Two good sources (books preferably) that show the leading and most reasonable arguments for/against "trickle down economics"?

This is a very large subject, where the terms have not even be well defined. I find it very unlikely that you will find an answer. Before even attempting to do so, you should define concisely what is meant by the terms. And particularly, are you talking about stabilization(short run) or structural(long run) economics? Because those two things are entirely different. One strategy is to study the classical and Keynesian schools of economics, since generally it at least to me appears that classical economics is called supply side economics, while keynsians are called demand siders.

Since the question was partly related to a person and not schools of economics, you could define "Reaganomics" as what actions he actually took, and what happened as a result. Upon doing this you will probably find that he wasn't really a strident supply sider in the first place. His strategy seemed to be to reduce taxes and pay for it by taking debt. Since it was not even a recession, this can be hardly classified as an economic policy, but a political strategy. Promise something for nothing and get votes is what seemed to be his plan in light of the data, and it worked as far as politics was concerned (he won twice).


Why are real interest rates so non-volatile compared to investment?

In most countries, interest rates are actively managed by the government or central bank in pursuit of various policy objectives (some closely linked to investment, some, like stable foreign exchange markets, not).  Investment in turn is determined by a wide range of factors other than interest rates.  Basically I don't think that your assumption of a close link is valid.


The classic reference on this topic (as suggested by my professor) is the book;

Theory of Cost and Production Functions by Ronald Shepherd.


Algebraic demand curve in a perfectly competitive market for a firm

If we're considering the canonical case of one firm facing perfect competition, then we're faced with a demand curve (for each firm's goods) that's perfectly flat- regardless of how many units any given firm produces, consumers are willing to pay a certain market price $p$ and no more (all of this is just a restatement of what you've mentioned in the question, of course).

What we can do is then consider how to have a model that incorporates this definition of perfect competition with your given definition of the demand facing firm $i$. As you point out, the derivative of the demand as you've defined it is $\beta$. (Again, all a restatement of what you've pointed out).

The next question to ask, then, is "what is $\beta$?" Effectively, it's the slope of the demand curve each firm faces. If we assume perfect competition, then we assume a flat demand curve, which leads us to conclude that $\beta=0$. I'd suggest that your reasoning didn't go wrong anywhere, just that the two threads need to be directly connected!


Signaling is the informed side taking actions to reduce (or maintain, depending on the private types) the information asymmetry. For example, high skill workers getting certifications to signal their productivity so as earn a higher wage. Or low skill workers trying to mimic the high-skilled's behavior as much as possible so that they cannot be separated.

Screening is the uninformed side taking actions to reduce the information asymmetry. For example, monopolists use price discrimination strategies to identify customers with high vs low willingness to pay and charge them accordingly.


The Ω matrix is the matrix of the variance of the error term for each observation. Since we do not observe the true error term, we cannot find the true Ω, but we can try to estimate it.

There are different ways of estimating Ω, and there is some debate in econometrics as to which method is the best but the most common method I think would be to take the square of the observed error divided by (1-h) where h is the projection matrix of your matrix X.


Very elastic supply + very inelastic demand

Consider the inverse functions

$$Q^d = A-bP$$

$$Q^s = C + dP$$

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

Equilibrium price and quantity are

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

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

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

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

while

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

Comparing the two in absolute terms, we get

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

... from which we conclude:

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

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


Consumer Econometrics: Identifying nature of goods

There are few things that need to be clarified before we want to understand the nature of goods.

First concept is elasticity: which is just change of one variable in response to change in another variable, here increase/decrease in demand for good as a result of change in its price or consumer income.

Mathematically:

Price (point) elasticity: $\varepsilon_{price} = \frac{P}{Q_{d}} \frac{\partial Q_{d}}{\partial P}$

If certain good has $|\varepsilon_{price}| < 1 $, it is inelastic meaning that any change in price will have low impact on your quantity demanded (think about drugs, which are very inelastic). Opposite works for $|\varepsilon_{price}| > 1 $.

Income elasticity: $\varepsilon_{income} = \frac{I}{Q_{d}} \frac{\partial Q_{d}}{\partial I}$

The idea here is the same as in case of price elasticity but now income will have and impact on your demand.

In example you provided the prices are constant, therefore we cannot measure price elasticity of demand. However, it is relatively simple to calculate income elasticity of demand. We can either calculate it by hand or use simple OLS model. For sake of convenience I will use the latter (as it also was what you asked for).

I create simple linear model where my dependent variable is the demand for good x and independent variable is income. The result will be just measuring unit impact. In case you are interested in measuring % change you have to take logarithms on both sides.

$$demand_{i} = \alpha + \beta_1 income_i + \varepsilon_i$$

Good 1 (normal):

            Estimate Std. Error t value Pr(>|t|)
(Intercept)  5.31579   20.82775   0.255    0.841
income       0.03421    0.13674   0.250    0.844

Good 2 (inferior):

            Estimate Std. Error t value Pr(>|t|)
(Intercept) 22.89474    6.24832   3.664     0.17
income      -0.09474    0.04102  -2.309     0.26

As you can see there are only 3 observations so the results are not very robust but should give you main idea. Furthermore, as there is not enough data we can only hypothesize about characteristic of a good, there is more information needed to distinguish between normal and luxury goods.

Nevertheless, current data shows that demand for first good increases as income increases. The case is opposite for the second good.

EDIT: As noted by @luchonacho in order to generalize into income and price elasticity we would have to include price into our regression. The resulting model would look as follows:

$$demand_{i} = \alpha + \beta_1 income_i + \beta_2 price_i + \varepsilon_i$$

Now one has to be careful with interpretation of the coefficients. $\beta_{i}$ shows and effect of 1 unit increase in income\price on the demand for good (elasticity), keeping all other variables constant (ceteris paribus).


How do I best prevent cheating using a credible threat in a two-person, non-cooperative, positive sum game?

There aren't two payoff matrices. If there's a random choice between the two payoff matrices, then the overall payoff matrix will just be a linear combination of the two matrices you've presented, according to the probabilities. For instance, if the probability of getting caught is 10%, then each entry in the overall matrix is .9 times the corresponding entry in the first matrix, plus .1 times the entry in the second matrix. Since the two matrices are identical but for the bottom right, only that square will depend on the probability. If the probability of getting caught is $p$, then the payoff in that square will be $4(1-2p)$. More generally, if they have probability $p$ of getting a fine $f$ instead of the regular payoff, then the overall payoff will be $4(1-p)-pf=4-4p-pf=4-(f+4)p$. As you say, a higher probability of getting caught means less of a fine is required, and vice versa.

You have the payoffs for both players being equal, but suppose the Supplier and Consumer have different expected payoffs for the bottom right, SEP and CEP respectively. For the Supplier, any positive SEP will be an incentive to choose Corrupt. But for the Consumer, they need a CEP>2 to have an incentive to choose Corrupt. So we can remove the Nash Equilibrium by punishing just the Conusmer, and the required probability/size of the punishment for the Consumer will be lower than for the Supplier.

You say that even if you disincentivize the Consumer from Corrupt, the Supplier can go to another Consumer, but if the other Consumer has the same payoff matrix, then from a game theory point of view, as soon as we get a matrix for which the Consumer will choose Honest, the Supplier shouldn't be able to find any Consumer to be Corrupt.

Keep in mind that any game theory analysis will be based on only what's in the payoff matrix, so if there's some phenomenon that you think will affect the result, then for it to be included in the analysis, the payoff matrix needs to reflect it somehow. One way to analyze a party's ability to move on to another counterparty is opportunity costs. Suppose I have a painting, and one potential buyer might pay 100k, while another might pay 90k. You might think that the payoff for getting the first buyer to buy it is 100k, but by selling it to the first buyer, I'm giving up the opportunity to sell it to the second. So making sure the first deal goes through might be worth only 10k to me. Similarly, even if a Supplier gets 2 units of utility for selling something, if they're giving up the opportunity to sell it to someone else, then it might be appropriate to consider their payoff to be less than 2.

Besides subtracting a NE we don't like, we can also look at how we can add one we do like. Currently, the Supplier's choice matter only if the Consumer chooses Corrupt; otherwise, they are indifferent. Thus, the only way to induce them to choose Honest is by changing the payoffs when the Consumer chooses Corrupt. If the Supplier's payoff in the bottom left corner were less than 2, then they would have an incentive to choose Honest when the Consumer chooses Honest. This would make (Honest, Honest) a Nash equilibrium. So if the Supplier had a chance, no matter how small, of being punished every time they choose Corrupt, regardless of whether the Consumer chooses Corrupt, then the upper left would be a NE.

They would then be in a situation where are two NE. They would prefer the bottom right one, while you prefer that they be in the top left. Such a situation is heavily history-dependent: once they're in one NE, getting into another requires coordination. So one strategy would be to first put a lot of effort towards catching and punishing the Consumer, lowering the payoff in the bottom right and eliminating it as a NE. Once they're in the top left NE, you could reduce the enforcement. This would re-introduce the bottom right as a NE, but they would now be in the upper left NE and would have to coordinate getting to the other one. You can then put in some effort into punishing the Supplier whenever they choose Corrupt but the amount of effort to keep that a NE would be less than that need to keep (Honest, Honest) a NE would be less than that needed to keep (Corrupt, Corrupt) not a NE.

An even better solution would be adding a "Snitch" option; if Honest players had the option of snitching on Corrupt ones, and were rewarded for doing so, then that would make Corrupt much less attractive.


GDP Growth QoQ vs YoY: Why do the figures not match?

Because those data are Seasonally adjusted annual rate: https://en.wikipedia.org/wiki/Seasonally_adjusted_annual_rate


In the US, do high wages in regions like New York and California offset the high cost of living?

TL;DR Wages offset the high cost of living in most states.  In NY and CA specifically, wages are insufficient to offset the high cost of living.  In New York City specifically, wages do not even come close to offsetting the high cost of living.

