Name of example of irrationality of proportional and absolute cost

I think you're referring to the jacket-calculator problem, first proposed by Tversky and Kahneman (1981) as their Problem 10. The paper illustrates the idea of mental accounting with several problems regarding uncertainty, and problem 10 illustrates "the temporary devaluation of money":

  The following problem, based on examples by Savage and Thaler, further illustrates the effect of embedding an option in different accounts. Two versions of this problem were presented to different groups of subjects. One group ($N = 93$) was given the values that appear in parentheses, and the other group ($N = 88$) the values shown in brackets:

    Problem 10: Imagine that you are about to purchase a jacket for (\$125) [\$15] and a calculator for (\$15) [\$125]. The calculator salesman informs you that the calculator you wish to buy is on sale for (\$10) [\$120] at the other branch of the store, located 20 minutes drive away. Would you make the trip to the other store?

  The response to the two versions of problem 10 were markedly different: 68 percent of respondents were willing to make an extra trip to save \$5 on a \$15 calculator; only 29 percent were willing to exert the same effort when the price of the calculator was \$125. ... By the curvature of $\nu$, a discount of \$5 has a greater impact when the price of the calculator is low than when it is high.

  ...

  Many readers will recognize the temporary devaluation of money which facilitates extra spending and reduces the significance of small discounts in the context of a large expenditure, such as buying a house or a car. This paradoxical variation in the value of money is incompatible with the standard analysis of consumer behavior.


An Introduction to Econometric Theory by James Davidson might be worth a look. It satisfies all your condition at a slim 256 pages.


How can banks pay interest to the central bank?

You anticipate the answer when you ask:

  This question can be easily answered if there were any way in which
  new money can leave the central bank without being paid back. Are
  there such transactions I don't know about?

Indeed, there is always a way that money leaves the central bank without being paid back: the central bank does something with its net interest earnings, usually sending them to the central government, which treats them as part of its revenue, and is therefore able to get by on a little less tax revenue than it would otherwise need. For instance, in 2013 the Federal Reserve remitted $78 billion in profits to the US Treasury.

Let's incorporate this observation into an augmented version of your example. Suppose that the central bank keeps the supply of money at \$10, with a corresponding loan of \$10 to banks, and the annual nominal interest rate is 10%. Suppose that the central government spends \$5 per year and runs a balanced budget.

Each year, banks pay \$1 in interest to the central bank. This is profit and is sent to the central government, which then only needs to raise \$4 in taxes to pay for its \$5 in spending. The net effect of this is to put \$1 in the hands of the public, which ultimately finds its way to paying for the \$1 in interest that banks owed to the central bank. (After all, these banks are presumably lending out the money and collecting interest from the public themselves.)

One can make the example much more intricate, but the key point is that we don't get an exponentially growing debt owed to the central bank by the rest of the economy - because the central bank sends its profits to the government, and then they're recycled into the rest of the economy.

(As user4385 points out in a comment, the situation is similar for any kind of debt. Suppose, for instance, that Connecticut is a net creditor to the rest of the country - where does the rest of the country get the money to pay interest to Connecticut? The answer is that Connecticut eventually spends its interest earnings on goods and services from the rest of the country - funds flow in both directions.)


When the global optimal is outside of the constraint set, what will be the demand?

Argue that, given your assumptions on the utility function, $x^*$ is the essentially unique (and hence global) maximum. (You need this because there may be local maxima when the assumptions on the utility function is relaxed - this will violate the proposition you're trying to prove).

Now simply use the definition of global optima: for any $x\leq x^*$, $u(x)\leq u(x^*)$. This should be enough to give you the result.


Drug pricing, amount of sales and R&D costs

The previous +1 answer gives the correct economic mechanism but let me give you some case specific answer here.
First of all there actually already is another drug that targets the same disease called Spinraza (see here) with cost of \$750,000 for the first year and then \$350,000 per year after that, so about \$4 million a decade.  Assuming people with this deasease can live up to 70 years (which would cost patient \$28 million over life time) that means the Zolgensma drug is already $92.5\%$ cheaper than their competitors over patients lifetime (although the figure is less impressive if this person dies earlier - but even at 10 years it is already almost half the price of the other treatment). Sure this does not answer question why it could not be even more cheaper - but it already puts the high price tag in some perspective.
Given that these more expensive therapy exists I assume that the market for it wont be 0. Even if the cost is high it can be manageable with insurance that spreads the high cost over large number of people. I doubt most patients will pay the price out of the pocket.
Second, the article you cited says that this drug was developed for a rare disease that affects only about 1 in 10000 people, so it is not like this drug can be sold by thousands.
Let us just do some back of an envelope calculation. These gene therapy treatment is particular valuable and applicable to those diagnosed in early childhood. According to the Our World In data the population increase in 2019 was about 80 million. Now many of these people will live in countries without sufficient infrastructure/supply chains etc to administer any treatment. Especially in sub-Saharan Africa there are issues even with giving people cheap deworming pills due to conflicts/anarchy, people living in rural areas without clinics, lack of education etc. so no matter what is the price it won't be accessible to about $33\%$ of world population. That gives us about 50 million.  Since the disease will affect about 1 out of 10000 people that means yearly the market for the drug is about 5000 people.
Next, we actually know exactly in this case how much the medicine costs because it was not developed by the company but acquired from another company reportedly for $8.7 billion from US firm AveXis. Furthermore, patents for drugs last 20 years from the day they are patented and since the FDA approval process takes some time and there is always a threat of a new competitor coming up in with a new drug it is not reasonable to say company will have all 20 years to recoup costs. Let's for a sake of argument say that it will have 10 years. Furthermore, these are just development costs. As far as I understand gene therapy is not as easy to manufacture as regular pill (but I am not medical professional), plus there are all other associated with running the business but let us forget about those for a second.
Well that gives us the total market for this drug over 10 years to be about 50000. Now we need to spread all the 8.7 billion over 50000 people. Hence to break even (just on development costs and nothing else) the drug would have to be priced at \$174000. Again this is just development cost so I would guess that at your proposed \$200000 the company would still not break even.
In addition any company needs also some healthy profit because R&D is risky business any wins have to pay for all failures to successfully develop drug. Even in cases like here where R&D was done by different firm there is still an issue that you never know when the new competitor arrives. If we would change the above assumption that the company will enjoy monopoly for 10 years to just 1 year because maybe better treatment will come next year suddenly just to break even on development the treatment would have to cost \$1740000 which is much closer to current price.
In fact according to  Institute for Clinical and Economic Review, that took into account wide range of factors the new gene therapy would be justifiable at cost \$1.1 million to \$1.9 million per treatment. Now this is still lower than the \$2.1 million per treatment but less so.
Now this answer is actually complementary to the answer of Bayesian above since undoubtedly thanks to their monopoly on the drug the company charges more than it would if there would be more competition and this mechanism is correctly described by Bayesian, but the point is that even without this issue assuming that price would have to cover the development cost etc it would still have to be priced around million.


Why use the income approach to approximate GDP if it relies on the value produced by the expenditures approach?

The definition of the expenditure measure of GDP is:
$$GDP_{EXP} \equiv C + I_g + G + X_n$$

The definition of the expenditure income measure of GDP is:
$$GDP_{income} \equiv I_n - I_f - C_c$$

As I understand it, $s$ is not part of it. $s$ is defined as the difference between the two measures:
$$s \equiv GDP_{EXP} - GDP_{income}$$

Apparently it is also possible to define it with the RIPSAW approach:
$$GDP_{income} \equiv R + I + P + S + A + W$$
R = rents, I = interests, P = profits, SA = statistical adjustments (corporate income taxes, dividends, undistributed corporate profits, and W = wages.

And yes, it is useful to calculate GDP with multiple methods. Among other things, it reduces noise in GDP estimates:

  Two often-divergent U.S. GDP estimates are available, a widely-used
  expenditure-side version $GDP_E$ , and a much less widely-used
  income-side version $GDP_I$ . We propose and explore a “forecast
  combination” approach to combining them. We then put the theory to
  work, producing a superior combined estimate of GDP growth for the
  U.S., $GDP_C$ . We compare $GDP_C$ to $GDP_E$ and $GDP_I$ , with particular
  attention to behavior over the business cycle. We discuss several
  variations and extensions

Improving U.S. GDP Measurement: A Forecast Combination Perspective Aruoba, Diebold, Nalewaik, Schorfheide, and Song (2012, ungated here)


New-Keynesian Model: Log-linearizing the firm's FOC

$$(\sum_{k=0}^\infty \theta^k E_k(Q_{t,t+k} Y_{t+k|t} (P_t^*/P_{t-1} - \alpha MC_{t,t+k} \beta_{t-1,t+k}))) = 0 $$

Log linearize around the zero inflation steady state.

$$p_t^* - p_{t-1} = (1 - \beta\theta) \sum_{k=0}^\infty (\beta\theta)^k E_t(\widehat{mc}_{t+k|t} + p_{t+k} - p_{t-1}) $$

Where $$\widehat{mc}_{t+k|t} \equiv {mc}_{t+k|t} - mc$$
In other words,
$$p_t^* = \gamma + (1 - \beta\theta) \sum_{k=0}^\infty (\beta\theta)^k E_t(\widehat{mc}_{t+k|t} + p_{t+k}) $$
where $\gamma \equiv log \frac{\epsilon}{\epsilon + 1} $

If I remember correctly, this model uses Calvo pricing, so inflation is just from wage stickiness. So if you set $\theta = 0$ (no price stickiness)
$$p_t^* = \gamma + mc_t + p_t$$

See what you can work with from there.

