will find volumes sold somewhere in the text of the annual report (before the financial statements start)
You will find revenues at the start of the financial statements (p.228 in the above report example)
Further breakdown of revenues can be found in the notes to the financial statements (i.e. some point beyond p.228 - the note I refer to on p.253 is the note on revenue in that annual report, so naturally breaks the revenue out. You can find out which notes refer to which items in the financial statements by looking at the financial statements on p.228 - there you will see a '4' next to revenue which means you want to look at note 4)

I would recommend of doing a mix of looking through annual reports for a given company over time, and also multiple different companies' reports.


How do I obtain a correlation between two variables? Can I differentiate a quadratic regression model formula with the form
$$Y_i=\beta_0+\beta_1 X_{1i} +\beta_2 X_{1i}^2+\epsilon_i$$
(added to this formula would be other control variables e.g dummy variables) to obtain the correlation between X and Y holding everything else constant? Also, if I were to add a female dummy variable, how would the correlation of X and Y differ between men and women? Or would the correlation be the same?

For the above equation is differentiable, and hence the partial derivatives will exist:
$\frac{\partial Y}{\partial X_2}= 2\beta_2X_2$.
Adding a dummy variable should not affect the above derivative for all practical purposes - the function will be differentiable a.e.
(note that you can't differentiate with respect to a dummy variable though)
Edit:
After the question was modified, the new expression of the partial derivative would be:
$\frac{\partial Y}{\partial X_1}=\beta_1+ 2\beta_2X_1$.


Replicate Blundell and Bond (2000) results using R I want to replicate Blundell and Bond (2000) Table III in R. I'm using the function pgmm from package plm, which (apparently) replicates the approach of Stata's xtabond2 (Roonman, 2009). The estimates I get are qualitatively similar, but not the same, the Arellano-Bond test of serial correlation suggests the moment conditions are invalide....and I'm sad to say I don't yet see how to recover the production function coefficients.
The authors of plm have a useful companion textbook: Millo and Croissant 2018 Panel Data Econometrics in R. I get the data from there (associated packaged pder), and follow section 7.5 for set-up and diagnostics. Here is a self-contained example:
library(plm)
library(pder) # contains the Blundell and Bond dataset
#detach(package:dplyr) # if loaded, dplyr::lag masks plm::lag

data('RDPerfComp')
str(RDPerfComp) #n.b. - variables already in logs (see ?RDPerfComp)

And now to replicate some of the columns from Blundell and Bond 2000 Table 3:
# "OLS levels"
ols<-plm(y~lag(y,1) + lag(n,0:1) + lag(k,0:1),
             data=RDPerfComp, index=c("id","year"),
             effect="twoways", model = "pooling")
summary(ols)

# "Within groups"
within_groups<-plm(y~lag(y,1) + lag(n,0:1) + lag(k,0:1),
                   data=RDPerfComp, index=c("id","year"),
                   effect="twoways", model = "within")
summary(within_groups)

# "SYS t-2"
sys_t2<-pgmm(
  y ~ lag(y,1) + lag(n,0:1) + lag(k,0:1) |
    lag(y,2:99) + lag(n,2:99) + lag(k,2:99),
  data=RDPerfComp, index=c("id","year"),
  effect="twoways",model="onestep",
  transformation="ld"
)
summary(sys_t2,robust=TRUE,time.dummies=FALSE) # both options can be provided directly in pgmm()

# "SYS t-3"
sys_t3<-pgmm(
  y ~ lag(y,1) + lag(n,0:1) + lag(k,0:1) |
    lag(y,3:99) + lag(n,3:99) + lag(k,3:99),
  data=RDPerfComp, index=c("id","year"),
  effect="twoways",model="onestep",
  transformation="ld"
)
summary(sys_t3,robust=TRUE)

The results are very similar for the pooled OLS model, almost identical for fixed effects/within model, and only "qualitatively similar" (magnitudes, signs) for the SYS-GMM models, with some exceptions (notable the estimate for the y_t-1 coefficient). More concerning, the Sargan-Hansen test appears to reject the null of valid instruments for both the SYS-GMM models:
sargan(sys_t2) # same statistic as reported by summary()
sargan(sys_t3)

...and the Arellano-Bond moment condition test appears to reject the null of no serial correlation, suggesting that the moment conditions are invalid
mtest(sys_t2) # you can make this robust using vcovc =
mtest(sys_t3)

So my questions:

Am I specifying these wrong (probably - my first try with gmm) or are we just looking at the results of different machinery?
What could explain the diagnostic test results, which appear to say the SYS-GMM models aren't valid?
How do we get Beta_n, Beta_k, and rho (the production function parameters, as given in the  middle panel of Table III) from these results? (EDIT: OK, as stated in the paper, via testing and imposing the coefficient restrictions using "a minimum distance estimator" see eq'n 2.3 and text below in original paper)

(yes these are 'advanced undergrad' type questions, no this is not coursework)