Having now researched this a bit, I can give a very concrete answer to the Lou/Nue hypothetical, and I think a pretty decent answer to the general idea.  Let me just say up front, I am not an economist, I'm taking a best guess based on the data published by real economists.  These are layman's conclusions, and, as BKay pointed out, can't possibly capture the complexity of the real world.  That said...

Nue runs out of money first.  Here's why:

The regional price parity (RPP) in NYC is 136.  That means, a purchase which costs \$100 for an average American will cost \$136 for an average resident of NYC.  The median income in NYC is \$50,711.  This is 97% the national median income.  This means that a days work which pays \$100 for an average American pays \$97 dollars for an average resident of NYC.

The regional price parity in Louisiana is 91.  A purchase which costs \$100 for an average American will cost \$91 for an average resident of Louisiana.  The median income in Louisiana is \$40,462.  This is 77% the national average.  This means that a days work which pays \$100 for an average American pays \$77 dollars for an average resident of Louisiana.

In addition to Lou and Nue, also let us consider Medie.  Medie earns exactly the national median income, and her cost of living is exactly the national average, i.e. RPP = RWP = 100.  (Sidebar: to the extent that such a person exists, they probably live in Pennsylvania, which comes the closest to conforming to both wage and price averages).  So let's compare a hypothetical wage and price for Medie, Lou, and Nue:

Medie earns \$100 per day
Apples cost \$1 each in Medie's home town
Medie can buy 100 apples per day

Lou earns \$77.81 per day
Apples cost \$0.91 each in Lou's home town
Lou can buy 85 apples per day

Nue earns \$97.63 per day
Apples cost \$1.36 in Nue's home town
Nue can buy 71 apples per day

Note, this effect only holds for New York City proper.  If you compare New York State with Louisiana, they are dead even.

To answer the question more generally, all other things being equal it pays to be in a high wage, high cost of living state, though there is major regional variation.  To try and answer this more fully, let's look at the data BKay supplied above, and expand the hypothetical from the original question.  Regional Price Parity data is fairly easy to come by (i.e., "for every dollar spent by an average american, how many dollars must a person from region X spend to get the same result?").  Regional Median Wage data is also pretty easy to come by.  From the Regional Median Wage we can trivially calculate Regional Wage Parity (i.e. "for every dollar earned by an average American, how many dollars can a person in region X expect to earn?").  This is a term I'm making up, so I know it's not exactly scientific, but I think it give a good gestalt for the situation.  This gives us:

$$
\frac{Regional Wage Parity}{Regional Price Parity} = HowMuchStuffYouCanBuy
$$

"How much stuff you can buy" is really the figure that this question is trying to get at.

The state with the highest "apples per day" value is New Hampshire (126) followed by Virginia (123).  As I said, New York and Louisiana do the worst.  DC and Georgia conform exactly to the national average.  Here are these value's graphed:

Note, while local wages seem to predict well for this "how many apples" measure, prices do not seem to predict at all.  Goes to show, cheap != affordable.

Here's the raw data I used for this if you want to play around with it:

+----------------------+-----------------------+----------------------+------------------+
|        State         | Regional Price Parity | Regional Wage Parity | How Many Apples? |
+----------------------+-----------------------+----------------------+------------------+
| Louisiana            | 91.40%                | 77.81%               |               85 |
| New York             | 115.40%               | 99.14%               |               86 |
| New Mexico           | 94.80%                | 83.12%               |               88 |
| Mississippi          | 86.40%                | 77.30%               |               89 |
| Arkansas             | 87.60%                | 78.39%               |               89 |
| Montana              | 94.20%                | 84.35%               |               90 |
| Kentucky             | 88.80%                | 80.21%               |               90 |
| North Carolina       | 91.60%                | 83.45%               |               91 |
| Florida              | 98.80%                | 90.60%               |               92 |
| Tennessee            | 90.70%                | 83.27%               |               92 |
| South Carolina       | 90.70%                | 83.53%               |               92 |
| West Virginia        | 88.60%                | 81.89%               |               92 |
| Nevada               | 98.20%                | 91.10%               |               93 |
| Alabama              | 88.10%                | 83.07%               |               94 |
| California           | 112.90%               | 109.39%              |               97 |
| Arizona              | 98.10%                | 95.31%               |               97 |
| Hawaii               | 117.20%               | 115.16%              |               98 |
| Maine                | 98.30%                | 97.09%               |               99 |
| Ohio                 | 89.20%                | 88.24%               |               99 |
| Delaware             | 102.30%               | 101.61%              |               99 |
| District of Columbia | 118.20%               | 118.01%              |              100 |
| Georgia              | 92.00%                | 92.23%               |              100 |
| Indiana              | 91.10%                | 91.93%               |              101 |
| Michigan             | 94.40%                | 96.26%               |              102 |
| Oklahoma             | 89.90%                | 91.71%               |              102 |
| Idaho                | 93.60%                | 95.86%               |              102 |
| Pennsylvania         | 98.70%                | 101.48%              |              103 |
| Illinois             | 100.60%               | 103.93%              |              103 |
| Texas                | 96.50%                | 100.33%              |              104 |
| Vermont              | 100.90%               | 105.73%              |              105 |
| Oregon               | 98.80%                | 103.97%              |              105 |
| Kansas               | 89.90%                | 96.16%               |              107 |
| Rhode Island         | 98.70%                | 106.07%              |              107 |
| Missouri             | 88.10%                | 95.00%               |              108 |
| New Jersey           | 114.10%               | 124.36%              |              109 |
| Alaska               | 107.10%               | 118.71%              |              111 |
| South Dakota         | 88.20%                | 98.39%               |              112 |
| Wisconsin            | 92.90%                | 104.50%              |              112 |
| Washington           | 103.20%               | 116.72%              |              113 |
| Wyoming              | 96.40%                | 109.30%              |              113 |
| Colorado             | 101.60%               | 116.78%              |              115 |
| Iowa                 | 89.50%                | 103.26%              |              115 |
| Massachusetts        | 107.20%               | 123.79%              |              115 |
| Nebraska             | 90.10%                | 105.34%              |              117 |
| Connecticut          | 109.40%               | 128.66%              |              118 |
| Utah                 | 96.80%                | 115.15%              |              119 |
| North Dakota         | 90.40%                | 107.59%              |              119 |
| Minnesota            | 97.50%                | 117.62%              |              121 |
| Maryland             | 111.30%               | 134.28%              |              121 |
| Virginia             | 103.20%               | 126.95%              |              123 |
| New Hampshire        | 106.20%               | 133.56%              |              126 |
+----------------------+-----------------------+----------------------+------------------+

Sources:
Wage data (Direct XLS Download)
Price Data (PDF)


How do small firms survive in an oligopoly?

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


How does price fixing work if it requires an almost universal agreement?

In the real world, "price fixing" is very difficult to accomplish.  In most industries, it would be very easy for a new seller to enter the market and offer their goods at the lower price, stealing the customers from the "price fixing" sellers.  For these sectors of the economy, "price fixing" is not an option unless the "price fixing" sellers can convince/coerce any entering sellers to commit to the existing fixed price.

Ordinarily, "price fixing" occurs in industries with either a monopoly or an oligopoly.
In a monopoly, there is only one seller.  So, they alone are able to dictate the price of the good or service.
In an oligopoly, there are only a few sellers.  These few sellers can easily conspire with each other to elevate the price.  However, even then, there is always the danger that one of the sellers will eventually drop their prices and try to steal the consumers from the other sellers.


How do we find a competitive equilibrium price when 2 firms operate with different marginal costs?

Ignoring the previously mentioned possibility that the problem may be written incorrectly: The concept of "residual demand" will be helpful here.

As with any sequential game, it's good to work backwards. From the perspective of firm 2, firm 1 has quoted some price $p_1$, and firm 2 has an opportunity to respond.

Firm 2 knows that if it sets $p_2<p_1$, it will take the whole market, and will face the whole demand curve $Q = 30-p_2$. It can choose the profit-maximizing $p_2$, as long as $p_2<p_1$.

Similarly, if it sets $p_2=p_1$, it will share the market.

Finally, if it sets $p_2 > p_1$, it will face the residual demand left over after firm 1 makes its sales. Assuming that $p_1\leq 25$, firm 1 will sell its five units and then not be able to sell any more. The demand left over for firm 2 to sell to after firm 1 makes its sales will then be $q_2=30-p_2-5$, or $q_2=25-p_2$. Firm 2 can choose its profit-maximizing price given this demand curve.

In each of these cases above, Firm 2 is selecting the profit-maximizing quantity by first setting up profit:

$$\Pi_2 = p_2q_2 - 6q_2 = (p_2-6)q_2$$

Plug in the appropriate $q_2$ using the demand functions determined above, then take the derivative with respect to $p_2$ and set the derivative equal to 0, solve for $p_2$. In each case you're constrained by what $p_2$ can be. If you're working with the $Q=30-p_2$ demand function (which you only get if $p_2<p_1$), then if profit-maximizing price is $p_2>p_1$, then you'll actually want to set $p_2$ just a hair underneath $p_1$ (you can just call it $p_2=p_1$ for simplicity).

Now you've got the optimal price for Firm 2 to pick given that it's decided to go for $p_2<p_1$, $p_2=p_1$, or $p_2>p_1$. To figure out which of those three it wants, you'll want to calculate Firm 2's profit under each of those scenarios. These profits should be dependent on $p_1$, since $p_1$ determines the boundaries of what $p_2$ can be while still satisfying $p_2<p_1$, $p_2=p_1$, or $p_2>p_1$.