Edit: If you're wondering how this is done, then "An Old Man in the Sea"'s resource in the comments is helpful, in sections 3.2 and 3.3. It will show how to do the First-Order Taylor Expansion to derive the result.


What happens to undated government stocks when interest rates dip below the coupon rate?

This is a pretty standard bond pricing issue. The short answer is yes, the market value of the bond can and often will exceed its par value if interest rates are below the coupon rate, just so long as the call option is structured such that the government must pay any interest that has accrued between the last coupon date and the time that the call option is exercised. However, the extent to which the bond will pay more than its face is a question of how the call option is structured: whether it can be called at any time, or whether it can only be called on coupon dates.

Consider an example where the government has issued a \$100 bond paying 4% per period and (for whatever reason) chooses not to exercise the option immediately, the prevailing interest rate is 3% per period, and the coupon rate is 4% per period:

Period 1: \$4 payment, discounted present value is \$3.88
Period 2: \$4 payment, DPV is \$3.77
Period 3: \$4 payment, DPV is \$3.66
Period 4: \$4 payment, call option exercised, \$100 principal returned, DPV is \$92.40

Total value: \$103.72 (difference due to rounding).

Now consider the case where the bond is outstanding, rates drop to 3%, and the bond is immediately called— the bond pays out \$100, plus whatever interest has accrued.

US government bonds are discretely callable— they can only be called on the coupon date, as in the first example. So in the case you give they'll generally trade above par at any date between coupon payments. UK bonds can be called at any time, so there's a lot more uncertainty— it's possible that you could buy the bond today and have it called immediately. However, given that there's little reinvestment risk and that in the event that they're called they will pay out the face value plus accrued interest, the lower bound of their value should be right around par. Thus, to the extent that there's uncertainty as to whether and when the call option will be exercised, it's reasonable to expect that they will trade strictly above par.

Interestingly, as the interest rate drops and the spread between a callable bond and market rates becomes larger, the likelihood that the bond will be called increases, so the value of the bond continues to increase, but at a decreasing rate. This is known as negative convexity. It's a common feature in US mortgage markets, because most borrowers in US mortgage markets (unlike mortgage markets in many other countries) have an implicit option to prepay at any time without penalty. As a result, mortgages and mortgage-backed securities display significant negative convexity, making hedging interest rate risk a big deal for mortgage lenders. For this reason, your question is actually closely related to the question, "Why do lenders dislike early loan repayments?".


I have not heard of such a study and I have a feeling studying how a daily news item would affect an annual measurement value would be a pretty futile experiment.

However, there are some studies on how announcements from central banks or other financial authorities might affect expectations in the short run. My collaegue actually did her licensiate thesis on how ECB board announcements affected the growth path of euro inflation.

A pretty recent article would be Moessner, R.: "Effects of ECB balance sheet policy announcements on inflation expectations." in Applied Economics Letters and that might be a good place to start looking.


If aggregate demand and supply do not have a specific value, what is the point of the formula?

This should have been a comment, but I have less that 50 reputation and I am new to this site as are you.

First, I think the point is clear and concise, but you may be misinterpreting it slightly.

Think of demand or supply like a pendulum swing that is being pulled by two forces.

For supply this is prices and output, prices can be pulled by output and output can be pulled by prices.

However, you're right, you can get specific values, you can use the formula.

The formula is particularly useful for averages, the prices and output over time.


The omitted variable bias in gravity model is an important issue given that some factors are unobserved or difficult to quantity. To solve this issue trade economists tend to rely on various fixed effect estimators. But, the question is what is your variable of interest?

Exporter-by-year and importer-by-year fixed effects

For instance, if you are interested in evaluating the effect of trade costs on trade, you can introduce exporter-by-year and importer-by-year fixed effects to absorb GDP, GDP per capita, price indexes etc.

Exporter-by-importer fixed effects

If you are interested in evaluating the effect of one country-specific variable on trade, you can introduce exporter-by-importer fixed effects to absorb distance or contiguity effects.

Exporter-by-year, importer-by-year + exporter-by-importer fixed effects

If you are interested in evaluating the effect of a time-varying bilateral factor, like free trade agreements, on trade (see Baier and Bergstrand, 2007), you can introduce exporter-by-year, importer-by-year + exporter-by-importer fixed effects to absorb distance or contiguity effects as well as GDP, GDP per capita, ....

References

Baier, S. L., & Bergstrand, J. H. (2007). Do free trade agreements actually increase members' international trade?. Journal of international Economics, 71(1), 72-95.
Baldwin, R., & Taglioni, D. (2006). Gravity for dummies and dummies for gravity equations (No. w12516). National Bureau of Economic Research.
Head, K., & Mayer, T. (2013). Gravity equations: Workhorse, toolkit, and cookbook. This last reference is a must to read to construct a gravity model.


How does the Austrian School view land rents?

From what I heard, Austrian economics is descriptive, not prescriptive; for example, being an Austrian economist and a communist may not be a contradiction. However, the following represents the view of an average Austrian economist on land rents, based on my experience.
Land can be acquired by property transfer or by homesteading. Homesteading is mixing land with labor. Property rights to land can be lost by property transfer or by abandonment. Same as with any other property, the owner of land can rent to others.


How to calculate standard deviation of a portfolio?

You could say the return on Johnson & Johnson is a random variable $R_J$ with expected value $\mu^{\,}_J$ and variance $E[(R_P-\mu^{\,}_P)^2] = \sigma^2_J$, and on Ford is $R_F$ with expected value  $\mu^{\,}_F$ and variance $E[(R_F-\mu^{\,}_F)^2] = \sigma^2_F$

$R_J$ and $R_F$ perfectly correlated means $\frac{\mathbb E[(R_J-\mu^{\,}_J)(R_F-\mu^{\,}_F)]}{\sigma^{\,}_J\,\sigma^{\,}_F}=1$ so $\mathbb E[(R_J-\mu^{\,}_J)(R_F-\mu^{\,}_F)] = \sigma^{\,}_J\sigma^{\,}_F$

Now consider your portfolio $60\%$ Johnson & Johnson and $40\%$ Ford.  It has return $R_P= 0.6 R_J +0.4 R_F$ with expected value $\mu^{\,}_P= 0.6 \mu^{\,}_J +0.4 \mu^{\,}_F$ by linearity of expectation, so the actual return and expected return are $40\%$ of the way from the corresponding figures for Ford to the figures for Johnson & Johnson

Now consider the variance of the return on the portfolio $$\sigma^2_P = \mathbb E[(R_P-\mu^{\,}_P)^2] \\= \mathbb E[(0.6 (R_J-\mu^{\,}_J) +0.4 (R_F-\mu^{\,}_F))^2] \\ = 0.6^2 \sigma^2_J +2\times  0.6 \times 0.4 \sigma^{\,}_J\,\sigma^{\,}_F + 0.4^2 \sigma^2_F \\= (0.6 \sigma^{\,}_J + 0.4 \sigma^{\,}_F)^2 $$
so taking square roots gives $\sigma^{\,}_P = 0.6 \sigma^{\,}_J + 0.4 \sigma^{\,}_F$, i.e. the standard deviation of the return on the portfolio is  again $40\%$ of the way from the corresponding figure for Ford to the figure for Johnson & Johnson


What is aid money for natural disasters spent on?

One thing such funds get spent on is corruption:

Do Public Fund Windfalls Increase Corruption? Evidence from a Natural Disaster
(Nikolova and  Marinov (2015))

  We show that unexpected financial windfalls increase corruption in
  local government. Our analysis uses a unique data set on flood-related
  transfers, and the associated spending infringements, which the
  Bulgarian central government distributed to municipalities following
  torrential rains in 2004 and 2005. We build an index of corruption
  using information from the publicly available audit reports, and
  exploit the quasirandom nature of the rainfall shock (conditional on
  controls for ground flood risk) to isolate exogenous variation in the
  amount of funds received by each municipality. Our results imply that
  a 10% increase in the per capita amount of disbursed funds leads to a
  12.2% increase in corruption. We also present suggestive evidence that more corrupt mayors anticipated punishment by voters and dropped out
  of the next election race. Our results highlight the governance
  pitfalls of non-tax transfers, such as disaster relief or assistance
  from international organizations, in weak democracies.

Weathering Corruption (Leeson and Sobel (2006))

  Could bad weather be responsible for U.S. corruption? Natural
  disasters create resource windfalls in the states they strike by
  triggering federally-provided natural disaster relief. Like windfalls
  created by the ìnatural resource curseî and foreign aid, disaster
  relief windfalls may also increase corruption. We investigate this
  hypothesis by exploring the e§ect of FEMA-provided disaster relief on
  public corruption. The results support our hypothesis. Each additional
  $1 per capita in average annual FEMA relief increases corruption
  nearly 2.5 percent in the average state. Eliminating FEMA disaster
  relief would reduce corruption more than 20 percent in the average
  state. Our Öndings suggest that notoriously corrupt regions of the
  United States, such as the Gulf Coast, are notoriously corrupt because
  natural disasters frequently strike them. They attract more disaster
  relief making them more corrupt.


