Do large- and mid-caps try to shun low share prices?

I have no expertise in this area whatsoever, but I've taken a quick look and see a significant body of research on reverse stock splits. Although there are many reasons that reverse stock splits occur, overall findings on the hypothesis of an optimal share price are inconclusive.

Here is a review of 26 articles published about reverse stock splits in international journals from 1970 to 2010. I'll quote from the abstract:

  Reasons attributed by firms for initiating a reverse split are ‘image
  improvement’, ‘artificial increase of price’, ‘reduction of
  stockholder servicing expenses’, ‘improving marketability’ ‘increase
  the stock's investor base’ ‘trading range hypothesis’ ‘signaling
  hypothesis’’ liquidity hypothesis’, ‘regulatory norms’ ‘facilitates
  going private’ and ‘compulsions from creditors, in case of a
  bankruptcy’. In the case of hypothesis testing, it is noticed that,
  researchers are not able to reach in a consensus on the outcome.

Section 3.5 of this review focuses on "a widely accepted belief that forward stock splits and reverse splits are intended to keep the stock price within some 'optimal range'." Radcliffe and Gillespie (1979) "commented that reverse split cannot achieve an optimum range." Studies that focus on the Hong Kong market in particular do no support an optimum trading range hypothesis, at least not in the case of reverse stock splits. However Jain et al. (2004) "documented a significant increase in institutional ownership for stocks with prices of $5 after the reverse split." Jog and Zhu (2004) "found that institutional share holding increases after reverse split which helped them to conclude that an optimum price can reached (at least to institutional investors) through reverse split."

So while there are numerous reasons that companies may benefit from reverse splits, there is not strong evidence for the existence of an ideal share price range. If there were such a price range though, the study by Jain et al. suggests that the minimum might be around $5.


What is an example application of a quasilinear utility function?

Quasilinear utility functions are useful in much of the demand estimation literature, particularly in discrete choice. For instance, check out Berry 1994,Berry Levinsohn Pakes 1995 and the many applications in Nevo's papers on demand estimation (here's a "practicioner's guide"). Ken Train's book on it is available for free here!

To summarize, they can lead to indirect utility of the form $$u_{ijt}=\alpha_i\underbrace{(y_i-p_i)}_\text{real income}+\underbrace{X{jt}\beta_i}_\text{observed product characteristics$*\beta_i$}+\underbrace{\xi_{jt}}_\text{unobserved product characteristics}+\underbrace{\epsilon_{ijt}}_\text{mean zero stochastic term}$$
where $i$ represents individuals $i=1,\dots,I_t$ in each of the $t=1,\dots,T$ markets selling $j=1,\dots,J$ products. Here, $\alpha_i$ represents the marginal utility of income and $\beta_i$ represents the marginal utility from the product characteristics observed in $X_{jt}$.

Suppose that we restrict the heterogeneity across consumers to only enter through the stochastic term $\epsilon_{ijt}$. Then both the individual specific parameters $(\alpha_i,\beta_i)$ must be equal to $(\alpha,\beta)$ and the market share of each good can be represented by
$$s_{jt}=\frac{exp(X_{jt}\beta-\alpha p_{jt}+\epsilon_{jt})}{1+\Sigma_{k=1}^{J}exp(X_{kt}\beta-\alpha p_{kt}+\xi_{kt})}$$

The equation for the market share is a function of variables that only vary at the product-market level, so you only need information on prices and quantities (and product characteristics) for a crude estimation. However it gives some quirky results. Particularly regarding the elasticity of market share wrt own price and cross price (market share) elasticities, and consumer subsitution patterns. Things can get more robust the more you read on demand estimation, you can introduce consumer characteristics and get results that have more desirable substitution properties.

There are also many criticisms of the conclusions that this type of modeling can draw, but I'll leave that up to you to imagine should you want to read on the topic.


Soft question: How do you create/draw/plot economic graphs digitally?

Give @Giskards comments I'll put up my answer in the comments as answer. I usually fake the data and then use my favourite plotting program. For example here is the requested income substitution graph challenge created with R and GGplot2. For completeness I add the code, but given that it's quite long I add it to the end of my answer. Added bonus of GGplot/R is that if one is well versed with it it is simple to include LaTEX annotation.

Making a similar graph in Excel is also doable. I'll admit though that Excel becomes a pain once we want multiple axes and scales, and the same probably applies to GGPlot. And of course Excel doesn't work well with LaTEX.
Code to generate graph (all parameters can be adjusted, the only thing that needs to be fixed afterwards is the vertical position of the arrows and the text).
#Packages
require(ggplot2)
#Parameters
#Using a CD utility function for convenience and because it generates easy demands
#As the A in that function is just for scaling we'll set it to 1
#Exponent on utility function
alpha <- 0.5
#Price of goods
p_x <-1
p_y <-1
#Price of x after price increase
p_x2 <-4
#Budget
M <- 10

#Basic numbers as input
df<-data.frame(x_amount=seq(0,M/p_x,by=0.1))

#Budget constraint 1 & 2 (formulated in y-x plane)
df$BC_1 <-(M-p_x*df$x_amount)/p_y
df$BC_2 <-(M-p_x2*df$x_amount)/p_y

#Calculating utility for correct indifference curves
#By the marginal spending rule alpha/(1-alpha)*(y/x)=p_x/p_y
#Therefore y=((1-alpha)/alpha)*(p_x/p_y)*x
#By the budget constraint y=(M-p_x*x)/p_y
#Using that and solving gives x=(M*alpha)/p_x and y=((1-alpha)*M)/p_y
#Utility indifference curve 1
U1<-((M*alpha)/p_x)^alpha*(((1-alpha)*M)/p_y)^(1-alpha)
#Utility indifference curve 2
U2<-((M*alpha)/p_x2)^alpha*(((1-alpha)*M)/p_y)^(1-alpha)

#Indifference curve 1
df$indif1<-(U1/(df$x_amount^alpha))^(1/(1-alpha))
#Indifference curve 2
df$indif2<-(U2/(df$x_amount^alpha))^(1/(1-alpha))

#To find the final budget constraint first identify the x and y value
#To do this we set the first derivative of indifference curve 1 equal to
#the new -p_x2/p_y and find its root
f1 <- function (x) -alpha*(U1/x^alpha)^(1/(1-alpha))/((1-alpha)*x)+p_x2/p_y

Solution_x <- uniroot(f1,c(0.1,20))$root
Solution_y <- (U1/(Solution_x^alpha))^(1/(1-alpha))
#Determine the intercept

f2 <- function(M) M-p_x2*Solution_x - p_y * Solution_y
M2 <- uniroot(f2, c(0,30))$root

df$BC_3 <- M2/p_y - p_x2/p_y * df$x_amount

#Reshaped dataframe to long format
df_2 <- data.frame(x_amount=rep(df$x_amount, times=5),
                   y_variables=c(df$BC_1,df$BC_2,df$indif1,df$indif2, df$BC_3),
                   role=factor(rep( colnames(df)[2:6], each=length(df$x_amount)))
)

ggplot(data = df_2) +
  aes(x_amount, y_variables,colour=role)+
  geom_line(size=1)+
  ylim(0,20)+
  geom_vline(xintercept = Solution_x, size=1, linetype=3)+
  geom_vline(xintercept = (M*alpha)/p_x , size=1, linetype=3)+
  geom_vline(xintercept = (M*alpha)/p_x2, size=1, linetype=3)+
  geom_segment(x=(M*alpha)/p_x, y=3,yend=3, xend=Solution_x, colour="black", arrow = arrow(length = unit(0.25, "cm")))+
  geom_segment(x=Solution_x, y=5,yend=5, xend=(M*alpha)/p_x2, colour="black" ,arrow = arrow(length = unit(0.25, "cm")))+
  geom_segment(x=(M*alpha)/p_x, y=0.8,yend=0.8, xend=(M*alpha)/p_x2, colour="black", arrow = arrow(length = unit(0.25, "cm")))+
  annotate("text",x=3.2, y=3.7, label = "Substitution effect", size=3)+
  annotate("text",x=1.9, y=5.3, label = "Income effect", size=3)+
  annotate("text",x=3, y=1.2, label = "Total effect", size=3)+
  ylab("Amount of y")+
  xlab("Amount of x")+
  theme(legend.position = "none",
        panel.background = element_rect(fill = NA),
        panel.border = element_rect(linetype = 1 , fill = NA))


What happend to the dollar value in the time of the housing crisis

It is not immediately obvious precisely when the recent US housing crisis took place: prices started declining in 2006 (https://fred.stlouisfed.org/graph/?g=cvjE) causing disruption in the financial markets in 2007. The peak of the crisis was possibly in September 2008 when Lehman Brothers failed and the mortgage securitizing enterprises Fannie Mae and Freddie Mac were taken over by the federal government.

US consumer prices fell slightly in the second half of 2008  (https://fred.stlouisfed.org/graph/?g=cvjm) while it was rising both before and after that period, so you might say money became slightly more valuable in terms of goods and services

In the same period, the value of the US dollar rose against other currencies (https://fred.stlouisfed.org/series/TWEXB), typically described as a flight to safety by worried investors during the worldwide financial crisis

There is no particular reason to believe exactly the same things would happen in other housing crises or in other countries, but it is reasonable to expect a housing crisis to reduce consumption (the construction sector shrinks while others feel poorer) possibly leading to a recession and perhaps lower inflation.


Positive productivity shock with a fall in output

It seems that a possible explanation is that the productivity shock was too persistent such that capital flow from one country to the other in order to exploit the higher return to capital. Capital is mobile while labor is not.


Labour Market: simple macroeconomic modeling

To find demand for labor, solve the firm's profit maximization problem :
\begin{eqnarray*} \max_N & \ P(2N - 0.5N^2) - WN\end{eqnarray*}
Differentiating the objective with respect to $N$ and setting it equal to 0 yields the demand function for labor :
\begin{eqnarray*} N^d = 2 - \frac{W}{P}\end{eqnarray*}
Corresponding supply of output is

\begin{eqnarray*} Y = f\left(2 - \frac{W}{P}\right) = \left(2 - \frac{W}{P}\right)\left(1 + \frac{W}{2P}\right) =  2 - \frac{1}{2}\left(\frac{W}{P}\right)^2\end{eqnarray*}

Given the supply of labor is
\begin{eqnarray*} N^s = \frac{W}{P}\end{eqnarray*}

Equilibrium in the labor market occurs where $N^d = N^s$. Solving it, we get equilibrium employment, real wage, output, profits as follows :
\begin{eqnarray*} N^* & = & 1 \\ \left(\frac{W}{P}\right)^* & = & 1 \\ Y^* & = & 1.5 \\ \pi^* & = & 0.5 \end{eqnarray*}


Keynesian Cross and Balanced Budget Multiplier

The fiscal multiplier in (iv) would arise from

$$ Y = C+I+G$$

$$ Y = a + c(Y-T)-d\alpha Y +G+I.$$

This can be rearranged as

$$Y(1-c+d\alpha)=a-cT+G+I,$$

and, therefore, the fiscal multiplier would be

$$\frac{1}{1-c+d\alpha}.$$

In order for this to equal $1$, you just need $d\alpha=c.$

Note that setting $d\alpha=c$ in your "multiplier" does not yield 1:

$$\frac{1}{1-c}+\frac{1}{1-d\alpha}=\frac{1}{1-c}+\frac{1}{1-c}=\frac{2}{1-c}.$$


Intermediate macroeconomics: optimal bundle for quasilinear utility?

