Do the republican tax cuts cost more than forgiving student loan debt?

While many folks treat reductions in government revenue as equivalent to spending, they’re not actually the same thing. Tax cuts don’t “cost” anything. Tax cuts represent less money coming in, while government spending (such as repayment of student loans) represent more money going out. So your first thought when seeing the two things treated as if they were the same should be “somebody has an agenda here” and to view anything that follows with a skeptical eye.

That said, it’s certainly valid to ask whether the tax cuts decrease government revenue by more than the cost of the repayment of student debt.  The short answer is “nobody knows” because both things represent such huge financial transfers that they would distort the economy.

Nobody denies that tax cuts increase economic activity — the question is by how much.  Many Republicans argue that tax cuts increase economic activity by so much that they “pay for themselves” because the smaller slice of a much larger pie works out to more overall. Most Democrats dispute this.

Similarly, nobody denies that government spending stimulates the economy — the question is by how much. Democrats often argue that government spending is a more effective (or at least more fair) way of stimulating the economy, than letting businesses (or the wealthy) hold onto the money and spend it themselves. Republicans dispute this.

Every facet of this issue is so politically charged, and what little hard data exists is so up to interpretation, that I don’t think you’ll really get the kind of definitive answer you’re probably after.  The bottom line is that it’s not really possible to conduct the kind of controlled experiments necessary to come to a solid conclusion. Which isn’t to say that people can’t make very reasonable (or persuasive) guesses. Just be aware that they are, in fact, guesses — and politically motivated ones, at that.


Solving Utility Maximization with Lagrangian

You have added inequality constraints $x_1 \geq 0$ and $x_2 \geq 0$.
Hence, you now have Kuhn-Tucker conditions for complimentary slackness:
$$
\mu_1 x_1 = 0 \text{ and } \mu_2x_2 = 0
$$
So whenever $x_i > 0$, by the complimentary slackness condition, $\mu_i = 0$.
See Karush-Kuhn-Tucker conditions. It also contains regularity conditions you ask for.


Axiom: More is Better; But when is more better?

You seem to be talking about (strong) monotonicity rather than non-satiation (which is closely related to but different from monotonicity).
(Strong) monotonicity says that we prefer one bundle to another if the first bundle has strictly more of at least one good and no less of any good. A bit more precisely and in a two-good setting,

Let $B_1=(x_1,y_1)$ and $B_2=(x_2,y_2)$ be two bundles. Suppose the preference $\succsim$ satisfies (strong) monotonicity. Then $(x_1,y_1)\succ(x_2,y_2)$ if either of the following is true:

$x_1>x_2$ and $y_1\geq y_2$
$x_1\geq x_2$ and $y_1>y_2$

So, to your Q2: If $x_1>x_2$ but $y_1 < y_2$, then (strong) monotonicity says nothing about which bundle is preferred. (This is not to say that the preference does not have any ordering over the two bundles, but merely that strong monotonicity alone won't tell us anything about this ordering.)


Economic Overview of Pacific Island Nations

As a group, there are similarities. They are all small and remote island economies. None have a population over 1 million people. Fiji is the largest with a population of roughly 900k. It is important to remember that they are still different countries and it can be unhelpful and misleading treating them all as identical.

The Pacific island region has considerable potential for development, especially in the areas of tourism, fisheries, forestry, mining, and agriculture.

Challenges

Small size
limited natural resources (diversity and capacity to capitalise on)
narrowly based economies (small populations and isolation limit capacity to diversify production.)
large distances to major markets
vulnerability to exogenous shocks, can affect growth and have often led to a high degree of economic volatility.
They are some of the most vulnerable nations in the world to disaster. In particular, climate change and rising sea levels.

Long term viability of economies has been questioned. Fiji is the only one approaching independence from aid.. Many Pacific Island economies have found it difficult to achieve sustained economic growth and hence sustained growth in living standards

See this link for a brief overview by the world bank.


I would recommend Tim Harford's "The Undercover Economist" for an easy way to get some exposure to how economists think, without having to go through all of the dry academic mathematics etc.

To get a sense of the shape of the economics discipline, you might also like to look at "Economics: A Very Short Introduction" by Partha Dasgupta.

Lastly, if you really want to get into the discipline and you want a slightly more formalised/academic treatment then any good introductory textbook should do. N. Gregory Mankiw's "Economics" is a popular choice.