How do you show welfare changes with limited entry versus perfect competition?

I think calling this 'trick' is a bit of a misnomer because there is nothing particularly tricky about it.
When you make any welfare analysis of some change (tax/quota etc.) you need to compare situation after change with situation before change. For that reason you calculate the deadweight loss (DWL) of policy as a difference between consumer surplus before policy and after policy.
In your case the problem (including new restricted supply $S_R$ - painted in red color) would look like in the following picture I made (I linearized the problem in order to make the picture easier to render).
In order to calculate deadweight loss here you would first calculate the area of big triangle bounded by the original supply and demand (in black) and then subtract the area of the trapezoid that is created by the new restricted supply (in red).
I am surprised they call it a trick in that textbook since this is how DWL from a policy is defined. Following Mankiw Principles of Microeconomics 8th ed. pp 157:

Deadweight Loss: the fall in total surplus that results from a market distortion, such as a tax

To calculate what a fall in CS is you need to either implicitly or explicitly take into account what the original situation was. One way of how to calculate this explicitly is to see what the original supply and demand was and comparing it to the new situation.


Here you have a possible answer (although I am not 100% sure about it):

You said Brand counts 50% and price 50%. We can consider that with higher brand utilities we get higher chance of buying, while with higher prices we get lower chance of buying the product. Following this idea, I made this equation in which both chances (of product A and B) should be equal, since it would lead us to an equilibrium in which it would be the same for the custumer to buy the product A or the product B:

$U_A - P_A = U_B - P_B$

We substitute according to our values:

$50 - 80 = 30 - x$

We simplify:

$-30 = 30 - x$

Again:

$-60 = -x$

And again:

$x = 60$

So 60\$ would be the price of indifference between product A and B. So we should make it a bit lower if we want people to buy product B: 59.9$, the correct answer of your problem.

I hope it helps.


Return on two different ways to construct a portfolio

I'm not sure I follow, but do the two portfolios mean the following?

For portfolio (1),
$$
r_i - r_f - b(r_m - r_f) = r_i + (b-1) r_f - b r_m
$$
and for portfolios (2)
$$
r_i - b r_m - (1-b) r_f = r_i + (b-1) r_f - b r_m.
$$
So, writing them out like this, they look the same.


Could lexicographic preferences on N^2 be represented by a utility function u: $N^2$ to $Z$?

If it is a lexicographic preference on $R^2$, the question sounds weird and I don't know if it can be represented by a utility function from $N^2$ to $R$. The domain of the utility should be the same as the domain of the preference relation, otherwise they cannot represent each other for sure.
Now suppose that, you mean, we have a preference on $R^2$, but we are only taking some data from the $\mathbb R^2$, for example only those data in $N^2$, and see that if we could represent those $N^2$ data by a utility defined on $N^2$. This way, I think the problem becomes more interesting and meaningful.  (Ok, so now the question is edited this way.)
If it a lexicographic preference on $N^2$, I think it can be represented by a utility function from $N^2$ to $R$.
The proof should be obvious in this case. A simple construction suffices.
If you have further questions on this case, please do let me know in comment.
Now let's think about the case of $u:N^2\to Z$. This problem becomes more complicated. To solve this problem, you first need to get used to the proof that a lexicographic preference on $R^2$ cannot be represented by utility function with $R$ as codomain. By applying the same method, you'll see that a preference on $N^2$ cannot be represented with a utility with $N$ as codomain. Then going from $N$ to $Z$ will not take much efforts.


Relationship between Revenue-Elasticity and Price-Elasticity

Let's denote the elasticity of $X$ to $Y$ at $Y_0$ with $\eta_{X, Y}(Y_0)$ and solve for the demand ($Q$) elasticity in terms of the revenue elasticity ($R$).

We know that the elasticity is always given by

$$ \eta_{X,Y} = \frac{d X(Y)}{dY}\frac{Y}{X}$$

or equivalently (showing the equivalence is a useful exercise),

$$ \eta_{X,Y} = \frac{d \log X(Y))}{d \log Y}$$

Now,

$$ R(p) = p Q(p) \\
\eta_{R, p}(p) = R'(p) \frac{p}{pQ(p)}\\
\eta_{R, p}(p) = (Q(p) + pQ'(p_0) ) \frac{p}{pQ(p)} \\
\eta_{R, p}(p) = 1 + \frac{pQ'(p_0)}{Q} \\
\eta_{R, p}(p) = 1 + \eta_{Q, p}(p) \\
$$

Given that the left-hand-side elasticity is $-1$ at the initial price $p_0$, the right-hand-side elasticity must be $-2$:

$$-1 = 1 + \eta_{Q, p}(p_0) \Rightarrow \eta_{Q, p}(p_0) = -2$$

Your mistake

You are being sloppy with the mathematics. First you state

$$ Q = \frac{TR}{P}$$

But then you claim

$$ Q = \frac{0.8TR}{1.2P}$$

These two equations just cannot be true at the same time.

Perhaps you want to look at initial $TR_0$, at total revenue after price change $TR_1$, and then state that $TR_1/TR_0 = 0.95$.


Why does the European Union give subsidies to farmers?

Markets are extremely poor at pricing events that have very low probability and catastrophic impacts. In part because we're very bad at estimating low-probability events: by definition, they're rare. And in part because the catastrophic impacts fall on pretty much all the population, so any single purchase has very widely-spread potential negative externalities.

And there are strongly asymmetric risks here - if civilisation collapses, it can take centuries to rebuild it. If one country falls under the control of another, it becomes extremely expensive and messy to reverse this.

As such, societies decide - in order to avoid those catastrophic impacts - to pay a kind of insurance premium. A high risk of some market distortion is an acceptable premium to pay, in order to avoid catastrophic loss.

Food is probably the most obvious market where a dramatic loss of supply could lead to catastrophic failure. (the carbon market is another) By subsidising farmers, we ensure the continuity of the domestic supply of food: this helps ensure the availability of food locally, so the population gets fed; and reduces the strategic international risks that would arise from high imports of essential foods.


Question about an interpretation of the MRS

Writing out the expression with Leibniz notation, we get $\frac{\frac{du}{dx}}{\frac{du}{dy}}$, or the marginal utility of $x$ divided by the marginal utility $y$.
For example, let's imagine I get 10 utils from another apple and 5 utils from another cabbage. In that case, the MRS is therefore $\frac{\frac{10 utils}{1 apple}}{\frac{5 utils}{1 cabbage}}$, or, $\frac{2 cabbage}{1 apple}$, matching the marginal rate of substitution of 2 cabbages per apple.
A bit of simplification will easily get you $\frac{dy}{dx}$, which is the rate of change of $y$ with respect to $x$, the interpretation we're familiar with.


Why is deflation not considered the opposite of inflation?

People think that inflation is bad when it gets out of control, say when its more than 3 or 4% a year. The idea is that we all make economic decisions based on prices and its harder to make those decisions when the prices are constantly changing! Moreover, we try to avoid holding on to money and committing to a price for a long time, because we know those become meaningless over time. Also people associate inflation with the ills of fiat money, and other such things.

Deflation would seem to be not a big deal. You hold on to your cash, it buys more things as time passes! But, it turns out to be a big deal. Deflation turns the real interest rate paid by cash into a positive number. And that means that when the fed wants to lower rates a lot to get you to spend and borrow, it can´t lower them below that real rate. So it can't get you to spend and borrow -> economic fragility! Fed is powerless! So people are now scared to death of deflations! Even small ones seem to be hard to turn around. Japan has been flirting with deflation for a long time, unable to escape from its cold grip....

Therefore, to answer the question:
 Inflation and deflation can be defined as opposites: inflation is a positive rate of change of prices sustained over several periods while deflation is a negative rate of change of prices sustained over several periods. However, the effect of inflation and deflation on the economy are not opposites from each other, and policy-maker's concern for one and the other are different, but not the opposite of each other either.


Can the stock market show indefinite exponential growth?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2010 commentary:

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

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

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

The Great Horse Manure Crisis of 1894:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


Why absolute value in elasticities and marginal rate of substitution?

I think there are pedagogical advantages to discussing both the raw numbers and the absolute values and I think the benefits of both explain why they both show up (sometimes in the same text, even).

Each elasticity number gives two bits of information. First, the absolute value with respect to 1 and second, the sign. Now, clearly, if you had a negative elasticity, you could compare it to -1. However, it becomes somewhat difficult to teach when using phrases like "greater than" or "less than" -1 to discuss a good being (in)elastic, since "greater than -1" is actually inelastic if the elasticity is negative. It is much more intuitive to be able to discuss the ratios of percent changes if "greater than" does in fact mean that the top is bigger than the bottom and vice versa for "less than".