3. How do we recover parameters from production function estimates (INCOMPLETE ANSWER - will be updated with how to do this in R once I have time to figure it out, or if somebody else knows...)
Blundell and Bond aren't estimating the parameters of a Cobb-Douglas production function. They're estimates the parameters of a "dynamic (common factor) representation" of a production function, specifically:
$(1) \ \ y_{it} = \beta_n n_{i,t} - \rho \beta_n n_{i,t-1} + \beta_k k_{i,t} - \rho \beta_k k_{i,t} + \rho y_{i,t-1} + (\gamma_t - \rho \gamma_{t-1}) + (\eta_i(1-\rho) + e_{it} + m_{it} - \rho m_{i,t-1})$
...which they get by quasi-differencing their production function and doing something weird with the $v_{it}$ term (not shown above). Changing the symbols, they re-write this as:
$(2) \ \ y_{it} = \pi_1n_{it} + \pi_2 n_{i,t-1} + \pi_3 k_{it} + \pi_4 k_{i,t-1} + \pi_5 y_{i,t-1} + \gamma^*_t + (\eta^*_i +w_{it})$
Where the * presumably indicates steady-state values, but again, I wish I had access to a teacher to explain precisely why they write that. Anyway, what their SYS-GMM estimator returns is a vector of parameter values $\boldsymbol{\pi} = (\pi_1,...,\pi_5)'$. We now have to use this to get the vector of parameters $\boldsymbol{\theta} = (\beta_n,\beta_k,\rho)$.
The only place I can find an explanation of how one does that is this paper applying SYS-GMM to Cuba. They refer to Woolridge 2002 (I don't have it), and assert that one can consider the problem as defined by the relationship $\boldsymbol{\pi} = h(\boldsymbol{\theta})$. We have $\boldsymbol{\pi}$, we need $\boldsymbol{\theta}$, and we will have to employ some function h() to make the link. It sounds like h() is taken to be an instance of a general class of minimum distance estimators, and we can (according to Woolridge 2002, apparently) solve the problem by solving:
$min (\boldsymbol{\theta}) = (\hat{\pi}-h(\theta))'\Omega(\hat{\pi}-h(\theta)) $
where $\Omega$ is some weighting function. And again, apparently $\Omega$ should be chosen as the variance of the matrix of parameters, obtained by "the delta method".
...but now it gets confusing, because although it's easy to find info on the delta method online, the matrix of parameters includes the unknowns $\boldsymbol{\theta}$. I guess the way to tackle this is to multiply it all out and plug into optim, using some arbitrary choice on starting values (factor shares of output, if $ valued?). I will update if I get a chance to try that...
In going from equation (1) to (2) it is pretty obvious that:
$$h(\beta_n,\beta_k,\rho) = \begin{pmatrix} \beta_n \\ - \rho \beta_n \\ \beta_k \\ - \rho \beta_k \\ \rho \end{pmatrix}= \begin{pmatrix} \pi_1 \\ \pi_2 \\ \pi_3  \\ \pi_4 \\ \pi_5 \end{pmatrix},$$
and $$\Omega = var(\pi)$$


How to approximate stochastic volatility model with finite-state Markov chain? A common practice when computing solutions to stochastic dynamic optimization problems is to approximate an exogenous forcing process $z_{t+1} = \rho z_t + \sigma \epsilon_{t+1}$ with a finite-state Markov chain, e.g. by Tauchen's or Rouwenhorst's method. What would be a good way to discretize AR(1) process with stochastic volatility?

That is, if the original AR(1)-SV process looks something like this:
$$
\begin{split}
z_{t+1} &= \rho_z z_t + \mathrm{e}^{v_t} \sigma_z \epsilon_{t+1} \\
v_{t+1} &= \rho_v v_t + \sigma_v \eta_{t+1}
\end{split}
$$
with $\epsilon, \eta$ being independent standard gaussian shocks, my goal is to obtain values $z_i$ and transition probabilities $p_{ij}$ ($i,j=1,\dots,n$) such that the corresponding Markov chain approximates the original continuous-valued process.

You could do a binomial-tree approximation to the process for $z_t$ and then have a different process control the number of steps you take on the tree. This preserves recombining property and it is essentially the method explored in On the Computation of  Continuous  Time Option Prices Using Discrete Approximations (Amin (1991))

  We  develop  a class of  discrete, path-independent  models to
  compute prices  of American options  within the Black-Scholes  (1973)
  framework,  including  models in which state variables have
  time-varying volatility  functions and models with  multiple  state
  variables. Time-varying volatility  functions are illustrated with
  applications  to term structure models developed by  Vasicek  (1977)
  and  Heath, Jarrow,  and Morton  (1988), (1990).  Distinct from
  previous  work in the  literature,  the multivariate models suggested
  in this  paper are consistent with  arbitrarily large, though
  constant,  covariance functions. Finally,  we compare  and contrast
  the numerical  accuracy  of a  large  number of models with simulation
  results.

You could then use a binomial AR(1) process for the number of steps.


AR(1) in Discrete Version of Stochastic Growth Model If I assume a stochastic growth model in discrete time and the production function is defined as $F(K_{t}(s^{t-1}), L_{t}(z^{t}))$ where $z^{t}$ is history of the technological shock up to time $t$. A government also exists in the economy and the government spending at period $t$ is $g_{t}(z^{t})$. Can I assume that the government spending follows an AR(1) process given the setting in a stochastical process? If not, do you have any suggestions on modeling the change in government spending? Thank you!