So now Firm 1 knows how Firm 2 will respond to whatever $p_1$ is. And so Firm 1 will set $p_1$ in a way that maximizes Firm 1's profit. This step is a bit easier, since Firm 1 makes nothing under $p_2<p_1$, so it's unlikely that Firm 1 will want to set $p_1$ so that Firm 2 picks $p_2<p_1$.

To make this a bit more clear, let's do an example for Firm 2 making their decision.

Let's say Firm 1 had picked $p_1=10$.

If Firm 2 sets $p_2<p_1$, it is dealing with the demand function $$q_2 = 30-p_2$$. So we set up profit

$$\Pi_2 = (p_2-6)(30-p_2)$$
$$\frac{\partial \Pi_2}{\partial p_2} = 36 - 2p_2 = 0 \Rightarrow p_2=18$$

which is above $p_1=10$. Since profit is strictly increasing in $p_2$ for $p_2<10$, firm 2 will maximize its profit while holding $p_2<p_1$ by setting $p_2=10$ (a hair below 10, really, but let's just say 10). The profit from doing so is

$$\Pi_2 = (10-6)(30-10) = 80$$

And, of course, Firm 1 sells nothing and makes a profit of 0. Now if Firm 2 sets $p_2>p_1$, it's dealing with the demand function

$$q_2 = 25 - p_2$$

and wants to maximize profit

$$\Pi_2 = (p_2-6)(25-p_2)$$
$$\frac{\partial \Pi_2}{\partial p_2} = 31 - 2p_2 = 0 \Rightarrow p_2=15.5$$

which is above $p_1=10$, satisfying $p_2>p_1$. This price leads to the profit

$$\Pi_2 = (15.5-6)(25-15.5)=90.25$$

In this case, Firm 1 sells their five units and makes a profit of $(10-3)5=35$.

You will also want to check the $p_2=p_1$ case once it's clear what that actually leads to.

And so, if Firm 1 sets $p_1=10$, Firm 2 will want to set $p_2=15.5$, since a profit of $90.25$ is better than a profit of $80$.

This example is worked out with a specific $p_1$, and this particular $p_1$ makes Firm 2 not undercut Firm 1. The next step is to find out what the highest price that Firm 1 can set without getting Firm 2 to prefer undercutting. This will be $p_1$ in equilibrium, and Firm 2's best response to that $p_1$ will be $p_2$ in equilibrium.


It's from King and Rebelo (2000) "Resuscitating Real Business Cycles". Here is a link to the NBER working paper version. The graph is in Figure 8 on p.94.


Why don't economists recommend voluntary childlessness to fight poverty?

Despite the initial shock value provided for the question, and the high possibility for this question to become heated, political, or otherwise delve into an off-topic conversation, I will do my best to provide an answer to this question.

  Voluntary childlessness would be a functionally ineffective suggestion. This is not only too vague a suggestion to be widely useful or create policy for, but there are better focuses for economists to study in order to fight poverty.

If adults are practicing female infanticide for cultural or economic reasons, would these adults seriously consider simply not having children if you ask them? If adults are withholding post-natal care in particular circumstances, then how is this an economic failure rather than a moral one? If we are focusing on the family unit, and argue that every family has its own smaller market economy in who provides what sort of labor for the family, then shouldn't we argue that each family economy should be informed on how to make better choices, and be restricted from making unethical choices such as murder?

In some cases, maybe a family might consider not having kids if they can't support them. The consideration for whether someone will have a reasonable quality of life of course is subjective. In some parts of America there is extreme poverty, same as there is in India or China or many other countries. Yet happiness or "utility" has always been a subjective experience, and families continue to have children in these conditions.

Consider this statement from Indian economist and Nobel Prize winner Amartya Sen:

  "There is considerable empirical evidence that even as people in many parts of the world have become richer, with much more income to spend in real terms than ever before, they have not felt particularly happier than before.1 "

As with all things this may not be universally true. Some studies find suicide rates are not sensitive to income or unemployment. 2 But what is a bad living standard for some is not an insurmountable living standard for others. Is it wrong for people to bring children into the world where they must overcome suffering? Answering this question requires imposing a hard standard for what standard of living is a basic right, which frankly, is not the intellectual right of economists over everyday people.

Responsible economists, if looking at this issue, would rather prevent the miniature market failures within the family unit. Sometimes, trying to make policy that greatly restricts choice at the small scale would be impractical, or too prohibitive to be ethical, as economists generally like to allow for individual freedoms. So economists tend to look at broader policy through taxes or social welfare programs to combat poverty. One thing that is clear is that to prevent the most egregious consequences of poverty, there must be a way to hold those accountable who commit atrocities such as female infanticide or other such actions.

  "It was mentioned in the last chapter that no major famine has ever occurred in a functioning democracy with regular elections, opposition parties, basic freedom of speech and a relatively free media (even when the country is so poor and in a seriously adverse food situation)....Despite China's greater economic success than India's in many economic fields, China - unlike independent India - did have a huge famine, indeed the largest famine in recorded history, in 1958-61, with a mortality count estimated at close to 30 million. Though the famine raged for three years, the government was not pressed to change its disastrous policies3"

If transparency and public accountability are required to prevent and act on national tragedies that greatly reduce welfare, then on the smaller scale, the culture within a community is what will determine whether poverty or crises of resources will be answered with some sort of aid or assistance, or whether they will be answered with more drastic measures.

One cannot ignore in this conversation that many modern economies actively encourage population growth. As mentioned above in the comments, some places like Communist China had a one-child policy to restrict population growth. That policy has been repealed in the face of the changing demographics that China is undergoing, where there will be a much larger proportion of older people who live longer. The one child policy was a contrived way of dealing with issues like food shortages. Because the government tried to completely control markets, they created weird market failures and dealt with them in ways that were clearly detrimental.

Does this mean policies such as giving tax breaks to those who marry or giving welfare based on household size are bad policies? Is there moral hazard in subsidizing child creation in some sense? First off, why do these policies exist? An economy can grow both with the creation of technology, and the creation of capital and labor which pair together at some "efficient" ratio, depending on the market. To perhaps oversimplify, growing labor is one of the ways of growing an economy and trying to keep it productive and competitive with other countries.

Thus, economists should study how welfare programs for families affect the incentives families have for working or having children, etc. Which they already do. A cursory search of the literature:

Maru, Rushikesh M. "Incentives and disincentives in the Indian family welfare program." Studies in family planning 17, no. 3 (1986): 136-145.
Knox, Virginia W., Cynthia Miller, and Lisa A. Gennetian. Reforming welfare and rewarding work: A summary of the final report on the Minnesota Family Investment Program. Vol. 8. New York: Manpower Demonstration Research Corporation, 2000.
Keane, Michael, and Robert Moffitt. "A structural model of multiple welfare program participation and labor supply." International economic review (1998): 553-589.
Dahl, Gordon B., Andreas Ravndal Kostøl, and Magne Mogstad. "Family welfare cultures." The Quarterly Journal of Economics 129, no. 4 (2014): 1711-1752.
Schoeni, Robert F., and Rebecca M. Blank. What has welfare reform accomplished? Impacts on welfare participation, employment, income, poverty, and family structure. No. w7627. National bureau of economic research, 2000.
Lundberg, Shelly, and Robert D. Plotnick. "Adolescent premarital childbearing: Do economic incentives matter?." Journal of Labor Economics 13, no. 2 (1995): 177-200.

At the end of the day, economists are not concerned necessarily with changing the minds of individual family members and encouraging them to not have children. A family may not even find this "optimal", as children are a source of not just future support into old age, but of companionship in a harsh world (and other non-pecuniary incentives). Energy is better directed at guiding the hand of government towards policy that can effectively alleviate poverty and increase the welfare of society as a whole.

Additional citations:

1 Sen, Amartya Kumar. The idea of justice. Harvard University Press, 2009. 272.
2 Andres, Antonio Rodriguez. "Income inequality, unemployment, and suicide: a panel data analysis of 15 European countries." Applied Economics 37, no. 4 (2005): 439-451.
3 Sen, Amartya Kumar. The idea of justice. Harvard University Press, 2009. 342.


What accounts for the high GDP of the United States?

Looking at gross output (which includes using the outputs of other industries) and value-added (largely wages and profits) by industry you get numbers like this for 2017 in USD trillion.

Adding up the value-added gives total GDP, and you can see that there is a lot more to the economy than manufacturing

                                                         Gross output  Value-added
Agriculture, forestry, fishing, and hunting                       0.4  0.2
Mining                                                            0.5  0.3
Utilities                                                         0.4  0.3
Construction                                                      1.5  0.8
Manufacturing                                                     6.0  2.2
Wholesale trade                                                   1.7  1.2
Retail trade                                                      1.8  1.1
Transportation and warehousing                                    1.1  0.6
Information                                                       1.7  0.9
Finance, insurance, real estate, rental, and leasing              6.2  4.1
Professional and business services                                3.8  2.4
Educational services, health care, and social assistance          2.8  1.6
Arts, entertainment, recreation, accommodation, and food services 1.4  0.8
Other services, except government                                 0.7  0.4
Government                                                        3.7  2.5

Total                                                            33.7 19.4


Why salaries counted under Government expenditure in GDP

The expenditure measure of GDP counts final expenditure, i.e. consumption by individuals and government and foreigners (exports) plus all capital formation (i.e. investment), and then subtracts imports since that part of final expenditure is not satisfied by domestic production.

The salaries of government employees count as government consumption in the same way as the government's purchase of services from private companies also count as government consumption.  So the effect of paying for this work is the same whether the individuals are employees or contractors.


There’s two things of interest: interest rate risk, and liquidity risk.

For liquidity risk, you could compare short-term liabilities to short-term assets. This would be just a ratio. The long-term buckets (1-5) and (5+) aren’t going to add much information. Banks are in the business of rolling over 1-5 year term deposits, so that bucket will always be big. And since bank loans are often amortising, while the deposits have a bullet maturity, the mismatch between a 5-year deposit (bank liability) and a 10-year loan (bank asset) is much smaller than the maturity date suggests. This is why I would just look at ratios with the mid-long buckets merged.