The above describes how you might go about learning about economics. But from your question, it seems more like you are more interested in learning about finance, which is the discipline that encompasses the study financial markets, etc. I learnt finance from a book called "Introduction to Finance" by Lawrence J. Gitman and Jeff Madura, but there doesn't seem to be a recent edition so perhaps someone else can recommend a more recent introduction to the subject.


Set of Bayes Correlated Equilibria when complete information is not available

You can certainly do it. However, keep in mind that the BCE will not be a lot "smaller". This is because there are many information structures that are almost perfectly informative, or that fully reveal some states but not all of them. Therefore, by disallowing the complete information structure you are simply removing one element in the boundary of the set of BCE's. Keep also in mind that this set has, in general, infinitely many elements. Since it is a convex set, any convex combination of two elements in it is also in the set, for example.

Going back to your question, there are many ways to rule out complete information structures. The one that comes to mind stems from the fact that a fully informative signal will correspond to a BCE where for each $y\in Y$, the support of $P_{V|Y}$ is a singleton. Notice that if this is the case, learning what action you should take implies learning the state of the world.

Therefore,  the extra constraint would be that $P_{Y,V}$ must satisfy that there exists a $y^*\in Y$ such that the cardinality of the support of the conditional probability of the states given that action is bigger than 1, i.e. $|P_{V|y^*}|>1$. This is consistent with the idea that at least in some cases the DM remains uncertain about the state of the world after receiving the recommendation to choose action $y^*$.

Notice that a signal that fully reveals all but one state of the world, and instead induces a posterior belief for such a state of $99.999\%$ will not be ruled out by the extra constraint, so including the constraint will have very little effect.


The reason why marginal benefit is measured in cans of soda is that this economy only has two goods: pizza and soda. So instead of using money we may as well use soda. Alternatively, in the absence of money this economy is an exchange economy, and the only way to pay for pizza in that case is with soda.

When you move beyond two goods willingness to pay is often measured in money value. However, measuring willingness to pay in money value is just a convenient way of saying: a bundle of "everything else that is available".

In a two good economy,given the current amount of pizza that you have, an additional slice of pizza may thus be worth 5 cans of soda to you. In a multiple good economy it may be say 5\$ where the 5\$ stands for "all the other (combinations of) goods you could get for 5\$.


If the borrower is a firm, lower prices means your output is selling for less, so you need to sell more units in order to repay the debt (assuming a constant profit margin).

For an individual, the buried assumption is that wages are also falling in the deflation. In which case, the debt is increasing relative to your wages. However, if your wages have not fallen, falling prices will make it easier for you to repay the debt (you can consume the same amount, and have more money left over to repay debt).

It makes more sense at the macro level, as deflation is normally associated with lower growth and a higher unemployment rate.


Why is Uber worth almost as much as Boeing?

A big part of the answer to this question must surely be network effects.

Yes, Ford has a lot of engineering talent. But so has GM. This means that Ford has to compete with GM to sell cars, and this competition limits that amount of profit that Ford can make.

Ride sharing is a different story altogether. Suppose you write software that completely replicates the functionality of the technology used by Uber. How many drivers will want to use your software? Probably few or none because all of the people looking for a ride are using the Uber app and drivers want to be where the customers are. How many end customers will use your technology? Probably few or none because all of the drivers are using Uber and consumers want to use the platform where they can easily get a ride. As you say, people can easily open the new competing app to check it out, but if they find nobody else using it then they will just switch back to Uber. The only way to a competitor to overcome this challenge would be if many users simultaneously decided to switch at once, but such coordination is fairly rare in practice, and usually only happens if the new technology is vastly superior to the old one.

This property—that a product's value depends upon how many other people are using it—is known as a network effect, or network externality.

If you think about it, you will see that many products that have this network effect property are monopolised (or at least have relatively little competition). For example,

a social network website is more useful if more of your friends are on there (a network effect)—and Facebook is a pseudo monopolist in this market.
Developers write software for computer operating systems that have many users and users want to use the system with a lot of software available. These netwrok effects helped Microsoft to a position of dominance.
Blu-Ray players are more useful if lots of shops sell blu-ray discs and shops will sell blu-ray discs if many people own a blu-ray player. The network effects here explain why the competing HD-DVD format died out and we were left with a single dominant high-definition media format.