I find it difficult to just say government spending follows an AR(1) process this is because you will end up with violating the "No Ponzi Game Condition" on most models including government.
To model changes in government spending you would simply have to concider different ways of shocking your model.
If you are thinking about optimality in your model and if there is a place for government, formulate your environment in the context of a planners problem and check how optimality looks and if in fact there is space for government.
I hope this helps


What oil price will minimise new resource extraction? A higher oil price would increase incentives to develop new oil resource extraction, but it also increases the competitiveness of sustainable energy sources.

Conversely, a low oil price might mean less development of new resource extraction, putting projects such as hydraulic fracturing or offshore Arctic drilling on hold.

What I wonder is: what oil price will lead to the lowest level of new resource extraction?  Or, in other words: suppose that I strongly oppose the development of new resource extraction with potentially very high environmental costs (such as hydraulic fracturing or Arctic offshore drilling), should I be glad when oil prices or low... or when they are high?

An oil price of 0 will make any extraction of oil unprofitable and hence imply no further oil extraction.

You should think about how prices carry signals. A low oil price (even if not 0) carries the signal that we, as society, do not value that oil as much. The conclusion is imminent.


Free rider problem in game theory Suppose a town is building a bridge, and it costs $B$.
There are $n$ villagers.

Each village's valuation of the bridge is private information, $v_i$.

It is common knowledge that this valuation is drawn from a uniform distribution $[0,1]$. $B\in[0,1]$.

Villager can only submit $0$ or $B$.

If one villager submits $B$, then the bridge is built and every other villager pays their submission.

If no bridge is built, everyone gets $0$.

How do I construct an expected payoff a village $i$?

What I got down to is having 2 scenarios: $v_i>B$ and $v_i\leq B$.

But in each case, I have two possible payoffs. For the former case,

  if every other player submits $0$, $i$ should submit B, because $v_i-B>0$.
  if someone pays $B$, $i$ should submit 0, because she gets $v_i$.

You get a similar type of for the other scenario.

But how would I incorporate this into expected payoff of $i$ and how should I go about constructing a social welfare function?

I feel like this is just a variation of all-payout auction with discrete action space for each $i$.

Let $b_i\in\{0,B\}$ be $i$'s strategy. Then $i$'s payoff depends on the strategy profile $(b_i,b_{-i})$, where $b_{-i}=(b_j)_{j\ne i}$.

\begin{equation}
u_i(b_i,b_{-i})=
\begin{cases}
v_i&\text{if $b_i=0$ and $b_j=B$ for some $j\ne i$}\\
0& \text{if $b_i=0$ and $b_j=0$ for all $j\ne i$}\\
v_i-B&\text{if $b_i=B$}
\end{cases}
\end{equation}

Thus, $b_i=B$ is a best response if
\begin{equation}
u_i(B,b_{-i})\ge u_i(0,b_{-i})
\quad\Leftrightarrow\quad
v_i-B\ge (1-\Pr(b_j=0,\;\forall j\ne i))v_i.\tag{1}
\end{equation}

Since the game is ex ante symmetric, we could further assume that every $i$ adopts a threshold strategy, i.e.
\begin{equation}
b_i=\begin{cases}
0&\text{if $v_i\le\overline v$}\\
B&\text{if $v_i>\overline v$}
\end{cases}\tag{2}
\end{equation}
where $\overline v$ is some common threshold value. Then, the probability in $(1)$ can be written as
\begin{equation}
\Pr(b_j=0,\;\forall j\ne i)=\Pr(v_j\le \overline v,\;\forall j\ne i)=(\overline v)^{n-1},\tag{3}
\end{equation}
where the last equality is obtained from the assumption that $v_j$'s are i.i.d. and $v_j\sim U[0,1]$.

Consolidating $(1)$ to $(3)$, we can solve for the cutoff value $\overline v=B^{1/n}$.


Significance of Y-axis in Aggregate Supply curve (AD-AS model) This question is considering an AD-AS model, with Price on the Y-axis and Real GDP on the X axis. The AS is composed of the Keynesian (horizontal), intermediate (upward sloping) and classical (vertical range.

I read that one explanation for the upward slope of the intermediate range is that as price level increases, output prices may increase beyond input price (due to rigidity). Hence, real value of inputs/costs falls, and it becomes more profitable to produce the good, and hence output increases.

Regarding this uneven increase in the nominal value of outputs and inputs, are they both reflected in the y-axis? Meaning, does the y-axis's aggregation of price contain both intermediate as well as final goods, or is it merely an estimation of final goods. I would think that in the former case, the rise in GPL on the graph (inducing increase in real GDP) contains both increases in output and input. In the latter case, the rise in GPL contains only output price increases, but the increase in input prices which lags behind is reflected off the graph.

I would think that in both cases, whether the increase in input prices is reflected on the y axis or not, the shape of the intermediate range still holds. Hence, is may not be significant. Is it simply a choice of what metric (CPI, etc.) I use to estimate price on my y axis?

