GDP(Expenditure view of GDP): /Why aren't investments categorized as non-final goods?

Well first of all the story why we only record final consumption is not completely straight - it’s not because we only care about activity of “real person” or consumer. But because counting it all the way would mean we double count the value of the good.

For example imagine the following situation. A wood is produced and sold for 15\$ to furniture company and then furniture is sold to consumers for 30\$. Well it’s not that we don’t care about the 15\$ because it was bought by company, but because the 15\$ value is already “hidden” in the value of the final good. Counting both would give you value of 45\$ but thats double counting the 15\$ is already "hidden" in the final price (of course final price could be sometimes lower if the second business by mismanagement manages to destroy value - i.e. producing something with lower value then value of the inputs - then you would want to record only the final price still to account for the fact that the process destroyed part of the old value).

Even when business purchases something which is not used for further consumption it counts as final good, purchasing catering for some firm celebration would be reflected in consumption since the catering is final good.

However, while we can’t really count let’s say wood that will later (same year) be used for furniture production we can count spending on machinery because there would not be any double counting since it’s not like you just modify the machine and sell it later as some final good.

This is because GDP basically tries to measure output at current prices. You can do that either by income approach since by definition output is equal to income or by spending approach because all output is going to be used or “spent” in one way or other. Investment also represents spending the produced output so it should definitely be there.

The same question you are asking about gold plated machines can be asked about any final good. If a consumer wants gold plated PC instead of normal PC is that any less or more rational than business owner wanting gold plated machine? The answer is if you want to assume people are rational the business owner will only invest in golden machine if that’s somehow relevant to business process otherwise it would be outcompeted away by other business. If you want to relax the rationality assumption then why should we assume consumers are rational and business not? If we count irrational purchases by consumers we should not discriminate irrational investment.

Regarding the auxiliary question about depreciation. Depreciation actually is not reflected on GDP because it is Gross Domestic Output. However, there is also NDP - net domestic product that controls for depreciation.


Who took utimatum game and dictator game as the evidence against Homo Economicus assumption of individual utility maximization?

Utility maximization is a proposition that can neither be confirmed nor refuted. For one thing, "utility" does not even exist as an entity; it's a mere conceptual construct. For another, "maximization" as a motivation is inherently unobservable. Even behavioral economists, who are adept at finding so-called empirical "anomalies" --- behaviors that apparently contradict economic predictions --- talk of "rationalizing" those anomalous behaviors by coming up with models in which the anomalies are outcomes of some maximization process. See, for example, Thaler's review of the literature on ultimatum/dictator games which he pioneered.

What the experimental results from ultimatum/dictator (and trust) games tells us is merely that people are not income maximizers. It is nevertheless invalid to conclude that people do not seek to maximize some other criterion or objective, which may or may not be part of what economists call "utility".

As economists, we understand that the specific measures we use for utility, like income, satisfaction, or selfishness, are adopted because of analytical convenience for the problem at hand, not because we seriously believe that those measures reflect human nature in any deep philosophical sense.

In a way, it's unsurprising that no economist, famous or otherwise, would declare utility maximization "wrong", since doing so would first require a precise definition of what "utility" is. Such a definition, despite nearly two hundred years of intellectual endeavor, remains frustratingly elusive.


How effective it will be in the end depends on how the policy is shaped and enforced exactly.

Buying garbage is in fact the same as subsidizing people to pick-up the garbage. In theory, by setting the subsidy at the appropriate level (where the marginal damage of an additional kg of litter on the street equals the marginal cost of picking up that garbarge and handing it in) one would achieve the "optimal amount of litering".

I do see a problem though,especially for the longer term. If people get paid for handing in their garbage, there are no incentives to reduce the overall amount of garbage, in fact people might be tempted to buy products that come with extra packaging so they can cash in on the garbage.

I think a better solution in the long term would be a tax on material that is likely to end-up on the streets.


To answer your first question: it depends on the subsample that you want to use.

A representative or stratified sample is constructed by dividing the population of interest into non-overlapping subsets, drawing a random sample from each subset, and then computing weights to adjust for the fact that not all elements from the sample had the same probability of being selected from the population.

The advantage of using a representative or stratified sample is that you can use information that you have about the population to construct your sample and so have more reliable estimates of statistics computed for the population of interest. The disadvantage is that the weights that you computed are right for the stratified sample that you constructed but if you want to explore characteristics that differ between the strata then these weights might very well be the wrong weights. Your estimates would be biased and you probably wouldn't be able to adjust for this bias.

As for propensity score matching. You can only match on what you can see. You'll still have to deal with the problem of omitted variable bias. It's possible that propensity score matching increases rather than decreases the bias. How effective it is depends on what assumptions you make and on whether these assumptions hold.


Question regarding social welfare in the presence of externalities

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

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

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

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

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

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


Can lying be disincentivized without serious curtailments of free speech?

If free speech is narrowly defined to only include true claims, true and false claims can be perfectly distinguished, the harm of false claims perfectly measured, and all claims are either true or false, then false claims are really no different than other forms of pollution. A standard pigovian tax should internalize the externalities and encourage the socially optimal level of truth telling. The social planner just has to tax each lie enough to discourage the social harm it does.

However, I maintain that in practice all of these assumptions are false. All experience seems to show that using the legal system to purge public discourse of lies leads to concentrating enormous power in those who make the lie / truth determination and that they will use that power in a way that is often inconsistent with objective truth And, when there is no objective truth there will still be those who would use the legal system to control public discourse in the name of protecting it.

In addition, the real world's imperfect legal processes are expensive and painful to participate in. That means that many true things that may be confused with lies will not be said, and that will further restrict freedom of speech.


To start with the question in the title:

Why don't economists do regression diagnostics?

People do regression diagnostics. I don't know of any respectable researcher that would not perform regression diagnostics and virtually any paper will have hints that the regression diagnostics was performed. For example, in tables with regression results you will find remarks on White or HAC errors being used to either correct for heteroskedasticity or autocorrelation or both, or references to corrections for cross-sectional dependence etc.
Only very unscrupulous scholars would make claims about these issues being/not being present without some testing.  So scientists (or at least the good ones) always perform regression diagnostics.
To address the question in the body:

in economics research papers nobody actually reports residual plots, collinearity checks etc. Is there any reason for this?

Yes, almost all scientific journals have very strict page limit of between 30-60 pages with most journals having page limit around 40 pages. In addition shorter articles are often more preferred and attract wider readership because people usually prefer to read shorter papers. Also, note that page limits are usually inclusive of list of references which often can eat up another 1-5 pages and also all other stuff. Only online appendices are excluded from page limit.
Now documentation of regression diagnostic can easily eat up 10 pages if you want to do it properly with all the plots (or even more). Moreover, regression diagnostic is not of much interest in itself. You preform it in order to know how to properly specify your model or what identification strategy to use. Once you figure that you just use the appropriate model, so by itself regression diagnostic has little value for reader as it carries very little information about research result. As mentioned in the first part of the answers people will still mention in their paper that there was autocorrelation or heteroskedasticity and how they corrected for it (and so on for other problems), so there is not that much point in additionally wasting space in the paper on showcasing all the auxiliary diagnostics. Any mistrustful researchers can just request their data and rerun that diagnostic themselves.
Consequently, the reason for that is simply that there is not enough space for it in the paper, and because you always have to economize on the space given. If you would really want to do it, it would usually end up eating 1/3 of a precious space, You would be surprised how common problem it is for researchers to actually fit their research in the page limit. Often you will be forced to relegate even main derivations to online appendices just to fit in the limit. In the end anything that is not of great importance to support or interpret the main result will simply not make the cut.
As mentioned in the comments this can sometimes cause issues with reproducibility, but nowadays the solution to that is that journals require scholars to post their code that was used to derive results (where you would find also regression diagnostics) rather than actually report it in the paper, for the reasons mentioned above.


GDP of domestic and foreign economic activities of a country

You can calculate domestic economic activity by calculating GDP and subtracting net exports. Any activity that requires dealings with foreign country will be recorded as either export or import. Once you subtract exports and imports from GDP you are left just with domestic activity.


Has the ban of single-use plastics sparked innovation in biodedgradable recyclable plastics?

Not sure if this question is suitable for this site but here's some (unsubstantiated by data) information and some other interesting points relating to economics behind it.
Rationale of the ban is not unfounded. It is based on a rather simple concept famously known as the Porter's Hypothesis. However, there is more economics at play (explained below). But that later
Coming to innovation: there is some evidence of innovation in biodegradable plastics. For example, in flights the plastic spoons/forks and knife given with packed food are now made of biodegradable plastic. Now the biodegradable plastic material is not even remotely as strong or malleable as regular plastic. But with right mechanics and design, the industry has finally been able to come up with usable (not necessarily affordable) cutlery. This we can definitely consider innovation.
But that is not all that is happening. One can certainly argue that if it were possible to make biodegradable plastic cutlery why did it not happen earlier? The simple answer is it was expensive. The biodegradable plastic cutlery is heavier compared to plastic counterpart and the raw material (which comes by weight) is also more expensive. It was because of regulation that industry was forced to take away from market the cheaper (and at that time - far better) alternative.
This is step one. Step two of the intended consequence is the new product becoming economical. So interestingly (unfortunately, I am unable to find the article now), the price of biodegradable plastic (usually corn byproduct or similar something) is increasingly becoming more affordable (economies of scale). The design is being copied and adopted by many take-away restaurants. So you see, perhaps in foreseeable future, even if the regulation is removed, industry may continue to keep using biodegradable products.
So if all goes well, it becomes a win-win in few years time.
As an economics student, what's of interest is that a pareto improvement outcome (an outcome which is favourable for some and not unfavourable for any) was just lying there. However, market outcomes are seemingly not that far-sighted and therefore often requires a nudge to set it moving in the right direction.
You can relate this to many things: fuel efficient car engines, battery driven cars, lending to small entrepreneurs and what not!


"risk free interest rate" in Black Scholes

Generally speaking, a risk-free rate refers to the yield you get on a government bond (read more here).

On a checking account there's a possibility that the bank would fail. Yes, it's FDIC insured, but up to \$250K.