From the utility function it seems L is leisure.

a) I think you went about a) in a wrong way. For a, simply you want to work as little as possible but be able to pay 11 in taxes. So you will want to earn exactly 11USD and not more (earning more means working more, which you want to minimize). So at 0,50USD an hour you have to work 22 hours. Since h=24 the maximum leisure you can have is 24-22=2.

b) Where you are going wrong in your analytical approach for b) is not including the budget constraint in your problem (when taking derivatives), which you should as you explained for the graphic analysis.

For consumption you have expenditures - income: p*c=wage*labor - T (technically an inequality, but in this case you can assume it holds with equality). I would suggest using a langrangian with this constraint. You also have the constraint that Leisure=24-labor. This you can plug in directly and is advisable so that your problem only has two unknowns (c and labor).
Solving this problem now should do the trick.


There's three important dimensions for programs/languages:

Convention: Having a program that everyone uses helps you to get feedback/help, work with coauthors, use other people's codes
Ease of use: Since many uses in economics are routines, having the program doing these for you and making your implementation of the use easier is a big bonus
Adaptability: A program that allows you doing covering most of your needs and learning only one syntax versus having to work with different programs at the same time

In terms of frequency of usage among academic economists, here's my ranking:

Top tier

For econometrics, by far, STATA. Mostly because of convention and ease of use.
For dynamic programming, and to some extent monte carlo, by far, Matlab. Mostly because of convention and ease of use

Second tier

For time series econometrics, Eviews (ease of use)
For all kinds of econometrics, R (adaptability, somewhat convention)
The swiss knife of really anything, Python (adaptability)

Specialists

SAS, for huge data sets
Fortran, for efficient prebuilt routines and large scale computation

This list is of course my personal opinion, and for academic economists only. I believe that no one will dispute the top tier, but the second tier/specialists can be somewhat debated. And then there's some more who are even more specialist (for example, Octave as a open source Matlab alternative)


Books to self-study applied econometrics

Experts can provide better suggestions if you give more information about your background, preferred programming language, etc. An absolute beginner myself, I am trying to learn Stats and Econometrics, and their applications using R language, the lingua franca among stats community. So far I have consulted primarily Springer's Use R series and free resources available on CRAN. I found the following particularly useful:

Introductory Econometrics: A Modern Approach by Jeffrey M. Wooldridge
Applied Econometrics with R by Kleiber & Zeileis

These are rather elementary books. Have a look at CRAN Econometrics Taskview to learn about applications of more advanced topics and even most recent Econometrics research.


Extraction of Inflation Expectation from bond yields

Yes, the number you give is an approximation. If you wanted to calculate the true economic breakeven, you would need to include the effect of the lag used in the indexation process (which includes known inflation information), coupon cash flows, seasonality of inflation, etc. If there is a maturity mismatch, then you would need to decide how to handle that as well.

However, the deviation between the economic breakeven and the approximation is normally small. In fact, the market convention is (or at least it was) to ignore compounding and just use the spread between quoted rates.

You would need a full fixed income pricing suite to calculate the true economic breakeven, so a course would stick to the approximation.


Have you tried writing down your intuition? Maybe the preference relationship of the electorate as a whole is transitive, but not complete, or complete but not transitive, etc.

I would start, for example asking the electorate, which one is preferred Biden or Warren? 2 voters would prefer Biden and one would prefer warren, so using the majority rule, we can conclude that for the electorate as a whole: Biden $>_{elect}$ Warren. Keep going with all the pairs and conclude whether the  preferences are complete or transitive.


Is a Nash equilibrium anything more than what it is?

The conventional definition of Bayesian Nash equilibrium (BNE) is as follows:

  A pure strategy BNE is a profile of
  type-contingent strategies $$(s_i(\theta_i),s_{-i}(\theta_{-i}))=(s_1(\theta_1),\dots,s_{i-1}(\theta_{i-1}),s_i(\theta_i),s_{i+1}(\theta_{i+1}),\dots,s_m(\theta_m))$$
  such that for each $i\in P$,  $$ s_i(\theta_i)\in\arg\max_{s_i'\in
 S_i} \sum_{\theta_{-i}}p(\theta_{-i}\mid \theta_i)
 u_i(s_i'(\theta_i),s_{-i}(\theta_{-i}),(\theta_i,\theta_{-i})). $$

If we want to define BNE with the language of beliefs about the other player's actions, we may propose the following definition:

  A pure strategy BNE is a profile of type contingent strategies
  $(s_i(\theta_i),s_{-i}(\theta_{-i}))$ and a profile of beliefs
  $b^*=\{b_i(\theta_{-i})\}_{i\in P}$, where $b_i(\cdot)$ is a
  distribution over $S_{-i}(\cdot)$ conditional on $\theta_{-i}$, such
  that

  $s_i(\theta_i)$ maximizes $i$'s expected utility (expectation over $\theta_{-i}$) given $b_i(\cdot)$ and a prior on types; and
  $b_i(\cdot)=s_{-i}(\cdot)$, i.e. beliefs in $b^*$ are correct.

Thus if the type distribution is degenerate, the definitions of BNE and NE coincide. Nevertheless, the correctness of beliefs (about the opponents' strategies) are present in both definitions.
The difference is that in BNE, players' beliefs are over a set of functions (due to the fact that in Bayesian games, strategies are type-contingent).


Do the efficiency savings of mergers indicate a type of waste or inefficiency in a market?

Are the cost savings mentioned in the article indicative of a
  fundamental inefficiency caused by a competitive market, that wouldn't
  be present in, say, a nationalized industry (or total monopoly)?

That "causation" is mischaracterized. It is not that a competitive market causes inefficiencies, but that it encourages their removal. Inefficiencies also exist in a state-controlled economy, but there the government pursues other policies because it does not need to be concerned about the risk of being left out of the [state-controlled] market.

The title of the article you shared serves to illustrate the point. The fact that the unions "welcomed" the merger reflects how they typically object to mergers (elsewhere, the article quotes one union officer in terms of having "made great sacrifices"). The historical friction from unions is antithetical to the optimization that eventually becomes indispensable in a market-based economy. Here, it appears from the article that the unions understood that Trump's tariffs on steels and the imminent consequences from Brexit are compelling reasons to reach an agreement and accept the merger.

A natural monopoly is the only monopoly that could thrive in a competitive market because, by definition of natural monopoly, the existence of competitors would not result in improvements in the market or economy.


Why don't consumers subsidize monopolies?

As you pointed out, the problem of inefficient supply by a profit maximizing monopolist can be solved via subsidizing the monopolist to increase his marginal revenue. The subsidy can be paid by the consumers or by a central government.

Consumers unfortunately perceive the problem as a collective action problem: The marginal utility gain from subsidizing the monopoly is much lower than the marginal welfare gain of society, making individuals reluctant to subsidize the monopoly.

Governments, however, can solve the collective action problem by raising a tax and thus financing the subsidy. However, governments usually do not only pursue efficiency but also interpersonal equity. If the government cannot transfer the monopolist's earnings lump sum to the consumers, then this may conflict with the goals of interpersonal equity.

To give a simple example: Suppose rich individual A owns a monopoly on water. There are many consumers of water who are all poor. A sets the profit maximizing price/quantity. If the government maximizes total utility and all consumers have identical concave utility functions, the government would like to impose the efficient subsidy and tax the rich individual A lump sum to finance the subsidy and possibly transfers to the poor. However, if the lump sum tax on A is not available, we are in what is called a second-best solution. In this case, it may be optimal for the government to permit some inefficiency from the monopoly rather than taxing the poor to pay for the subsidy.

As an aside: Most interestingly, if there is an omniscient government which maximizes social welfare and can make lump-sum transfers, then under some regularity conditions the collective action problem disappears without the government imposing the subsidy! Thus, I would have an interest to subsidize the monopoly on my own. This is because the utility possibility frontier is pushed outwards by the subsidy and the government will reimburse me lump sum for my cost.


What happens when a reserve bank runs out of foreign currency reserve?

This is an excellent question and it deserves a good answer and I will try my best here.

So what is a reserve currency? A reserve currency is a currency that other nations use for making global payments, loans and foreign exchange reserves.

The four currencies that are considered global are the US dollar (USD), the Euro, the Japanese Yen and China's RMB (yuan).

Now, what happens to a bank when it runs out of reserve currency, well, it depends who the bank is, where its located and what the reserve currency is that they have run out of.

If you are one of the four currency nations then you are exporting your currency, but you have to export enough into the global system to support the demand for payments, loans and reserves.

Central banks in general could also issue lines of credit which require payment in one of the four reserve currencies mentioned above.

This becomes part of someone's job at these banks to ensure that there is a harmonious balance on the balance sheet at all times between exporting currency, issuing credit and demanding payments.

Lets take a case study such as the EU banks where they had issued loans in Euros, and the fatal consequence of that started to become clear in 2016. Emerging market borrowers were forced to default as their currencies weaken against the Euro and the USD, driving the costs of servicing their debt denominated in Euros and USD higher.

Someone mentioned Venezuela above and yes this is what happened to them. Not that they ran out of foreign currency, but that the cost of servicing their debt denominated in USD and Euros soared to the extent that it weakened their own currency, in addition to their policy of expropriating businesses that did not belong to the government and other policies which finally lead to foreign investment high tailing it out of there and a vote of no-confidence for the now dead Bolivar.

Even nations have credit reports and credit ratings and you can imagine when they run into that kind of trouble, their ratings drop.