I didn't quite well understood your question, but from what I could make of it I have answered the relation behind the formation of the Short run aggregate supply

In the short run, nominal rigidities , and/or imperfect information, make the AS
curve positively sloped (SRAS - Short run aggregate supply)

The position of the SRAS curve is determined by the factors
contributing to equilibrium in the labour market. In particular, an increase
in the expected price level makes workers bargain for higher wages (for
any given unemployment rate). The increase in the wage raises the actual
price that firms set. As a result, an increase in the expected price level
causes the AS curve to shift upwards

Diagrammatically , the SRAS curve should shift upwards ;

This equation states that the deviation of the actual price level from the
expected price level, P – Pe, is proportional to the deviation of output
from its natural level, Y – Yn

If you are confused between Workers negotiation and AS fall or rise - you should read about the WS-PS model. The WS stands for wage setting, PS for price setting.


Relationship between the Tragedy of the Commons and negative externalities? I've read that the tragedy of the commons can be seen as a negative externality. That is, $MSC > MPC$. However, I'm having trouble understanding why the supply curve actually shifts downwards due to this.

I know, graphically, that the $MSC$ curve will be above the $MPC$ curve. But, what do the external costs mean in this context and how would it all look graphically?

The reason why it boosts supply is that the costs are not born by produces. For example, since you can’t own fresh air due to lack of property rights (tragedy of the commons) firms don’t need to pay for using up the clean air by pollution and hence it does not enter their cost functions.

Recall decrease in costs shifts supply right as at lower cost firms are willing to supply more at any price.

I created a graphical example of this for you in overleaf. As the graph show in presence of externality the supply $S$ shifts right and new supply is $S_E$. Demand remains unchanged because the externality affects production costs not preferences or other factors affecting demand. The new equilibrium will be at the intersection of $D$ and $S_E$. In this new equilibrium price is too low and quantity too high compared to social optimum which would be at the intersection of demand and supply without the externality.

The vertical distance between the supplies is the value of the external costs (externality).


Central Banks and Price Stability Are there any empirical studies on the question of whether independent central banks cause price stability?

I am seeking to understand if independence (of the central monitory authority) is part of the market function that determines price stability at all, and if there are any studies conducted in this area.

The case I have seen arguing for independence leading to price control from here, in an article titled

  Nobel-Winning Economist Kydland Backs RBI's Anti-Inflation Policy

  In his speech, Mr Kydland observed that independence of the central bank is key to achieving the broader goals of policymaking, and interference by the executive is not desirable.

The case against (probably) from here

  The 1995 Reserve Bank of Zimbabwe Act legislated a greater degree of autonomy
  for the central bank. After 1995 the bank had its own budget and could decide on its own
  finances. The act also established the control of inflation as the unique objective of monetary policy,

  Clearly, increased CBI (Central Bank Independence) did little to restrain Zimbabwe’s subsequent monetary policy.

Your question has been addresses in different ways. Kydland and Prescott (1977) argue that a central bank should follow defined policy rules instead of active stabilization methods because the latter contributes to economic instability. Barro and Gordon (1983) prove that under a discretionary regime, the central bank has an incentive to print money to improve the economic performance in the short run, but this doesn't happen in the long run. Walsh (1995) discuss the way central bankers incentives should be design in order for the central bank to follow a socially optimal policy.

On Central Bank Independence (CBI), Grilli, Masciandaro and Tabellini (1991) and Cukierman, Webb and Neyapti (1992) developed a methodology to assess CBI  from different countries, and how the degree of independence impacts on the economic performance of this countries. Alesina and Summers (1993) studied 16 OECD countries and they compared the countries CBI score against economic performance measures (GDP growth, unemployment rate, and inflation). Then, there are several papers that cite these researches and build upon them.

The CBI scores are based on multiple criteria, Grilli et al., have a different approach than Cukierman et al. Alesina and Summers used a combination of both, so for the case of Zimbabwe you'll have to analyze if the laws of its central bank have the characteristics that the researches take into account when they build their indices.


Maximizing units under a budget constraint and increasing costs Consider two columns.

Column A has total cost per day, Column B has units bought that day. The marginal cost of each unit is increasing because of limited supply.

My goal is to estimate total possible units under a certain budget.

What I did for this was run a LOGEST estimation to get the information in the form of cost = b+ m^units
My reason for doing this is because of the increasing marginal cost per unit.

I got the function :
y = 1.00077^x + 0.24

But when maximizing it, the numbers I'm getting for units are too small under this budget.

I also ran a LINEST and got that each unit bought increases the cost per unit by approximately 0.0005814009591 $. I have been unable to make a model that uses this estimation.

Any suggestion or different approach will be much appreciated,
Thanks.

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

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

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


Relationship among universal type space, Aumann's semantic knowledge model and Samet's syntactic knowledge model What's the relationship among universal type space, Aumann's semantic knowledge model and Samet's syntactic knowledge model?

Here's my confusion:

Regarding universal type space and the model in Aumann's Agreeing to disagree, I used to think they're really the same thing from two different angles. The type space construction is a bottom-up construction. It starts with all the payoff relevant parameters from players' point of view, and generates a set of states of world in the end. Aumann's model is top-down. The set of states of world and players' knowledge as partitions are exogenous. Interesting results are derived by imposing some consistency rules.

It seems to me, there's a one-to-one correspondence between a player's type in the former and a cell( or atom, block) in the selfsame player's partition in the latter, because a player's strategy has to be measurable with respect to them in these settings.