Debt accumulation equation derivation: valid given that it rests on calculus and the time period is a year? (nowhere near infinitesimal?)

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

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

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

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

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

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


A good way to think about this is to think about the cases where there are a finite number of goods, indexed by $\omega \in \Omega$. In this case, the partial derivative is
$$
p(\omega) = \frac{\partial}{\partial c(\omega)} \sum_{\omega' \in \Omega} p(\omega') c(\omega').
$$
The case in which $\Omega$ is a continuum of goods follows as a sort of limiting extension. See that even this finite sum can be expressed as an integral, given the proper measure $\mu$:
$$
\sum_{\omega \in \Omega} p(\omega) c(\omega) = \int_{\Omega} p(\omega) c(\omega) \,\mu(\mathrm d \omega).
$$

You mention,

  This is puzzling to me since the derivative of a indefinite integral
  of $c_t$ should be $c_t$, not 1.

If you provided your reasoning for this, it would be easier to see where the confusion is. In any case, hope this helps!

Also, this guide may provide further assistance: The basics of “Dixit-Stiglitz lite”


Since it doesn't change the money supply, how can an "expansionary" fiscal policy alone spur economic growth?

In an open economy, Government might be borrowing money from abroad and so the logic of how that capital might have anyway been employed to a  productive end doesn't work out. (Also sale of forex reserves or taking up loans would depreciate domestic currency leading to increased exports and higher AD).

Also, money supply itself doesn't determine the pace or level of economic growth. It is the consumption and Saving patterns that spur demand, leading to the virtuous cycle of increased incomes and investment.

Provided that the C and S patterns are themselves a function of trust and market expectations (especially during times of economic crisis such as recession or slowdown), government through it's expansionary fiscal policy and the popular credence attached to it, incentivise increased activity and growth.


A dummy variable is a binary variable, that does need to be logged. You can use them as they are. Also, if the variable is set to 1 for a given result and zero otherwise, by taking logs you will turn your variable to 0 and a missing value because the log of 0 does not exist.

update: Instead of a plot, why not simply calculate pairwise correlation coefficients. Here is an example using Stata

. sysuse auto, clear
(1978 Automobile Data)

. * Create a dummy variable
. gen byte big= weight>3020

. ta big

        big |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         35       47.30       47.30
          1 |         39       52.70      100.00
------------+-----------------------------------
      Total |         74      100.00

. * Correlate big with price
. pwcorr big price

             |      big    price
-------------+------------------
         big |   1.0000
       price |   0.3469   1.0000

Both are positively correlated.

. * Add a other dummy and compute new correlations

    pwcorr price foreign big

             |    price  foreign      big
-------------+---------------------------
       price |   1.0000
     foreign |   0.0487   1.0000
         big |   0.3469  -0.5682   1.0000


What is the relationship between the demand for loanable funds and investment?

Assuming loanable funds are all used for investment, loanable funds = investment.

The interest rate can be though of as the price for loanable funds. Take a look at the following graph.

You can think of the change from point A to C in two steps, with B as the intermediary, even though in reality both steps probably happen simultaneously.

First the shift in demand from D to D2 (decrease in demand for loanable funds) is reflected by the move from A to B. Price has not yet changed at this point.

Then, a new equilibrium is reached with quantity demanded moving down the new demand curve (as price decreases) to point C. In this step price decreases so the quantity demanded actually increases. But it does not reach the quantity demanded at the original point A.

So as the demand curve shifts to the left both price and quantity demanded decrease.


Money creation in textbooks since McLeay et al

Textbooks still include discussion of money multiplier together with more nuanced discussion of central banks setting interest rates (compatible with story in McLeay et al 2014). In fact they did so already before the paper was published in 2014.
I think in order to answer this question it will be important to first correct a misconception you seem to have about what the paper implies regarding to textbook story. You state:

The paper is damming about the description of the monetary system as given in many undergraduate level textbooks.

No. If you actually read McLeay et al 2014 they state:

While the money multiplier theory can be a useful way of
introducing money and banking in economic textbooks, it is
not an accurate description of how money is created in reality.
Rather than controlling the quantity of reserves, central banks
today typically implement monetary policy by setting the
price of reserves — that is, interest rates.

Consequently, the paper was certainly not damming of the textbook money multiplier story (and no fair reading of the paper can conclude they went as far as damming the description of whole monetary system in textbooks which goes way beyond just money creation), and going by this statement I doubt that the authors would even want to remove this story from textbooks as they themselves consider it useful. I also can't see anything else in the paper that would suggest that multiplier should not be included in the textbooks as a didactic tool (e.g. analogously most markets are not perfectly competitive,  yet I don't think that economic textbooks will ever be able to efficiently introduce more complex market structures before discussing case of perfect competition no matter how unrealistic such market structure might be).
Now onto your main question, one of the main point of McLeay et al (2014) is that:

Rather than controlling the quantity of reserves, central banks
today typically implement monetary policy by setting the
price of reserves — that is, interest rates.

Now this is something that was already discussed in textbooks quite long time ago. Let me give you some examples:
Blanchard et al. Macroeconomics an European Perspective. 2nd ed. Widely used mainstream textbook  with 2nd edition published in 2013 (year before the paper came out), states pp 69-70 (square brackets contain my remarks):

We have described the central bank as choosing the money supply and letting the interest rate be determined at the point where money supply equals money demand [i.e. the multiplier story]. Instead, we could have described the central bank as choosing the interest rate ... Why is it useful to think about the central bank as choosing the interest rate? Because this is what central banks, including the ECB, the Bank of England and the Fed, typically do...

the textbook then proceeds to give simplified down narration of what you could have read in the 2014 paper (but remember this is undergraduate textbook everything is simplified there).
Mankiw Macroeconomics 8th edition - originally published in 2012, states:

Although it is often convenient to make the simplifying assumption that the
Federal Reserve controls the money supply directly, in fact the Fed controls the
money supply indirectly using a variety of instruments. ...
There are various ways in which banks can borrow from the Fed. Traditionally,
banks have borrowed at the Fed’s so-called discount window; the discount rate
is the interest rate that the Fed charges on these loans. The lower the discount
rate, the cheaper are borrowed reserves, and the more banks borrow at the Fed’s
discount window. Hence, a reduction in the discount rate raises the monetary
base and the money supply.
In recent years, the Federal Reserve has set up new mechanisms for banks
to borrow from it. For example, under the Term Auction Facility, the Fed sets a
quantity of funds it wants to lend to banks, and eligible banks then bid to borrow
those funds. The loans go to the highest eligible bidders—that is, to the banks
that have acceptable collateral and are offering to pay the highest interest rate.
Unlike at the discount window, where the Fed sets the price of a loan and the
banks determine the quantity of borrowing, at the Term Auction Facility the Fed
sets the quantity of borrowing and a competitive bidding process among banks
determines the price. The more funds the Fed makes available through this and
similar facilities, the greater the monetary base and the money supply.

In fact the last paragraph was addition to the 8th edition that was not there in 7th edition (published in 2010) so you can see these textbooks usually catch pretty quickly.
Burda & Wyplosz Macroeconomics: A European Text 217-218 3rd ed, originally published in 2009:

Nowadays, ... most central banks choose to control the interest rate ... a central bank can set any interest rate it chooses, provided it stands ready to provide or withdraw liquidity in any amount needed to meet the derived demand corresponding to this rate.

the textbook then proceeds to discuss basically what is the point of the 2014 paper already in 2009.
The newer editions of the books that were printed post 2014 still contain this explanation. But given that they already addressed this issue prior 2014 I would not attribute it to McLeay et al paper per se. As clearly shown above textbooks addressed this issue already in 2009.
You can see these chapters being further expanded in the newer editions of the Mankiw and Blanchard et al Macro textbooks. Perhaps this further expansion can be attributed to influence of McLeay et al paper. Arguably Blanchard et al do this at much greater length then in Mankiw textbook.
In addition, it is worth to point out that I do not think that the above shows that McLeay et al were being duplicitous in their 2014 paper. In fact, if you read the paper carefully they never state that textbooks do not cover how money is being created by modern central bank. They always refer to money multiplier story (that admittedly is given perhaps too much space) in the textbooks that they are trying to 'debunk' but they actually never state that textbooks do not cover that modern central banks conduct monetary policy through interest rates.

Response to Edits:

I would suggest that there are two distinct issues that McLeay et al are complaining about:

A) Incorrectly suggesting that banks lend deposits rather than correctly stating that lending creates deposits.

I cant find a passage where McLeay et al state that textbooks got this point wrong, but if they state that somewhere it would be incorrect.  In fact, this is a picture that is from the above cited Blanchard et al Macro textbook pp 71 from 2013!

The picture clearly shows that demand for deposits creates demand for reserves which is exactly the point of McLeay paper. In addition there is nothing wrong in principle also arguing that from supply side the increase in supply of reserves would lead to increase in borrowing and deposit accounts. It is not the mode of behavior that modern central banks would choose but it is not wrong in itself as they could do that. The relationship in the diagram above has to hold but of course central bank has discretion in deciding whether to change interest rate (which affects the demand for money and then you get the effects coming from deposits) or to change supply of money directly where the effect would go opposite way. It is correct to state that modern central banks usually choose former rather than latter (and as proven above textbooks acknowledge that), but that does not mean it’s wrong to say that central banks could conduct monetary policy via direct changes in money supply.

B) Incorrectly suggesting that the money supply has a ceiling set by reserve requirements in practice.

Regarding, the B they nowhere say that reserve requirements do not create celling for lending. They state instead that banks will lend out money and then seek to raise their reserves by purchasing them on interbank market in order to maintain the mandatory reserve ratio - but they have to maintain that ratio.
First of all, as you can see from the statistics on excess reserves below (which is discontinued now as reserve requirements were abolished in 2020), prior 2009 banks held virtually no excess reserves. In such situation the amount of reserves supplied by central bank is hard cap for lending of commercial banks. If they would lend more they would literally break the law (as a tidbit in such situation the multiplier story still applies as the ratio to reserves and broad money should be approximately given by the multiplier). After 2009 market held excess reserves, in that situation you can think of every individual bank be unconstrained by reserve requirement because without central bank doing anything any individual bank can borrow excess reserves from any other bank to maintain their reserve requirement (this is what they mean in the paper when they say banks are unconstrained by reserves).   However, the banking system as a whole (all banks taken together) is still constrained by the reserve requirement and amounts of reserves. Even in this situation banks could not all at the same time lend more than they can given the reserves and reserve requirement. So this is not something that textbooks, which are written from the perspective of whole system rather than single bank, get wrong (and again I cant see them calming that textbooks do that in the paper). In fact here you could actually coitize the McLeay et al for not being careful enough about explaining this.