In my opinion, the system of reserve currencies is dysfunctional for everyone, creating and incentivizing fatal imbalances in trade, yields and debt. Some look to a basket of currencies from the World Bank known as Special Drawing Rights or SDRs as the solution, but all this does is tighten the coherence of a system that's already dangerously hyper-coherent, that is, highly susceptible to contagion.

But the concept of reserve currency and the balancing act that banks have to go through with it is not perfect and even gold had its limitations. Anyway, I hope this is some semblance of an answer or gets you closer to your answer.


Why does a firm make profit in a perfect competition market

The first order condition for profits here (with respect to quantity, since firms are price-takers) is
$$p - 4q_i = 0 \implies q_i^* = \frac 1 4 p,$$
which is the supply function of its firm. So market Supply is
$$nq_i^* = \frac{180}{4} p = 45p,$$
and equilibrium market price
$$45 p = 100 - 5 p \implies p^* = 2$$
and equilibrium market quantity
$$Q* = nq_i^* = 180 \cdot\frac 1 4 (2) = 90$$
Per identical firm we have
$$q^*_i = 0.5$$
The profits are
$$(2)*(0.5) - 2* (0.5)^2 = 0.5$$
...indeed.
So what happens here?
Well "perfectly competitive market" among others things means costless and free entry. But the problem above was solved for a fixed number of firms.
At this number of firms, each firm makes an economic profit. This will induce other firms to enter the market, driving equilibrium price down and economic profits to zero.
I guess the OP can understand how one can compute the number of firms required so as to have zero economic profits (hint: it is not finite).


Why is economic profit for a monopoly per unit demand minus ATC?

Price minus marginal cost gives you marginal profit.

\begin{align*}
\text{Total profit}&=\text{Revenue}-\text{Total cost}\\
\frac{\text{Total profit}}{\text{Quantity}}&=\frac{\text{Revenue}-\text{Total cost}}{{\text{Quantity}}}\\
&=\frac{\text{Revenue}}{{\text{Quantity}}} - \frac{\text{Total cost}}{{\text{Quantity}}}\\\\
\text{Per-unit profit}&=\text{Price}-\text{Average total cost}
\end{align*}


How a countries interest rate (official cash rate in NZ) and inter-bank network determines retail interest rates?

The first thing to understand is that banks lend to each other as part of the normal functioning of the banking system. Banks transfer money between themselves based on customer transactions, and banks that end up losing flows typically borrow from banks with the excess. They do this on an overnight basis, since the flows can reverse the next day.

Central banks have a policy rate, the details of which depend upon the country. Typically, it undertakes actions to keep the private sector interbank lending rate near this target. It does not necessarily have to lend money to banks itself to do this.

  So is the official cash rate set by the central bank (or equivalent central bank rates overseas) the rate which banks lend to one another, or is it the rate the central bank lends to retail banks?

As explained above, the central bank announces a target for the overnight rate between banks. There are a number of ways to achieve this objective (repos, outright purchases of bonds, borrowing/lending, discounting bank assets). If you wish, you can search for those terms individually, or consult central bank websites for primers.

  And how does this ultimately affect normal people borrowing from
  retail banks?

Lenders compare the risks of potential borrowers, and charge a yield premium - a spread - for riskier borrowers. Lending to the central government is normally the least risky form of lending, and then lending to other banks. The implication is that all other forms of lending are riskier, and so they borrow from banks at a positive spread to the interbank rate. This means that the interbank rate is the benchmark for other borrowers, and explains why central banks guide the interbank rate.

(In the midst of a crisis, almost all forms of lending can be viewed as risky, and lending rates can be quite unstable. Central banks need to take actions to eliminate these credit stresses.)


Why there are no famous software/IT companies in Europe? (unlike USA)

In Europe there is typical more regulations and more and higher taxes on profits, financial transactions, and on products and services. This means there is less incentive for entrepreneurs to create their businesses since they face for example higher yields and higher interest rate coupons, environmental regulations, state bureaucracy which increases the cost and decreases the incentive (profit). Since most of innovative companies are generally start-ups such as Facebook was, there is higher cost of funding once these companies are considered riskier. In Europe that cost is further increased by the tax system for example.   There are also other factors such as education quality that differs. Europeans generally regards the US universities to be more prestigious and this is a decisive factor that makes lots of Europeans, typically the brightest to migrate to the US for further studies and higher wages since Americans can afford to pay more since there is less state interventionism.
I hope I gave you some ideas of what might be going on. In economics there is no definitive answer so keep on investigating and asking other people. Sorry for the lack of data.


OLS estimator derivation: second-order condition to prove global minimum?

It seems that you working on the right lines. By multiplying out the brackets, it can easily be verified that $n\sum{X}_i^2 - (\sum{X}_i)^2 = n\sum{(X_i - \bar{X}})^2$ where $\bar{X}$ is the mean. As you yourself spotted, this is basically a standard expression for the variance. From this, it follows that $n\sum{X}_i^2 - (\sum{X}_i)^2 > 0$ provided that $X_i \neq \bar{X}$ for some $i$.

Incidentally, you also need to verify that one of the second derivatives is positive (say $SSR{_{\alpha\alpha}}>0$) which follows directly from your Hessian.


What does Eugene Fama mean "variance of price changes over multiple days should be less than the multiple of the variance over a day"?

Thanks whoever asked this at r/econometrics.

abcxyd 9 days ago
I don’t see how Fama’s reply relates to the initial comment at all. But what he means is if you calculate price changes over a longer horizon (e.g. a week), the variance of those price changes is not necessarily lower than the variance of daily price changes when the variances converted to the same frequency. I.e. the annualized variance of weekly price changes is not necessarily lower than the annualized variance of daily price changes. Here’s a well known paper that demonstrates this: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1540-6261.2012.01722.x.


Understanding distortions in investment in human capital

I assume WH Hutt is referring to long-term effects. Here's what I understand. If "the price of any commodity is raised above the free market level by strike threat or action or by state edict," so that the price is above marginal cost. Then firms earn a "free" mark-up (=price - marginal cost) and need not be as productive as in a competitive market. As a result, they may hire less productive workers or offer less productive jobs, distorting investment in human capital in favor of low productivity and low-paying jobs.


Two things:

Capital not being put to work reveals no profit. This capital could have been invested into something else which may (or may not) have resulted in profit for the bank. Opportunity cost of capital could be rather big. This means that the bank is actually loosing out on potential profits.
Capital (in form of equity) does not necessarily mean the company is profitable. Many (often smaller) companies are 100% equity financed - this has no relation to profitability what so ever. Increasing the equity/debt ratio does not say anything about if the company is profitable. It could be because the company has build up equity (yay, this means profits), but it could also be because the company has gotten a capital injection (not affecting profits). It works other ways as well - perhaps a company is very profitable (building equity and not paying dividends), but at the same time they increase their debt, keeping the ratio constant; in this case you cannot see if it is profitable or not. Debt is not the same as “not profitable”. Actually most companies have debt because they may be able to invest the debt at a better rate than their interest rate (eg in machinery to increase production resulting in profits).

Increasing the gap between assets and liabilities is exactly the same as described above. Assets = (Equity + Liabilities).


Why are property price-to-rent ratios relatively low in the US?

Reviewing their methodology, they make a number of assumptions that will affect their results. They don't provide the sources of the data they use as inputs, so it's impossible to fully evaluate their methodology, but it is worth noting their description:

  Price to Rent Ratio - is the average cost of ownership divided by the
  received rent income (if buying to let) or the estimated rent that
  would be paid if renting (if buying to reside). Our formula to
  estimate rent per square meter assumes 1 bedroom apt has 50 square
  meters and 3 bedroom apartment has 110 square meters. It doesn't take
  into account taxes or maintenance fees.

Given the relatively simple assumptions, lack of transparency regarding input data, and reliance on assumed homogeneity in housing stock both internationally and intra-city, I wouldn't rely on these data to arrive at any conclusions, let alone the conclusion that price-to-rent ratios are particularly low in the US.


Calculating Market Concentration without sales data

Why not using the number of workers? And simply replacing sales (or output) by workers in the HHI or C4 indices. I saw this in the literature, but where? May be in a report of the German "Monopolkomission"...

EDIT: I found an example for France. The share $C_{10}$ of the production of the 10 biggest firms is very correlated with their share in total employment (at the sectoral level). The correlation coefficient is about 0.96. Note, however, that their production share often tend to be higher than their employment share, maybe due to increasing returns to scale.
Source: Insee, GR2 – Concentration des groupes : part des 4 ou 10 premiers groupes (NES 114 postes)
https://www.insee.fr/fr/statistiques/2381764?sommaire=2381775&q=concentration


How does this demand function satisfy the Weak axiom if it doesnt satisfy the necessary and sufficient conditions?

Your equivalence result is incorrect. The correct results are:

If $x(p,w)$ satisfies Walras' law, homogeneity of degree zero, and the weak axiom, then the Slutsky matrix is negative semidefinite, that is, $v \cdot S(p,w) v \leq 0$ for any vector $v$.
If the Slutsky matrix is negative definite for all vectors $v$ that are not proportional to $p$, that is, if $v \cdot S(p,w) v < 0$ for such vectors $v$, and if $x(p,w)$ satisfies Walras' law and homogeneity of degree zero, then it satisfies the weak axiom.

Therefore, there is no contradiction in the fact that your demand function satisfies the weak axiom while its Slutsky matrix is only negative semidefinite (and not negative definite).


(The question about perpetual debt was covered by the link to the description of a perpetuity.)

There are two sides to the "is it really possible"?

Could a country that controls its central bank (e.g., Canada, Japan, United States) replace its debt with money issued by the central bank?
Could the ECB do the same thing?

The answer to (1) is that it appears theoretically possible. (In fact, the economic school of thought known as Modern Monetary Theory advocates this.) There is the question of whether this would be a good policy, and the answer to that would be controversial. It should be noted that Quantitative Easing policies of the Federal Reserve and the Bank of Japan involved large purchases of government bonds by the central bank, and there have been no obvious side effects (for example, inflation) yet. These policies represent a step towards the central bank buying up all government debt.

The answer to (2) - could the ECB follow such a policy - is a technical question. The actiona of the ECB are limited by treaties; the usual interpretation of those treaties says that the ECB cannot do this. Certainly, the ECB limited its buying of Greek debt based on its interpretation of the treaties. There would have to be a move to change the treaties that restrict the ECB's actions to allow such a move, which seems like a difficult task.

From the perspective of French policy, the answer to question (2) is more important than (1).