Of course, there is also a bunch of information tied up in the sign of the elasticity. We get the Law of Demand out of own-price elasticity, we get compliments/substitutes from cross-price elasticity, etc. So it is important to still make sure students understand the importance of the sign.

When I am teaching, I try to discuss both parts explicitly, but make clear that the elasticity itself includes the appropriate sign. I think most books are trying to capture these two bits of information in one way or another. In any case, the formal definition of elasticity should include the sign, but if one is just talking about how elastic a good is, the absolute value could be reported (with the note that it is the absolute value of the elasticity, not the elasticity itself).

As for MRS, it's usually not the absolute value, per se, that we report, but rather the negative of the derivative dy/dx. This is quite standard, since it has the intuitive interpretation of the consumer being willing to give up so many units of x for so many units of y. Since indifference curves are usually convex, this derivative is negative, thus changing the interpretation (and intuition) somewhat if we don't negate it.


Is there any mainstream criticism of the Benes-Kumhof conclusion that the Chicago Plan would improve the US economy nowadays?

On the Equivalence of Private and Public Money is a 2019 working paper by Brunnermeier and Niepelt that addresses this issue:

  We propose a generic model of money and liquidity.  We provide
  sufficient conditions under which a swap of private (inside) against
  public (outside) money leaves the equilibrium allocation and price
  system unchanged. We apply the results to Central Bank Digital
  Currency,  the “Chicago Plan,”  and the Indian de-monetization
  experiment.

This is their exercise:

  As a result of these developments, debates about the “right” monetary
  architecture resurface and classic questions about the nature of money
  return to the fore.  A key point of contention concerns the optimal
  balance between public and private money. Proponents of a strong
  government role fear that private money creation breeds instability
  and shifts seignorage rents from taxpayers to shareholders.  In the
  “Chicago Plan” of the 1930s and the  recently  rejected  Swiss
  constitutional  referendum  on  “Vollgeld”  (sovereign  money), they
  propose to severely restrict or even ban money creation by anyone
  except the central bank.  Less drastic proposals aim at electronic
  Central Bank Digital Currency (CBDC) for use by non-banks.  Monetary
  authorities in countries such as Canada, Singapore, and Sweden
  currently evaluate the introduction of such “Reserves for All;” the
  Banco Central del Uruguay has successfully tested the model; and other
  central banks consider it.

  Skeptics, on the other hand, warn of severe macroeconomic risks due to
  the replace- ment of private by public means of payment.  In their
  view, a reduction of bank issued inside money will hamper credit
  extension by banks to firms and households, with negative
  implications for growth;  and the introduction of CBDC will provide a
  safe haven asset for depositors to run into at the slightest hint of a
  crisis, rendering bank runs more likely and thereby threatening
  financial stability.

  To assess these arguments, we develop a generic model of money and
  liquidity.  Within this framework, we establish sufficient conditions
  under which it is irrelevant whether the public  or  the  private
  sector  issues  means  of  payment.

They summarize their results as follows:

  We  apply  our  results  to  two  proposals  for  monetary  reform:
  CBDC,  and  the  more drastic “Chicago Plan.”  We find that the
  introduction of CBDC need not change macroeconomic outcomes,
  independently of whether deposits are subject to bank runs or not.  If
  bank runs are a feature of the current system then the equivalent
  monetary regime with CBDC has state contingent transfers from the
  private sector to the central bank; if it does not, for instance due
  to a generous deposit insurance scheme, then no such transfers are
  needed.

  Contrary to the prevailing view that CBDC would make bank runs more
  likely, our analysis concludes that it might well make them less
  likely.  With pass-through funding, the central bank becomes a large
  depositor that internalizes run externalities, unlike small
  depositors.  This makes the financial system less fragile. Regarding
  the Chicago Plan, we also find that the conditions for equivalence are
  met provided that banks receive appropriate compensation for lost
  seignorage rents, or that the  ownership  structure  of  banks  is
  aligned  with  the  distributions  of  tax  burdens.   An important
  motivation for the “Vollgeld” proposal to outlaw banks from creating
  liquid assets  was  that  banks  should  be  forced  to  relinquish
  these  rents.   This  would  transfer seignorage from bank
  shareholders to taxpayers, undermining wealth-neutrality.

  We also apply our results to the recent Indian de-monetization
  experiment.  We find that it could not have been neutral because
  cash-based transactions at black-market prices could not have been
  replaced by deposit-based transactions.

In contrast, there is a Bank of England working paper that strongly disagrees.The macroeconomics of central bank issued digital currencies by Barrdear and Kumhof (2016):

  We study the macroeconomic consequences of issuing central bank
  digital currency (CBDC) -- a universally accessible and
  interest-bearing central bank liability, implemented via distributed
  ledgers, that competes with bank deposits as medium of exchange.  In a
  DSGE model calibrated to match the pre-crisis United States, we find
  that CBDC issuance of 30% of GDP, against government bonds, could
  permanently raise GDP by as much as 3%, due to reductions in real
  interest rates, distortionary taxes, and monetary transaction costs.
  Countercyclical CBDC price or quantity rules, as a second monetary
  policy instrument, could substantially improve the central bank’s
  ability to stabilise the business cycle.


What does Varoufakis mean by 'banks can make up money' in 'Talking to my daughter about the economy'?

Banks and the finance industry have an essential function of allocating capital to productive uses, intermediating between savers and investors, and managing risk. However, banking deregulation, beginning in the 1970s (and not "centuries ago" as claimed by Varoufakis), has moved this industry toward rent-seeking activities. So, since then, bankers do not lend money from savings accounts deposits. This is "the legend". They offer financial services. They are engaged in lending by trading bonds and securities. They are engaged in futures markets (central financial exchanges where standardized futures contracts are traded - see wikipedia).

By the way, deregulation has been a very lucrative change because finance has become more profitable relative the rest of the economy. Philippon and Reshef show convincingly in a QJE paper that salaries in the financial sector have skyrocketed.


Why couldn't the Karush-Kuhn-Tucker optimization find the solution?

As @user32416 pointed out the first order stationarity conditions are not enough. Specifically it seems that you violate Slater's condition, which states that "the feasible region must have an interior point". There are no $x,y$ for which
$$(x+y-2)^2 < 0.$$

If you rephrase the problem to
$$\max (xy)$$
$$x+y-2 = 0$$
$$x,y \geq 0$$
Slater's condition is met (for linear conditions no interior points are necessary) and you can apply Karush-Kuhn-Tucker.


Computation of Different Axiomatic Barganing Solutions

The answer depends on the "following solution concepts", which you did not specify. I guess the Nash solution and the Kalai-Smorodinsky solution will be among them.

The frontier functions you seem to propose are of the form $y_n(x)=\sqrt{1-\frac{100x^2}{n^2}}$, where $n\in\{1,2,\ldots,100\}$.

For the Nash solution you maximize $xy_n(x)$ and after substituting for $y_n(x)$ and setting the derivative to zero you will find $x_n=\frac{n}{\sqrt{200}}$ and $y_n=\frac{1}{\sqrt{2}}$. For the KS solution you set $y_n(x)=\frac{10x}{n}$ and after substituting you will again find $x_n=\frac{n}{\sqrt{200}}$ and $y_n=\frac{1}{\sqrt{2}}$. Graphing these solutions is easy.

Remark:
That the solutions coincide is not a coincidence. The different frontier functions are constructed in such a way that they are all just horizontally "compressed" or "stretched" versions of the frontier function $y_{10}(x)=\sqrt{1-x^2}$. This means that they are really all equivalent in the sense that they result from each other after some rescaling of $x$ (the utility of agent 1). But the frontier function $y_{10}$ just describes the quarter unit circle in the positive orthant, which is symmetric w.r.t. the agents. In symmetric feasible sets the Nash and the KM solutions are known to coincide.


Why is basis point defined as "1/100 of a percent"?

The way in which basis points are almost invariably used is as a spread relationship (at least in fixed income). That is, it is the difference between two yields.
Yields are quoted as percent. (If you wish, percentage points.) Most spread relationships involve yields that are close to each other, so they are multiplied by 100 - so we get basis point spreads.
A change in yield is the spread between the yield now and where it was previously, so it is once again a difference, and so there is no ambiguity in the meaning. If a yield goes from 1% to 1.01%, it is a $100(1.01 - 1.00) = 1$ basis point rise.
Some people might quote low yields in terms of basis points. E.g., they might say that a bond yielding 0.1% has a “a yield of 10 basis points.” This is an non-standard usage of basis point, since it is referring to an absolute yield.
(The only exception I can think of for the usage convention I outlined is for management fees that are low - e.g., an index fund has “a management fee of 10 basis points.” However, since people think of that as a reduction in the return by 10 basis points, it slips through. Equity investors might use basis points for intraday returns. Since they do not quote spread trades in basis points, they have less reason to distinguish the terms.)


What is a suitable exponential to model a currency or cryptocurrency price increase?

If I understand correctly you are asking for a model of the price of bitcoin based on the number of transactions.

This is impossible for a number of reasons.
1) Theres not necessarily a relationship between those two variables

2) Even if there is a relationship between the two variables then there may be other variables which have an equal or stronger effect (very likely) making the variable a bad predictor.