Do granting subsidies always cause allocative inefficiency?

Your intuition is correct: in cases of market failure when the price under-represents the marginal value to society as a whole (for example if positive externalities are present) then granting the subsidy would improve allocative efficiency. As long as the subsidy is not greater than the positive externality, then the only loss in that case arises from the overhead in managing the subsidy - the bureaucratic cost. This is typically less than the inefficiency resulting from the market failure, so society gets a net gain from the subsidy.

The same thing applies with taxes and negative externalities. For the original work on this, see Pigou's seminal "The Economics of Welfare" (1924)


As denesp mentioned, your solution is incorrect. To check whether there is envy, you have to compare the two bundles from the point of view of the same agent. So in our case we have:

For agent A: the utility of his own bundle is $4 \alpha$ and the utility of the other bundle is $\alpha+5$. So he feels no envy as long as $4\alpha \geq \alpha+5$, which is equivalent to: $\alpha \geq 5/3$.
For agent B: the utility of his own bundle is 5 and the utility of the other bundle is 0. So he never feels envy.

This means that the correct answer is (c).


How long are consumers willing to wait in order to find a bargain?

Check this paper out:

The Value of Time Spent in Price-Comparison Shopping: Survey and Experimental Evidence
Author(s): Howard Marmorstein, Dhruv Grewal and Raymond P. H. Fishe
Source: Journal of Consumer Research, Vol. 19, No. 1 (Jun., 1992), pp. 52-61

With a bit of hand-waving, you can say that consumers are willing to search as long as value of time < amount saved.


How to convert an historic value denoted in foreign currency to a modern value in local currency?

For what purpose?

Money over time acts as inflation rate, wage bundle, production good bundle, %gdp, %gdp/capita. Each represents a different “meaning” of money over time.

The US and UK economies have different consumption bundles, wage structures, skill structures, industrial structures, government policy, market agents and social meanings. 1968UK and 2018UK also vary and 1968UK and 2018UK vary in these domains.

Your question is unanswerable without the commodity or expense, the volume or market (wholesale, retail, government) and the purpose.

See measuringworth.com for essays.


Does the theory of contestable markets apply to industries where there is a natural monopoly?

Natural monopolies may exist because the cost structure is such that the market could not sustain two firms. This is usually explained by large sunk costs and relatively small demand - if there were two firms the average cost for at least one would have to be above the equilibrium price.
If there are no sunk costs at all - as set forth in the ideal case of a contestable market - then the long-run average cost function is likely not decreasing, hence this phenomenon cannot occur.


Proof that utility is nonincreasing in prices

That follows $v(p_1,y)$ being the highest utility one can get from a bundle affordable given prices $p_1$ and income $y$. Let $x_1$ be such a utility maximizing bundle. Then $p_1\cdot x_1\le y$ and $u(x_1)\ge u(x)$ for all $x$ such that $p_1\cdot x\le y$. In particular, $u(x_1)\ge u(x_0)$ since $p_1\cdot x_0\le y$ (this is what the argument you have shows.) Therefore,
$$v(p_1,y)=u(x_1)\geq u(x_0)=v(p_0,y).$$
Intuitively, if prices are lower, one can buy from a richer set of options, and with more options one can always get at least as high utility.


What are the defining features of Capitalism?

In this article, sociologist Erik Olin Wright provides a definition of
capitalism (from a socialist tradition):

  Many people equate capitalism with the idea of a market economy. Capitalism is not simply an economy in which markets play a central role in
  coordinating economic activity; it is a specific kind of  market  economy,  one  in  which  workers  do  not own and control the firms in which they work, capital  is  privately  owned  and  allocated  to  alternative purposes  on  the  basis  of  private  economic  returns  (or, equivalently, on the basis of private profit-making),  and  labor  is  allocated  to  economic  activities through labor markets.


The following approach seems to work in this case:

look for the stead state formula of $T_t$. You can do this by taking (2.8) and the formula for $T_t$, and combine them. Then, get rid of all $t$ index:

$$ T = \frac{1-\delta}{p}\left(B - \frac{B}{1+i}\right) + \frac{T}{1+i}$$

Then, rearrange until you get $T$, the steady state formula for $T_j$. You should get:

$$ T= (1-\delta)\frac{B}{p} $$

Guess what the time indexes are, and confirm they are correct. To do this,  lag the equation for $T_t$ (so you get rid of expectations), and replace $T_{t-1}$ and $T_t$ with your guess. If the equality holds, your guess is correct. If not, try again. For example, let us assume  $T_t= (1-\delta)\frac{B_{t-1}}{p_t} $ (the correct one).

Then, the equation is:

$$ (1-\delta) \frac{B_{t-2}}{p_{t-1}} = \frac{1-\delta}{p_{t-1}}\left[B_{t-2} - \frac{B_{t-1}}{1+i_{t-1}}\right] + \frac{T_t p_t}{(1+i_{t-1})p_{t-1}} $$

After simplifying and rearranging you get:

$$T_t= (1-\delta)\frac{B_{t-1}}{p_t} $$

which is correct.

Now, I don't know how general this method is. This is not my area of knowledge. But at least it works here.


More direct way to derive indirect utility function from expenditure function

Make e (p, V (p, r))=r, hence f (V (p, r)) g (p)=r. Then use the inverse function theorem:
V (p, r)=h (r/g (p))
Where h is the inverse of f.


The Lucas model does not address at all the points that you address of people losing jobs, as it utilizes just one agent that simply has a perfectly steady (perhaps growing at a constant rate) consumption path. A model with heterogeneous agents where they have the possibility of losing their jobs and having some periods with, supposedly, very low consumption, would give a much higher cost of business cycles.

Further, in a paper using robust preferences Sargent and some coauthors find that if the agent has fear that his model of where income fluctuations are drawn from is misspecified, the costs of business cycles are much higher.


Formulas or rules regarding End of Life for vehicle

There is no one general standardized formula for the value of a car. That is not how prices work. The price of a used car is going to depend on what other people are willing to pay for it, not some depreciation formula that you can just plug numbers into. This inherently means there is some uncertainty in trying to determine the value of a used car.

With that said there are resources out there to approximate what people generally are able to buy/sell a used car for such as the Kelley Blue Book which records the average selling price for models of used cars after a certain number of years. These resources should give you an approximation for what a used car could go for but it will never be exact and is location and time dependent.


Does my research prove market inefficiency?

The efficient market hypothesis does not imply that there are no patterns!

As Eugene Fama pointed out decades ago, any test of market efficiency is a joint test of market efficiency and an asset pricing model. The EMH on its own is not a testable theory.

If I understand your statement properly, you're claiming that forecasting variance would violate market efficiency? For that to be true, you would need to assume an asset pricing model where variance is not forecastable. That's a strange claim. It would imply that risk free government bonds must have the same volatility as small biotech firms (otherwise, I can forecast volatility based upon whether a security is a stock or a bond).

It well known that volatility is forecastable, both in the cross section and in the time series. For example, there is the widely used GARCH model and all kinds of other stochastic volatility models. Forecasting volatility is interesting, but it in no way constitutes a per se violation of market efficiency.

This answer of mine goes into greater depth on what the efficient market hypothesis actually says and how to test it.

References

Fama, Eugene F., 1991, "Efficient Capital Markets: II," Journal of Finance


A lottery is essentially a probability distribution. So the variance of a lottery is the variance of the probability distribution it represents, which is given by the formula
\begin{equation}
\mathrm{Var}(L)=\sum_{i=1}^np_i(x_i-\mathbb E(L))^2,
\end{equation}
where $p_i$ is the probability that outcome $i$ occurs, $x_i$ is the monetary value of outcome $i$, and $\mathbb E(L)$ is the expected value of the lottery.

Take the lottery $L_2=0.5[0]\oplus0.5[4]$ for example. We can easily verify that $\mathbb E(L_2)=2$. By the formula above, then,
\begin{equation}
\mathrm{Var}(L_2)=0.5(0-2)^2+0.5(4-2)^2=4.
\end{equation}

I'll leave you to finish the rest of the question.


Does the minimum of short-run average cost equal the minimum of long-run average cost in the long run for perfect competition?

So to understand why the long run average cost curve and short run average cost curve  have the same minimum in perfect competition, as well as some of the other stuff you ask, you have to understand the different assumptions that underlie the models you're working with.

Let's start with what the short run and long run mean here. In this context, the short run is when a firm is stuck with some fixed costs. It may be able to vary labor or raw materials, making those things variable costs, but some other things (e.g. contracted salaries, rental rate of capital) are fixed costs. It may be hard to expand the size of a factory quickly or find a new place to move production.

So here we see 3 different short run average cost curves. Each of these factories of course want to minimize cost per unit produced (average cost), and then set a price equal or above that (otherwise they'd be losing money!), so you have 3 different quantities that the firms will want to produce. You will notice that some of these firms will have to set a higher price than that firm with the production in the middle, so you can imagine which firm is going to get the customers in perfect competition.

Why are the SAC's shaped like this U shape? It is because generally there are economies of scale up to a certain point before things get too big to handle. A school can more efficiently allocate teachers by bumping up classroom size from 1 to 5 for example. But if you try to give the teacher a 1000 child classroom, you would expect things to be absolute chaos.

So now what happens in the long run? In the long run all these things we would normally consider fixed costs are actually variable costs. We can change the amount of capital we rent or other such things.

So given enough time, firms can change how much they want to produce along this line (LAC). We assume everyone moves along the same line because in perfect competition, we assume firms are identical, so that includes the technology and efficiency the firms have to produce the goods. So firms will naturally want to set production to the minimum of the long run average cost curve, so that they can set those low low prices meant to attract customers.