Phenomenon of equal prices without price collusion

I know you are at pains to say you are not looking for 'collusion' as an answer, but what you describe sounds very much like tacit collusion. Here's a quote from Competition Policy by Massimo Motta (pp138–140):

  I briefly characterise the concept of collusion from the point of view of industrial economics. Note that here I will not use the term "collusion" as a synonym for "collusive agreement that should be outlawed". Indeed, one of the main themes of this chapter is that whereas in economic theory collusion is defined as a market outcome (i.e., "high prices", in a sense to be specified further below), anti-trust authorities and judges should consider as illegal only practices where firms explicitly coordinate their actions to achieve a collusive outcome.

  [...]
  In economics, collusion is a situation where firms' prices are higher than some competitive benchmark. [...] In any case, in economics collusion coincides
  with an outcome (high-enough price), and not with the specific form through
  which that outcome is attained.

  [...] It is important to stress that [colluding firms need] not talk to each other, neither directly nor through intermediaries: collusive prices will arise through purely non-co-operative behaviour of the sellers. In other words, if detection of deviations is rapid, and if (market) punishments of deviations are likely and credible, then tacit collusion can arise: firms do not necessarily have to talk to each other, let alone agree on complicated schemes, for a collusive outcome to be sustainable. All that is needed is the awareness that a deviation will be identified, and that a "punishment" will follow.

The 'punishment' that Motta refers to is exactly the idea that, if one firm cuts its price to break the tacitly collusive status quo, other firms will 'punish' it by responding with a price cut of their own.

Sometimes, tacit collusion is known by the alternative name conscious parallelism to reflect the idea that firms are consciously mimicking each others' strategies. Particularly among legal scholars, the term conscious parallelism is used to mean coordination of prices without an agreement, whereas the term collusion is reserved specifically for the case in which an agreement has taken place. Among economists, as Motta explains above, both practices are known as (respectively, tacit and explicit) collusion and the conscious parallelism terminology is less common.


The only reason I can see right now could possibly be pedagogical. While that term does indeed just equal zero, there could be generalizations where the agent works a high amount with probability $\tau$ and a low, but positive, amount with probability $1-\tau$. In this case, the term would still go through. There are also plenty of functional forms that would result in that term not being zero (taking away the -1, for example, which is often done in applied work). At any rate, this is an idiosyncratic enough case that the professor might have thought it best to show the process of rearranging terms for future reference and to give help with other scenarios. On the other hand, he may just not have noticed it. :)


Is there any historical example that a market is shrinking down after competition?

According to The Economist, 2015-09-26, pornography (the "adult" industry) may be one such industry. Due to the entrance of YouTube-like porn aggregators, industry revenues have shrunk dramatically in recent years:

  In America the number of porn studios is now down from over 200 to 20 ... Performers who used to make \$1,500 an hour now get \$500 ... Revenues are well below their peak; how far below is hard to say, as most porn producers are private. Just before the tubes took off, plausible estimates put worldwide industry revenues at $40 billion-50 billion. Mr Thylmann thinks they have fallen by at least three-quarters since then.

Here though we must perhaps be careful about defining "market size". If we define it by such measures as industry revenue and profits, then "market size" has indeed shrunk. But if we define it by say quantity traded (e.g. "number of hours of porn watched"), then probably "market size" is no smaller than before.


Why did Malthus thought that population increases geometrically while resources increase arithmetically?

As mentioned in the question the exponential population growth was argued to exist because it is based on the 'natural growth' that can be empirically observed anywhere in nature where the resources are abundant. So you already answered that part pretty much yourself.
When it comes to the arithmetic growth of resources, the word resource is actually not appropriate modern economist would call things like food and shelter output not a resources which are factors of production (the wikipedia in this article uses the word resources improperly see Samuelson & Nordhaus Economics). Resources are inputs not outputs of production.
The reason why Malthus thought that output/production would grow arithmetically is due to diminishing marginal product of factor of production. Diminishing marginal product means that although output increases when you use more factors (resources like land, labor, capital) the output increases at a diminishing rate. The diminishing returns as argued by many economist must apply otherwise even single plot of land could produce enough crops to feed whole world. At some point just throwing more labor and capital at a plot of land will simply lead to smaller output.
Malthus thus reasoned that due to these diminishing returns output will over time grow only arithmetically as given the fact that amount of land is fixed in the world at some point no matter how much machinery and labor force you apply to it at some point the output will increase only minimally (e.g. having 3 tractors for one acre field might increase output significantly compared to having 1 but having 100 tractors as opposed to 97 will not make much difference).
However, Malthus turned out to be wrong because he did not taken into account the effect of technology on production. A Malthusian production function would look something like:
$$Q=K^{0.3}L^{0.2}$$
which exhibits diminishing returns to scale as more and more inputs of labor and capital (resources) are put in the output will always increase but at diminishing rate (in fact if you would plot this curve you would see that as factor inputs increase the output increase becomes more and more ‘flat’ and ‘linear-like’ e.g. imagine a plot of square root function).
However, modern economists realize that technology plays a role in production process too. A modern production function would look like:
$$Q=AK^{0.3}L^{0.2}$$
where $A$ would be the level of avaiable technology. So as long as technology keeps accumulating and growing sufficiently fast enough to keep output with population growth Malthusian trap will not occur.


Has anyone peer-review researched investors buying another, but similarly spelled, ticker?

Yes, this has been done. Balashov and Nikiforov (2019) studied firms with similar tickers and found 25% had comovement in turnover and estimated 5% of turnover was due to investor confusion


Why is the Total Current Account Balance of World positive and does it mean that the world has a net Trade Surplus?

Since we are not trading with aliens (yet), you are right in assuming the global account balance ought to be zero. Your data contradicts this because it is collected by numerous statistical agencies who differ in their capability and their methods. Examples for different outcomes could arise from:

different degrees of border control. The fact that an export is registered in country A does not mean it is registered as an import in country B.
different capabilities in processing and collecting data. In some development countries, a substantial share of the economy is informal, i.e. outside the scope of any authority.
different statistical concepts applied.

There are datasets which try to overcome these difficulties by correcting them such that the global account balance is zero.


Select examples from a book suggestion due to @markleeds, Optimal Control Theory with applications in Economics:

Polluting growth has action $\int(bz-\dot{z}+\ddot{z})dt$.
Optimal extraction of a natural resource has action $\int(C(-\dot{x},\,t)+q\dot{x})e^{-st}dt$.
Consumption vs rapid attainment of production capacity has action $\int[\dot{x}-x+q-a]dt$.
Resource extraction in an open economy has action $\int-U(\bar{c}-e^{rt}\dot{x}+ay-\dot{y})dt$.
Consumption versus investment can give rise to many actions, including:

$\int(\dot{x}-1)U(x)dt$
$\int e^{-\rho t}(\dot{K}+\delta K-f)U(K)dt$
$\int\frac{dt}{K-\dot{K}}$
$\int e^{\dot{K}-aK}dt$
$\int(\dot{K}-cK)^ae^{-bt}dt$


Paying Filipino workers in USD. What should the inflation rate be?

Your employees are at risk of PHP inflation; you are not, so you should be paying in USD, and adjusting for USD inflation if you want to.

Yes your reasoning is correct. If you increase their pay by US inflation, in theory the exchange rate to PHP should increase MORE due to the higher PHP inflation (relative to USD). So when they convert their USD to PHP, their resulting PHP income would reflect PHP inflation.


Understanding at a quote about externalities in law and economics

You don't give the source of the quote, but presumably what is meant is this.  Whether X's production or consumption of a good affects Y (in a physical way such as smoke from X's factory or noise from X's playing loud music, not merely through the workings of the price system) is a matter of fact.  On the other hand, whether X is required (assuming a negative effect) to bear the costs of the harm to Y, is a matter of law.  The implication seems to be that an externality is present only if the law does not so require.

However, some writers would exclude the legal aspect from the definition of an externality.  Baumol & Oates, for example, state (quote found here, top of page 5):

  "An externality is present whenever some individual's (say A's) utility or production relationships include real (that is, nonmonetary) variables, whose values are chosen by others (persons, corporations, governments) without particular attention to the effect's on A's welfare."

An advantage of this type of definition is that it avoids the implication that an externality is no longer present when it has been addressed by law as above. Instead, we can say that the externality is still present but has been internalized.


Is the lack of information on customer behaviour good for banks?

Basel II opened the possibility towards "your individual interest rate" by allowing (and encouraging) banks to use more advanced methods of estimating Credit Risk, individualizing even, customer-per-customer, for example using Advanced-Internal ratings-based approach.

This means that the banks can lower interest rates towards clients that score better according to these presumably more sophisticated methods of credit risk assessment. They are not obliged to do so (to the degree that interest rates are determined by the interaction of market participants and not decided by the state). On the other hand, by making credit risk assessment more accurate, banks can select the customers with good credit ratings because this, in the end, lowers their overall credit risk exposure and ultimately, lowers also the obligatory capital that they must hold.

So indeed, individual credit rating and individual interest rates may increase the competition among firms and bring contractual interest rates down, reducing the banks' nominal profit rate -while it may keep intact the actual profit rate, since credit risk (and so, statistical losses) will also go down.
Moreover this may lessen the burden of capital reserves. In some cases (and I would say, in the current situation), banks may even care more about the latter than the former.


A property tax:

In the short run, a property tax will have no effect on rent, as the supply of homes is fixed (i.e., supply is totally inelastic in the short run), and demand is relatively inelastic but not completely so, so the incidence will fall on property owners. In the long run, a property tax will increase rental costs because supply of new units (i.e., construction) is highly elastic and long-run demand for housing looks just like short-run demand— relatively inelastic. As a result, the incidence of the tax will fall on occupants (both renters and owner-occupiers).

Intuitively, one could think of it this way: the cost of ownership will increase due to the tax, so for someone to see it as worthwhile to buy a newly-constructed home to rent out, the rental income would have to be relatively higher in the presence of a property tax than if one were not in place.

A tax on rental income:

The tax will increase rent; it will decrease the supply (and demand) of rental units (and increase the supply and demand of owner-occupied units). This will happen because the tax will reduce the return on apartments as revenue assets, causing some number of landlords to sell them to owner-occupiers, taking them out of the rental market. More importantly, though, there will be some renters who do not have the option of switching to owner-occupancy, and they'll bear the incidence of a tax on rental income.

I am assuming that there are three populations:

Landlords, who can choose to purchase homes for rent, but live elsewhere, so their choice to buy a unit to rent out can be analyzed separately from their own housing consumption
Renters, who must rent, due to some frictions (inability to afford a down payment, poor credit, unstable or difficult-to-document income history, etc.)
Potential owner-occupiers, who can choose between owning their own home and renting from a landlord, and who have some set of preferences between ownership and rental

Thus potential owner-occupiers and landlords compete for units for sale, while renters and potential owner-occupiers compete for rental units.