3) If there is a relationship, and that relationship is not causal then knowing the relationship would cause it to cease to exist as people begin to trade on arbitrage with that model which would cause it to stop being effective.

4) If I could model the price of bitcoin I certainly wouldn't be telling you, instead I'd be living it up on some private island.

The question makes no sense and is by far too complicated of a question. This is the type of topic that requires a research paper and will not necessarily provide results.

This is why you are getting downvoted. Because there is no logical answer to what you are asking.


Development economics papers that used Difference-in-Differences

A very good paper that I had in my MA curriculum is Jaychandran and Pande, AER 2017: https://www.aeaweb.org/articles?id=10.1257/aer.20151282 (I believe this paper has open access, maybe on one of the authors' websites).
Working through this paper should help you understand DID quite thoroughly. The paper also employs double and even triple DID.


Several international organisations provide open access to macroeconomic data such as national debt - usually the World Bank, economic development organizations such as the OECD and the African Development Bank, as well as public institutions in the USA (data.gov) and in Europe (as an example the ECB data warehouse). The national central banks should also provide the data you need, but its ease of access might vary.

The World Bank Open Data has the data you need, both in LCU (local currency) or in % of GDP, but only up to 2000 for the specific case of South Africa.

The IMF also collects data for several countries, so check if the page for South Africa has the data you are looking for.


What is the difference between trade deficit and current account deficit?

They are very related concepts but they are not completely same.

Current account deficit occurs when country spends more on imports than it receives in imports.

Trade deficit means that more imports are being sold than exports by a country.

A trade deficit is also a part of current account deficit as current account can be decomposed as:

$$CA=X-M+NI+NT$$

Where $X-M$ is the trade balance and and if $X-M<0$ we say country has a trade deficit, but as you can see the current account also includes net income which is income of country’s resident minus income paid to foreigners and NT is net transfers which includes things like foreign aid and remittances. A current account deficit occurs when $X-M+NI+NT<0$.

So although they are related and trade deficit is usually a big component of current account deficit they are definitely not same. It’s even possible for country to have current account surplus while having trade deficit.


(This is an English language question, not an economic one. Next time consider asking at English Language & Usage.)
A surprise is negative, if it is a bad surprise (for someone). In this context they probably mean that the revealed value of the indicator (PMI) is lower than they expected, which shows that the economy is in worse shape than they expected.
(For different indicators, such as the unemployment rate, it could be that the negative surprise is a higher than expected value.)


Does it make sense to talk about Bitcoin 'inflation' when little to no goods and services are listed in Bitcoin currency?

The answer depends on what inflation we are talking about since the definition you mention in your question is not the only type of inflation in use. There are several different inflations used by economists. When economists talk about inflation without qualification we mean inflation of goods and services, as you mention in your question, but beside that in economics we have concepts such as asset price inflation, or even house price inflation etc.
In principle, you can view bitcoin as a speculative asset not as a currency Baur et al (2018), there is actually not clear consensus on what bitcoin is because it has some characteristics of speculative asset. If you decide to view bitcoin as an asset, and construct some price index for price of an asset (what would be bitcoin exchange rate if you want to view it as a currency) then you can call change in that price index 'bitcoin price inflation', the same way as some call change in the housing price index house price inflation.
If we are talking about inflation more specifically about just goods and services inflation, then you cannot talk about bitcoin inflation, but note you cannot talk about USD or euro or pound inflation either (even if I seen people loosely talking about USD inflation, it is a misnomer).
Inflation is by definition  (see Mankiw Principles of Economics pp 13):

an increase in the overall level of prices in the
economy

In turn economy is by definition (ibid, pp 5):

Whether we are talking about the
economy of Los Angeles, the United States, or the whole world, an economy is just
a group of people dealing with one another as they go about their lives.

Hence inflation is about measuring change in prices in an economy (which could even be a household or just some region) and it does not matter how prices are quoted. As a matter of fact inflation is completely unitless quantity (in fact even CPI change of which gives you inflation is itself unitless, but if you would measure inflation observing growth in actual prices the units would still cancel out).
Consequently, it is misnomer to talk about USD or euro or bitcoin or any other currency inflation.  Euro is good example to illustrate this. The 'euro inflation' in France is different than 'euro inflation' in Euro-area and 'euro inflation' in Portugal. You can see that yourself by looking at Eurostat's inflation statistics for both EU and individual Euro-zone members (see Eurostat here). Heck, as Eurostat shows you can even calculate inflation for EU and not whole EU even uses the same currencies. More properly you should be talking not about USD, euro or bitcoin inflation but about inflation of USA, Euro-zone and so on. Inflation in USA is measured by change in CPI derived from prices quoted in USD because that is the official currency of US economy, but if half of USA are would use different currency you would still be able to calculate inflation for USA. Moreover, if you want to measure inflation of goods and services in some economy (e.g. some community of people) where people use bitcoin you can do that as well, although again it would be misnomer to call it bitcoin inflation, it would be inflation of that economy (and again the economy could be as small as you want).


Where can I look up a companies Herfindahl index?

HHI index cannot by definition be on companies. It is the squared sum of market shares of all the companies in a country. So, if you are looking for companies' market shares, you should look at each country individually.

But if you want HHI index on countries (which is a correct way of framing the question) then you can use this WorldBank data: https://tcdata360.worldbank.org/indicators/hh.mkt


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

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

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

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

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

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

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

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


Perfectly functioning credit markets and consumer saving

I did some quick research online and think I understand better. My basic understanding is that credit market imperfections restrict a consumer's capacity to borrow or to lend, thus his or her saving ceases to be a "neutral"/"fully" endogenous variable. (Rather than being a means to an end--maximize lifetime wealth--it becomes more and more of an end in itself?)


Three-player games are notoriously tricky to analyze. The ideal way to display them would be a three-dimensional array of cells, each containing three payoffs. But this is difficult to write down on two-dimensional paper. So typically an $n\times m\times l$-game is displayed as $l$ different $n\times m$-matrices. In your example you might think about it in this way:

Player 1 chooses the row (upper row, $A$, or lower row, $B$)
Player 2 chooses the column (left column, $A$, or right column, $B$)
Player 3 chooses the matrix (upper matrix, $A$, or lower matrix, $B$)

Therefore, to highlight the best payoff of player 3, for each of the 4 choices of players 1 and 2 (for each of the 4 cells in the matrices) you have to compare the player-3-payoffs between the upper and the lower matrix. So in the $(A,A)$-cell you highlight the $70$ in the upper matrix, since it is greater than the $60$ in the lower matrix. For the $(A,B)$-cell you highlight $23$, which is greater than $0$, and so on. In the end, the $(A,A)$-cell of the upper matrix (corresponding to the choice of $A$ by player 3) will have all three payoffs highlighted, and the same will be true for the $(B,B)$-cell of the upper matrix (again corresponding to the choice of $A$ by player 3). So the pure NE are $(A,A,A)$ and $(B,B,A)$.


What branch of Economics does 'e-governance' fall under?

This is Public Economics, under the JEL code H11:

Examples of such papers on e-Governance using the H11 JEL code are:

https://ideas.repec.org/a/ekz/ekonoz/2003311.html
http://www.sobiad.org/ejournals/journal_ijebeg/arhieves/2009/01ajay_kr_singh.pdf
https://ideas.repec.org/p/cpr/ceprdp/11761.html
https://ideas.repec.org/a/eco/journ3/2016-04-38.html
https://ideas.repec.org/p/wiw/wiwrsa/ersa14p905.html

Note that papers usually have multiple JEL codes. That is the case of the last three papers given above. Some also use codes related to Economic Development (Under JEL codes O), if they refer to developing countries. But the common denominator is Public Economics.


How to see that upper-semicontinuity and supermodularity are equivalent in a supermodular game context?

Your observation about topology and order is somewhat inaccurate. First definition make use of partial order on $S_i$ while the second make use of topology on it, but both structures are almost always specified by the assumption, that $S_i$ is a sublattise of $R^n$ and so it is equipped with usual subspace topology and partial order. This is the first point in the definition in the material you have referred to. So this worries are misplaced.

However there is some indications (see, for example, chapter 4 in Supermodularity and Complimentarity by Topkis), that the requirement of upper-semicontinuity is stronger and implies the first one. I'm not ready to provide an accurate proof, however.


What is the state of the art in capital theory?

My impression as a non-economist is that there has not been much interest in the 21st century in these debates and it is not taught to students.

This is misconception but understandable one (I will get to the understandable part at the end). According to The New Palgrave Dictionary of Economics (Becker, 2017) - leading source for economic terminology - capital theory is defined thusly:

Capital theory examines the special role played by time in resource allocation studies. The determination of the interest rate and functional distribution of income as well as how rational agents invest are analysed within single- and multi-sector general equilibrium frameworks. Here, agents exercise perfect foresight over alternative consumption and capital accumulation programs. Efficient programs are characterized. Representative and multi-agent infinitely lived households are studied. Equivalence principles link the equilibrium programs and optimal paths. Heterogeneous agent models with borrowing constraints are reviewed. A behavioural model of intertemporal choice is also compared to its constant discounting counterpart.