At least...that's what we would expect naturally, right? The last piece of putting it all together is seeing that the marginal cost equals average cost when average cost is minimized. I give a boring mathematical proof here. I assume you need no explanation for why firms set price equal to marginal cost.

  So, price equal to short run average cost means that the firm produces its goods, sells each of them for the price, and breaks even. Thus we say no economic profit. Price equal to long run average cost means that all firms want to expand or contract their production so that they all produce the same amount of goods and basically all look identical. So all firms compete and push price down to the minimum of the long run average cost curve. They neither make nor lose money. So firms are indifferent between operating and not operating. It doesn't really make a difference to them. Thus, firms don't really want to enter or exit.

Edit: To answer the last part, why is the long run cost curve not tangent at the minimum of each short run cost curve, consider the following: For almost all cases, we should expect the minimum of the short run cost to lie above the long run average cost curve. In the short run, you can vary only some inputs, and in the long run you can vary all inputs. So for any given quantity you are trying to produce, it's easier to find a cheaper combination of inputs in the long run than it is in the short run.

This particular question on the tangency has been asked before, with a good top answer here.


Why is the inverted yield curve a good predictor of impending economic recession?

There is a fair amount of ambiguity to this question. The first question is: what is the yield curve? A fixed income investor may refer to the yields across all maturities as the yield curve, while economists pick the difference in yields between two arbitrary maturities as the yield curve. Which two? Typical choices are the spread between the 2-year and 10-year bond, or the spread between the 3-month Treasury bill rate and the 10-year. The quality of a recession indicator depends which pair you choose.

The second question is: what country are we talking about? The yield curve is often described as a good recession indcator for the United States (which can be seen by looking at the time series of the 2-year/10-year Treasury spread, and compare them to recession dates. It is less clear how well it works for other countries.

There is a simple theoretical reason why it works. Under any modern financial model of the risk-free interest rate curve, we can see that term interest rates are roughly equal to the average of the expected overnight rate to its maturity, plus a term premium. (Technically, the average is a geometric average, since we are compounding an investment at the overnight rate.) As long as the term premium is not significantly negative, an inverted yield curve implies that the expected path of short-term rates is heading lower. The usual reason for a central bank to cut rates significantly is a recession (either domestically, or in trading partners).

In other words, if an inverted yield curve is a good recession indicator, it is just telling us that bond investors may be good at forecasting recession odds. Do we have reason to expect that they are perfect forecasters? Probably not. There’s any number of things that could distort bond market pricing, or else bond investors could herd into a poor forecast. Attempting to do statistical analysis of the yield curve without taking into account the changing institutional structure of the bond market is problematic.

I am not aware of any reason that suggests the inverted yield curve causes recessions under current institutional arrangements. (I am admittedly biased.) This is because developed country banking systes have much tighter control of interest rate risk now. This was not the case earlier (e.g., 1970s), and it may be that for some countries now, interest rate risk is not being hedged.

If you are interested in that question, I suggest asking it in a separate question, and you should specify what countries and eras you are interested in. The title of the question refers to prediction; a lot of readers would not relate that to causing recessions.


An interest rate is the percentage that is paid for borrowing money, and that one gets for lending. If it is negative that means you have to pay so that someone takes your money for a while. So how could that even work, why should anyone lend money under such conditions? Normal savers would just keep their money with them, even if that bears the risk that it might get stolen more easily than from a bank. What can however happen is that the real interest rate is lower than zero and people still keep their money at the bank. The real interest rate is the (nominal) interest rate minus inflation. In times of high inflation this can easily happen, and as you see here in the world bank data it frequently happens in many countries: http://data.worldbank.org/indicator/FR.INR.RINR

In times of crisis and low inflation central banks can even lower the short term nominal deposit interest rate below 0 in order to give incentives to commercial banks to lend out money that because of mistrust they would otherwise rather just store at the central bank and wait for better times. There is no consensus if this is good or bad and if it works and how it affects the economy and the people. The European Central Bank adopted this strategy since mid 2014 because of the severe crisis, and the Japanese central bank followed in January 2016.(WSJ) The idea is to stimulate the economy, which should lower unemployment. It should also make the currency unattractive, so its value should decrease compared to others and that makes exports easier as long as other central banks do not do the same. Some say this goal can be achieved better with the negative interest rate than the goal to stimulate the economy via increased lending of commercial banks, and especially in smaller economies like Denmark, and Switzerland, the mechanism seems to have helped to protect companies from getting too much harmed by currencies getting too strong too quickly.(ST)
In March 2016, the European Central Bank even started to offer commercial banks a negative interest rate for loans, rewarding lenders.(NYT)

There are also bonds that have negative interest rates.(BBC) This phenomenon needs some additional explanation and has its own question here.


The primary source of the recent ruble collapse has almost certainly been the falling international oil price, aggravated by some other features of Russian politics and its economy.

Petroleum products account for over half of Russia's export revenue, and most remaining export revenue comes from other commodities, whose output it cannot easily adjust. When oil prices fall, this lost export revenue must be replaced by some combination of

(1) more (presumably non-oil) exports

(2) fewer imports

(3) a larger net capital inflow.

For the most part, these adjustments will be made in response to an equilbrating decline in Russia's exchange rate. Since Russia's export mix is so commodity-heavy, the short run response of (1) to the exchange rate is very weak; since consumers tend to be sluggish in responding to price changes, (2) is weak in the short run as well. For a modern economy with good access to international capital markets, (3) is the main short-term buffer for shocks like these, but Russia is currently suffering from Western sanctions and was not particularly well-integrated into international capital markets in the first place.

For all these reasons, a very large decline in the exchange rate is needed to induce enough of (1), (2), and (3) to offset the decline in oil export revenue. Meanwhile, skittishness about the political situation in Russia (and its dubious historical record on monetary stability) don't help.

By the way, the dependence of commodity exporters' exchange rates on commodity prices is a staple of international finance; it has even been used to forecast commodity prices.


Why is it possible to calibrate your subjective probabilities?

Empirically yes, it seems confidence has a positive correlation with correctness. One reference is Bordalo et al. 2018 Beliefs about gender, see Fig.1 for example. The actual probability of a correct answer is different from own or other people's estimate of the probability of a correct answer, but if the estimated probability is higher, then the actual probability is higher.

As to the axioms or theoretical assumptions - you can just assume that people's estimates of their correctness are increasing in the correctness. Or assume Bayesian updating about own correctness, in which case past correct guesses would increase the guesser's confidence in own correctness. The number of past correct guesses in turn is positively correlated with the guesser's actual correctness (by the Law of large numbers).


Who performs the checks for regulatory compliance at trade borders?

The most simple and universal answer is that it is up to each government to decide if checks should be made and if so by whom.  Some have none, either because of international agreements, because they see no need, or because they lack the capacity to do so.

The most common case is, as you say, that officials from different ministries inspect goods, and food/agriculture are the most common because it's too late if you find out that pests or diseases have been imported once they're past the border.

But otherwise, countries often make efforts to reduce and simplify border checks by doing risk assessments of traders or containers (and inspecting only the risky ones), by improving cooperation between ministries, or by improving enforcement of regulations and standards behind the border.


You can find in many textbooks (for example Mas-Collel, Winston and Green) that the Independence of irrelevant alternatives axiom implies that preferences over lotteries are linear with respect to the probabilities of each event.

Then, a compound lottery is of the form: $\mathcal{L}''=\alpha\mathcal{L}+(1-\alpha)\mathcal{L}'$, If $A$ and $B$ are the outcomes of the simple lottery $\mathcal{L}$ and $C$ and $D$ are the outcomes of the other simple lottery, $\mathcal{L}'$. Then, the compound lottery can be seen as a simple lottery with four outcomes, given the linearity in probabilities: $\mathcal{L}''=\alpha\left(\beta A+(1-\beta)B\right)+(1-\alpha)\left(\gamma C+(1-\gamma)D\right)$.


negative interest rate lending ripple effects

Decreasing the nominal interest rate to a negative value will cause businesses to have to raise their prices in order to maintain 0 economic profit. This is because wages are "sticky," and cannot change in a general quarterly or annual period.  People who live in the country have not been given any higher incentive to spend, but since prices are increased - aggregate demand will decrease.  Additionally, in order to survive the cut in demand and rise in prices, firms will look to lay off workers - raising unemployment.  Consumption should decrease as a result of a negative interest rate charged by the Central Bank.  In what was an attempt to increase GDP - output will decrease.  --> Stagflation is likely to occur


Why do we say that trade and specialization according to comparative advantage lead to one-time increase in PPF of given country?

For this you first have to put some numbers on the problem to be able to draw PPF and consumption. Lets assume that Cheestopia can produce 1 cheese at 1 labor, and 1 wine at 2 labor and Winetopia 1 cheese at 2 labor and 1 wine at 1 labor, and both country has 100L avaiable for production, this gives you the following PPFs for both countries in autarky (the chart was created by 1muflon1):

Now, I wont post full solution for a Ricardian model because it is not part of your question but in this case valid solution would be that the trade prices will be 1 cheese for 1 wine (if you want to know why maybe post it as a separate question about solving Ricardian model). Now under this trade scenario both cheestopia and Winetopia can produce only the good in which they have comparative advantage (i.e. only cheese in Cheesetopia and only wine in Winetopia) and at the trade 1ch for 1 w they can now access all the following points in consumption (note the points for two countries overlap but I ploted them next to each other so you see that second country does not disapear):

Now, whether anyone agrees that this increases a PPF it is indisputable that it increases the consumption possibilities of two countries. Thats plain from the picture. So now a question is following. Can we call this expansion of consumption possibilities increase in PPF? I think yes and also many textbooks call it like that for the following reasons:

From economic point of view there is no difference between producing, say, X of wine and between producing Y of cheese and then trading Y of cheese for X of wine. Just imagine that there a wizard/machine that converts Y of cheese in X of wine. From an economic perspective trade is like having access to production technology of the other country. Also macroeconomically consumption must be in long run equal to income and income in the long run must be equal to production.
By standard measures of production (such as GDP) this increases the production at any other point than the vertex (100ch, 0w) which overlaps with autarky PPF and PPF is by definition all possible combination of production. To show that this is the case lets consider one point on the new consumption line and lets use one standard output/production measure - GDP.