In this case, the choice of landlords to exit due to taxes will not pass through perfectly to the rental market due to the fact that while potential owner-occupiers who are currently renting can escape the tax by switching to ownership, there are some renters who are renting whose demand for renting is pretty inelastic— these people will bear the incidence of the tax.

Interestingly, in the US there is such a tax on rental income, though it's implicit. We have a bunch of incentives for home ownership, notably the exemption from capital gains for owner-occupied homes, but most importantly the fact that income on rental properties is taxed like any other business income, while owner-occupiers effectively rent their homes to themselves without paying tax on the implied rental income. (As an aside, people often point to the income tax deduction for mortgage interest payments, but this actually just creates tax equivalence between homeowners and landlords, who can deduct interest as a business expense.)


tldr: The core is a very general concept that can be used in a vast amount of models. Applying it to the setting of a general equilibrium, you can show that every competitive equilibrium is in the core.
The core
The core is a concept that can be defined for very abstract environments.
Consider a population of agents $N$ and an space $\Omega$ of outcomes. Assume that every agent has nice (transitive and complete) preference relation $\succeq_i$ over the elements in $\Omega$.
In addition, agents can form coalitions $A \subseteq N$ and for every state $x \in \Omega$ and coalition $A$ there is a correspondence $\Gamma_A: \Omega \rightrightarrows \Omega$ that determines to which states the coalition $A$ can deviate to when starting at $x$.
For example if $y \in \Gamma_A(x)$ this means that at state $x$ the coalition $A$ has the power to move to state $y$.
We say that a state $x$ dominates the state $y$ by coalition $A$ if:

$y \in \Gamma_A(x)$
for all $i \in A$: $y \succeq_i x$ and there is at least one $j \in A$ such that $y \succ_j x$.

Condition 1 states that $A$ has the power to move from $x$ to $y$. Condition 2 requires that every member of $A$ (weakly) prefers $y$ over $x$ and at least one member strictly prefers $y$ over $x$. If both conditions hold, then you can say that $x$ is not a stable situation as $A$ can find a better state $y$.
Now given such structure $(N, \Omega, (\succeq_i|i \in N), (\gamma_A|A \subseteq N))$ we can define a the core as the set of all states $x \in \Omega$ that are not dominated by some other state. In other words, no coalition can find a profitable deviation from $x$.
Exchange economies and perfect equilibria
Now give this, let us show that for an exchange economy, the competitive equilibrium is in the core. An exchange economy consists of a set of agents, $N$, a set of goods $J$. Each agent has a locally non-satiated utility function $u_i: \mathbb{R}^J_+ \to \mathbb{R}$ and an endowment $\omega_i \in \mathbb{R}^J_+$. A price vector $p \in \mathbb{R}^J_+$ together with an allocation $(x_1, \ldots, x_N)$ for the agents in the economy is a competitive equilibrium if for all agents $i \in N$:
$$
x_i \in \arg \max_{q} u(q) \text{ subject to } p' q = p' \omega_i
$$
(equality of the budget constraint holds due to locally non-satiation) and:
$$
\sum_{i \in N} x_i = \sum_{i \in N} \omega_i
$$
This second condition requires demand to be equal to supply.
To show that every allocation of a competitive equilibrium is in the core, we first need to get a mapping from our exchange economy to the structure given above:

The set of agents is simply the set $N$

The set of states $\Omega$ can be any allocation $(x_1, \ldots, x_N)$ such that $\sum_{i \in N} x_i = \sum_{i \in N} \omega_i$.

The preferences $\succeq_i$ are the ones that correspond to the utility functions.
$$
   (x_1, \ldots, x_n) \succeq_i (y_1, \ldots, y_N) \iff u(x_i) \ge u(y_i).
   $$

Now for the possible deviations of a coalition $A$, we assume that each coalition can move to an allocation by simply reallocating their own endowments. This means that they can move to a new allocation for their members as long as the total consumption within the coalition does not exceed the total endowment of the members in the coalition. (There is an issue here as I am not specifying what happens to the consumption of the members outside the coalition once a coalition deviates, but we will see that this does not really matter for the argument).

Given this, let us show that any competitive equilibrium is in the core.  Towards a contradiction, assume that $(x_1, \ldots, x_N)$ is a competitive equilibrium with price vector $p$, and assume that coalition $A$ has found a profitable deviation $(y_i| i \in A)$. This means that:

for all members $i \in A$:
$$
   u_i(y_i) \ge u_i(x_i),
   $$

for at least one member $j \in A$
$$
   u_j(y_j) > u_j(x_j).
   $$

The total consumption in $A$ must not exceed the total endowment of members in $A$
$$
   \sum_{i \in A} y_i \le \sum_{i \in A} \omega_i
   $$

Let us show that these three conditions lead to a contradiction. First, using a simple revealed preference argument it follows from  $u_i(y_i) \ge u_i(x_i)$  that:
$$
p' y_i \ge p' x_i.
$$
Indeed, otherwise $p' y_i < p' x_i \le p' \omega_i$ which means that $y_i$ was cheaper than $x_i$. This however contradicts the assumption that $x_i$ was utility maximising for $i$ at prices $p$. Also using a similar revealed preference argument, we can show that $u_j(y_j) > u_j(x_j)$ implies:
$$
p' y_j > p' x_j.
$$
So adding these inequalities across $i \in A$, we get:
$$
\sum_{i \in A} p' y_i > \sum_{i \in A} p' x_i.
$$
On the other hand from the budget constraint conditions and 3. we also have that:
$$
\sum_{i \in A} p' x_i = \sum_{i \in A} p' \omega_i = p' \sum_{i \in A} \omega_i \ge p' \sum_{i \in A} y_i = \sum_{i \in A} p' y_i
$$
a contradiction.


Iso-elastic utility is defined as a function $U(w)$ where for all $k \gt 0$ you have $$U(kw)=f(k)U(w)+g(k)$$ for some functions $f(k)$ and $g(k)$ independent of $w$, i.e. an affine transformation of the original utility function

This is iso- because this kind of utility function leads to identical (or at least proportionate) decisions: it means that the optimal risk/reward behaviour at given level of wealth $w$ is also optimal for another level of wealth $kw$ if you multiply all the original investments by $k$.  For example, if at some wealth level you would put a third of it into a particular risky investment and two-thirds into a particular safe investment, then with an iso-elastic utility function you would do the same with at any wealth level

Both your formulations are iso-elastic in this sense, since they only differ by a constant $\frac{1}{1-\mu}$ and so lead to identical distribution decisions.  The difference between them is that the first has $u(0)=0$ and $u(1)=\frac{1}{1-\mu}$ while the second has $u(1)=0$, and since that difference has no real-life implications it might be unreasonable to claim the two utility functions had different properties

Those who use the second formulation often associate it with a logarithmic utility function as the limit function as $\mu \to 1$.  This limit cannot be done without subtracting the $\frac{1}{1-\mu}$ (no longer a constant, since $\mu$ is changing), so they take the second formulation for arithmetical convenience


Where to find the face value in a US treasury bond announcement

The entry “offering amount” is the total par value that is being auctioned. (In the example given, this is a reopening of an existing issue, so it is the increase of par value for the issue.)

From the perspective of a bidder, the “par value” is what they are awarded, which will only be a portion of the total par value of the issue. (There is a maximum bid size specified, which prevents a single bidder from taking down the entire offering.)


Intuitively, a higher price for pears means that I have to give up more apples to be able to afford an extra pear (or, conversely, if I give up one pear then the number of extra apples that I can afford increases). This is going to make me want to reduce my pear consumption and increase my apple consumption (in orther words, to substitute away from pears towards apples). Graphically, this corresponds to a change in the slope of the budget constraint and is known as the (Hicksian) substitution effect.

This substitution effect is, however, moderated by a second consideration. If I increase one or more prices then the total amount of "stuff" that I can afford to buy decreases, so it is as if my income has decreased (which would correspond to a shift of the budget constraint towards the origin). This is known as the income effect and will usually mean that my consumption of apples decreases if the price of pears rises.

When the income and substitutes effects are put together, you get the total effect of an increase in the pear price upon the demand for apples. This total effect gives rise the the notion of gross substitutes: apples and pears are gross substitutes if the following is true

  increasing the price of pears causes the consumer to demand more apples.

Formally, this is written as $$\frac{\partial X_a}{\partial p_P}>0,$$ where $X_A$ and $p_P$ are the demand for apples and the price of pears respectively.

To arrive at the notion of net substitutes we simply take a price change and shut-down the income effect. The hypothetical exercise works like this:

we increase the price of pears, which induces both an income effect and a substitution effect.
to compensate the consumer for the income effect, we give him exactly enough extra money to ensure that (even though one of the prices is higher) he can still afford to get onto the same indifference curve as before. Hence his utility will remain unchanged.
We look at how his demand changed, which now depends only on the substitution effect (since we have compensated the consumer for any change in real income).

Two goods are net substitutes if, after making this adjustment, we find that the demand for apples has increased. Thus, we say that two produces are net substitutes if

  Increasing the price of pears while compensating the consumer for the resulting decrease in his real income causes the consumer to demand more apples.

Formally, $$\left.\frac{\partial X_a}{\partial p_P}\right|_{\text{constant }U}>0,$$ where $X_A$ and $p_P$ are the demand for apples and the price of pears respectively, and $U$ is the consumer's utility.

It is not true to say that "a competitive equilibrium [does] not exist if the products are net-substitute". Indeed, most of the time, products that are gross substitutes will also be net substitutes as well. Thus, most examples of gross substitute preferences supporting a competitive equilibrium will also be examples of net substitutes doing the same.

The reason why it doesn't make sense to state the existence condition for competitive equilibrium in terms of net substitutes is that net substitutes is a purely hypothetical construction in which a fictitious agent intervenes to shut down the income effect and keep the consumer's utility constant. The whole point of a competitive equilibrium is that there is no such intervention: the equilibrium is entirely decentralised and is sustained purely by finding prices such that the market clears when consumers pick their optimal demand.


Why would a rise in the discount rate stop foreign gold drain and make banks fail?

An increase in the discount rate increases the cost of borrowing for commercial banks.  Their normal response would be to

(a) Offer higher interest rates to depositors to replace loans from the Reserve System, and

(b) Increase commercial interest rates on the loans they offer to pass on their higher costs to customers.

This makes it more attractive for individuals (including foreign ones) to deposit gold or pay back loans, together "arrest[ing] withdrawal".