But after having a skimming of an unpublished paper by Robert Simon,The Common Prior Assumption in Belief Spaces: An Example, I found it's not the case.

In that paper, he actually imposed a partition on Merten and Zamir's type space(he claimed so) for each player, so there's no such correspondence.

Another thing that is weird is that it seems to me he's actually not working on on a belief space. It looks like he's working on a model in Dov Samet's Ignoring ignorance and Agreeing to Disagree, which is homeomorphic to a Cantor set, a set which is generated by assigning truth values on underlying propositions and the use of non-repeated knowledge operators of the same player. It seems to me Dov Samet's model is not homeomorphic to Merten and Zamir's type space, because we might need to add operators of belief from probability 0 to probability 1 in Dov Samet's model to do that, and the generated set of state of state of world will have a cardinality strictly larger than a Cantor set.

There is no "universal Aumann model", as shown in Heifetz & Samet, GEB 1998, "Knowledge Spaces with Arbitrarily High Rank
", even though there is a universal type space.

On a less technical level, Aumanns model does not allow for wrong beliefs. A generalization, so called Kripke structures, do however.


Data on average/typical retail markups Can anybody provide a reliable source that gives data on retail markups? My end goal is to make a fairly high-level statement along the lines of "a typical retail markup (across all industries) is X%", or "the average markup in industry Y is X%", so fairly aggregated data would be fine.

I recommend the Comp-Net database. It is a firm-level data for European countries. It includes a large range of variables, including mark-ups:

Check the documentation for more details.

Many researchers have also used the Amadeus database, also for Europe. A nice summary about it is here.

For the US, take a look at this paper. The authors use three different sources of markups: Compustat, NBER Census of Manufacturing, and IRS (Inland Revenue Service). The first two are micro-data whereas the latter is aggregate at industry level.


Why can't goverments print money to fund their economies? In previous questions I understood that printing money and injecting it in the economy generates inflation because there is a bigger demand for the same offer (please correct me if I'm wrong) so it's not a good idea. After thinking this, a new question arose. Why can't goverments print money to fund the productive sector? In that way, it can get money in circulation while generating more offer so there is no inflation. I can't understand what prevents goverments to do that.

The first thing to be aware of is that money is continuously being created and destroyed through the process of fractional reserve banking (which according to the Bank of England and others is incorrectly explained in most textbooks). Under this system there can be periods in which, in the absence of central bank intervention, there will be a fall in the money supply and deflation. In these periods there would be little risk of inflation if the government printed money for whatever purpose they liked. Indeed some economists have advocated direct money printing instead of QE.

With regard to the idea that creating money for productive purposes causes less inflation because more is produced - I know that this is something that Prof. Richard Werner has emphasised in the past, though I don't have a specific reference for that to hand.


Why would investors from other countries want to invest in a country with a large CA deficit? According to my textbook, the current account and financial account must balance; therefore, a country w/ at large CA deficit will need to fund this by a financial account surplus (i.e. they need to receive FDI funds, encourage foreign investors to buy their bonds etc.)

But why would a country want to invest in another country that has a structural CA deficit (as a structural CA deficit implies the country is uncompetitive and therefore it is a risky investment).

Its all relative when evaluating investments:

A) It might be risky but pay a relatively high return. It could be the case that the local interest rates are high even taking into account a potential devaluation, or it could be the case that the investment is denominated in foreign currency, in which case the devaluation doesn't change the principal (although it does change the likelihood of default). Typically currencies appreciate after the central bank increases the rates in local currency, as foreigners are willing to tolerate more risk when the return goes up. (The "Sharpie ratio" is one way to measure the return relative to riskiness.)

B) The country can be temporarily uncompetitive. That is, if investors think it will be relatively better later on (less uncompetitive ), then they will be willing to bet on the country. (In other words, $R=(Dividend +Future Price)/Current Price$, which means that even if you expect low dividends or interest payments, your expected return could be high because the expected future price is high.


Why are banks allowed to resell mortgages? It just seems like a way to get around money creation limits imposed by liquidity requirements. For example if a bank creates new money by extending new morgages then securitizes them and resells them, the bank is effectively printing money and giving it to itself to boost it's liquidity ratio, which in turn allows the bank to extend more morgages and resell them ad infinitum!

Maybe it's actually good that banks can do this? I'd like to know if this is a responsible business practice that's good for the economy as a whole (maybe allowing for cheaper mortgages) or if it's only in the interest of bank shareholders (at the expense of destabilizing the economy).

A bank selling mortgages does not, by itself, increase the money supply.

To see this, work through the balance sheet implications step-by-step:

A bank makes a mortgage loan, swapping cash assets on its balance sheet for a mortgage asset. The customer receives cash. At this stage, the money supply has been increased.

2a. A bank sells a mortgage to another bank, swapping cash and mortgage assets between the two, but without increasing the money supply.

2b. A bank sells a mortgage to something that is not a bank, reversing what it did when it made the mortgage loan: the bank ends up with a cash asset and loses the mortgage asset, while the not-a-bank entity loses cash, decreasing the money supply.