Lets select Cheesetopia and lets select point of consumption (0c,100w) which is a point of consumption only accessible by trade. Now if you claim that this point does not represent new PPF, at this point the production then a consumption point (0c,100w) should not show up on aggregates as GDP which measures the production as that would imply that production is outside PPF which by definition must include all production possibilities of a country. To calculate GDP we have to choose some good as numeraire (money) it does not matter which one we choose lets do cheese. So at the consumption point 0 cheese and 100 wine the components of GDP will be C= 100ch (here ch is the currency cheese they actually consume wine), X = 100ch (they export cheese) and M = 100ch (they import 100 wine and again cheese is the currency here). So GDP in this case is GDP = 100 + 100-100 = 100. So here we have a contradiction and there is only two ways how to resolve this contradiction:

You will say that GDP does not measure production. Which I dont think even the biggest critics of GDP would say.
PPF must be at consumption point (0ch,100w) at least 100 because by definition PPF is the combination of all production possibilities of the country, so if GDP measures production it must be within PPF it cannot be outside.

Now you can pick your 'poison' from the above option. Economically, the second makes sense. Intuition is that there is no meaningful difference between producing cheese at home and via trade transform this production of cheese into production wine and between actually being able to produce wine at home at the terms of trade. Or another way how you could express that intuitively is that in the new PPF any combination of goods can be produced by producing just cheese which is the highest point on the pre-trade PPF and which is also the single point where pre and post trade PPF will be exactly same.

Furthermore, to see that this is the same lets consider this scenario. 1 Winetopia gets destroyed by a tsunami so only Cheesetopia is left in the world. Now imagine that Cheesetopia will send some scubadivers to recover the Winetopia's wine production technology hence now Cheesetopia can produce both wine and cheese at 1 labor. Now the PPF is exactly the same as with the trade (meaning there is no meaningful economic distinction between trading.)


$u_1(x, y) = -(x-1)^2 - (y-1)^2$

$u_2(x, y) = -|x-1| - |y-1|$

are examples of utility functions that are concave, and therefore represent the preferences that are convex. Also, these preferences are not monotonic.


What are the most popular technical models used for forecasting exchange rates in international economics?

Writing as an academic modeller who would use the outputs of such models, what's required (and what I look for as a reviewer) is:

reproducibility: the algorithm is described with sufficient detail to enable someone else to reimplement it;
validation, using data that is completely distinct from the calibration dataset; and
that the output is a distribution of forecasts, not just point values.

Such a distribution can then be fed into ensemble modelling. So instead of using a single forecast of the future value of a currency pair, I could feed in the distribution to a monte carlo simulator or similar.

It doesn't need to have the right expected value, nor a correct value for volatility (or any other moment).

All that makes it essentially useless for trading. And that's a good thing, because no one of sound mind would give away a profitable forex forecaster: such a forecaster would immediately render itself obsolete as it entered common use.


How to estimate long term exchange rate?

I kept digging and found the following references. Hope it will help someone else.

IMF: Estimation of Equilibrium Exchange Rates in the WAEMU: A Robustness Approach
IMF: Estimating the equilibrium real exchange rate: an application to Finland


Log-linear version of the uncovered interest rate parity

It’s derived as follows. First start with original equation.

$$(1+i_t)=(1+i^*_t)\frac{S_{t+1}}{S_t}$$

Take natural logs of both sides:

$$\ln(1+i_t)=\ln(1+i^*_t)+\ln(S_{t+1}) -\ln(S_t)$$

Now you just use the following:

$$s_t=\ln(S_t)$$

And use the well known fact that for small values of $i$ the following approximation holds:

$$\ln(1+i)\approx i$$

And rearrange to get

$$\hat{i}_t-\hat{i}^*_t=\hat{s}_{t+1}-\hat{s}_t$$

PS: Also actually the equation you derived is not log-linearized as it’s not linear in its log parameters


Does net exports has to do with borrowing and lending?

Maybe this will help: imagine that trade is done in the currency of the foreign country.
Suppose you are American, you are standing on the border of Mexico, and you sell a hot dog to a Mexican for 20 pesos. Now you want to buy tacos from him, but you want 30 pesos of tacos. So he lends you 10 pesos, then you buy the tacos.
So X=20, M=30, and net exports= -10 and you borrowed 10.
Side note: some poor, risky countries (e.g. North Korea) can't have negative net exports, because no one will lend to them.


Why is every action considered to be in the support while calculating mixed strategy equilibrium?

It is not, only in intro problems.

You have already seen counterexamples: The prisoner's dilemma has an equilibrium, yet it does not have full support. (But it is a pure strategy equilibrium! So? All pure strategies are just very particular mixed strategies.)

Mixed strategies with full support are called completely mixed strategies.

It is a good exercise to show that strictly dominated pure strategies are never in the support of mixed equilibrium strategies. Using this you yourself can construct a simple example where the only equilibrium is a mixed but not completely mixed strategy profile.


What's wrong with the "airline marginal cost pricing" argument?

One possible answer is that Mankiw's argument takes consumer demand for airline tickets as fixed and given. I would speculate that cheap last-minute tickets are a substitute good for regularly priced tickets, and that if enough people came to prefer them, demand for regularly priced tickets would fall and the airlines would lose revenue. In other words, instead of paying full price, too many customers would deliberately hold out for the heavily discounted tickets.
This is the same reason why so many stores destroy their obsolete/stale inventory instead of selling it cheaply or donating it, and is an example of a perverse market incentive, as it leads to unnecessary waste.


Does the PBoC work like the Fed in having meetings where they discuss changes in monetary policy?

I haven't posted here in a while, but I saw this question and thought I ought to respond.

No. That is the short answer to your question.

After having been living and working in China for a year, I realized that nothing about its economy can be viewed separately from politics and social psychology of mainland Chinese population. Simply put, everything is different.

People's Bank of China is defacto a part of executive branch of government. It sets monetary policy decisions in accordance with the government's social and economic policies, which are ultimately curated by the Chairman of the Communist Party (a.k.a the President). This makes it very predictable. If the growth target is set to 6.5%, the PBOC will provide enough liquidity to hit the target, pretty much at all costs.

In China's political culture collective debates are ubiquitous, but when something is being discussed, everyone tends to converge on the leader's opinion very quickly.

However, one can only speculate how PBoC board makes their decisions. It is not very transparent, like most of the political culture in the country. Everyone seems to be happy though that it is, at least, predictable.


Where can I find charts with the amount of treasuries in existence?

SIFMA: US Marketable Treasury Issuance, Outstanding, and Interest Rates

The hint here is that repurchases are relatively rare and prepayments are not an option so gross issuance that hasn’t yet matured is a decent proxy for outstanding amounts.


Where to get historical intraday trading data from?

I work at Quandl and we have intraday data here: https://www.quandl.com/vendors/as

The databases include S&P 500 One Minute Bars, NASDAQ 100 One Minute Bars, Dow Jones Transportation Average One Minute Bars, Dow Jones Industrial Average One Minute Bars and Dow Jones Utilities Average One Minute Bars.

The databases cover five years of history and include OHLCV data and all additions, removals and changes to the index.

You can use our API with every dataset. Each database has a section explaining API usage and bulk download. You can also check out our detailed API documentation here: https://www.quandl.com/docs/api

Hope this helps!

Also, we apologize for the shortcomings of our site's search features - we are working very hard to improve this to better help users find the data they need.


Intuition: Difference in price elasticities of demand due to different bases

The solution to this issue is called "Arc Elasticity", used for "large" absolute changes. On the surface, the formula for Arc Elasticity is the familiar one, for example for price elasticity of demand

$$\eta_{arc}= \dfrac{ \text{
Percentage change in quantity demanded }} {  \text{ Percentage change in price } }$$

But the thing is how these percentage changes are calculated: If we went from quantity $q_a$ to quantity $q_b$, then while we "usually" calculate the percentage change as $(q_b-q_a)/q_a$ for the Arc Elasticity we divide by the mid-point of the interval -not by the point we started with. Same for price. So

$$\eta_{arc}= \dfrac{ \text{
Percentage change in quantity demanded }} {  \text{ Percentage change in price } } = \frac {\frac {q_b-q_a}{(q_b+q_a)/2}}{\frac {p_b-p_a}{(p_b+p_a)/2}}$$

$$\implies \eta_{arc} = \frac {q_b-q_a}{p_b-p_a}\cdot \frac{p_b+p_a}{q_b+q_a}$$

Re-arrange the terms at will to suit your own mnemonic triggers.

The Arc Elasticity has the convenient properties

(1) it is symmetric with respect to the two prices and quantities,
(2) it is independent of the units of measurement,
(3) it yields a value of unity if the total revenues (price times quantity) at the two points are equal.

See Allen (1933).

P.S. to OP: Use this for your other question.


GDP projections for the fifty American states

Official forecasts seem not to be available. The Bureau of Economic Analysis did produce these forecast in the past, but not anymore.

Forecasts from academic economists are scarce. US studies are usually only available for employment and not for GDP (for example, this paper). A working paper from late 2014 reviews the literature on regional forecasting (not only for the US) and the state-of-the-art methodology of such exercises. You can see in Table 1 a summary of studies between 1975 and 2015. None of them focuses on GDP for US states. Notice however that there are such studies for Germany (Wenzel, 2013) and Europe (Baltagi et. al. 2014), so maybe in the future an equivalent for the US will be produced.


Existence of market sharing equilibrium in hotelling model

Market sharing simply means that both platforms have some market share. So the condition can probably be obtained by finding the closed-form solution for market shares (not only implicitly as in (7)) and imposing the condition that all market shares are positive. This is akin to each platform having an interior solution.

I am not sure which Hessian you are referring to, but my guess is that you mean the hessian of a firm's optimization problem (choosing both of their prices) taking the prices of the other platform as given. In that case, if the Hessian is negative definite, regardless of the other firm's prices, an interior solution exists.


What is the need for a special purpose entity/vehicle in mortgage backed securities

Here are a few reasons that build on @Dismalscience's answer.