I'm not sure it would and couldn't find this implied in the text.
Because their cost of borrowing has gone up sharply.  If they can't get rid of this cost by calling in loans or attracting savings, or offset it with profits, then they'll go under.  And if they quickly pass on higher interest rates to borrowing customers, this is likely to lead to bankruptcies and foreclosures, so they have to write off loans, and go under.


Why does Denmark have such a huge disparity between its income and wealth Gini coefficients?

The disparity exists because a high income taxes level income inequality but do little to fix wealth inequality.

  Wealth inequality is always higher than labor income inequality, due to income originated from wealth (or capital income), such as rents, dividends or royalties and the increase of asset values [6]. This source of income accounts for a large portion of the national income (˜ 20%-35% [11]), hence its substantial effect on wealth inequality. Additionally, though labor income accounts for most of the national income produced in all western economies, only a relatively small fraction of it contributes to accumulating personal wealth due to taxation and spending. [...]

  There is an obvious positive correlation between wealth and income inequality. However, it is a characteristic of mainly poor countries. The correlation between the Gini indices for the middle-high and high levels of income is 0.23, while for the low and middle income countries it is 0.68.  [...]

  Mathematically, increasing the average tax rate reduces the disposable income, hence effectively reduces savings. However, the relatively limited range of average income tax rates makes its effect on wealth inequality relatively low, in practice. Therefore, it can be concluded that progressive income tax is likely to be an impractical measure for affecting wealth distribution, as suggested previously [20, 25, 36, 52]. This non-trivial effect of income on wealth inequality is originated from the imperfect correlation existing between income and wealth [18, 21, 23, 24]. When income tax is increased, the top earners, who are not necessarily the wealthiest individuals in the population, have a larger difficulty of accumulating wealth, with respect to the wealthiest. On the other hand, it barely affects the wealthiest individuals. Therefore, such an increase might even deepen the wealth gap. When decreasing income tax, the opposite effect will therefore occur. In addition, progressive taxation, which might have a significant effect on the distribution of income, will have a small effect on wealth inequality. Therefore, we conclude that affecting income inequality or changing the average income tax in order to effect wealth inequality are likely to be ineffective means. An evidence for this can be found in the economies of Denmark and Sweden, two of the most equal countries in terms of income in the world, with a high tax burden, in which wealth inequality is among the highest within the OECD countries [53].

If I can find out why wealth inequality is so high in Denmark, I'll add more details about that, but the above address why one should not really expect super strong correlation between wealth and income inequality, which I take it to be the main question here.

What I could find out quickly is that wealth inequality in Denmark continued to rise, as of 2015.

  The new figures reveal that the poorest 10 percent in Denmark had average assets of 211,000 kroner in 2015, 13,000 kroner less than the year before, while the wealthiest 10 percent owned average assets of 6.76 million kroner – an increase of 375,000 kroner compared to 2014. [...]

  The figures revealed that Denmark’s richest 10 percent now own as much as 70 percent of the rest of the population put together – a clear indication the government didn’t need to consider any more reforms aimed at benefiting the wealthiest Danes.

This actually gets even more intriguing because until 1998 Denmark had one of the highest wealth taxes.

There might be an explanation with the data from the graph above, which is from the early 2000's, because pension funds were not included in wealth back then, as calculated by the Danish tax authority:

  The Danish wealth data are considered of a very high quality, and they have been fruitfully
  used to study retirement savings (Chetty et al. 2014), intergenerational wealth mobility (Boserup
  et al. 2014), and the accuracy of survey responses (Kreiner et al. 2015). The data does have two
  limitations, however. First, they exclude funded pension wealth before 2012, because such assets
  were not subject to wealth taxation. [...] Second, there is a break in the data in 1997 when the wealth tax was abolished. After 1997, while the Danish administration continued to collect wealth data from third parties, it stopped
  asking households to self-report assets not reported by third parties.

I guess this emphasizes why wealth inequality is a lot harder to measure (than income inequality). If "very high quality" wealth data has those kinds of issues...

Anyway, here's a more detailed analysis of wealth inequality trends in Denmark:

  Figure 1 shows wealth shares in three broad classes: the bottom 50%, the next 40%, and the top
  10%. Measured in this way, wealth inequality has been relatively stable in Denmark over the last
  three decades. Throughout the period, the bottom 50% of the distribution owns a tiny fraction of
  aggregate wealth: their assets are barely higher than their debts. Therefore, almost all wealth is
  owned by the richest half of the population, and it is shared about equally between the middle
  40% and the top 10%. While the wealth shares in the figure are overall stable, wealth inequality
  did increase somewhat from the mid 1980s to the early 1990s. During this time, the top 10% wealth
  share grew while the bottom 50% wealth share shrank. This evolution was driven by the dynamics
  of asset prices, in particular housing prices, which fell significantly during this period. Because the
  share of housing in asset portfolios tends to be decreasing in the level of wealth, housing slumps
  hurt the bottom more than the top, leading to a rise in wealth inequality.

So if you want to know the source of the wealth inequality in Denmark, you have too look further back in history, and unfortunately there's apparently not much good data for that.

The same paper goes on comparing the rise in wealth inequality with the US, and finds that in Denmark it was raising more slowly, especially in the top 1% and top 0.1%. They also find that dropping the wealth taxes didn't change this pattern, however, they attribute this to an "equalizing force":

  One important confounding reason why wealth inequality has stabilized in Denmark (despite wealth tax cuts) is
  likely to be the sharp rise of pension wealth, from around 50% of national income in the late 1980s to 178% in 2014.
  Because pension wealth is relatively equally distributed, rising pension wealth tends to reduce inequality. As shown by
  Chetty et al. (2014), automatic employer contributions to retirement accounts increase pension and total wealth substantially
  for middle-class Danish households.


Sample used in calculating the sample regression function

It is not very clear what you're asking, but if the model is of the form

$$
y_i = \beta_0 + \beta_1 x_i + \epsilon_i \tag{1}
$$

Then the sample regression function (SRF)

$$
\hat{y}_i = \beta_0 + \beta_1 x_i \tag{2}
$$

indeed only considers one value of $x_i$ at the time. If you have a situation in which several observations $y$ are associated with the same value $x_i$, then a linear model is perhaps not appropriate for describing your data


Virtual valuation when the distribution is discrete

Virtual valuation is the derivative of the expected revenue function with respect to the quantile $q$ that is then evaluated at value $v$. The Revenue function is

$$R(q) = q\cdot v(q),\;\;\; q = 1-F(v),\;\;\; v(q) = F^{-1}(1-q) \tag{1}$$

and

$$r(v(q)): = \frac{dR(q)}{dq}=  \frac{d}{dq}\big[q\cdot F^{-1}(1-q)\big] \tag{2}$$

written, after the calculations, in terms of $v$, so

$$r(v)=v - \frac{1-F(v)}{f(v)} \tag{3}$$

If $v$ is discrete we have

$$q_j = 1-F(v\leq v_j),\;\;\; j=1,...,k \tag{4}$$

where now $F$ is a distribution function of a discrete rv, an where $j$ counts the ordered discrete values that $v$ may take, $v \in \{v_1,...,v_k\}$.

Discretizing the relationship we could define

$$r(v(q_j, q_{j+1})):= \frac{R(q_{j+1})-R(q_j)}{q_{j+1}-q_j} \tag{5}$$

which in terms of $v$ becomes

$$r(v(q_j, q_{j+1})):= \frac{v_{j+1}\cdot [1- F(v\leq v_{j+1})] -v_{j}\cdot [1- F(v\leq v_{j})]}{1- F(v\leq v_{j+1})-1+F(v\leq v_{j})} $$

$$=\frac{v_{j+1}\cdot Pr(v > v_{j+1}) -v_{j}\cdot Pr(v > v_{j})}{-Pr(v=v_{j+1})}$$

Using

$$Pr(v > v_{j}) = Pr(v=v_{j+1}) + Pr(v>v_{j+1})$$

we get

$$r(v_j,v_{j+1}) = v_{j} - (v_{j+1}-v_j)\cdot \frac{Pr(v>v_{j+1})}{Pr(v=v_{j+1})}$$

or

$$r(v_j,v_{j+1}) = v_{j} - (v_{j+1}-v_j)\cdot \frac{1-F(v_{j+1})}{Pr(v=v_{j+1})} \tag{6}$$

Since to a first approximation, if $v$ is continuous, and $v_j,v_{j+1}$ are "close enough" we have

$$Pr[v \in (v_j,v_{j+1})] \approx f(v_{j+1}) \cdot (v_{j+1}-v_{j})$$

It is clear how the obtained relation for the discrete case can be seen as the analogue of the continuous case.

For practical applications, one could think also of using a "continuity correction" for the probability in the denominator of $(6)$.


Detecting the presence of measurement error

Suppose we observe only $\tilde{x}$ and $\tilde{y}$ which are the true values measured with error:
$$ \tilde{x} = x + u$$
$$ \tilde{y} = y + v.$$
We would like to estimate:
$$ y = \beta x + \epsilon$$ but all we can really estimate is
$$\tilde{y} = \hat{\beta} \tilde{x} + \zeta$$

However, if  y is measured without error ($\tilde{y}=y$) we can use reverse regression to bound the measurement error in regressions. The regression is:

$$ y = \hat{\beta} \tilde{x} + \epsilon$$

You also run the reverse regression
$$ \tilde{x} = \hat{\frac{1}{\beta}}y  + \hat{\frac{1}{\beta}}\epsilon+ u$$
Define the reverse regression beta as $\hat{\beta}_r = \frac{1}{\hat{\frac{1}{\beta}}}$. It turns out that the results from
the standard regression and from the reverse regression will bracket the true
coeffcient, i.e. $plim\  \hat{\beta} \leq \beta \leq plim\  \hat{\beta}_r$.

This interval is small when the variance of $u$ and $\epsilon$ are small. If one of the two are zero then one of the inequalities hold exactly. Unfortunately, in practice this interval may be large and therefore this approach not very helpful.


If anyone ever wonders the same, I´ve just tried weighting the monthly parameters and that leads to the correct interest rates :) you take 1 / 12 * ∑ (12 values of the respective parameter for the respective year). The answer was way easier than I thought :D


What is value in the context of microeconomic analys for case of monopoly profit maximization

The demand curve represent the marginal value that consumers put on a good. That is, the marginal value for the $Q$-th unit of the good is the height of the demand curve at $Q$.

The total value from consuming $Q$ units of the good is therefore the area under the demand curve from $0$ to $Q$.