For interest rate risk, the duration gap is what matters (plus interest rate shock simulations; see below). (Although I write duration, that is just habit. Technically, you need something like a DV01: how much money is gained/lost on a 1 basis point rise in yields? This can be inferred from an estimated duration.)

A part of the question is unclear - you are looking at a financial report of a real world bank? There might be a memo item buried in the notes on the financial statement that gives the exact mismatch. The bank and the regulators know what the mismatch is, it is unclear whether that is public information. Since it is sensitive commercial information, it is highly possible that the net duration information is not public. (I obviously do not know.)

You could try approximating the duration for each bucket of assets and liabilities, and then add them up. The problem is that this answer could easily be wildly incorrect, and the exercise is probably a waste of time.

It ignores the optionality of mortgages (for a US bank). So straight duration is somewhat misleading, you also need to look at large shifts in the yield curve (which is another standard stress test applied by regulators and the bank’s risk management.)
A bank can own or issue long-term floating debt. So even if the maturity is 10 years, the duration is at money market length.
It ignores the fact that banks use interest rate derivatives (swaps) to hedge their duration risk.

If you dig into the regulator’s documentation (obviously depends on the bank’s jurisdiction), they should publish the risk limits for interest rates that they allow. Obviously, the bank’s internal models will give a number within the limits, as even the most incompetent regulator would notice a deviation. It may be that the bank has some exotic interest rate risk that does not show up on those stress tests, but you would never know by looking at public information anyway.


Neo Keynesian Modelling and the Lucas Critique

Before gravity was conceived as a physical phenomenon and studied by Isaac Newton, gravity was not microfounded. So before Newton, modelling the real world should assume away gravity, because it was not microfounded. We should instead create models into which humans could walk on air.

When a phenomenon appears stable, while attempting to understand and decipher it (to micro-found it), we should be wise enough to accept its existence and include it in our models, of course in an "ad hoc" manner since we haven't decipher it yet.

Whether firms "cannot" or "choose optimally not to" change their prices everyday, makes little difference, as long as we haven't settled on the optimization framework into which such an optimal choice could come about. It makes little difference because in the absence of knowledge it can be seen as a semantic issue: I can re-interpret "cannot" as "an optimizing agent cannot do what is suboptimal -it goes against every inch of its existence".

Nevertheless, bashing for micro-foundations of an observed regularity (and it is a prevailing observed regularity across time, space, cultures and economic systems that firms don't changes their prices continually), is a good thing, in that it keeps up the pressure to finally find those microfoundations.
I just hope the bashers don't argue in addition, that in the meantime, we should only be modelling people as walking also on air -sorry, be modelling firms only as being able to change their prices continually.

And to send the ball back, I have never seen in my life any convincing "micro-foundation argument" for the assumption that prices are perfectly elastic.


Determining the elasticity of a supply/demand curve visually

Generally speaking it is not possible to tell if demand/supply is elastic/inelastic just by looking at steepness (although there are some exceptions).
Rigorously, the price elasticity of supply/demand is given by:
$$EL=\frac{\frac{\partial Q}{Q}}{\frac{\partial p}{p}}= \frac{\partial Q}{\partial p}\frac{p}{Q}$$
The slope of demand/supply curve will be given by $\frac{\partial Q}{\partial p}$ so looking at the slope can only tell you whether the first term is high/low but it does not tell you what the second term is $p/Q$. Consequently, generally speaking it is not possible to tell what the elasticity of supply/demand is just from the picture.
This is further complicated by the fact that what matters is the slope of the demand/supply function $\frac{\partial Q}{\partial p}$, but typically what you see on picture is not a demand/supply function but inverse demand/supply function, because by convention we plot price on $y$-axis, so what you see is not $Q(p)$ but $p = f^{-1}(Q)$.
This holds especially for linear supply/demand curves. For example general linear demand is given by:
$$Q = - a p + b$$
(where $a$ is the slope) hence general price  elasticity for demand curve would be:
$$EL= -a \left(\frac{p}{-ap+b}\right)$$
(general formula for linear supply would be almost identical except $a$ would be positive) so as you can see above for linear function the price elasticity with change with price, and consequently knowing slope (steepness) will not help you to know whether the demand is elastic or not. For example, suppose that the slope is $-10$ (which is quite steep), then $\frac{-10p}{-10p+b}$ can still turn out to be less than 1. For example, for $p=0$ the elasticity here would also be zero.
There are some exceptions though. If the whole supply/demand is horizontal flat (as judged when looking at plot of $p=f^{-1}(Q)$ which means that $Q(p)$ is vertical) then we know that slope is infinity. Since, infinity multiplied by any scalar is still infinity we know that in this case the elasticity will be infinite (i.e. such supply/demand will be perfectly elastic) even just by looking at the picture.
Similarly, if the whole supply/demand is vertical (as judged when looking at plot of $p=f^{-1}(Q)$ which means that $Q(p)$ is horizontal) we know that the slope of demand/supply curve will be zero. Since anything multiplied by zero is still zero the whole elasticity will be zero in such case (i.e. such supply/demand will be perfectly inelastic).
Consequently, save for special cases it is not possible to know if a demand/supply is elastic or inelastic just by looking at a steepness of a slope. This is especially true for linear demand and supply where elasticity will range from $0$ to $\infty$ as price change along the demand.

Even more confusingly, I read from some sources that any supply curve that is upward sloping from the origin has a constant unitary elasticity regardless of the value of the slope of the supply curve.

This is true because a linear supply curve that goes through origin is generally given by $Q_s= ap$ which implies that elasticity is:
$$EL_{Q_s} = a \frac{p}{ap}=1$$
This actually holds also for linear demand function passing through origin since general linear demand that passes through origin would be given by $Q_d=-ap $ so the elasticity is:
$$EL_{Q_d} = -a \frac{p}{-ap} = 1$$
So this is another special case where you can exactly tell what a demand or supply elasticity is just by looking at it.


Is there a correlation between pharmaceutical prices and drug dealers?

Direct correlation seems unlikely. You would probably have to control for population or even better, population density. Leaving prices unchanged a city with ten times the population can support ten times as many drug dealers. Differences in average income levels would present a similar problem.

Finding reliable data, such as number of drug dealers and a good measure of price levels will be a challenge as well.


What are the most used approximations in economics?

There are four categories of approximations used in economics.  Unfortunately, none of them are economic approximations, but rather mathematical or statistical approximations.  As such, they do not appear in the economic literature, so much so as in the mathematical literature.  You are not seeing in the economic literature because students should be exposed to the content by mathematicians.

The difficulty comes from the type of math used in economics.  There are two ways you could look at calculus.  One is that it is the study of change.  The other is that it is the study of approximations.  All of calculus is a set of approximations, though if you will mentally agree that $\lim_{n\to\infty}\frac{1}{n}=0$ then you can get "exact" answers.  Imagine, however, that the smallest unit is a penny, then you cannot go to zero and now you have an approximation if a penny is the smallest possible size.  The question economists have to answer within the profession is whether or not the difference has a large enough impact to matter.

It is rare in economics for anything to be anything except an approximation.  There are some categories though to these approximations.

The first category can be thought of as either equilibrium approximations or local approximations.  Mathematicians would use the phrase "local approximations."  The main one of these is the Taylor expansion, though there are others.  In classes, I have to be very careful when I teach undergraduates because they often substitute their own mental approximations for the actual ones in work.  While it is wonderful that they are trying to work problems through from first principles, its usually the ones who didn't study the answer in the book and who are panicking.

The second one can be thought of as functional approximations.  The actual functions in the real world are discrete and usually created by the separate functions of many different firms.  While there are certain mathematical properties created by the topology of the problem.  We know that certain types of problems are forced to have a certain general form, but the specific form will be unique to the real world problem.  As an example, a taxi company needs one driver per cab.  If you add cabs but no drivers then no revenue gain is created.  Likewise, if you add cab drivers but no cabs, you get not revenue gains.  Indeed, in both cases you can take losses from paying the cabies and the costs for the cabs such as insurance.  So the production function, which is a Leontief production function is assumed to be present almost all the time, ignoring cabbies who quit, or wrecked cabs resulting in a temporary mismatch between workers and cabbies.

There is also the issue that utility functions are ordinal and any function that preserves preference ordering is equally valid.  This is not an approximation so much as an arbitrary choice for convenience.

The third category could be thought of as model approximations.  For example, using game theory, is an arbitrary choice as a way to model something.  The use of a general equilibrium method versus a model that is sub-game perfect will create different approximations in the end.  Of course the goal is for empiricism to judge between the modeling methods, but for your purposes they should both be thought of as approximations.

Finally, all of statistics is a form of approximation.  The danger is to believe statistical models and all economic models are statistical models.  They can be excellent or poor.  Statistical significance is not enough, it needs economic significance, that is "what is the effect size."  Likewise, how sensitive is the statistical model to the data and to reality.  You can easily create a statistical model that is not at all robust.  That will make your approximations very fragile.

There isn't a list.  The most common are Taylor expansions, finding the slope, $\hat{\beta}$ in models as an approximation of the derivative, and production functions.  The best way to tell you are dealing with an approximation will always be seeing $\Delta$ in a problem.  If you see $\Delta$ then you are dealing with an approximation of $\mathrm{d}$.  Although $\mathrm{d}x$ is really an approximation of $\Delta{x}$, economics always solving inverse problems so in economic practice $\Delta{x}$ is an approximation of $\mathrm{d}x$.


Is there any work on equality in a market versus friction?

The key theoretical work, at least in the area of education, comes from Milton Friedman and his "Theory of School Choice". Important references are:

Friedman, M. (1962), The Role of Government in Education. In Capitalism and Freedom. Chicago: University of Chicago Press.
Friedman, M. and Friedman, R. (1980). Free to choose. New York: Harcourt
Brace Jovanovich.