They key here is that expansions or contractions of the money supply arising out of banking have everything to do with the the extent to which banks in the aggregate are lending cash that has been deposited with them (i.e., deposit liabilities). It’s a stock, not a flow, so you have to analyze the balance sheet impacts of what happens when banks sell an asset, paying attention to how the buyer is financing the purchase, to understand what the effect on the money supply is.

The (glaring) exception to this is that many entities that hold mortgages act effectively like banks, but aren’t banks. They’re often referred to as “shadow banks.” There are a lot of different types of entities that do this, but a simple, clean example is a mortgage REIT. If a REIT buys a mortgage security, it will likely fund it by doing a repo (basically borrowing money but with collateral) with a money market mutual fund, which is lending out its depositors’ money, just like a bank.

One note: In responding, I’m deliberately ignoring the part about liquidity requirements, because money creation by banks can be (and has historically been) bound at different times and for different entities by liquidity, capital, or reserve requirements, but liquidity requirements in the US are not generally intended to constrain money creation per se, but rather as a prudential measure. More specifically, GSE MBS is a Level 1 “high-quality liquid asset” under the liquidity coverage ratio, so swapping mortgages once they’ve received a GSE wrap doesn’t actually do anything to improve a bank’s liquidity ratio.


Ownership in Neoclassical Economics/Property Rights Question I'm currently looking at New Institutional Economics and I can't get my head around the assumption of the neoclassical irrelevance theorem stated by the neoclassical economics.

It doesn't matter whether the factors of production are owned or rented by their users
(see Samuelson 1 957, 894: "Remember that in a perfectly competitive
market it really doesn't matter who hires whom: so have labor
hire ' capital, ' . . ." )

I can't seem to find an explanation for that statement. Can someone explain it in terms of neoclassical thinking?

Best Regards

As far as I'm aware, this is what it means:
When we say a capitalist 'hires' labour, we are talking about the power dynamic here, where the capitalist has control over what the worker does, his/her wages etc. But in Samuelson's world, a perfectly competitive markets implies that contracts are complete, which means that the worker when agreeing to work for the capitalist has complete information over what the job is going to be like, when and whether their wages is going to be paid etc. If the worker didn't like the future work/wages, they wouldn't accept the job. So here with complete contracts, the hierarchy is irrelevant, it doesn't matter who hires whom, since both knows exactly what the future job conditions are. As you can see this assumption abstracts away from power dynamics and wouldn't be very useful in analysis of real world labour issues.


Why don't researchers use regularized probit model? I know that a regularized logistic regression can be done to reduce training error, but I haven't found any economics research that uses a regularized probit model, only a regular probit model from what I have been able to find. Why don't economic researchers use a regularized probit model?

Thank you

I have spent three days thinking about how to answer your question.  I still haven't really decided how it should be answered, so this answer is more in the way of a set of observations.  I can readily imagine a formal treatment of general linear models or limited dependent variables models could do better than this answer.

The first thing I would observe is there is probably no answer to your question.  Instead, you should consider constructing such a solution.  It is probably impossible to talk about why something did not happen.

The second is that every academic tradition tends to have traditions about what and how to use a statistical model.  There is a lot of discretion in a pretty wide range of problems.

Some of that tradition is influenced by computability and the size of data sets.  Many fields have been heavily influenced by the role punch-card computing had on a choice of solutions.  For older fields, where tables or slide rules were used, you see its influence.  At least some of the question is likely due to a field feeling the need to explore some methods more than others.

Other parts are influenced by the frequency of some type of problem.  If a field commonly runs into censoring, for example, it still influences the thought even when censoring isn't present.  Economists generally cannot perform randomized experiments and are being asked by policymakers to make decisions almost for them.  The economics profession loves to assume normality, even when it cannot be present, because it makes for tractable solutions.

Another observation is that all regularization methods map to some Bayesian point estimator under highly stylized assumptions.  That is not trivial because it biases the estimator.  The small loss in accuracy can lead to a substantial improvement in precision.

That would matter more for sampling distributions that have heavier tails than others.  The mean of the normal distribution has better sampling properties than the mean of the logistic distribution.  To see this, I created ten thousand samples of size one thousand and found the mean of each sample and plotted its density plot.  Each sample has a mean of zero and a variance of one.

The density plot of the means of the normal distribution are in red and the logistic are in blue.

The purpose of regularization is to make the leptokurtic sampling distribution of the mean for the logistic distribution become closer to the mesokurtic distribution of the mean of the normal distribution.

That,  of course, can be the side effect of a well constructed Bayesian prior distribution.  Indeed, it is one of the reasons Bayesian models are less likely to overfit.  Of course, they have their own unique problems that Frequency-based models lack.

Each of these densities is the "test" distribution given a known distribution.  Because the slope of the regression, or the mean here, is easily pulled away from the true parameter value when compared to the normal mean you can reduce the width of the test distribution by not weighting all values on the real number line as equiprobable.

So one of the likely answers would be that the advantage of regularization would produce smaller gains for probit.  Nonetheless, Stein's paradox would still hold, though in a strange form, and there would be gains.

Indeed, the entire point of Bayesian estimation is to impute real outside knowledge into the estimator.  If something is unexpected, then the weighting implicit in a Bayesian estimate pulls any point estimator away from the sample on the logic it is an outlying sample.  Of course, the potential conceit is that the researcher would be able to identify a sample that is unusual.