The net value (i.e. net of cost) from consuming $Q$ units of the good is consumer surplus, which equals total value (defined in the previous paragraph) minus total cost (represented by the sum of the two shaded rectangles in your graph).


You may want to consider this as the difference between the potential to pay and the actual means to pay on hand. Since government revenues will ultimately come from GDP (excepting foreign aid etc.), you will be certain that debt to revenue will be higher (smaller denominator).

How useful is this as a measure? I suppose, as with all things, it depends. Debt to GDP is a well understood and widely used statistic, and so it lends itself to comparison between other nations. Ultimately GDP is a pool from which the government, in principle, could raise revenues from.

In contrast, revenues are your means to pay right now. Debts generally don't all need to be paid at once, and so your means of paying right now may not matter as much as the fact you are able to pay them when they're due (after all, the money you have right now may be better put to use in some productive activity that will enhance your means of paying the debt in the future). If the bill collectors are at the door, suddenly your revenues matter quite a bit!

I suppose the closest I can get to a direct answer to your question might be that if you doubted the ability of a government to tap into these potential revenues (ie. people won't pay taxes), then debt to revenue would likely be more appropriate given that it is an accurate portrayal of the means to pay.

I'll close with a numerical example. Suppose there were two governments that were identical across all respects, only tax to cover their expenses and have \$10 billion in debt with two different payment plans. Country A must pay back \$1 billion a year over 10 years and Country B must pay back \$2 billion a year over 5 years.

Country A's debt to revenue would be 10, while Country B's debt to revenue would be 5. The numbers are different, but we haven't really learned much about the health of these economies.


If you are interested in Tobin's (average) q,  you might find useful A Simple Approximation of Tobin's q (Chung and Pruitt (1994)). That paper has a highly accurate approximation for Tobin's Q using Compustat. While the JSTOR copy I linked to is pay-walled, other versions appear not to be.


What is the economic purpose of increasing the minimum wage?

Opinion of Economists

What makes you think that economists are so aligned against the minimum wage? Take a look at the IGM Forum that polls top academic economists. There is substantial disagreement about the effects and welfare implications of a minimum wage hike.

IGM Forum: Minimum Wage
NYTimes Blog Post about it

Theory about the minimum wage

Also, it's worth pointing out that besides empirical studies (like Card and Krueger), there are in fact theoretical reasons why a minimum wage might be welfare improving---see Lee and Saez (2012). (I'm just saying they exists, not commenting on the strength of the results.) In the Handbook of Public Economics, chapter 7, "Optimal Labor Income Taxation", they say this about that paper:

  Lee and Saez use the occupational model ... with endogeneous wages and prove two results. First, they show that a binding minimum wage is desirable
  under the strong assumption that unemployment induced by the minimum wage hits the
  lowest surplus workers first. ...

  Second, when labor supply responses are along the extensive margin only, which is
  the empirically relevant case, the co-existence of a minimum wage with a positive tax rate on low-skilled work is always (second-best) Pareto inefficient.A Pareto improving policy
  consists of reducing the pre-tax minimum wage while keeping constant the post-tax
  minimum wage by increasing transfers to low-skilled workers, and financing this reform
  by increasing taxes on higher paid workers. Importantly, this result is true whether or not
  rationing induced by the minimum wage is efficient or not.This result can also rationalize
  policies adopted in many OECD countries in recent decades that have decreased the
  minimum wage while reducing the implicit tax on low skill work through a combination
  of reduced payroll taxes for low skill workers and in-work benefits of the EITC type for
  low skill workers.


This is a really big topic and you're essentially questioning why don't we calculate price levels using Paasche's indexes instead of Laspeyre's. Well, one "simple" answer is that's it's very expensive to maintain a detailed account of what a representative consumer basket should be.

There's people trying alternatives to this, like the Billion Prices Project, but their estimated inflation is very close to the one we estimate through traditional, constant consumer basket method.


Did/does a decline in crime rates encourage materialistic values?

  These are interesting claims but Shiller does not seem to offer
  anything to back them.

Much of it sounds quite logical, whence I would not expect the author to present evidence on that. But, despite my consistent preference for neoliberalism, I think the author's conclusion is unverifiable and is rather an opinion that leaves several gaps unaddressed.

People seek and compete to impress and to be admired. That is part of our nature. For that purpose, some people develop their talent & skills, others --regrettably-- get tattoos, and others who can afford it show off goods and services that they think will make them stand out. Unlike a talent or a tattoo, objects such as jewelry, cars, or the latest iPhone can get stolen or at least vandalized. Thus, it is entirely reasonable that a generalized perception of safety will make the materialistic sector uninhibited to go out and engage in a materialistic competition.

Likewise, the author's remark on terrorism follows almost from definition. A terrorist's targets are those he views as strategic to his political motive: typically public figures, and/or masses whose support of a regime or institution would weaken upon terrorist acts. By contrast, targeting a merely wealthy person or household would not significantly impact the public's mindset in a way that advances the terrorist's purpose.

But, as I mentioned above, the author's conclusion that

  [t]he declining crime rates in the U.S. made a capitalist lifestyle seem
  a better model for the entire world

is hardly susceptible to verification, research, or consensus. That conclusion entails multiple facets and subjectivity gaps that the author apparently did not address.

For instance, Marxists will disagree with the author's conclusion by portraying the state as the mechanism specifically devised to preserve the elite's capitalist lifestyle. In short, Marxist will refute any link between "declining crime rates" and "capitalism as a better model".

Likewise, an analyst will dispute the adequacy of extrapolating a trend of "declining crime rates in the U.S." for reaching conclusions about what exactly would be "a better [economic] model for the entire world" (brackets and emphasis added). Much of the capitalistic lifestyle in the U.S. relies on its indebtedness, whereas already in the 1920s Hjalmar Schacht was concerned about how the capitalistic lifestyle (perhaps frenzy) in Germany was undermining the German economy.

An environmentalist, a Catholic priest, or a Buddhist monk will refute the notion that materialistic values are any beneficial for a single country --let alone for the entire world--, no matter how the idea of "declining crime rates" is slid in the argument.


Is there a name for this family of games (Binomial games?)?

OK,  Erel Segal Halevi's comments have placed me on the right track for finding what I was looking for;

This family of games is called "Resource Selection Games", and it has quite a few papers written on it (such as this one).


If South America were to unite as one country would they become an economic superpower?

In answer to the narrower question of how significant an economy South America would be, here's a rough comparison of current (2016) GDP:

The Caribbean is included in Latin America for good measure (and because that's the way the World Bank cut up the data).  The US is 3.5 times the size, the EU 3.1 times, and China 2.1 times.  The economic area would be almost 3 times the size of the Brazilian economy.

In terms of pros and cons, there are probably larger political than economic issues involved.

Source


Converting my comments into an answer...

In the infinitely repeated game, if the players want to collude on $(L,L)$, then there needs to be an incentive for each to stick to the plan, i.e. a punishment if one of them deviates from playing $L$.

As you have figured out, this amounts comparing the discounted payoffs from playing $(L,L)$ with a one-shot deviation of playing $H$ against $L$, and then playing $(H,H)$ forever.


How do I confirm that the constraint set wL + rK < Q is convex

Consider an arbitrary pair of vectors $(L_{1},K_{1})$ and $(L_{2},K_{2})$ that satisfy $wL_{i} + rK_{i} \leq Q$ for $i = 1, 2$. To show that constraint set is convex, we need to show that any convex combination of that (arbitrary) pair of vectors lies in the constraint set. Namely,
for all $\gamma \in [0,1]$ we have

$$\begin{split}
w\left(\gamma L_{1} + (1-\gamma)L_{2}\right) + r\left(\gamma K_{1} + (1-\gamma)K_{2}\right) &= \gamma \left(w L_{1} + r K_{1}\right) + \left(1-\gamma \right)\left(w L_{2} + r K_{2}\right)\\
&\leq \gamma Q + (1-\gamma)Q = Q
\end{split}$$
Thus the vector, $(L_{3},K_{3})$, is also in the constraint set (where $L_{3} := \gamma L_{1} + (1-\gamma)L_{2}$, and $K_{3} := \gamma K_{1} + (1-\gamma)K_{2}$) and so the set is convex.

Your answer (or at least the rearranging of inequalities in your answer) is largely correct. However, it is important to note that you've shown this inequality for an arbitrary vector in the set and for an arbitrary convex combination and not for a particular one.


"Tightness" of political elections and public attention

Yes, you should look at the regression discontinuity literature in political economy that uses close elections as the identification strategy. For example, see http://sekhon.berkeley.edu/papers/CaugheySekhonRD.pdf  and http://www.polmeth.wustl.edu/media/Paper/EggersetalRDD.pdf


Does stronger regulation of economic activity impede economic growth in constitutional democracies with basic constitutional rights?

Broadly speaking regulation can be defined as done by OECD see Khemani and  Shapiro (1993):

Regulation is broadly defined as imposition of rules by government, backed by the use of penalties that are intended specifically to modify the economic behaviour of individuals and firms in the private sector.

This is broad definition that includes anything from price controls via regulations on export/imports to antitrust laws.
Research shows that inclusive institutions which include things that would very well fall under the label regulation like antitrust laws, laws that enforce competition, prevent firms from creating barriers to entry and so forth do promote economic growth (see Acemoglu 2008, Acemoglu & Robinson 2000a, 2000b, 2001, 2006, 2008; Olson 1984, Bates 1981, 1983, 1989 and sources cited therein*).
On the other hand extractive institutions, such as government grants of monopolies, restrictions on who or what classes of people can participate in labor market (e.g. like many apartheid regulations that restricted blacks form some professions) many of which again would fall under the label of regulation, tend to depress growth (see the same sources as above).
So growth is neither retarded or supported by 'heavy regulation' per se, it all depends what sort of regulation we are talking about. Regulation that fixes market failures, promotes openness and competition generally supports growth whereas regulation that creates market failures, closes economy and favors concentration generally retards growth.
An important caveat is that under a more narrow definitions of regulation such as the definition used by  Breyer et al (2016):

governmental actions to control price, sale and production decisions of firms in an avowed effort to prevent private decision-making

which is more narrow the answer might change as literature is less kind to price controls and command and control regulations, but still the answer would depend on what sort of regulation are we talking about.
In literature,  the focus is not really on how 'heavy' regulation is, but on regulation quality. For example, Jalilian et al (2007) show that developing countries with higher regulatory quality grow faster, where regulatory quality is defined as "burden on business via quantitative regulations, price controls, and other interventions in the economy" (where more burden means lower quality - but burden is not the same as having many regulations as one can implement large quantity of well designed regulations that jointly might have smaller burden than few very badly designed regulations).