Given the above broad definition of capital theory, virtually the whole corpus of modern macroeconomic theory is preoccupied with capital theory. The above broad definition of capital theory as a field would include models of economic growth such as the famous Solow-Swan model or Romer model and virtually any growth model that accounts for capital formation be it endogenous or exogenous. It would also include many overlapping generations models with dynamic capital formation and so on. For an overview of state of the art growth models you might want to look at Barro and Sala-i-Martin Economic Growth 2nd Edition (it is graduate level text so it has state of the art models), but really I can't think of a single macro - or even general economics textbook that would not at least briefly cover these issues (for example Blanchard et al. Macroeconomics: A European Perspective which is prominent macro textbook and deals with these issues).
In addition the above definition easily encompasses general equilibrium business cycle models as well. This is another large area of study in current macroeconomics. Presently this is theoretically covered mainly by the New Keynesian IS-LM models and Real Business Cycle theory. For state of the art examples of such models see Romer (2008) Advanced Macroeconomics 4th ed. For undergraduate treatment you can have look again at Blanchard et al. textbook mentioned earlier.
The areas mentioned above without any doubt the largest areas of research interest in macroeconomics (even throughout presently macroeconomics is becoming more empirical rather than relying on theoretical models as you can see in  Angrist et al. 2017). Consequently, the research interest in capital theory can be presently argued to be quite strong and ubiquitous.
However, In my first paragraph I stated that the misconception you hold is understandable. This is because the term 'Capital Theory' fell out of favor and it is mostly used to describe particular historical sets of theories on capital (especially those you mentioned in your opening question) rather than an area of interest. Hence nowadays when someone publishes theoretical paper that will be about the theory of capital (e.g. Becker, and 1987 - just a random example)  it will be often given different specific name rather than just capital theory (although occasionally I see people still using the term in non-historic context).


How to prove a generalised function is quasiconcave?

Note first that the function $r\mapsto A(r)^{\mu/p}$ is strictly increasing on $\mathbb{R}_+$. When you look at the minimum in the definition of quasi-concavity, you can therefore ignore this part and it suffices to show that the function
$$(x_1,x_2,\ldots,x_n)\mapsto a_1x_1^p+a_2x_2^p+...+a_nx_n^p$$
is quasi-concave. Actually, the function is even concave. The sum of concave functions is concave, so it suffices to show that the function
$$(x_1,x_2,\ldots,x_n)\mapsto a_ix_i^p$$
is concacave for each $i=1,\ldots,n$.


Percentage/proportion of published papers with DSGE models

You may have been thinking of a chart originally from The Economist Nov 24th 2016 article "Economists are prone to fads, and the latest is machine learning" though I cannot see it there.  There is a copy of the chart visible at Noah Smith's blog

It shows an analysis by The Economist of the key words in working-paper abstracts published by the National Bureau of Economic Research, with lines for laboratory experiments, randomised control trials (RCTs), difference-in-differences, regression discontinuity, machine learning or big data, and DSGE


Firm 1's profit maximization problem is :
\begin{eqnarray*} \max_{q_1} & \ p(q_1 + q_2 + q_3)q_1 - c(q_1) \end{eqnarray*}
Firm 1's response to firm 2's and 3's quantity choices will satisfy the following:
\begin{eqnarray*} p(q_1 + q_2 + q_3) + p'(q_1 + q_2 + q_3)q_1 - c'(q_1) = 0 \end{eqnarray*}
Likewise, we'll get the implicit best response functions for the other firms as well.
\begin{eqnarray*} p(q_1 + q_2 + q_3) + p'(q_1 + q_2 + q_3)q_i - c'(q_i) = 0 \end{eqnarray*}
for each $i \in \{1,2 ,3\}$.

There is a symmetric equilibrium of the above game if there exist $q^*$ such that
\begin{eqnarray*} p(3q^*) + p'(3q^*)q^* - c'(q^*) = 0 \end{eqnarray*}
To show that there exist one, consider the following function
\begin{eqnarray*} g(q) = p(3q) + p'(3q)q - c'(q)\end{eqnarray*}
Observe that $g(0) = p(0) - c'(0) > 0$. Also, given that $p(q)$ is decreasing and concave, there exist $\overline{q} > 0$ such that $p(\overline{q}) \leq 0$. Consequently, $g(\overline{q}) \leq 0$. Therefore, by intermediate value theorem, there exist $q^* \in [0,\overline{q}] $ such that $g(q^*) = 0$ i.e.
\begin{eqnarray*} p(3q^*) + p'(3q^*)q^* - c'(q^*) = 0 \end{eqnarray*}
Also, $g'(q) = 4p'(3q) + 3p''(3q)q - c''(q) < 0$. Since $g(q)$ is decreasing in $q$, $q^*$ is unique.
So there is a unique symmetric equilibrium. To show that it is the only equilibrium, we'll show that there is no equilibrium where at least two of the firms choose different quantities. To do so, let us subtract the implicit best response function of firm 1 from that of firm 2,
\begin{eqnarray*} p'(q_1 + q_2 + q_3)(q_2 - q_1) = c'(q_2) - c'(q_1) \end{eqnarray*}
Notice that the above equality only holds for $q_2 = q_1$. This is because

when $q_2 > q_1$, $p'(q_1 + q_2 + q_3)(q_2 - q_1) < 0$ and $c'(q_2) - c'(q_1) > 0$,
when $q_2 < q_1$, $p'(q_1 + q_2 + q_3)(q_2 - q_1) > 0$ and $c'(q_2) - c'(q_1) < 0$.

Therefore, there is no equilibrium satisfying $q_2 \neq q_1$. Likewise, there is none satisfying $q_2 \neq q_3$ or $q_1 \neq q_3$.


What is the service equivalent of an economic 'bad'?

Any labor may be considered as a 'bad' (service) for which you are compensated by the firm by paying you salary/wages.
In modeling labor market, this is generally described in the opposite sense, i.e., consuming leisure. When you work you let go of leisure, which is a good. So that, technically, makes supplying labor (which is a service) as an economic bad.


What happens if an expensive thing goes into high supply for a limited time?

a lot of factors go into this. If a product in low supply and high demand suddenly becomes high in supply, with the same level of demand, as you mentioned, the price will in theory drop from \$1,000 to \$400. But the issue is the elisticity of demand, and the opportunity cost of selling the product at a lower price when demand rises. If the price is at \$400, and demand increases as supply dwindles, but there are substitutes to the product, consumers will simply buy the substitute. If there is no substitute however, demand is high, and price elasticity is high, the price can rise fairly quickly in that scenario.


$$dx_t = \mu dt + \sigma dz_t \\
y_t = f(t, x_t)$$

A key idea here is that $\left( dx_t \right)^2=\left( \ldots \right)dt^2 + \left(\ldots\right) dzdt + \sigma^2 dz_t^2 = \sigma^2 dt$. The loose reasoning is that $\left( dz_t\right)^2 = dt$ and all the other terms (i.e. $dt^2$ and $dz\, dt$) are infinitely smaller than $dt$.

Horribly loose intuition for $dz_t^2 = dt$ is that $dz_t$ is normally distributed with variance $dt$, and hence the expectation of the square of $dz_t$ is $dt$.

In any case, we then have:

\begin{align*}
\quad dy_t &= \frac{\partial f}{\partial t} dt + \frac{\partial f}{\partial x} dx_t + \frac{1}{2} \frac{\partial^2 f}{\partial x^2} dx^2_t\\
&= \frac{\partial f}{\partial t} dt + \frac{\partial f}{\partial x} \left( \mu dt + \sigma dz_t  \right)+ \frac{1}{2} \frac{\partial^2 f}{\partial x^2} \sigma^2 dt \\
&= \left(\frac{\partial f}{\partial t} + \frac{\partial f}{\partial x}\mu + \frac{1}{2} \frac{\partial^2 f}{\partial x^2} \sigma^2 \right)  dt + \left( \frac{\partial f}{\partial x}\right)\sigma dz_t
\end{align*}

Which is Ito's lemma.


What does it mean to "kickstart the economy"?

In short, the belief this reflects is that cheap money is spent more freely.  Since GDP counts the sum-total of value-added transactions in the economy, in principle this means that monetary policy affecting the velocity of money can in turn affect GDP.  Theoretically, this is valid to the extent that debt-servicing costs are a significant friction in the economy.

Thinking of money as blood in the circulatory system of the economy, lowering rates is like taking blood thinners to avoid clots.

Whether it works out that way in practice or not is difficult to ascertain, and in practice there are countervailing forces (lower interest rates discourage household savings, high inequality suggests a high degree of misallocation, etc.) that simple changes to interest rates cannot address.


Elasticity of demand equals -1 but income decreases!

We discourage numeric questions as they are unlikely to be useful for future visitors but this is a very good example of why using non-marginal quantities can be misleading.