There are many other such examples.

Since people understand that markets with network effects tend to "tip" to monopoly, and since monopolies tend to be extremely profitable, investors think that Uber is a good bet for future profitability.


Perfect Complements - Walrasian Equilibrium

If the prices $p_1$ and $p_2$ are positive than as you pointed out the equations
\begin{eqnarray*}
    \frac{30p_1}{p_1+p_2} + \frac{20p_2}{p_1+4p_2} & = & 30 \\
\\
    \frac{30p_1}{p_1+p_2} + \frac{4 \cdot 20p_2}{p_1+4p_2} & = & 20.
\end{eqnarray*}
hold. This is troublesome, because subtracting the first equation from the second yields
\begin{eqnarray*}
\frac{3 \cdot 20p_2}{p_1+4p_2} & = & -10
\end{eqnarray*}
which has no solution for positive prices. However if a good has zero price, than the demand equations are different as no one minds buying superflous goods as long as they are free. For $p_2 = 0$ you would have
\begin{eqnarray*}
    \frac{30p_1}{p_1+p_2} + \frac{20p_2}{p_1+4p_2} & = & 30 \\
\\
    \frac{30p_1}{p_1+p_2} + \frac{4 \cdot 20p_2}{p_1+4p_2} & \leq & 20.
\end{eqnarray*}
This is because $\frac{30p_1}{p_1+p_2} + \frac{4 \cdot 20p_2}{p_1+4p_2}$ is a minimum that the buyers need but they do not mind having more as good 2 is free. There is also a formulation of equilibrium, the 'value-equilibrium' which is that for good $i$
\begin{eqnarray*}
p_i \cdot D_i(p) = p_i \cdot S_i(p) \mbox{ and } D_i(p) \leq S_i(p)
\end{eqnarray*}
meaning that there can be oversupply of zero price goods.
(Think about air. Would you buy air from someone?)

Unfortunately this equation system would still imply
\begin{eqnarray*}
\frac{3 \cdot 20p_2}{p_1+4p_2} & \leq & -10
\end{eqnarray*}
which has no solution in non-negative prices. On the other hand, for $p_1 = 0$ you would have
\begin{eqnarray*}
    \frac{30p_1}{p_1+p_2} + \frac{20p_2}{p_1+4p_2} & \leq & 30 \\
\\
    \frac{30p_1}{p_1+p_2} + \frac{4 \cdot 20p_2}{p_1+4p_2} & = & 20.
\end{eqnarray*}
which implies
\begin{eqnarray*}
\frac{3 \cdot 20p_2}{p_1+4p_2} & \geq & -10.
\end{eqnarray*}
As $p_1 = 0$ any positive $p_2$ is a solution for this.


Employment Volatility and the Relevance of Aggregate Wage Rigidity

Wage rigidity is not the only solution to the Shimer Puzzle (Shimer, AER 2005) that has been proposed in the literature, so I wouldn't say that it is the only relevant metric to consider when thinking about labor market dynamics in this context. However, as I understand the question, it aims at the role of wage rigidity in a Diamond-Mortensen-Pissarides (DMP) model and not on alternative solutions to the Shimer Puzzle.

Thus, here are a few thoughts on the rigidity of wages of newly hired workers:

The baseline DMP model is essentially a model of new hires. The wage formation mechanism as it is described in Pissarides (2000) does not differentiate between newly hired workers and ongoing employment relationships. The Nash bargaining solution dictates a surplus sharing rule that splits up what is being produced in every period, no matter how long the employment spell lasts. The bargaining powers are exogenous. In the baseline model, the elasticity of wages with respect to labor productivity is simply 1. Wages are fully flexible and immediately adjust to changes in labor productivity. This model feature lies at the heart of the Shimer puzzle. The model's inability to generate dynamics consistent with volatilities we observe in the data is due to the fact that wages adjust upwards too much in response to a positive shock, thereby lowering incentives of firms to post additional vacancies.

Since the theoretical model treats every match in every period like a new match, the rigidity of new matches is of primary empirical interest for the calibration and analysis of this class of models.