* Note this research is also summarised in Acemoglu & Robinson: Why Nations Fail? which is book that is written in a way that is more accessible to laymen readers than the papers mentioned above).


What is equilibrium dependent upon in Generalized Second-Price Auctions?

The surplus is the value of the object obtained minus the price paid. In your first example, the surplus would be $10-7 = 3$. The reason why you don't find examples where BOTH players are not using optimal strategies is because $b=v$ is weakly dominant. Unlike a lot of games where you need to consider best response functions, this one can be solved simply by removing dominated strategies.

Using your first example, there exists no bids that will give a higher payoff than $b_i=10$ regardless of what $b_{-i}$. Suppose we look at player 1, then consider all cases:

$b_2 < b_1 < v_1$: surplus is the same as $b_1=v_1$

$b_1 < b_2 < v_1$: surplus is 0, $b_1=v_1$ is profitable deviation

$b_1 < v_1 < b_2$: surplus is the same as $b_1=v_1$

$v_1 < b_1$ surplus is negative or 0 (depending on $b_2$), $b_1=v_1$ is profitable deviation

Also, auctions are usually used for a non dividable object, which means that examples with multiple players with the same value require a tie breaking rule. Whether or not this weak dominance survives depends on this tie breaking rule.


This regression may work. Two issues, however.

How do you identify the "trade costs of war" given that trade and war are potentially endogenous?
Dropping the developed countries, which are the main exporters, may affect the estimates of the bilateral and multilateral trade resistance terms. But this is easy to check by comparing the estimates with and without the main exporters.


How do EMH proponents explain Black Monday (1987)?

Different proponents of efficient market hypothesis  (EMH) will have different explanations because EMH does not say which fundamentals/variables should drive prices. EMH just states that prices reflect avaiable information but it does not say which avaiable information is important and which isn't.
There are actually several versions of efficient market hypothesis  and answer might be slightly different for each of them (in details but not much overall). However, generally speaking efficient market hypothesis is not theory about why market prices fall or go up.
Efficient market hypothesis is a hypothesis about informational efficiency of market. As explained in Miskin & Eakins, Financial Markets and Institutions 8th ed. pp 158 :

Efficient market hypothesis (also referred to as the theory of efficient capital markets) ... states that prices of securities in financial markets fully reflect all avaiable information.

authors further explain:

The efficient market hypothesis views expectations as equal to optimal forecasts using all avaiable information. What exactly does this mean? An optimal forecast is the best guess of the future using all avaiable information. This does not mean that the forecast is perfectly accurate, but only that it is the best possible given the avaiable information.

Consequently, EMH does not say why prices go up or fall. It just says they contain all avaiable information and also refers expectations of future prices and again just says that these expectations will be the best forecasts given all publicly avaiable information. It does not even say these forecasts will be correct as they are just forecasts.
In order to say why prices increase or decrease you would have to combine EMH with some asset pricing theories that actually try to explain stock price behavior. For example capital asset pricing model (CAPM) could be used to explain what drives returns (which are changes in prices) and CAPM can be modeled together with assuming EHM but it can also stand separately. Furthermore, CAPM is just one example of a model that tries to explain asset prices, there are many more and in principle all can be combined with EHM.
For example, Stout (1997) uses EMH together with CAPM to show that in such model stocks might be sometimes undervalued (when there is large amount of uncertainity). So Stout who is proponent of EMH (at least to the extent that he uses it in his research) could say this might be because market undervalued stocks due to uncertainty.  The point here is that in order to know what proponents of efficient market hypothesis think about what caused Black Friday you need to enquire about what asset pricing model they are using. Different proponents of EMH will give you different explanations because being proponent of EMH does not mean you are necessarily 'married' to single asset pricing model. For example, if someone argues stock prices are given by present value of their dividend (something that could hold whether EMH holds or does not hold) would say that Black Friday was caused by expected net present values of dividends dropping and EMH would just state that those expectations were formed by all publicly avaiable information.


Is there contradiction between automation created resilience and the full employment (with high wages)?

There is not necessarily any contradiction. Full employment does not mean every single person in economy is employed. Full employment is (Worswick; 1987):

Full employment does not mean zero unemployment. There can be dislocations where large
numbers of workers are displaced from their present employment, and time is needed before new
workplaces can be created. This can happen at the
end of a war, or following some major technological change. Apart from such special cases, regular
allowance must be made for frictional and seasonal unemployment. Policy would not aim,
therefore, at zero but at the elimination of unemployment attributable to demand deficiency.

So generally speaking the technological change per se might only reduce the rate at which economy will attain its full employment. In addition, the concept of full employment is somewhat vague. In order to make it operational it will often be measured by the non-accelerating inflation rate of unemployment. It is completely possible for NAIRU to become higher as a result of technological change.
Next, automation does not necessarily create unemployment (see Nakamura et al 2018). Automation, can as well increase the number of jobs avaiable through effects on increasing aggregate demand. Of course, it is possible that it would create more unemployment, but empirically that did not happen in economies such as US till now (excluding current pandemic where it is hard to say what unemployment is due to automation and which due to other issues).
There is research that examines impact of automation on resilience of supply chains (see for example Hosseini et al 2020), but there does not seem to be a paper that would look at a tradeoff between resilience and full employment (or at least google scholar search did not show anything up).


Finding Bertrand equilibrium with no demand function explicitly given

This is not a Bertrand equilibrium. Altough both firms set prices and they do so simultaneously, the products are not perfect substitutes because the travel distance differs for most consumers.

What this seems to be is the second stage of a Hotelling model. The usual assumptions are that a continuum of buyers are spread out uniformly along the line and that every buyer's reservation price is very high compared to the transportation cost, so in equilibrium all buyers will be served. The total quantity of buyers may be scaled to one for simplicity.

Given these assumptions you can derive the demand function each firm faces.


How can I control for trade between UK and Australia in my difference-in-difference trade model?

I can’t imagine what dummy could you use there. Here trade is your dependent variable if you would use dummy you would have to switch to some non-linear probabilistic model such as logit or probit.

Most of the time I see papers using just exports from country i to j as proxy for bilateral trade. But there are multiple ways how you could in principle measure it, and it’s not easy to provide some short review of all possible ways. For example, more sophisticated metric would be to measure it in terms of value added like here. It would really depend on exact situation, I would maybe recommend starting with the exports from UK to AU for UK and vice versa for AU and then move onto more fancy measures, it might be good idea to do extensive robustness checks using different possible metrics.


EmpirIcal evidence on effects of price floors and ceilings

There is different evidence for price controls in labor market and different evidence for price controls in general.
Minimum Wage
When it comes to minimum wages there is evidence that they do not cause as much unemployment as was thought in the past. According to the literature review by Neumark & Wascher (2006):

Our review indicates that there is a wide range of existing estimates and, accordingly,
a lack of consensus about the overall effects on low-wage employment of an increase in the minimum
wage. However, the oft-stated assertion that recent research fails to support the traditional view that
the minimum wage reduces the employment of low-wage workers is clearly incorrect. A sizable majority
of the studies surveyed in this monograph give a relatively consistent (although not always statistically
significant) indication of negative employment effects of minimum wages. In addition, among the
papers we view as providing the most credible evidence, almost all point to negative employment
effects, both for the United States as well as for many other countries.

However, at the same time there is evidence that at least some of the negative effects might be due to publication bias (see meta analysis of Doucouliagos and Stanley, 2009) so the problem might be even bit less severe than the above excerpt suggest.
Nonetheless, this is likely due to peculiarity of labor market imperfections. For example, there can be  significant quasi rents that usually go to employers due to their better bargaining position, which means that rising minimum wage would have no effect on employment up to the point that all quasi rents are assigned  the worker and only then it would start to have any employment impact. There are also further reasons for this, since your question is very broad I won't go into details but you can learn more in Borjas Labor Economics about these reasons.
In addition, there are also some further caveats. First,  US (where most of the studies on minimum wage come from) has one of the lowest minimum wages relative to average wages in the world, the employment effects are larger in countries with relatively high minimum wage to average wage ratio.  Second, it might have adverse effect on consumers, Peter Harasztosi and Lindner (2019) for example find that about  75% of effect of higher minimum wage in Hungary was passed onto consumers.
Despite of this it is fair to say that when it comes to minimum wage the effects are not as bad as it was originally thought and they can be even beneficial on net basis if set to appropriate level.
Other Price Controls
When it comes to price controls in general, for example on many goods and services markets the consensus still remains that they reduce overall welfare. There might be some exceptions, it is beyond the scope of economics stack exchange to provide literature review on every single price or category of prices there is, but generally speaking evidence shows that price controls either lead to lower quality of goods or scarcity.
For example, Davis and  Kilian (2011) estimate that price controls in energy prices in US had allocative cost on averaged $3.6 billion annually. This, is just one example of course but generally speaking evidence points relatively large adverse effects in most markets   (e.g. see discussions in Finley and Holt (2019); Glaeser, Edward, and Luttmer (2003); Rockoff 1984; Coyne et al (2015) and sources cited therein).


In the standard competitive-market supply and demand model, the prediction is that, when an above-equilibrium price leads to surplus, prices will naturally fall. You're asking why suppliers don't just sell less at the same price instead, yes?

The basic reason why this doesn't happen is that doing this would require coordination on the part of the sellers, and there are too many of them to all work together.

Imagine, for example, that the equilibrium price is 10, but the current price is 15, leading to a surplus, with $Q_s=20$ and $Q_d=10$.

In your scenario, you end up with sellers agreeing to sell 10 units at a price of 15 each, and no more. However, at this high price, each seller will have an incentive to produce just a little more. One of the sellers, let's call her Jane, will sneak an 11th unit into the market, and either try to sell it as one of the ten units in the market at a price of 15, hoping that one of the other sellers will end up with an un-sellable unit, or Jane will try to take over the market by offering at a slightly lower price of 14 (which she can certainly afford to do - 14 is still much higher than her marginal cost).

For the plan to fall apart, there just has to be one person like Jane willing to work in their own interest against all the other sellers. And since there are by definition many many suppliers in the market, surely there's at least one Jane sitting around drooling at the thought of all those sales.

Most of the sellers would be better off overall if they were able to stick to an agreement to have a high-price and sell a low-quantity (after all, this is basically what monopolies and oligopolies do). But because there are so many competitors, each of whom has an individual incentive to break that agreement, the agreement is going to fall apart, leading prices to drop and quantity-traded to increase up to the equilibrium point.