Check here for a not so old review of the literature on School Choice. Here is an interesting analysis of the Chilean education system, in the light of Friedman's ideas. Friedman had the idea that competition would increase quality across the whole spectrum of schools:

the quality of    all    schooling    would    rise    so    much    that    even    the    worst,    while    it    might    be
relatively    lower    on    the    scale,    would    be    better    in    absolute    quality”    (Friedman    and    Friedman 1980,    170)


How can one compute the CPI All items index from the component indexes?

I'm afraid that with the information you state, this is impossible.

Say there are three items in the CPI: housing, food, and energy. Define the weight of each component in total CPI, weight which can vary over period, as $w_{h,t}$, $w_{f,t}$, and $w_{e,t}$ respectively. By definition, they add up to 1. Similarly, define the CPI series of each item as $P_{h,t}$, $P_{f,t}$, and $P_{e,t}$ respectively.

The CPI index for all but energy goods, $P_{hf,t}$ is given by:

$$ P_{hf,t} \equiv \frac{w_{h,t}}{w_{h,t}+w_{f,t}}P_{h,t} + \frac{w_{f,t}}{w_{h,t}+w_{f,t}}P_{f,t}$$

Although you know $P_{hf,t}$, you do not know any of the other 4 terms, for each period. As such, this is an undetermined system. In the case of a CPI with $N$ items, the system has $2(N-1)$ unknowns.

If weights are constant, you cannot get much further either. Say that you have $T$ number of periods. Then, you have a system of equations like

$$ A_{t} = bX_{t} + cY_{t} $$

where only $A_{t}$ is known. This is also undetermined. You can only write $X_{t}$ as a function of $Y_{t}$, $b$ and $c$. (and viceversa).

A second best approach?

You have one option though. You could compute the "vector distribution" of the all-CPI index. To see this, notice that the total price index, $P_{t}$ is

$$ P_{t} \equiv w_{h,t}P_{h,t} + w_{f,t}P_{f,t} + w_{e,t}P_{e,t} $$

This is equal to

$$ P_{t} = (w_{h,t}+w_{f,t})P_{hf,t} + w_{e,t}P_{e,t} $$

But weights add up to one. Therefore,

$$ P_{t} = (1-w_{e,t})P_{hf,t} + w_{e,t}P_{e,t} $$

Or better:

$$ P_{t} = P_{hf,t} + w_{e,t}(P_{e,t}-P_{hf,t}) $$

Now, since you know the CPI index for energy-only ($P_{e,t}$) and for all-but-energy ($P_{hf,t}$), you could compute $P_{t}$ for a given assumption on the energy weight on total CPI. You can, for instance, look into other similar countries and see how much this weight is. Or look for related information on this respect. This number cannot be wildly different across countries. So you can still get a rough idea of general CPI.


Foreign produced goods will see price increases directly as a result of the tariff, which adds to the prices of these goods.  The full tariff may not be passed through, as these higher prices will reduce demand, changing the supply/demand balance

Domestically produced goods will usually see price increases indirectly as a result of the tariff, as demand for these domestically produced goods will increase as a result of the weaker competition from foreign produced goods, assuming an upward sloping supply curve

Your quotes translate these likely price effects from tariffs into "inflation pressure"


Firm $i$'s profits $(\pi_i)$ as a function of its own price $(p_i)$ and the other firm's price $(p_j)$ are as follows :

\begin{eqnarray*} \pi_i(p_i, p_j) = \begin{cases} (p_i-200)\min(1000- p_i, 300) & \text{if } p_i < p_j \\ (p_i-200)\min\left(\frac{1000- p_i}{2}, 300\right) & \text{if } p_i = p_j \\ 0 & \text{if } p_i > p_j\end{cases}  \end{eqnarray*}

, $i, j \in \{1,2\}$ and $i \neq j$.

We now find the best response correspondence of firm $i$ $(\text{BR}_i(p_j))$ by solving the following problem
\begin{eqnarray*} \max_{0 \leq p_i \leq 1000} & \ \ \pi_i(p_i, p_j) \end{eqnarray*}

and we'll obtain

\begin{eqnarray*}
\text{BR}_i(p_j) = \begin{cases} \{700\} & \text{if } p_j > 700 \\ \emptyset & \text{if } 400 < p_j \leq 700 \\ \{p_j\} & \text{if } 200 < p_j \leq 400 \\ \{p : p \ge 200\} & \text{if } p_j = 200 \\ \{p : p > p_j\} & \text{if } p_j < 200\end{cases} \end{eqnarray*}

$(p_1^*, p_2^*)$ is a Nash equilibrium of this game if it satisfy $p_1^* \in \text{BR}_1(p_2^*)$ and $p_2^* \in \text{BR}_2(p_1^*)$. This yields the following set of Nash equilibria :

$\{(p_1^*, p_2^*) : 200 \leq p_1^*=  p_2^* \leq 400\}$

i.e., any action profile where both firms charge the same price, and that price lies in the interval $[200, 400]$ is a Nash equilibrium of the game.


What's the role of money multiplier in the banking system?

At present, this question resembles three questions.

Are people on the internet saying incorrect things about bank money creation?
Is money creation by banks fraudulent?
Is money creation by banks limited by the fact that deposits are bank liabilities?

These are questions that mainly do not fit the desired format of this website, so I will handle them very quickly. If there are follow up questions, it might be best to create a new narrow technical question.

I would argue that bank creation of money has led to a lot of incorrect statements about it on the internet. Unless a particular statement is to be analysed, there is nothing else to say.
The belief that bank lending is fraudulent money creation show up in some popular Austrian economics writing. The answer requires delving into the definition of “fraud.” It is safe to day that no legal system accepts that view, as that would imply that a significant portion of the financial system would lose legal backing.
Yes, the fact that bank deposits are liabilities limits bank money creation. It is not the same thing as creating counterfeit banknotes, which are not liabilities.


Differences between international and national creditors

I think it's going to be hard to compare the price for a country with a large internal creditors and another one without, as such a price depends on many parameters apart from that.

But to answer the core of your question, it does have an influence. In many European countries, the public debt is considered a huge problem since the 2007-2008 crisis at it reaches the 100% of GDP. And it is a problem because, those countries have to spend a huge amount of the GDP to pay back that debt, with interests. They can't default without having much higher prices (see Greece, Spain or Italy around 2010). The 100% of GDP is a virtual barrier that is considered critical by many investors or specialised press.

In contrast, a country with a large part of national creditors, Japan, currently run with 217% of its GDP debt. Yet the market for the government bonds in Japan is quite stable.

This might crudely be explained by a link between the two elements of the debt. National have all interests that their own government functions. If their own government has money, they can invest in their economy, which profits directly the investors. If the investors are abroad, they would be less affected by a slow down or a crash or the economy, and thus ask for higher prices to compensate for the risk of defaults.


Looking for an article in Behavioral Economics about Inequality

Although your description is very detailed, there is plenty of research on this topic. I think you are looking for this current published paper:

Starmans, Christina & Sheskin, Mark & Bloom, Paul. (2017). Why people prefer unequal societies. Nature Human Behaviour. 1. Article number 0082. doi:10.1038/s41562-017-0082.

This paper covers the latest research about inequality. If its not the specific one you are searching for, please look at its 102 references and let us know.


Does elasticity vary along the Demand/Supply curve or is it a summary statistic of a curve?

Yes, elasticity varies along a curve. No, elasticity is not a summary statistic of a curve.

Definition. The elasticity of demand, $Q_D$, with respect to price, $P$, (or price elasticity of demand) is defined as this number: $$\frac{\partial Q_D}{\partial P} \div \frac{Q_D}{P}.$$

Example. Suppose $Q_D = 100 - P$. Then the price elasticity of demand (PED) is $$\frac{\partial Q_D}{\partial P} \div \frac{Q_D}{P}=-1\div\frac{Q_D}{P}=-\frac{P}{Q_D}=-\frac{P}{100-P}.$$

  More specifically, one of my lectures gives Elasticities of various items such as 0.09 for Gasoline and 0.8 for soda drinks. Are these values just taken on a specific point?

Yes. Elasticity estimates are usually point estimates.

Note though that sometimes they're some sort of a mean or average estimate. (In such cases anyone reporting such estimates should be very careful about how exactly these estimates were defined.)

  If yes, how can they be used to describe the complete curve of a specific item.

You're right. They don't describe the "complete curve".

Note. With soda, prices probably don't fluctuate too much. So elasticity estimates are probably reliable.

In contrast, with gasoline (or more generally energy), we have to be more careful. Indeed, there's an extensive literature on this topic with estimates all over the place.

Here for example is a table from a recent meta-analysis (Labandeira, Labeaga, and López-Otero, 2017) where ranges of elasticities from various studies are reported:


Is skills or abilities of the worker taking in consideration in Marx law of value?

Labour power is a commodity like any other. Its value is consequently a function of the labour embodied in it.

Taking your example,

product A (a webpage)
takes 10 hours
you need special skills (those of a webdesigner) that are hard to learn
only 14% of population already have those skills to build that
product

Versus

product B (a chair)
takes 10 hours
you do not need special skills (you do; those of carpenter. But those are easier to learn, compared to those of a webdesigner)
90% of the people (probably an exageration, but certainly more people have the skills of a carpenter than those of a webdesigner) already have those skills to build that product

A value = B value ?
the chair value = the web site value?

No.

While each of them requires 10 hours of labour, the labour embodied in each has a different value.

The labour of the webdesigner is more valuable.

Why?

Because it takes - say - 1,000 hours of labour to turn an unskilled labourer into a webdesigner, while it takes - say - 200 hours of labour to turn an unskilled labourer into a carpenter.