Regularization automates that conceit without asking the researcher if they do have actual knowledge from prior research.

There is no reason not to find a regularization for higher dimensional probit, but there is a need to do it with a high dimension logit.

It is certainly a feasible thing to do because Bayesian priors for logistic regression are discussed quite a bit in the literature.  Finding one that works well so that an analytic solution accepted by your peers can be found is quite another issue.


How does key currency work? When a country make too many of their currencies, it will eventually lower the currencies' value and inflation would occur.

But why won't key currency work like this? If the US is making more and more money, shouldn't the value get lowered at some point? Where did all that amount of money which has been coming out of US go? Is it because the world is still growing even now, and the circulation needs more and more Dollars constantly?

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


How do small firms survive in an oligopoly? How do small firms survive in an oligopoly if large firms already dominate a huge amount of market share in the market? in terms of the supermarket industry between large supermarkets and small grocery stores around the country.

When there are few big firms and many smaller firms with a small market share, economists speak about a market with a competitive fringe. The smaller firms are price takers, have higher marginal and average costs and a lower markup than bigger firms. They have often a lower rate of profit than big firms. Although markets with heterogeneous firms are often not presented in textbooks, the economic literature is full with contributions investigating heterogenous firms. This is more realistic, but somewhat more complicated than the homogenous firm framework. Existence and unicity of the short- and long-run equilibrium are not always guaranteed.
Small firms survive because they have often smaller sunk costs (entry and exit costs) than larger firms, and often pay lower wages.


Is local non-satiation enough to talk about Walrasian Equilibrium being subset of Core In Advanced Microeconomic Theory, the author mentions that the Cobb Douglas utility function is neither strongly increasing nor strictly quasiconcave over all of R+. But the condition of strongly increasing in R+ is used to prove that set of Walrasian Equilibrium allocations is a subset of Core. So we can't apply this result to Cobb Douglas utility functions to prove that Walrasian Equilibrium obtained is part of core. Is local non satiation sufficient to say set of Walrasian Equilibrium allocations is a subset of Core as Cobb Douglas satisfies local non satiation?

Yes, local-non satiation is sufficient for the result. In fact, the theorem holds as long as for every consumer every optimal consumption exhausts the budget. The wikipedia page has a proof which uses local non-satiation: https://en.wikipedia.org/wiki/Fundamental_theorems_of_welfare_economics#Proof_of_the_first_theorem.

As a side note: Cobb-Douglas preferences do satisfy strict monotonicity on $\mathbb{R}^{n}_{++}$. Thus, if you can argue that you may restrict attention to bundles where all entries are strictly positive, the arguments based on strict monotonicity applies.


Revenue maximization We have two firms with identical cost structure compete in a market

Demand function = $p=a-bq$

And $q=q_1+q_2$

They are identical in every way. However, firm 1 maximizes profit and firm 2 maximizes revenue as long as shareholders are satisfied, which he achieves by keeping profits nonnegative.

Both firms have constant and equal marginal cost c. So I want to find the quantities that they will choose.

———

What I did is...

For firm 1,

$$\pi_1=max[(a-b(q_1+q_2))q_1-cq_1]$$

FOCs for $q_1$

$$a-2bq_1-bq_2-c=0$$

So $$q_1={a-bq_2-c\over 2b}$$

For firm 2,

$$max [(a-b(q_1+q_2))q_2]$$

FOCs $$a-bq_1-2bq_2=0$$

$$q_2={a-bq_1\over 2b}$$

So,
$$q_1={a-b({a-bq_1\over 2b})-c\over 2b}$$

$$q_1^*={a-2c\over 3b}$$

And $$q^*_2={5a+2b\over 6b}$$

—-

The question says that “* firm 1 maximizes profit and firm 2 maximizes revenue as long as shareholders are satisfied, which he achieves by keeping profits nonnegative.*”

Because of this sentence, I am exactly not sure about my solution. Especially for firm 2.

I’m confused at this point. Please tell my mistakes. Thank you.

Firm 1's objective is to maximize profits :
$$\max_{q_1\geq 0} \ \ \left(a - b(q_1+q_2)\right)q_1 - cq_1$$

Solving the above problem, we get the best response function of firm 1 as
$$q_1 = \dfrac{a - c - bq_2}{2b}$$

Firm 2's objective is to maximize revenue subject to the constraint that its profits are non-negative :
$$\max_{q_2\geq 0} \ \ \left(a - b(q_1+q_2)\right)q_2$$ $$\text{s.t. }\left(a - b(q_1+q_2)\right)q_2 - cq_2 \geq 0$$

Solving the above problem, we get the best response function of firm 2 as
\begin{eqnarray*} q_2 =\begin{cases}  \dfrac{a - bq_1}{2b} & \text{if } a - bq_1 \geq 2c \\ \dfrac{a - c - bq_1}{b} & \text{if } a -  bq_1 < 2c \end{cases}\end{eqnarray*}

Solving the best response functions for $q_1$ and $q_2$ yields
\begin{eqnarray*} (q_1^*, q_2^*) = \begin{cases} \left(\dfrac{a-2c}{3b}, \dfrac{a+c}{3b}\right) & \text{if } a \geq 2c\\
 \left( 0, \dfrac{a-c}{b}\right) & \text{if } a < 2c \end{cases} \end{eqnarray*}


Is $\lim_{t \rightarrow \infty} B_t = 0$ at equilibrium in classical monetary model, where $B_t$ represents bond holding? At equilibrium of classical monetary model, does $\lim_{t \rightarrow \infty} B_t = 0$, where $B_t$ represents bond holding has to hold? I was wondering about this question because there is no ponzi solvency condition in classical monetary model, and usually when inequality exists as part of constraints in economics model, they often can be represented as equality at equilibrium.