Haefke et al. (JME, 2013) report empirical evidence for wage rigidity using US labor market time series data.  They find that the wage of new hires (both out of unemployment and after a job-to-job switch) corresponds almost one-to-one to changes in labor productivity. The estimated elasticity is around 0.8 (with quite a large standard error of 0.4). The wage of workers in ongoing employment relationships, on the other hand, shows little flexibility. The authors note that the elasticity of 0.8 is an appropriate calibration target for search and matching models.

Whether focusing on new hires only is too strong an assumption depends mainly on the country one looks at. The US labor market, for example, is driven by huge turnovers. Thus, in every period, a large share of employees can be considered new hires. For some European labor markets, on the other hand, the assumption might be less reasonable because average employment spells tend to be longer and labor market flows smaller.

References:

Haefke, Christian; Sonntag, Marcus; Rens, Thijs van: Wage rigidity and job creation. In: Journal of Monetary Economics 60 (2013), No. 8, pp. 887-899

Pissarides, Christopher A.: Equilibrium Unemployment Theory. 2nd Edition. The MIT Press, 2000

Shimer, Robert: The Cyclical Behavior of Equilibrium Unemployment and Vacancies. In: The American Economic Review 95 (2005), No. 1, pp. 25-49


I guess it depends on what precisely counts as "self-executing" but escrow transactions are very similar and quite common, particularly in real estate and certain kinds of online transactions.

  An escrow is a deposit of funds, a deed or other instrument by one
  party for the delivery to another party upon completion of a specific
  condition or event. It is an independent neutral account by which the
  interests of all parties to the transaction are protected.

What is Escrow? - Title One


Short-run and Long-run cost against the price of the variable input

Everything comes from the constraint

$$
C(p, \gamma^0) \leq S(p, \gamma^0, z^0_k) \tag{C.17}
$$

By construction at $p_0$ these two things are equal:

$$
C(p^0, \gamma^0) = S(p^0, \gamma^0, z^0_k) \tag{1}
$$

Consider a very small positive number $\delta p_i$, and note that (I dropped the other components of $p$ since they remain constant)

\begin{align}
C(p_i^0 - \delta p_i^0, \gamma^0) &<  S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) \\
C(p_i^0 - \delta p_i^0, \gamma^0) - C(p_i^0, \gamma^0) &<  S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) - C(p_i^0, \gamma^0)\\
C(p_i^0 - \delta p_i^0, \gamma^0) - C(p_i^0, \gamma^0) &<  S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) - S(p_i^0, \gamma^0, z_k^0) \\
\frac{C(p_i^0 - \delta p_i^0, \gamma^0) - C(p_i^0, \gamma^0)}{\delta p_i^0} &<  \frac{S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) - S(p_i^0, \gamma^0, z_k^0)}{\delta p_i^0}\\
\lim_{\delta p_i^0\to 0^+}\frac{C(p_i^0 - \delta p_i^0, \gamma^0) - C(p_i^0, \gamma^0)}{\delta p_i^0} &<  \lim_{\delta p_i^0\to 0^+} \frac{S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) - S(p_i^0, \gamma^0, z_k^0)}{\delta p_i^0} \\
-\frac{\partial C}{\partial p_i} &< -\frac{\partial S}{\partial p_i}
\end{align}

or in other words,

$$
\frac{\partial C}{\partial p_i} > \frac{\partial S}{\partial p_i} ~~\mbox{for}~~ p_i < p_i^0 \tag{2}
$$

or in plain English: $S$ is flatter than $C$ for $p_i < p_i^0$. You can repeat the same argument for $p_i > p_i^0$


The most obvious answer is Coasian bargaining. What Coase showed in his famous "The Problem of Social Cost" is that if there are no transaction costs and if utility is transferable then it suffices to allocate property rights—i.e. to give one party the right either to engage in the externality-causing activity or to prohibit it. The two parties will then engage in bargaining with the result that the socially efficient level of the activity is undertaken. The idea is that if an activity has private value $v$, but imposes external social cost $c$ on others then

if the private individual has the right to participate in the activity then others would collectively be willing to pay up to $c$ to persuade him not to. This offer will be accepted only if $c>v$ so the activity takes place only if it is optimal.
if others have the right to prohibit the activity then the private individual would pay up to $v$ for them not to do so. This offer will be accepted only if $v>C$ so again the activity takes place only when it is optimal.