The exact definition of the price elasticity of demand is
$$
\epsilon(p) = \frac{d D(p)}{d p} \cdot \frac{p}{D(p)}.
$$
(In your notation $D(p) = Q$.)
By straightforward calculation you can show
\begin{eqnarray*}
\max_p & & p \cdot D(p) \\
\\
p \cdot \frac{d D(p)}{d p} + D(p) & = & 0 \\
\\
p \cdot \frac{d D(p)}{d p} & = & - D(p) \\
\\
\frac{p}{D(p)} \cdot \frac{d D(p)}{d p} & = & - 1 \\
\\
\epsilon(p)  & = & - 1.
\end{eqnarray*}
Whether a marginal price change increases or decreases revenue when $\epsilon(p)  \neq - 1$ can be seen from a similar calculation.

Note that the reasoning used above only stated that $D(p)$ reached its local maximum. It is possible that several local maxima exist and the global maxima is elsewhere.

So $\epsilon(p)  = - 1$ implies that the revenue cannot be increased by small (marginal) changes in $p$. So far I have used the concept of point elasticity. But your textbook uses arc elasticity, which measures non-marginal changes:
$$
\frac{\Delta Q}{Q} / \frac{\Delta p}{p}
$$
Some reasons to do this:

Arc elasticity can be measured empirically, point elasticity can only be approximated.
In case of small changes the two should be reasonably close.
Point elasticity requires some knowledge of calculus.

There are however also some problems with this:

No guarantuees are made by the $\epsilon(p)  = - 1$ condition for non-marginal price changes.
What base you should use for arc elasticity is not clear at all. You used
$$
\frac{Q_{new} - Q_{old}}{Q_{old}} \cdot \frac{p_{old}}{p_{new} - p_{old}}.
$$
Why is the old quantity and price the reference for the rate of change? Why is it not the new quantity and price
$$
\frac{Q_{new} - Q_{old}}{Q_{new}} \cdot \frac{p_{new}}{p_{new} - p_{old}}
$$
or the average of the two
$$
\frac{Q_{new} - Q_{old}}{\frac{Q_{new} + Q_{old}}{2}} \cdot \frac{\frac{p_{new} + p_{old}}{2}}{p_{new} - p_{old}}?
$$

These bases give you different values for arc elasticity. The second base gives you $1.2\dot{2}$ so it seems to be the one your textbook expects. I guess it is best if you see the difference between point elasticity that is used by the rule and arc elasticity. Other than this you have to ask your professor what definiton of elasticity she/he expects you to use.


Why aren't we seeing carbon taxes in practice?

I think it’s mainly politics. For example, when France tried to implement increases in tax on  oil (indirect way of taxing carbon) it led to yellow jacket protest.

As you pointed out it’s easy to track who produces the carbon in the economy. Especially on industrial level in developed countries. The reason 1 could be problem in some developing countries though.
As you pointed out the revenue can offset any negative effect as with Pigovian taxes there is no deadweight loss - if set properly
Again you answered yourself plus I would add in a long run it’s better to undergo temporary shock to avoid higher cost down hill.
I don’t think you can say it’s unfair. In fact I would say the fact that the industries create externality in the first place due to lack of property right is unfair (at least if we agree that creating externality is not fair to society which I think most moral thinkers would - although that’s question for philosophy SE).
You again answered yourself.

If you look at the attempts to introduce carbon taxes then you will see 6-8 are the main culprits. In France you get yellow jacket protests in Netherlands farmers protests, in Washington voters refused carbon taxes in referendum last year (see here)etc. - all responses to trying to introduce Pigovian taxes of one kind or another. People of any political affiliations generally don’t like taxes when they are taxes on them as well. I suppose many people also are skeptical the government will make it revenue neutral later by lets say sending check to all people so their income stays the same. In case of redistribution some might not like that and others also don’t believe social spending will increase.


Perfect Bayesian Equilibrium in a two stage game with incomplete information

In your example, you would still use backward induction to solve for the Perfect Bayesian Equilibrium (assuming the distribution of private costs has full support). In fact, the second stage of your example is similar to a Bertrand competition with asymmetric information. You can refer to the following paper for a general solution of the second stage game:

Spulber (1995) "Bertrand Competition When Rivals' Costs Are Unknown", Journal of Industrial Economics 43:1-11.

The first stage decisions should follow in a straightforward manner.


Who invented these key notions in Finance?

Net Present Value (NPV) as a soft concept existed probably even in antiquity but it was formalized and made popular by Irving Fisher in his book the Rate of Interest.

Internal rate of return is basically a special application of NPV. It was also first formally introduced in Fisher's book although he called it 'rate of return over costs'.

Duration of bonds was introduced by Canadian economist Frederick Macaulay, but the concept was later greatly expanded by none other than Fisher together with Weil.

Law of One Price I was not able to trace this idea back to any single person. According to this article:

  The intellectual history of the concept can be traced back to economists active in France in the 1760-70’s, which applied the “law” to markets involved in international trade. Most of the modern literature also tends to discuss the “law” in that context.

But no exact names are mentioned. It might be that the original authors are unknown. As @Henry pointed out in his comment, these were most likely the French Physiocrats.

Time value of money this like the NPV, a vague notion that existed already in antiquity. You can find a lot of antique quotes that boil down to saying “time is money”, but more formally, it was introduced to the west by Martín de Azpilcueta of the School of Salamanca.

Stochastic Discount Factor - as in its modern mathematical representation can be traced back to the works of Harrison and Kreps (see 1), and Hansen et al (see  [2-5]). However, as pointed out in @Michael +1 comment, the concept can be already traced back all the way to Arrow-Debreu and Radner. Of course, on this subtopic, the list of sources is not exclusive.

1 Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets.
Journal of Economic Theory 20, 381-405.

[2] Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators.
Econometrica, 50, 1029-1054.

[3] Hansen, L. P., & Jagannathan, R. (1991). Implications of Security Market Data for Models of Dynamic
Economies. Journal of Political Economy 99(2), 225-262.

[4] Hansen, L. P., & Richard, S. F. (1987). The role of conditioning information in deducing testable
restrictions implied by dynamic asset pricing models. Econometrica 55(3), 587-613.

[5] Hansen, L., & Singleton, K. (1983). Stochastic Consumption, Risk Aversion and the Temporal Behavior
of Asset Returns. Journal of Political Economy 91(2), 249-265.


Can holding interest rates at zero (ZIRP) for a very long time cause the deflation it is trying to prevent?

While my answer would depend on how, why, and what the central bank said about why they pushed nominal interest rates to zero, I suspect in most situations the answer is no.

Consider the simplest case of quantitative easing. Continuously injects cash into the economy and uses it to purchase public debt and if that is exhausted private debts. With this massive increase in the money supply, and the expectation that the money supply would continue to increase in the future, it would be unlikely that prices would be falling (deflation) in such a situation.

Why? Recall Milton Friedman's quip that "Inflation is always and everywhere a monetary phenomenon." While it may not be an iron law, there does seem to be good evidence that when the money supply increases prices are likely to go up after.

  Is inflation always a monetary phenomenon? Many economists believe
  that the link between money growth and inflation in the U.S. has
  weakened over the last two decades due in part to the Federal
  Reserve's policy experiment in 1979–1982 and innovations in the
  financial sector of the economy. I find that the long-run relationship
  between money growth and inflation is strong in a statistical sense
  and important economically. The key result is that the trend or growth
  component in CPI inflation is entirely due to the trend component of
  monetary base growth.

THE LONG-RUN LINK BETWEEN MONEY GROWTH AND INFLATION (CROWDER (2007))

Since most zero interest rate policies are likely to hold rates down by increasing the money supply, it is unlikely they will be deflationary.

My major caveat is that a zero interest policy may be accompanied by overt or implicit indication that the central bank has a inflation target that is near zero. If the central bank tightens rates whenever they go above 0 percent they may have zero or even negative average nominal rates and deflation. But in that situation it it is the expectations of low future inflation and aggressive inflation fighting that hold down prices and the low inflation holds down the interest rates. Scott Sumner and others have argued that this was essentially the Japanese central bank's policy for many years.


Regarding a consumption aggregator: How do I differentiate under the integral sign?

Using your formalism above, you can think (heuristically) of the integral as $$ \sum_{i=1}^nC_t(i)^{(\epsilon-1)/\epsilon} $$

If we differentiate this with respect to $C_t(j)$, we get

$$ \frac{\epsilon - 1}{\epsilon} C_t(j)^{-1/\epsilon} $$

Which is exactly what we needed. To do this rigorously, you need a notion of taking derivatives on function spaces. Look up the Gâteaux and Fréchet derivatives.


Industrial Revolution: Induced technical change and factor shares

According to Allen (2001), real wages expanded throughout the 19th century in the UK. You seem to imply that they did not. The graph below shows that the UK (London) had higher wages+cost of living than the rest of Europe (except the Netherlands) for several centuries, whereas the rising productivity in the 19th century (because of industrialisation) enabled the possibility of rising wages (see more graphs and tables in the paper).