Capital requirements: Banks don't typically need to hold capital
against loans they originated but subsequently moved into an SPV. This might be regulatory arbitrage but it might be a socially efficient outcome meant to move assets and liabilities out of the banking system.
Market segmentation: Because SPVs can tranche (slice) their loans they can offer products with different assumed default correlations, prepayment risk, and aggregate credit risk. These products can appeal to customers with different beliefs and preferences over risk.
Bank business model: Banks may be better at finding customers, screening them, and handling the paperwork of making loans (broadly originating) then they are at proving inexpensive and patient capital to fund those loans. Securitization allows the bank to specialize in origination without also being the ultimate capital provider.
Information destruction: Because SPVs contain loans that are diversified over geography and borrower characteristics they can reduce market adverse selection, improving pricing and liquidity.


In your case there could be multiple solutions to the problem not just $y=0$. Any combination of $x$ and $y$ that would satisfy the budget with equality would be optimal in this case.
Hence I think it would probably be best just express demand for $x$ as:
$x=\frac{I}{P_x} - 4 y$
In fact this also gives you all potential optimum solutions to the problem since you can verify that for some parameters for example $I=100$ and $P_x=1$, when you consume 0 units of $y$ (implying that $x=100$) you get exactly the same utility as when you consume $x=96$ and $y=1$, or $x=92$ and $y=2$ and so on. So the $x= \frac{I}{P_x}-4y$ gives the combination of all possible optimum solutions. I personally don't see an reason to just assume that $y$ should be zero in such situation (unless this is for a classroom setting and that was recommended by instructor in these situations).


Is money lent by central banks to private banks counted in MB or M1?

Yes, it is in both but we have to be careful not to double count:

  The Fed’s definition of M1 is the sum of (1) currency outside bank
  vaults, (2) traveler's checks of nonbank issuers, (3) customers’demand
  deposits at commercial banks (with minor deductions), and (4) other
  checkable deposits, like negotiable order of withdrawal (NOW) and
  automatic transfer service (ATS) accounts. Basically, this is currency
  held by the public plus demand deposit balances outside the Fed. M2
  consists of M1 plus (1) savings deposits (including money market
  deposit accounts), (2) small-denomination time deposits (less than
  $100,000), and (3) balances in retail money market mutual funds.
  Individual retirement account (IRA) and Keogh account balances are
  excluded from M2. Excess reserves, required reserves, clearing
  balances held at the Federal Reserve banks, and the like, are
  components of the Fed’s monetary base but would constitute
  double-counting of the same factors if included in M1 and other
  monetary aggregates. Such accounts are readily spendable media of
  exchange (transaction accounts), but counterparts of these accounts
  already are included in M1, for example, as components of customers’
  demand deposits at commercial banks. The quantities of liquidity to
  fear for inflationary consequences are either monetary base or M1/M2,
  but not both simultaneously.

The Problem of Excess Reserves, Then and Now (Todd (2013))

What is the monetary base?

  In economics, the monetary base (also base money, money base,
  high-powered money, reserve money, outside money, central bank money
  or, in the UK, narrow money) in a country is defined as the portion of
  the commercial banks' reserves that are maintained in accounts with
  their central bank plus the total currency circulating in the public
  (which includes the currency, also known as vault cash, that is
  physically held in the banks' vault).

  The monetary base should not be confused with the money supply which
  consists of the total currency circulating in the public plus the
  non-bank deposits with commercial banks.

Wikipedia: Monetary base

This is how it works:

  Creating Money through the Discount Window.  When a bank needs new
  reserves to support loans and investments it has already made or
  anticipates making, it ordinarily borrows from other banks at the
  Federal Funds rate.  But during times of stress, which are reflected
  by a shortage of liquidity in many banks, the whole banking system
  needs new reserves — hence the Fed's discount window. When a bank
  borrows funds overnight from the Fed's discount window (at an interest
  rate the Fed sets, called the discount rate), the bank's reserve
  account at the Fed is credited with the amount borrowed (and the Fed
  adds to its assets the additional amount owed to it by the borrowing
  bank).  Since the borrowing bank gets new reserves and no other bank
  lost reserves, net new reserves have been created for the banking
  system as a whole.  If the amount is also \$10 million, the banking
  system as a whole has a new capacity to expand loans and deposits by
  as much as \$100 million.  Thus, the Fed's open market purchases and
  discount window loans have the same ultimate impact on the money
  supply, at least until the discount window loans are repaid.

How the Fed Creates Money (McTeer and Villarreal (2008))


Nash social welfare function with negative exponential utilities

I completely agree with @FooBar. Of course the utility function can be negative in some of its range. Conceptually, one could invoke the cardinality vs. the ordinality argument as a response to your question. I would think that your problem is as follows:

$$
\
max\, SWF=u(x_{1})\times u(x_{2})\times...\times u(x_{N})
\
 s.t
\
f(x_{1}....x_{N})\leq g
\
$$

The constraint(s) can be some resource constraint. All that matters here is that the SWF satisfies the normal properties associated with the existence of a maximum on the constraint set (You can invoke the assumptions of the Weierstrass Theorem here). Moreover, you should check Second Order Sufficient Conditions (in this case the negative definiteness of the Bordered Hessian) for a maximum. The value of the welfare function by itself is irrelevant as long as it is a maximum on the constraint set.


Exports: How can a small amount of export make really high income

What you're asking1 stems from a more general question

  "How can such a small amount of some export $Q$ make the most money out of all the exports?"

To that the answer is to simply recall the standard formula for Total Revenue.

i.e.

$$TR=P \times Q$$

Even though the quantity of export $Q$ is small it could be that the price for $Q$ (be that for whatever reason) be the cause for why it makes more revenue relative to the countries other exports.

Hope this is helpful!

1 I could be wrong


A graphic calculator for simple microeconomics problems

I wrote some silly program where you just fix endowment $e=(e_1,e_2)$ and utility functions $u=(u_1(x_1,y_1),u_2(x_2,y_2))$. The example provides an illustration for your utility functions and $x_1+x_2=1$ and $y_1+y_2=1$. I've drawn 100 indifference curves on an equally spaced grid of given utility levels $\bar u_1\in[u_1(0,0),u_1(1,1)]$ (blue) and $\bar u_2\in[u_2(0,0),u_2(1,1)]$ (red). The black line is the contract curve.

I added a second figure with some initial endowment $e_1 = (0.25, 0.75)$, $e_2 = (0.75, 0.25)$ and core.

e1 = [0.25 0.75];
e2 = [0.75 0.25];

X = 0.0:0.01:(e1(1)+e2(1));
Y = 0.0:0.01:(e1(2)+e2(2));

syms x1 y1 x2 y2 u1_bar u2_bar

u1 = x1.^2*y1;
u2 = x2*y2.^2;

I1_fun = matlabFunction(solve(u1_bar == u1, y1, 'PrincipalValue', true));
I2_fun = matlabFunction(solve(u2_bar == u2, y2, 'PrincipalValue', true));

u1_x = diff(u1, x1);
u1_y = diff(u1, y1);

u2_x = diff(u2, x2);
u2_y = diff(u2, y2);

u2_x = subs(u2_x, [x2,y2], [X(end) - x1, Y(end) - y1]);
u2_y = subs(u2_y, [x2,y2], [X(end) - x1, Y(end) - y1]);

contract_curve = matlabFunction(solve(u1_y/u1_x == u2_y/u2_x, y1));

u1_min = double(subs(u1, [x1,y1], [X(1), Y(1)]));
u1_max = double(subs(u1, [x1,y1], [X(end), Y(end)]));
u1_Array = linspace(u1_min, u1_max, 100);
I1_Array = zeros(length(X), length(u1_Array));

for i = 1:length(u1_Array)
I1_Array(:,i) = I1_fun(u1_Array(i), X);
end

u2_min = double(subs(u2, [x2,y2], [X(1), Y(1)]));
u2_max = double(subs(u2, [x2,y2], [X(end), Y(end)]));
u2_Array = linspace(u2_min, u2_max, 100);
I2_Array = zeros(length(X), length(u2_Array));
for i = 1:length(u2_Array)
I2_Array(:,i) = I2_fun(u2_Array(i), X);
end

hold on
[AX, H1, H2] = plotyy(X, I1_Array, 1-X, I2_Array)
set(AX(:),'YLim',[0 1]);
set(AX(:),'YTick',[0:0.1:1])
set(H1(1:length(u1_Array)), 'Color', 'b');
set(H2(1:length(u2_Array)), 'Color', 'r');
set(AX(2),'YDir','reverse')
axis(AX,'square')
%str1 = '\bullet e=(e_1,e_2)';
%text(e1(1),e1(2),str1)
plot(X, contract_curve(X), 'k', 'linewidth', 2)
hold off


Does quantitative easing appreciate or depreciate the domestic currency?

The exchange rate can be expressed in a simple classroom monetary model as:

$$S = \tilde{m} - \psi \tilde {y} + \lambda (\tilde i)$$

Where $S$ is the exchange rate $m$ is log of money supply, $y$ log of real output $i$, interest rate, $\tilde{}$ denotes differences between variable at home and abroad (i.e. $\tilde{x} = x_{home}-x_{foreign}$), and $\psi$ & $\lambda$ are just model parameters.

So the exchange rate depends both on log of money supply and on interest rate. Furthermore the interest rate itself depends on money supply.

The answer of @410gone focuses on the first order effect of monetary expansion through changes in $m$ whereas the answer on Quora mentions only the effect monetary expansion has on exchange rate through $i$.

However, the Quora answer omits any discussion of other effects, whereas @410gone mentions there are other effects so I would say the @410gone answer is more correct in a sense it mentions that also other effects exist whereas the Quora answer pretends that increase in money supply only affects exchange rate through the interest rate.


How are elasticity of demand, marginal revenue, and total revenue connected?

Marginal cost is irrelevant to total revenue. It's relevant to profit, but not total revenue.

Total revenue is just price x quantity.

Marginal revenue is a monotonic decreasing function. That is, as quantity increases, marginal revenue decreases. So, let's take the quantity Q to be the point at which marginal revenue is zero.

For quantities below Q, marginal revenue is positive, so total revenue increases with quantity.

For quantities above Q, marginal revenue is negative, so total revenue decreases with quantity.