Impact of Natural Disaster on Production Function

Suppose the Cobb-Douglas production function is $Y = AK^{\alpha}L^{\beta}$, and the effect of the disaster is to reduce $K$ from $K_0$ to $K_1$. If any change in $A$ and $L$ is insignificant, then you can look at this in two ways:

Focusing on a partial production function in terms of $L$ only (that is, treating $A$ and $K_i$ as fixed parameters in the short term), there has been a change from $Y=AK_0^{\alpha}L^{\beta}$ to $Y=AK_1^{\alpha}L^{\beta}$. With $K_1<K_0$, that implies a shift downwards, with labour productivity having decreased.
However, the full production function in terms of $K$ and $L$ is unchanged, and there has been a movement on the surface defined by the function. If the function were plotted in three dimensions, with $K$ and $L$ on horizontal axes and $Y$ vertical, then this would be a movement downward (and along the $K$ dimension).

These are both valid ways of describing the situation: which is more useful would depend on what you are trying to do.

One caveat. Although production functions often suggest otherwise, labour is not homogeneous. Even if only a few people are killed, the effect on production could be significant if those people happen to have key skills that are in short supply, or knowledge the loss of which would affect the technological level.


Why can an increase in inflation rate, increase interest rates?

In a free currency exchanges market, the central bank defined goal, in the general case, is to maintain price stability and inflation rate restrained, that is to keep inflation positive but at a low rate,
In order to encourage economic activity

Inflation can be manipulated by the amount of money - more money in the system, the lower its value, and higher prices respectively, and vice-versa.

The amount of money is manipulated by the central using interest rates: higher interest rates encourages deposits in banks and discourages taking loans, both actions leading to less money in the system, and vice-versa


Teaching: from Microeconomics to Open-economy macro

This is for Micro, entirely based on my own opinion and experience.

Syllabus:

The most useful topics would be those on production and cost and perfect competition. I see no point of talking about utility theory unless you will be covering intertemporal choice. This and basic demand-supply. If you will be covering ISLM, you might find it a good idea to discuss "shifting a curve versus moving along a curve" with demand-supply prior to moving to ISLM.

Books:
I personally find useful The Applied Theory of Price by Deirdre McCloskey. The math (read calculus) was usually in the footnotes or appendix and I really did not need calculus to cover almost all of the standard chapters - Consumer Behavior, Perfect Competition, Monopoly etc. The exposition was intuition based.

However, having used this book as an instructor, I personally needed to actually read and work through the examples before teaching it to my students - some of them could require a bit of very careful thinking.

The book is available on the author's webpage: http://www.deirdremccloskey.com/books/index.php

Depending on how much calculus you want to show your students, other open source books on micro could be the one by McAfee https://www.mcafee.cc/Introecon/
and the one by Yoram Bauman (can't find the link to it)


Why is collective bargaining by a group of employees not the same thing as price-fixing?

This is more of an elaboration of The Almighty Bob's answer:

It is true that if we start from a competitive market (i.e. large numbers of buyers and sellers), then granting market power to sellers (e.g. workers) by allowing the formation of a monopolistic cartel is bad for efficiency. Those sellers will use their market power to increase the price (and reduce the quantity traded), resulting in a deadweight loss. Thus, we tend to look suspiciously upon practices that create market power. Note that here, the policy intervention we have in mind is to break up the cartel and return us to a competitive world.

Why should the labour market be viewed differently? Part of the answer is that the relevant counterfactual has changed. Begin with a world without labour unions. The market will then typically not be competitive because there are often a small number of employers who themselves enjoy market power. Just as a monopolist seller can drive up the price, these monopsonistic (or oligopsonistic) buyers of labour can use their power to drive down the price.

Now we are faced with the following policy problem:

  How can we correct for employers' market power and restore wages toward the (higher) efficient level?

Two simple solutions come immediately to mind:

Reduce employer's market power by stimulating competition between employers. This is achieved, to some extent, by antitrust policy. But it's hard to do much more here short of forcing more businesses to hire more workers.
Allow workers to form unions so that both workers and employers have market power. If the firms try to use their power to drive wages down and the workers use it to drive them up then there is a sense in which the two will 'cancel out' and the result can be closer to the efficient wage than a market in which only employers have market power.

Whether the second solution indeed works or not depends upon a whole range of factors. Here are a few:

If the employer side of the market is, in fact, quite competitive then the correction will likely be too big and we will end up with wages that are inefficiently high.
If bargaining is very costly then it might be more efficient to have one side (e.g. the employers) unilaterally set the wage.
If there is uncertainty about the wage that firms are willing to pay/workers are willing to accept then bargaining may inefficiently break down (see the Myerson-Satterthwaite Theorem).


Negative growth rate with positive job growth

These measure different numbers. Dollar value of items sold can decrease while number of employed people can increase, so there is no contradiction here.


Could robots replace humans as consumers?

Short answer

Perhaps your concern about stimulating demand is explained by the broken window fallacy. The fallacy is the belief that there is a social benefit to income that is concomitant with a loss in a stock of wealth.  Instead of using a stone to break a window you want to use a robot.

Longer answer

You said "demand was so low because of automation". I think automation increases valuable output so it increases income so it increases demand. I think you suggested a nonsensical premise.

I think current day robots are economically viable since there is a market for them. As @Fizz correctly says they use spare parts and they also use energy, usually electricity. Presumably they produce more value than they consume, otherwise nobody would buy one. What is a robot and what is the owner of the robot are hard to separate since robots do not have what I might call autonomy under the law. They are chattel. As chattel, you might say it is the combined unit of the owner plus robot that is the consumer and the producer. The owner might be a corporation. Robots can mechanically pay for goods and services but since it's not an autonomous individual it is really the owner that is paying, using the owner's money. The robot itself does not own money.

If the law changes to recognize robots as autonomous individuals, not chattel, not slaves, then their individual output would add to GDP and their individual consumption of goods and services would add to aggregate demand. They already do add to these economic measures, but as part of a combined unit of owner plus robot.

You asked if robots can replace human consumers. Yes, robots as autonomous individuals can replace humans as consumers of goods and services. When a robot as an autonomous individual consumes a rival good, a human cannot consume the same. I think this is easy to understand if we consider electricity. If a robot as an autonomous individual runs, swims, and bicylces a triathlon, it will use energy that a human could not have used to air condition their condominium.

Link to a description of rival goods.

ADDENDUM

You have edited your question so I am posting an addendum. In this addendum I will assume that the law changed to recognize robots as autonomous individuals.

If elite consumption increases by one dollar and consumption by non-elites decreases by two dollars, aggregate consumption will decrease but that is a transitory problem. The lower level of consumption will soon be matched with a lower level of output. Nobody will persist in producing goods that will obviously fail to sell. I sense your question is about permanent effects and you did not specifically express a concern about transitory problems. One reason it is transitory is because when people stop producing goods that do not sell they switch to producing something that does and when that happens the economic recession comes to an end. Consider that there is the "permanent" phenomenon of productivity improvement which will eventually cause income and consumption to increase for elites and non-elites and so the lower level of non-elite consumption is temporary.

You asked if a robot consumer will "keep capitalism afloat". If the non-elite, motivated by a temporarily lower living standard, desire to vote to switch to a non-capitalism regime I think the robot consumer producer has an uncertain effect in that aspect. The robot consumer will consume some rival goods while also producing some rival goods. In the long run the robot producer consumer will be powerful and it will produce much and consume much. They will be part of the elite. Under a progressive tax system human elites and robot elites will be taxed at a higher rate than non-elites. It might be the progressive tax system, not as much the existence of robot consumer producers, that helps the non-elite.

Since I am assuming robots are recognized as autonomous individuals I will not answer the questions involving owners of robots and robots being sold and rented.

You seem very concerned about the cost to build and operate robots. These costs are always decreasing because of the permanent phenomenon of technology improvement.

You seem to persist in being concerned about stimulating demand. I refer you to the beginning of my answer that said low demand because of automation is nonsensical. We do not need robots to stimulate demand of rival goods. The destruction of rival goods is sufficient to stimulate demand.


How did the Hunt brothers' cornering the silver market drop gold prices in 1981?

Since nobody is answering this, I will point out that the answer is half there.

The cornering attempt directly affected the silver price, but gold went along for the ride. People treated gold/silver as an asset class - “precious metals” - and they traded them on a relative basis (the gold/silver ratio).
The rules were changed, and the Hunts were forced to liquidate. This directly drove down silver futures.
Gold went along for the ride. People who were long silver and gold got hit my margin calls, and they had to liquidate both. The gold/silver ratio would rise if gold did not move. Finally, people unaware of the details of the silver market would just view this as the end of the run for “precious metals.”
Beyond that, it’s just opinions.


How to estimate empirically a demand curve

I think You will have to account for various factors other than price. What is your purpose in estimating the demand curve?

This link will give you a good explanation on how to estimate demand curves if you are looking for simple exposition - assuming that sales and other factors have linear relationship.

If you are good at econometrics, you may want to consider simultaneous equations models. It is likely that your single equation model will suffer from simultaneity and omitted variable bias along with identification problems.


a) not sure what exactly you mean here by probability distribution but if you mean the distribution of potential Y given the distribution of estimated coefficient b and a it would be correct, although usually we look at expectation to get single number than on distribution in which case it would be $E(Y|X)$

b) is correct


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

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

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


The problem with $\rho>1$ is that it means the marginal product of factors is not decreasing ($\rho<1$) or constant ($\rho=1$) but increasing, which is an odd assumption. Such functions yield isoquants that are concave, and might lead to only one factor being used (as BKay said).