The author states:

  The high real wages in the northern Europe were the result of high nominal wages. These, in turn, reflected a growing productivity advantage that these economies enjoyed during the early modern period. [...] The advantage of northern Europe, therefore, did not lie in cheap labor but rather in high productivity: Exporters in northern Europe could successfully compete against those in the south and pay a higher wage only because their productivity was higher. By the same argument, the eighteenth century rise in English wages above those prevailing in the Low Countries or, indeed, anywhere else on the continent, attests to rising productivity in British manufacturing (cf. Temin, 1997; Berg and Hudson, 1992). The English labor market was so inflated in the late eighteenth century that even the winter wage of men in agriculture exceeded the wage of craftsmen in many parts of Europe. This premium became even greater during the industrial revolution. English construction wages leaped up again in the first half of the nineteenth century, and for this period we know that the wage advance was general. The only way that Britain could pay the highest wages in Europe and dominate export markets as it did was to have the most productive manufacturing sector. Wage history indicates the mid-nineteenth century preeminence was built up over several centuries.

A recent piece by the Bank of England presents a long series of data on different variables, including labour productivity and wage growth. The graph (below) gives further support to Allen's analysis.

Thus, even in a period of high capital deepening, if real wages (and employment) are rising because of Hicks-Neutral technical change (on top of labour-saving technical change) a rise in the labour share over that period is possible. This can also be seen mathematically.

Consider a constant returns to scale CES production function:

$$ Y = A\left[\alpha K^{\rho} + (1-\alpha)L^{\rho} \right]^{\frac{1}{\rho}} $$

In a competitive market, the real wage is:

$$ w = (1-\alpha)\left(\frac{Y}{L}\right)^{1-\rho} $$

The wage share is:

$$ \frac{wL}{Y} = (1-\alpha)\left(\frac{L}{Y}\right)^{\rho} $$

Adding capital to the right-hand side produces:

$$ \frac{wL}{Y} = (1-\alpha)\left(\frac{L}{K}\frac{K}{Y}\right)^{\rho} $$

Capital deepening means $\frac{L}{K}$ falls. In a world with a mild degree of Hicks-neutral technical change (growth in $A$, as you would expect in the industrial revolution and Allen argues), it is reasonable to expect $\frac{K}{Y}$ is falling. Therefore, the term inside the parenthesis is falling. In the case of $\rho<0$, i.e. relatively low substitution between capital and labour (as is the empirical regularity, at least in recent decades; maybe different around the industrial revolution?), such biased plus unbiased technical change leads to an increase in the labour share.

Notice that in the case of $\rho=0$, the CES degenerates to the Cobb-Douglas function, in which case the labour share depends only on $(1-\alpha)$ and not on the capital-labour ratio.

Finally, the above is a highly ad-hoc, not general equilibrium analysis.
I just wanted to make the point that the equations allow for labour-saving technical change to expand the labour share.


I've read Eric Reinerts book and I do not think it is conspiracy theory because he explains also the economic background of the both symptoms you show.

One point he describes is how free trade discussion prefers the developed countries. Industrial production profits a lot more from scale effects than agricultural production. So he says, it is not fair to hinder countries to develop an industrial sector. Your argument about the so called tiger states has 'roots' in another development strategy of Japan for neighboring countries. The so called flying geese paradigma was one the reasons why it is now possible to buy high technology products from east asian countries. So it is more an example that strengthens Reinerts arguments. There was no leader goose for many other areas in the global south. Maybe china now plays this role. With the BRICS countries the situation today is more complex.  But the fact that the world is changing, can't be an argument against a theory which tries to be rooted in history.

That Eric Reinert points out still valid issues can you see in the discussion about the Economic Partnership Agreements.


Static Profit Maximization Short Run Shut Down Decision

In the short run, you cannot sell your capital. To do so would be a violation of "short run" and would instead be the "long run".
Case 3 (and I would also contest Case 2) are outright forbidden by the definition of short run.
I would note that your question has a lot of narrative to it - which is good in some cases, but you want to keep the literal definitions in mind, not all actions you describe are valid options in the parameters you've established. Optimization is, at its heart, a simple fact of math.


If America's economy collapsed what would happen to all of the citizens? What if the whole global economy collapsed?

There is no simple answer to this question. She is just giving her opinion on the topic. However, so long as USD is the main reserve currency for other governments and oil is mainly traded in USD, Americans can keep buying their guns at low cost. Gun laws are more detrimental to Americans' lives and hence the economy than anything else in the foreseeable future. This is my view, there is more...


Is the mainstream against agent based modelling?

I'm an outsider, so I can't speak of what the boards of prestigious economic journals think of this, but...

I suspect it has something to do with the opacity of computer simulations using agent-based models (ABM) compared to math proofs or even the statistical models that are the staple of applied econometrics... although simpler computer simulations like Monte Carlo methods are well accepted.

E.g. Arnold Kling, who has some academic and some Federal Reserve credentials, writes

  My concern with ABM is getting a result and not really knowing why you got it. Alternatively, if you really understand how the ABM is getting its result, you should be able to show how to get that results in a simple model, perhaps with a numerical example.

He doesn't seem to be on the board of any journals, but I doubt his opinion is uncommon.

BoE economist A. Turrell has written a (lengthier) paper containing a fairly balanced (IMO) list of pros and cons of ABM. "Calibration and interpretation" takes most space there when it comes weaknesses. He also mentions the Lucas critique as relevant, and notes that the most fertile cases for ABM being behavioral-economics oriented, e.g. using bounded rationality, also makes them most difficult to proof against the Lucas critique.

At least currently, the staple of macro-economics models is DSGE, which nearly always include a representative-agent:

  All the different views mainstream macroeconomists have about the state of their field and about possible areas of improvement should not diminish the degree to which they converged methodologically in studying fluctuations. They all analyse such phenomena usually through a dynamic stochastic general equilibrium model with a representative agent, firmly grounded on microeconomic principles. Moreover, several of them agree with Chari (2010: 2) that “any interesting model must be a dynamic stochastic general equilibrium model. From this perspective, there is no other game in town.” Therefore, he continues, “a useful aphorism in macroeconomics is: ‘If you have an interesting and coherent story to tell, you can tell it in a DSGE model. If you cannot, your story is incoherent.’”

Generally DSGE models assume a representative agent (in part because they need to side-step Sonnenschein–Mantel–Debreu type results).

  The theorems of Hugo Sonnenschein, Rolf Mantel and Gerard Debreu in the early 1970s established that the restrictions that generate well-behaved individual demand functions do not constrain aggregate demand functions to exhibit the same properties [...]. The new classicals sidestepped the problem of aggregation either by imagining an economy composed of identical individuals or by assuming that there is one individual who represents the whole economy, so that the solution to the optimization problem of this representative agent gives the aggregate relationships in that economy.

There were more steps before the current new synthesis DSGE approach, but I don't want to get into that here. My point with this is that if you have an optimizing representative-agent (RA), you don't need much computer/behavioral simulation... Of course, RA models are criticized (Fagiolo and Roventini summarize RA/DSGE criticism from much more famous economists, Stiglitz etc.) exactly because of this, e.g. their inability to predict (or supposedly even explain) the Great Recession etc. But this criticism seems to not be enough to dislodge DSGE from the current mainstream macro, presently. (There is a bit more subtlety to RA than what I've covered here; RA can include some sources of parametric heterogeneity but assumes a sort of "structural" homogeneity, if I understand that correctly.)

Fagiolo and Roventini have a detailed comparison of DGSE with ACE/ABM  approaches, and while they find that the two approaches share some criticism, they point out the following difference:

  The last issue worth mentioning is specific to ACE and it concerns the comparability of
  different agent-based models. DSGE models are all built using a commonly-shared set of behavioral
  rules (e.g., representative agents solving a stochastic dynamic optimization problems)
  and their empirical performance is assessed with common techniques (i.e., VAR models). This
  allows to develop a common protocol about "how to do macroeconomics with DSGE models"
  and it eases the comparison of the results produced by competing models. Given the relatively
  infancy of the ACE paradigm, the lack of such a widespread agreement among the ACE community
  hinders the dialogue among different ABMs, reducing the comparability of their results,
  and possibly slowing down new developments. In that respect, the development of common
  documentation guidelines (Wolf et al., 2013a), dedicated languages and platforms can surely
  improve the situation, increase the exchanges among ACE scholars, and reduce the entry cost
  to agent-based modeling.

In other words, because of its infancy, there's a lack of standardization in ACE/ABM (unlike DSGE), which presently also hinders wider adoption for the former. (As minor point of terminology, they use ACE/ABM interchangeably: "ACE [agent-based computational economics] models (often called agent-based models,
ABMs)".)


Probability of history occurring at time $t$

You are right, it is the same thing. Actually, later on the book the density over the history $s^t = [s_t, s_{t-1}, \cdots, s_0]$ is written as

$$
\pi(s^t) = \pi(s_t|s_{t-1}) \cdots \pi (s_1|s_0)\pi(s_0) \tag{2.3.1}
$$

where $\pi(s_0)$ denotes the probability of the initial state (or $\pi_0(s_0)$ if you wish), and $\pi(s|s')$ is a transition probability.

Note that Eq. (2.3.1) encapsulates the the probability of obtaining a given history in a Markov process, since ${\rm Prob}(s_t|s_{t-1}, s_{t-2}\cdots,s_0) = {\rm Prob}(s_t|s_{t-1}) = \pi(s_t|s_{t-1})$. This just to show that $\pi_t(s^t)\color{blue}{\equiv}\pi(s^t)$