Hence Q is the turning point of the curve: it is the point of maximum total revenue.

Elasticity of 1 means that a tiny % change, $\Delta$ in price in one direction (equivalent to multiplying price by $1+\Delta$),  will be met by a reciprocal proportional change in quantity in the other direction, equivalent to multipying it by $\frac{1}{1+\Delta}$: that's straight from the definition of elasticity.

So total revenue, the product of price and quantity, remains the same:

$$(1+\Delta) P \times \frac{1}{(1+\Delta)} Q = P \times Q$$

Hence marginal revenue always 0, when elasticity is exactly equal to 1.


Where can I find real-time indicators of economic activity?

The projects developed by Alberto Cavallo and Roberto Rigobon could be a source of inspiation.

The Billion Prices Project is an academic initiative that uses prices collected from hundreds of online retailers around the world on a daily basis to conduct economic research. This page shows their most recent research leveraging high-frequency price data, as well as the US daily inflation index (updated monthly).

Here are the datasets on Online Micro Price Data, Global Retailers Data...


Producer's cost for buying full solution vs. buying parts

Some economists (Oliver Hart and John Moore are among the most prominent) have developed a "theory of the firm" which could help address some of the issues involved. One of the considerations in that theory is that the different parties involved in production can 'hold-up' each other. For example, in this case, the brake manufacturer or the auto manufacturer can suddenly threaten to cancel the relationship with the other party, unless the contract is improved.  This, in turn, means they don;t invest much in each other and production is inefficient.

Under that scenario, the optimal solution is for a single party to be the owner of all crucial processes.

This relates to your question in the sense that, from this perspective, the manufacturer is better off buying the individual parts because then it's much harder for anybody to hold it up. Put simply, it has more negotiating power. It will want to in-house processes that are simple, but which could hold it up.

alternatively, it will want to have some serious lawyer power writing the contracts with all its suppliers so that they can't come up with any surprises. That's hard to do. The principle that this is hard to do is called the 'incomplete contracts' principle.

(edits in response to comments:)
Other key authors in the theory of the firm are Ronald Coase, Oliver Williamson and Sandy Grossman. For Coase, as long as property rights are well-defined,  market allocation would be efficient regardless of who owns what. However, there are transaction costs in markets, maybe you can think of them as contracting or negotiating costs). The firm overcomes the costs of transactions by creating non-market relationships within itself. The boss does not negotiate with the worker every day. This can be more efficient than having all activity being performed in the marketplace.


What would happen if a company bought back of all of its stock? Would it own 100% of itself?

The New York Stock Exchange has a continued listing requirement of 300 shareholders and 200,000 shares. A company will want to consider whether continuing to be traded on a stock exchange is desirable before approaching these limits.

LINK to a NYSE reference document.

If a company buys back almost all of its shares the last individual or institutional owner (who ever owns the last outstanding share yet to be bought back) will will own all of the equity. This person or institution will control the company. The seller of the last outstanding share will want the highest possible price. If this trade must be done via the company buying it's own shares, because that is the premise of your question, the owner will direct the company to pay the maximum cash amount. The company will generate the maximum cash by liquidating the company.

Definition from Wikipedia...

  Liquidation is the process in accounting by which a company is brought
  to an end

LINK to Wikipedia article about liquidation.

If the last outstanding share can trade for more than liquidation value, there is no reason to liquidate the company. The owner can sell the share to a different investor in order to get the highest possible price.


Do wages differ in two perfectly competitive labour markets?

This will typically depend on if people can switch between the two markets. If switching is possible then the marginal worker has to be indifferent between working in market A and market B and this equalizes the wages in the two markets. This also assumes you mean wage rates and not wage bills. Wage bills also depend on hours worked per worker, and that decision need not be equal across industries because of sorting and other reasons.

If people can't switch between markets it can, but doesn't have, to be that wages do not equalize. Consider two workers on two different islands with residents that don't trade or even meet. Even if labor markets on both islands were perfectly competitive, it needn't be that their wage rates were equalized.


Uncovered Interest Parity (UIP) condition approximation

From the basic equation you get
\begin{eqnarray*}
\frac{e^E_{t+1}}{e_{t}} & = & \frac{1+i_t}{1+i^*_t} \\
\\
(1+i^*_t) \cdot e^E_{t+1} & = & (1+i_t) \cdot e_t \\
\\
e^E_{t+1} - e_t & = & i_t \cdot e_t - i^*_t \cdot e^E_{t+1}.
\end{eqnarray*}
Now comes the approximation. You divide either by $e_t$ or by $e_{t+1}^E$.

First method
$$
\frac{e^E_{t+1} - e_t}{e_t} = i_t - i^*_t \cdot \frac{e^E_{t+1}}{e_t} \approx
i_t - i^*_t.
$$
Second method
$$
\frac{e^E_{t+1} - e_t}{e^E_{t+1}} = i_t \cdot \frac{e_t}{e^E_{t+1}} - i^*_t  \approx
i_t - i^*_t.
$$
I would say there is no crucial difference, both of these just assume that the proportional change in the exchange rate multiplied by the interest rate is an order of magnitude lower than either the interest rate or the change in the exchange rate alone.


Aside from buying IPOs, what exactly is the point of shareholders?

The shareholder system is a way of distributing the ownership of the company - each shareholder owns a certain part of the company. Shareholders are the owners of the company, in several company legal forms, such as an LLC. They exist before and after an IPO (Initial public offer), meaning that both public (traded) and private companies may have shareholders.

The shareholders can fire and hire the Management team (CEO/CFO/ etc), which answers your questions 2 and 3. They usually signal the Management team which actions they expect the company to take to maximize the company value, reflected by the share value. If the shareholders have a short-term gain objective, this might harm the long-term sustainability of the company - a case where the management team and the shareholders might have different perspectives.

Raising funds through the sale of shares is attractive for companies because it is interest free, and might give you access to much more funds than you would ever be able to get from bonds - depending on how a company communicates its future potential. However, this comes with a loss of ownership. There is only so much unsecured debt one can sell - and debt is always paid back with interest.


Specification of the parameters of this utility function [Behavioral Economics]

As @Henry commented and according to https://meta.stackexchange.com/questions/117251/what-should-be-done-with-questions-that-have-been-self-resolved-as-a-comment-ins I made a community wiki with the answer:

  αi and βi are coefficients related to how much an individual i feels bad about being less wealthy or more wealthy than other people. max{xj−xi,0} is the difference between person j's wealth and person i's wealth if person j's wealth is higher than person i's wealth; otherwise it is 0. The division by n−1 to get an average is because there are n−1 individuals apart from person i for person i to compare to.


To be a Pareto optimum, there must not exist another feasible allocation that makes every agent at least as well off and one or more agents strictly better off.

So, let us consider the options here.

Answer B - look at the individual allocations here and consider them relative to the economy's total endowment. Since the allocations given here do not exhaust the economy's total endowment, we could make one of the agents better off by simply giving him some of what has not been allocated. Doing this would not make the other agent worse off. So B cannot be P.O.

Answer C - Consider the allocations here relative to the total endowment. Is such an allocation feasible?

Answer A - Has the total endowment been allocated? If so, is there any way to increase what one agent has without decreasing what the other has?


Are government income and government employee wages counted in GDP? (income approach)

The wages of government workers are counted as wages of individuals in the income measure of GDP. If the Government trades, then surpluses or profits of these activities are counted as income in the income measure of GDP.

If GDP is being measured at market prices then some indirect taxes (on production or on imports, less any subsidies) are also taken into account; other taxes such as income taxes are not

Meanwhile Government payments of wages in its non-trading activities are counted as government consumption in the expenditure measure of GDP and this amount also counts as Government production in the the production measure of GDP


Define and characterize equilibria of the following game

SOLUTION:

1) DEFINITION OF EQUILIBRIUM

\begin{equation} \begin{split}
&p \in \mathbb{R}_+\text{ is the price chosen by the firm in period 1}\\
&a_U \in [0,1] \text{ is the share of income the Uninformed consumer allocates in period 1}\\
&a_I \in [0,1] \text{ is the share of income the Informed consumer allocates in period 1}\\
&\Theta = \{I,U\} \text{ is the type of consumer: Informed, Uninformed}\\
& S_I = \{ a : \{\underline{p},\bar{p}\} \times \mathbb{R}_+ \to [0,1] \} \text{ is the strategy set of the I. consumer}\\
& S_U = \{ a : \mathbb{R}_+ \to [0,1] \} \text{ is the strategy set of the U. consumer}\\
& S_f = \{ p : \{\bar{p},\underline{p}\} \to \mathbb{R}_+ \} \text{ is the strategy set of the firm}\\
&\mu_U(p) = Pr(P =\bar{p}|p) \text{ : consumer of type U belief that the second period price is } \bar{p}, \text{ given } p\\
&\mu_I(P) = Pr(P =\bar{p}|p) \text{ : consumer of type I belief that the second period price is } \bar{p}, \text{ given } p\\
\end{split} \end{equation}

An equilibrium of the game is a triple of strategies, $s^*=(a^*_I, a^*_U,p^*)$ for each type of consumer and the monopolist, together with a system of belief $\mu$ such that: for each player $i$, $s_i^*$ is sequentially rational, and the beliefs are determined by the strategy profile and Bayes rule whenever it applies. \

In particular for each price $p$, the consumer of type $i \in \{U.I\}$ solves:
\begin{equation} \begin{split}
&a_i^*(p) = \text{ argmax } \sum_p \big[ ( \frac{a}{p} + \frac{1-a}{\bar{p}} )\mu_I(P) + ( \frac{a}{p} + \frac{1-a}{\underline{p}} )(1-\mu_I(P)) \big]
\end{split} \end{equation}

Also, in the case of the Informed consumer, we know that
\begin{equation} \begin{split}
 &\mu_I(P) = Pr(P =\bar{p}|p) =
\begin{cases}
1 &\text{ if } P =\bar{p}\\
0  &\text{ if } P = \underline{p}\\
\end{cases} \\
\end{split} \end{equation}

given the consumers optimal strategies and $P$, $p^*(P)$ maximizes the monopolist first period profits:

\begin{equation} \begin{split}
&\pi(P)^* = \text{ argmax } \alpha [a^*_I(p) p] + (1-\alpha) [a^*_U(p) p]\\
\end{split} \end{equation}