As in any generic CES, the marginal product of factor $x_i$ is

$$ MP_i = \left(\frac{y}{x_i}\right)^{1-\rho} $$

The derivative of this MP with respect to $x_i$ is, after some rearranging,

$$ (\rho-1) \left(\frac{y}{x_i}\right)^{1-\rho}\left(\frac{x_{-i}}{x_iy^{\rho}}\right) $$

For $\rho>1$, this expression is positive, which means that the productivity of a factor increases as more of that factor is used.

Regarding isoquants, you can find these by rewriting the production function as $x_2=g(y,x_1)$. In the generic CES, this is

$$ x_2 = \left(y^{\rho} - x_1^{\rho}\right)^\frac{1}{\rho} $$

These are linear in the case of $\rho=1$, convex in the case of Cobb-Douglas (where the function above is $x_2=\frac{y}{x_1}$, a hyperbole), and concave in the case of $\rho>1$. For example, select $\rho=2$ and you have:

$$ x_2^2 = y^2 - x_1^2 $$

which is the formula of a circle centered at $(0,0)$, with radius $y$. Normally, for production theory only $x_i \geq 0$ is interesting, which gives you the concave isoquants for different levels of $y$. The figure below shows an example, were for a given factor prices ratio, there is a corner solution (point A):

$\hskip3cm$

(Code for reproducing figure here)


I think you misunderstood what the supply line represents. The function takes as its argument the number of units sold. It then returns the lowest price which the supplier of the last unit requires such that he is willing to sell.

Thus, the profit would not be $10*5$. Instead, the last person willing to sell the good receives 0 profit as he is selling at the lowest price he is willing to accept. Counting in discrete units, we would have something like $10+7.5+5+2.5+0=25$ profit. Each additional seller of a unit makes less profit than the previous one.

The flaw in your logic was that the first seller can really only provide a single unit at price 10 and not 5 units. The next unit already costs a bit more in production all the way till the last unit makes its producer just break even.


How to design / interpret a difference in differences regression

The point of control group matching is to ensure similarity between the groups, to isolate the effect of the treatment variable. If are assuming that the development paths of all academics is identical, and at some point, all academics have a chance to become editors, and some do, then you a reasonable to match at career start.
That's not a good assumption. Academics differ widely in quality/competency/publication/citation over the course of their careers. Much better to find matches by identifying academics that were similar those the became editors, who (for whatever reason) didn't, so that your control group is identical to your treatment group.


How to evaluate if an activity is likely to produce a positive ROI?

Look into what similar/same products this platform and similar platforms are selling for compared to your pricing.

Ask yourself the following:

How does their pricing compare to yours? If you are equal to or above their pricing- too risky. If you are below their sales prices, compare their online shelf life to estimate your projected holding period and carry cost between your purchase and sale time?
Do the other sellers have strong reviews (credibility)? Are you starting out without any reviews, or are you an existing seller with reviews?
What are your profit margins? If your costs go up 10-20% does will the demand allow for an increase your sales price?

Finally, run a 3-5 year cash flow plan to estimate your total sales, costs, and profits. Compare your projections(profits) with the amount of time you anticipate it will take you on a daily, weekly, monthly, annually.

Remember, selling online has its challenges, don't underestimate the amount of time it will take out of your day.

There's this story about a paintball gun dealer who bought their products from China and sold them out of their store, plus online through a major online selling platform. Their online sales grew so large their online platform (partner) went direct to the manufacture in China and made a deal cutting out the reseller, selling it cheaper than the paintball company could. They became a victim of their own success.

Anyway, good luck! :)


Can higher working hours reduce productivity?

The closest study I could find was that by John Pencavel titled 'The Productivity of Working Hours.'

Abstract:

  Observations on munition workers, most of them women, are organized to examine the relationship between their output and their working hours. The relationship is nonlinear: below an hours threshold, output is proportional to hours; above a threshold, output rises at a decreasing rate as hours increase. Implications of these results for the estimation of labor supply functions are taken up. The findings also link up with current research on the effects of long working hours on accidents and injuries.


What are accepted econometric methods to find out if a time series is I1 or not?

An I(1) series is also known as a series with a unit root. Therefore, the econometric tests to inquire on the order of integration of a time-series are referred to as "unit-root tests".

There are three widely used unit-root tests: Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS).

The null hypothesis (H0) in the ADF and PP tests assumes the presence of a unit root. For KPPS it assumes no unit root.

The tests often give different results, and best practice would require to report all three statistics as a robustness check.

There are many drawbacks of using these tests. The major issue lies in the lack of power of PP and ADF to reject H0 when the series is I(0) but close to I(1), that is when the series is highly persistent but stationary. To avoid this low power, other tests have been devised by Elliot, Rothenberg and Stock (1996), as well as Ng and Perron (2001).


Do banks take money to repay deposits from required reserves?

When you get your \$200 back, the bank's required reserves go down by \$20 as well, so the bank can take that amount back from its reserves.

Operationally, the bank wouldn't go to the central bank and get this, as they probably would have \$200 in cash laying around already.


1st of all, banking regulation in different, in various countries, so there is no 1 accurate answer for all cases.

Having that said, In general, banks may buy stocks, but that won't be with any capital being held as a deposit reserve ratio, or Basel regulation recommendations.
This is because a bank has to keep enough capital allocated per loan.
Furthermore, when a bank recruits capital in order to lend it, it becomes its own debt, rather than capital. The bank lending money is its asset, which should be alternative to stock buying

When a bank buys a stock, its done from it Nostro account, dedicated for investments and is seperate from its "classic" activity

Of course diversions from the theoretical model do exist, in cases like the Sub-prime bubble of 2008. but, obviously,the large banks back then, in fully aware manner, broke their own business model rules, in a fraudulent way


Was there a drop in liquidity in the corporate bond market during the Global Financial Crisis?

"...if such a...cycle exists..."---i.e. in economic language, whether liquidity and demand are endogenous to each other. Yes, of course they are. Liquidity (or illiquidity) of any asset can be viewed as an equilibrium outcome where agents confirm each other's beliefs---similar to the liquidity/illiquidity of a bank. As such it has a self-fulfilling aspect. An asset is liquid because people believe it is and therefore are willing to trade/make markets for it. This in turn leads to demand for the asset, which makes it liquid.
There are many instances during the 2007-2008 Financial Crisis that illustrate this. In the US, the Fed took positions to restore confidence in illiquid markets. The Fed eventually took no loss on those positions. Of course, the Fed also took similar actions to prevent/stop runs on financial institutions.
There are also similar examples during the current Covid-19 episode. In March 2020, liquidity of corporate bond market returned as soon as the Fed announced its corporate bond purchase program---long before it was actually implemented. When the program was eventually implemented (which the Fed must, to signal its credibility), only a small portion of planned purchase was made. Market's belief in liquidity was maintained as long as the Fed is believed to be credible. (See also here.)


Is UK house price spiral connected to debt based monetary system?

The price of housesis determined by the supply and demand for housing. The consensus view is that house prices in the UK are so high because of low supply and buoyant demand. In particular, the UK is currently building houses at a rate of less than 150,000 per year, but is creating twice that many new households. This is a situation that has persisted for some time. If there are more buyers than sellers then sellers can increase their prices with little fear that they will be left without a buyer at the end of the day.

To understand the cause for high house prices, one therefore needs to understand the reason for supply being so low, and demand being so high. In the latter case, the availability and cost of credit is certainly an important factor. If banks are willing to lend (say, because the government provides guarantees or other subsidies for doing so--as in the Funding for Lending scheme), and if interest rates are low and stable then people will be very willing to take out a mortgage. This is an important precondition for strong demand because most people cannot afford to buy a house without a mortgage.

This, though, is only part of the picture. Note that many countries currently have low and stable interest rates, but have not experience the rapid inflation of house prices seen the in the UK. Here are some other factors that are important in the UK context:

Limiting supply:

The UK has a restrictive planning regime that makes housebuilding (especially in high-demand areas) difficult. This has, for example prevented the expansion of towns into green belt land, or large increases in the density of housing in major cities.
Much of the land best suited to development is so-called ``brown field'' land that was previously put to some other use. Cleaning and preparing this land for use in the housing sector is costly and represents a risk for developers.
House builders earn essentially zero profit on affordable homes, making the development of such homes unattractive. This role was previously filled by the British government, but social house building has fallen dramatically since the 1980s.

Promoting strong demand:

The UK government has introduced a number of policies that directly stimulate demand for housing (such as the Help to Buy scheme).
The UK has a net inflow of migrants of around 200,000 per year--all of whom need to be housed.
Demand is not evently spread across the country. The UK economy is unusually concentrated around London and the South East, which puts particular pressure on the housing market in this area. House prices elsewhere have seen more modest growth.
The British are unusually attached to the concept of home ownership (unlike, for example, many continental Europeans who are perfectly happy to rent). This means that British buyers are less sensitive to prices and will continue to demand houses even as the prices increase--as we have seen.
Related to the above, tennants have relatively few rights in Britain. This makes long-term renting less attractive, and pushes people to buy houses.
Anecdotally, there appears to be strong demand for UK housing from foreign investors who treat the property as an asset, but do not occupy it.

Many of these things could be fixed with appropriate market interventions. However, there is a political economy dimension to the problem in that most of the British electorate lives in an owner-occupied house and therefore has a vested interest in maintaining the value of their house and preventing additional development in the area to the greatest extent possible. This possibly explains why candidates in the forthcoming election have focused mainly on proposals to subsidise demand (which would only exacerbate the problem!) or vague promises to build more houses, rather than on concrete plans (e.g. to reform planning) that would put-off a lot of middle-class voters.


Sources on Educational intervention changing consumer preferences?

I found research on this topic from the recent October 2016 issue of the American Economic Journal: Applied Economics. However I could not find the PDF online from the site however I got it from a different source.

Titled as
The Impact of High School Financial Education: Evidence from a Large-Scale Evaluation in Brazil it is learned that its possible to change consumers habits via curriculum design.