In general, no.

As you correctly say, No-Ponzi and Transversality imply that the NPV of real bond holdings go to zero. Since we (in general) have not pinned down inflation paths, this does not imply $\lim_t B_t = 0$, as you correctly suspect.

If you can provide more information about what model exactly you work on or the situation you're looking at, I could update my answer.


Finding Nash Equilibrium Where would the Nash equilibrium lie in the pictured scenario? Whats confusing me is that both persons best response changes depending on the choice of the other person (there is no dominant strategy). Am I correct in thinking the Nash equilibrium is at (-1,-1) as both A and B want to betray as it would be most beneficial, but as they both betray they end up at (-1,-1)

The two (pure) Nash equilibrium in this game is (Betray, Silent) and (Silent, Betray).
Let us see why (Betray, Silent) is an equilibrium.
Let us look at person A.
Person B is playing Silent.

If she plays Betray, she gets $2$.
If she deviates to Silent, she gets $1$. So she would not play Silent.

Now consider person B.
Person A is playing Betray.

If she continues playing Silent, she gets $0$.
If she deviates to Betray, she gets $-1$. So she would not play Betray.

No player has an incentive to switch strategies. So this is an equilibrium.
The same argument holds for the (Silent, Betray) equilibrium.


Literature request: Any articles on the signalling theory / game theory / asymmetric information of the firms' recruiting process? I'd like to read more about the recruiting process of firms. Signalling theory and game theory can be a useful tool to better understand this phenomena.

For example:

Applicants, who ask for higher wages, tend to have a higher willingness to work. Then a good strategy is to ask for higher compensation, in order to get the job.
There are companies at Job Fairs, which try pretty aggressively to get e-mail addresses / cellphone numbers. Companies with higher reputation don't have to be that active on the job market, applicants will "automatically" gravitate to them.

Maybe the second case is a bit stupid, but I gave you a hint. Do you know any articles on the signalling theory / game theory / asymmetric information of the firms' recruiting process? Thank you in advance.

It sounds like you have a background in game theory. Here is a Game Theory text available for free through RAND if you (or anyone else) wants a refreasher: http://www.rand.org/pubs/commercial_books/CB113-1.html

Below are some articles from which you should be able to draw information. Most are not specific to recruiting, but the underlying theory is certainly applicable. If you continue to be interested in this topic, you will find a great deal of information in the literature on social capital, product value signaling (one article included below), and value signaling as it relates to credentials. Denesp recommended a great paper; plug it into google scholar and see which papers cite that one. Doing this you may find a ton of information.

Here is a paper published that takes a game theoretic look at the legal profession. It doesn't directly relate to your scenario, but the concepts and framing certainly do (this is on google scholar): Rasmusen, E., Raghav, M., & Ramseyer, M. (2009). Convictions versus conviction rates: the prosecutor's choice. American Law and Economics Review, 11(1), 47-78.

Here is an article, also available on Google Scholar, that contends with imperfect information: Rothschild, M., & Stiglitz, J. (1976). Equilibrium in competitive insurance markets: An essay on the economics of imperfect information. The quarterly journal of economics, 629-649.

Here is one specific to Signaling Games: Cho, I. K., & Kreps, D. M. (1987). Signaling games and stable equilibria. The Quarterly Journal of Economics, 102(2), 179-221.

Also about signaling: Kirmani, A., & Rao, A. R. (2000). No pain, no gain: A critical review of the literature on signaling unobservable product quality. Journal of marketing, 64(2), 66-79.

Related to employment: Leana, C. R., & Van Buren, H. J. (1999). Organizational social capital and employment practices. Academy of management review, 24(3), 538-555.


Does the GDP contribution of a service sector represent the gross profits of that sector? I couldn't find a simple answer to this question: does the dollar contribution of a service sector represent the gross profits of that sector? For instance, the GDP contribution of the financial sector of the US economy is 1.26 trillion dollars. Is that all of the profit? Or does it represent the profits + the wages paid to workers?

The second way of estimating GDP is to use "the sum of primary incomes distributed by resident producer units".
Gross domestic product on Wikipedia (emphasis mine)

If GDP is calculated this way it is sometimes called gross domestic income (GDI), or GDP (I). GDI should provide the same amount as the expenditure method described later. (By definition, GDI = GDP. In practice, however, measurement errors will make the two figures slightly off when reported by national statistical agencies.)

This method measures GDP by adding incomes that firms pay households for factors of production they hire - wages for labour, interest for capital, rent for land and profits for entrepreneurship.

So no, it is missing (at the very least) the wages and interest paid on the debt of the financial industry.