2) CHARACTERIZATION OF EQUILIBRIA

for any realization of $P$ in period 2, we have that
\begin{equation} \begin{split}
a_I(p)^* =
\begin{cases}
1 &\text{ if } p <  P\\
0  &\text{ if } p >P\\
\in [0,1] &\text{ if } p =  P \\
\end{cases} \\
\end{split} \end{equation}

\begin{equation} \begin{split}
a_U(p)^* =
\begin{cases}
1 &\text{ if } p <  \mu_U(p) \bar{p} + (1-\mu_U(p))\underline{p}\\
0  &\text{ if } p > \mu_U(p) \bar{p} + (1-\mu_U(p))\underline{p}\\
\in [0,1] &\text{ if } p = \mu_U(p) \bar{p} + (1-\mu_U(p))\underline{p}
\end{cases} \\
\end{split} \end{equation}

To define the optimal strategy of the monopolist consider the following cases, where $\pi$ denotes the monopolist first period profits:

a)Suppose $p=\bar{p}, \forall P$, then By Bayes rule $\mu_U(p) = 1/2$; also suppose that off the equilibrium path $\mu_U(p) = 1/2, \forall p \neq\bar{p}$ ; then the monopolist profits are given by:

\begin{equation} \begin{split}
\pi(P) =
\begin{cases}
\alpha \bar{p} a_I^*(\bar{p}) &\text{ if } P=\bar{p} \\
0  &\text{ if } P =  \underline{p} \\
\end{cases} \\
\end{split} \end{equation}
This is not an equilibrium strategy because the monopolist can deviate and increase its profits when $P=\underline{p}$ by setting, for example, $\hat{p} = 1/2\bar{p} + 1/2\underline{p}$; this will give him a profit of $\alpha a_U^*(\hat{p})  >0$.
Similarly it is possible to prove that no-matter what the off the equilibrium path are, there is always a profitable deviation for the monopolist. \

b)Suppose $p=\underline{p}, \forall P$, then $\mu_U(p) = 1/2$ and also suppose that off the equilibrium path $\mu(p) = 1/2, \forall p \neq\underline{p}$ ; then the monopolist profits are given by:

\begin{equation} \begin{split}
\pi(P) =
\begin{cases}
\underline{p} &\text{ if } P=\bar{p} \\
\underline{p} (\alpha a_I^*(\underline{p}) +(1-\alpha) ) &\text{ if } P =  \underline{p}\\
\end{cases} \\
\end{split} \end{equation}
this is not an equilibrium strategy because $\exists \epsilon > 0 $ such that monopolist will deviate and increase its profits when $P=\bar{p}$; for example by setting  $\hat{p} = 1/2\bar{p} + 1/2\underline{p} -\epsilon>\underline{p}$ which will give him a profit of $\hat{p}> \underline{p}$ .

c)Suppose $p=\underline{p}, \text{ if } P= \underline{p}$, $p=\bar{p}, \text{ if } P= \bar{p}$ and $\mu_U(p) = 1, \forall p > \underline{p}$ then

\begin{equation} \begin{split}
\pi_1^*(P) =
\begin{cases}
\bar{p}(\alpha a_I^*(\bar{p}) +(1-\alpha) a_U^*(\bar{p})) &\text{ if } P=\bar{p} \\
\underline{p} (\alpha a_I^*(\underline{p}) +(1-\alpha) a_U^*(\underline{p})) &\text{ if } P =  \underline{p}\\
\end{cases} \\
\end{split} \end{equation}
this represents an equilibrium as long as  $a_I^*(\bar{p}) = a_U^*(\bar{p}) = 1$; otherwise the monopolist can set a price $\hat{p}< \bar{p}$ and can achieve a profit of $\bar{p} - \epsilon >\alpha a_I^*(\bar{p}) +(1-\alpha) a_U^*(\bar{p})$

d) Suppose $p = 1/2\bar{p} + 1/2\underline{p}, \forall P$ then $\mu_U(p)=1/2$ and and also suppose that off the equilibrium path $\mu(p) = 1/2, \forall  p \neq ( 1/2\bar{p} + 1/2\underline{p}) $
\begin{equation} \begin{split}
\pi_2^*(P) =
\begin{cases}
(1/2\bar{p} + 1/2\underline{p})  (\alpha  +(1-\alpha) a_U^*(p)) &\text{ if } P=\bar{p} \\
( 1/2\bar{p} + 1/2\underline{p} ) ( 0 + (1-\alpha)a_U^*(p)) &\text{ if } P =  \underline{p}\\
\end{cases} \\
\end{split} \end{equation}
This is an equilibrium strategy as long as there are no profitable deviation; notice that the monopolist can set $p=\bar{p}$ when $P=\bar{p}$ and given $\mu_U = 1/2$ its profits would equal $\alpha \bar{P}a_I^*(\bar{p})$. Also, when $P=\underline{p}$ the monopolist could set $p=\underline{p}$ and get a profit of $\underline{p}$. So we need to insure that neither deviation is possible.

e) ?

We can therefore characterize the following (Perfect Bayesian) Equlibria:

1ST EQUILIBRIUM)
\begin{equation} \begin{split}
&a_I(p)^*  = 1, a_U(p)^* = 1 \\
&\pi_1^*(P) \text{ defined as above } \\
&\mu_U(p) = 1 \text{ both "on and off" the equilibrium path } \\
&\text{(that is, if the monopolist deviates } \\
&\text{from the equilibrium strategy } \mu_U(p)=1 \text{ still holds} \\
\end{split} \end{equation}

SET OF EQUILIBRIA)
\begin{equation} \begin{split}
&a_I(p)^* =1, a_U(p)^* \in[0,1] \\
&\pi_2^*(P) \text{ defined as above } \\
&\mu_U(p) = 1/2 \text{ both "on and off" the equilibrium path } \\
&\text{(that is, if the monopolist deviates } \\
&\text{from the equilibrium strategy } \mu_U(p)=1/2 \text{ still holds} \\
& \text{Also, The following two conditions below hold:}\\
&\alpha \bar{P}a_I^*(\bar{p}) < (1/2\bar{p} + 1/2\underline{p})  (\alpha a_U^*(\bar{p}) +(1-\alpha) ) \\
&\underline{p} < ( 1/2\bar{p} + 1/2\underline{p} ) (\alpha a_U^*(\bar{p}) +0)\\
\end{split} \end{equation}


Luce Choice Axiom, Quantal Response Equilibrium

A few quotes from Jessie and Saari (2015) may be of interest.

Regarding Luce Choice Axiom (LCA):

  The effect of LCA is to endow each alternative with an intrinsic level of likelihood that is independent of the particular set from which it is chosen. Mathematically speaking, in Luce’s formulation, the choice axiom implies the existence of a weight function $v(A)$ for an alternative $A$ in which the probability of selecting $A$ can be written as
  \begin{equation}
P_T(A)=\frac{e^{v(A)}}{\sum e^{v(B)}}\tag{1}
\end{equation}
  where the sum in the denominator is taken over all alternatives in $T$ (Luce, 1959). Because function $v(\cdot)$ does not depend upon the set $T$, it defines an intrinsic weight of the alternative. An important special case is when $v(\cdot)$ is a linear function; here Eq. (1) defines the multinomial logit model.

Regarding Quantal Response Equilibrium (QRE) [in a $2\times2$ normal form game, where Row player chooses between Top and Bottom]:

  Instead of perfectly observing the payoffs for a given strategy, assume that the subjects perceive the expected value plus a stochastic term $\frac{\epsilon}{\lambda}$, where $\epsilon$ is a random variable and $\lambda$ is a magnitude parameter. In this framework, Row strategically chooses Top if
  \begin{equation}
E(\text{Top})+\frac{\epsilon_1}{\lambda}>E(\text{Bottom})+\frac{\epsilon_2}{\lambda}
\;\Leftrightarrow\; \lambda[E(\text{Top})-E(\text{Bottom})]>\epsilon_1-\epsilon_2. \tag{4}
\end{equation}
  That is, Row’s choice of a probabilistic strategy combines the actual expected values with a measure of how it is recognized. A common assumption about $\epsilon_i$ is that they are independent and identically distributed type-I extreme value random variables. In the general case of several strategies, the probability $p_i$ that strategy $s_i$ is chosen is given by
  \begin{equation}
p_i=\frac{e^{\lambda E(s_i)}}{\sum_j e^{\lambda E(s_j)}}.\tag{5}
\end{equation}
  This expression is identical to the LCA multinomial logit expression in Eq. (1) with  being a strategy’s expected payoff, with an emphasis on preserving the LCA structure.

  The $\frac{\epsilon}{\lambda}$ form of the stochastic term in Eq. (4) makes it reasonable to treat $\lambda$ as a measure of “rationality”. This is because with small $\lambda$ values, the random terms dominate; indeed, with $\lambda=0$ (Eq. (5)), the subjects are completely insensitive to differences in expected value, so strategies are selected from a uniform distribution. In contrast, the effect of the random terms diminish as $\lambda\to\infty$, which means that the subjects become increasingly responsive to payoff differences; in the limit they reach the Nash equilibrium.


You are right to be sceptical of this statement.  Let's take it step by step.

Will developments in biotechnology increase world food production?  Almost certainly yes, provided other things are equal.  But the reality is that other things are not equal.  Climate change is likely, other things being equal to reduce agricultural productivity in some parts of the world. Whether the positive effect of biotechnology will more than offset the negative effect of climate change is unclear.

If world food production increases, will prices of agricultural products fall? Not necessarily.  Demand for food is rising due to rising population and to rising incomes in much of the world. Again, the net effect (of rising supply and rising demand) is unclear.

If agricultural prices fall, could this increase hunger for some people? Yes, this is certainly possible.  Those most at risk would be people in poor countries who have relied on farming for their income and, due to limited education and training and/or location, have limited opportunities for alternative employment or other income sources.  The book is right to imply that hunger is as much due to low incomes as to food supply.  But the argument that the overall effect of biotechnology will be to increase world hunger is unconvincing.