  We find significant treatment effects on spending behavior as well. In line with the concepts
  taught in the curriculum, the results show a 2.1-2.5 percentage point greater likelihood of
  comparison shopping before making purchases, and a 3.1-4.1 percentage point greater likelihood
  of negotiating price or payment method prior to purchases by students in treated schools. Further,
  the results show that 16 percent of students in treated schools made a list of monthly expenses as
  part of a budgeting exercise compared to 13 percent in the control schools in follow-up 1. These
  numbers are 17 percent and 14 percent respectively, in follow-up 2. All treatment effects are
  statistically significant at the 1 percent level.

  Overall, these results show a clear improvement in student behavior as a result of the financial education course, in line with concepts taught in the curriculum.

The article concludes

  Financial education in schools is an important policy focus in both developed and developing
  countries, yet its impacts are not well understood. This paper contributes to the literature by
  demonstrating that a financial education program targeted to youth in secondary school can
  improve both knowledge and behavior, as well as influence financial attitudes and preferences.

Excellent research, and a recommended reading.


Name for a tax that captures all goods and services produced?

Value-Added Taxes (VAT) are supposed to capture most goods and services produced in the private sector, but there can be exceptions within a country’s laws.

Even if the exceptions were eliminated, there are some non-market components to GDP that would be missed (e.g. imputed values, like the “rental value of owner-occupied housing”). (You need to go into each country’s GDP definition to find the list of imputations.)


Nobody has to loose in an arbitrage. Economic relationships are not necessarily zero-sum (in fact often they will not be zero-sum). For example, if apples in city A are sold for ${\\\$}5$ and apples in city B can be sold for ${\\\$}8$, and we assume zero transaction cost there will be an arbitrage opportunity to earn ${\\\$}3$ riskless profit per apple by buying apples in city A and selling them in city B. But nobody looses in the transaction.
The apple producers in city A clearly value ${\\\$}5$ more (or at least indifferent) than an apple otherwise they would not trade it and just keep the apple. So giving them ${\\\$}5$ will make them better off (or at least not worse off). Then in city B people who buy apples must value apples more than ${\\\$}8$ they are paying for it otherwise they would just keep the money instead of buying them (or at least they must be again indifferent).
Consequently, when people take advantage of arbitrage opportunities generally speaking nobody looses anything. There must be some other issues present that would turn the problem into zero-sum game.
Regarding the microeconomic implications the main one is that people will take advantage of the arbitrage opportunities until the prices on the markets equalize - in the example above until the prices in both cities would become equal. The law of one price is based on the concept of arbitrage. There might be other implications depending on precise setting where arbitrage occurs, to explore all of them would be beyond the scope of SE answer.


Theories about how lack of supply can feed into lack of demand

Lack of supply of a network good - a good associated with a network effect - may result in lack of demand for that good.  The greater the number of people who have or use such a good, the greater its value to any one person.  Hence a lack of supply of such a good to some people will probably reduce demand from those to whom it is available.  For example, if there were a temporary lack of supply of phone use in city A (eg due to technical connectivity problems) making it impossible for people to make or receive calls, then demand for phone use in other cities might be expected to reduce by the amount of calls that would normally have been made to or from city A.  More fundamentally, some goods with the potential to create network effects may never be supplied and used in sufficient quantity to establish such effects, so that demand for them remains minimal (even though it might, if supply had been large enough and other circumstances such as first-mover advantage had been favourable, have become very large).
Possibly not what you had in mind, but if X and Y are complementary goods, then lack of supply of X can result in lack of demand for Y.  For example, a shortage of pasta might result in reduced demand for pasta sauces.  Or closure of sports centres (eg due to Covid-19) might reduce demand for sports clothing.


What happened to the national debts after Bretton Woods

The Bretton Woods system was a fixed exchange rate regime, but local currencies existed. Debt was unaffected (other than any debt repudiations that may have happened after the end of World War II).


How does inflation in income go 'hand in hand with inflation in prices'?

In the situation you describe people's real purchasing power would indeed be reduced. However such a situation is not likely. If the employer was a monopolist, how come employees could afford more than the bare necessities in the first place? (See the works of Carl Marx.)

In real life it is more likely that if an employer does not raise wages when businesses are doing well another employer will make a competitive wage offer. Thus inflation will result in the rise of wages.

Mind that Mankiw's book is not a mathematical treatise, his statements are not precise. The book is merely a collection of stories aimed at students who are just familiarizing themselves with economic phenomena.


Calculating Service Contributions to GDP

Services will be calculated at the final price they are given in market. That price includes all value added items in providing the service. So, to calculate contribution of airlines in GDP, you just need to sum up the total value of tickets that are sold. Other things will automatically be counted in that.


How much better off would the average person be if we took away enough money from the top 1% to make them no richer than the average person?

I assume the following:

We redistribute wealth (not income) from the top 1% to the bottom 99%
Everybody among the bottom 99% receives the same amount.

Source for my data: World Income Database

In 2014, the average personal net wealth among the top 1% was around \$11 million in 2017 prices. The total wealth to be distributed is hence (3.3 million people in the top percentile $\times$ 11 million) = \$36.3 trillion ($3.63\times10^{13}$).

This means that everybody among the bottom 99% receives around \$111,000. How much this makes you better off depends on your initial state. Concepts of low- and middle-class are somewhat ambigious. According to the WID data, net personal wealth among the bottom 50% is essentially zero, and \$205,000 among the 50 to 90th wealth percentile.

EDIT:

Please note that this is a purely mechanical and unrealistic exercise. For starters, it ignores legal and administrative hurdles. A major concern is also that a substantial share of the private wealth of the top 1% is invested in productive firms which employ millions of people. What happens  to their employees if you expropriate the owners of these firms?


Does real GDP control for changing preferences?

I think the confusion here may be about the phrases "control for" and "account for".
Real GDP "controls for" prices, meaning that if prices change (say every price doubles), then real GDP shouldn't change either.
In contrast, real GDP does not "control for" preferences, because if preferences change, then real GDP will also change.

The phrase "account for" is ambiguous and could mean either "control for" (as described above) or "is affected by" (pretty much the exact opposite meaning).


What is the Gross Domestic Product (GDP)?

Gross Domestic Product
As per wikipedia, we learn that the OECD, an organisation of international recognition for economic policies and macroeconomy, defined the GDP as

Gross domestic product is an aggregate measure of production equal to the sum of the gross values added of all resident institutional units engaged in production (plus any taxes, and minus any subsidies, on products not included in the value of their outputs). The sum of the final uses of goods and services (all uses except intermediate consumption) measured in purchasers' prices, less the value of imports of goods and services, or the sum of primary incomes distributed by resident producer units.
-- OECD, Glossary

In somewhat simpler terms, it is a quantitative measure of the amount of values produced by all industries and services of a given country. For example, if a company buy some tomatoes and produce a tomato sauce, the difference between the money received for selling the sauce and the money spent for buying the tomatoes (and possibly other products) will be added to the GDP of the country where the tomatoes are being transformed1.
The GDP is based on price, and not all prices are known (for example, prostitution, black market, etc.) or need to be estimated, like public services. Therefore the determination of the actual GDP cannot be reached, but some statistical approaches offer various ways to estimate that number. One should note that the different approaches do not always provide similar results. Furthermore slight variations in the definition of the GDP may provide different results. Even if the GDP is used since decades everywhere, there are still some discussion about how to measure it. Some details are provided in Wikipedia and in the references therein. But one way, is to use the expenses approach where the GDP is calculated as
$$GDP = C + I + X - M + P$$
where $C$ is the consumption, $I$ the investments, $X$ the exports, $M$ the imports and $P$ the public spending. More details can be found here or in the already cited wikipedia.
The GDP number is used to indicate the performance of an economy. The higher it is, the more value the country's econmy produced. It is used to

compare two countries' economy, regardless of the types of industries they have,
see the evolution of a given country economy as a function of time.

Please note that those are only valid with a constant definition and equal estimation approach. One approach
It can be noted that the GDP value of a country is often normalised by the number of inhabitants of that country. This, to simplify the comparison between countries like Luxembourg and India, which have US\$54,940,000,000 (US\$111,716 per capita) and US\$2,308,018,000,000 (US\$1,627 per capita) respectively (as per IMF in 2014 and 2015 via the corresponding Wikipedia's lists: nominal and per capita). The higher the GDP/capita, the richer the population. But this, however is assuming a good repartition of the wealth, which is not always granted.
Discussions on the validity of GDP
The GDP is an indicator of the current state of an economy. However it tends to be used everywhere, every day by policy makers, economic analysts, journalists, etc. This overpowers other complementary indicators. Which, for policy making is probably insufficient.
As mentioned before, the GDP is used as a measure of how rich the inhabitants of a country are, but due to (sometimes very) inequal repartition of wealth, the GDP could be misleading. Apart from the document cited above, some claim that

neither GDP nor this balance sheet takes account of environmental degradation, insecurity or inequality.
-- François Lequiller, OECD

And, as can be found, there are some discussions about alternative indicators to replace or complement the GDP, which should indicate the wealth as well as environmental, equality and some other parameters.
1. That is the main difference with GNP, which concerns residents, that is to say where the company is registered. More on the subject can be found here.


Leontief input output model with column sum greater than 1

In terms of if and only if statements according to Peterson & Olinick (1982);

A substochastic matrix A is productive if and only if $I-A$ is
nonsingular.

In substochastic matrix the sum of entries by row or columns will not be greater than 1 so it is part of the condition but in addition the matrix $I-C$ should also be nonsingular. The nonsingularity is important for the invertibility of the matrix.
Consequently, I do not think that there are exceptions where the industries are unprofitable but the matrix is still productive. Rather there are exceptions where just because the entries sum to less to 1 and matrix is non-negative but it is singular and so we cannot invert it, in which case it would not satisfy conditions to be productive.