This example assumes a negative externality, but the same approach works in the case of a positive externality. For example, if the private benefit is $v$ (which may be negative if the activity is very costly) but there is an external benefit of $u$ then third parties would collectively be willing to pay up to $u$ to encourage the private individual to engage in the activity. Thus, the activity takes place only if $v+u>0$---i.e. exactly when it is efficient.

This solution is an important element of carbon trading schemes, which are one of the main ways that countries are attempting to tackle the problem of anthropogenic global warming.

The Coasian solution has the attractive feature that it is relatively decentralised (there is no need for a central planner to accurately determine the size of the externality). Although this solution appears to work very well, it has a couple of important drawbacks:

The zero transaction cost assumption is strong. This is particularly true when an activity imposes a small externality on a large number of people so that there is potentially the need for a large number of bilateral payments.
If the externality falls on a large number of individuals then paying a subsity creates a public good problem: each individual could try to free ride and hope that a large enough subsidy is paid by others.

The Coasian solution therefore works best when either

the externality falls mostly on a single 'large' agent who can therefore engage in Coasian bargaining without the fear of free riding and only incurring transaction costs once.

or

agents are able to use contracts, their government, or some other device to act collectively as if there were the single large agent in 1.


How is the GDP growing when nothing else seems to be?

There's a bit to unpack here.

Consistent wage growth seems in line with rising GDP. So does a steadily falling unemployment rate.

For other economic measures, the stock market is a whole other animal. It often responds to outside global events that aren't solely economic in nature. It may also be affected by the Federal Reserve's desire to steadily increase the interest rate, though we would expect that to also affect unemployment somewhat perhaps.

The most interesting point of contention here is the trade deficit. It's a common misconception that high trade deficits should imply slower GDP growth. During the Great Depression we ran a trade surplus. During 2001 and 2009, with some of the weakest GDP growth, we also had small trade deficits. One possibility as to why we are running a trade deficit is that with a booming US economy, domestic production demands more inputs, which we have to get from abroad for at least a little bit.

It's not really a matter of "less money in the economy" at the end of the day. You can also consider the typical textbook expression for calculating GDP:

$Y = C + I + G + (X - M)$

Where $Y$ is in GDP and $(X - M)$ is exports minus imports. From this equation, it looks like the more we import, the lower GDP gets, so if we end up running a trade deficit because imports keep rising or "money leaves the economy", then we should have smaller GDP.

What's easy to forget is that we have to do something with these imports. We either consume them, use them for investments, or the government buys them ($C, I, G$), so subtracting imports from the measure of GDP is just a way of preventing double counting.


You can interprete $c_1 \in \{0,1\}$ as "I have the tea" and "I don't have the tea", and this tea is valued $v=13$. $c_2$ is just a wealth transfer, i.e., it is $-p$ if the tea is bought and $0$ if the purchase is rejected.
Gain-loss utility is assesed separately in each dimension. Such that
$$n(c|r) = n_1(c_1|r_1) + n_2(c_2|r_2).$$

In your case the reference point is $\widehat r =(1,-30)$. In words, the buyer expects to purchase the good at price 30.
In a PE, it must be that given this reference point
$$U (\widehat r| \widehat r) \geq U ( c | \widehat r) \quad \forall c.$$
That is, the buyer prefers to execute his plan.

This leads to utility
$$U (\widehat r| \widehat r) = v * 1 - 30 + 0 = 13-30=-17.$$
Suppose instead that the buyer does not buy the good. In pure strategies and with a fixed price, there are only two options "buy at price 30", $(1,30)$ and not buying, $(0,0)$.
That is, she does not spend $p$ of her wealth and does not get the good with value $v$,
$$U ((0,0)| \widehat r) = v * 0 - 0 \:+ \quad \lambda(v*0-v*1) \:+ \quad (0-(-30)), $$
where the first part is the consumption utility from not buying, zero.
The second part is the loss-utility from not having the good weighted by the loss-aversion parameter $\lambda$. He does not have the good, so he feels a loss of $v$, the value of the good. The third part is the gain-utility from saving 30 bucks.
Hence,
$$U ((0,0)| \widehat r) =30 - \lambda v = -22$$
with the given parameters. We can verify the given PE.

$v$ is the value of the good. Think of this setting as separable consumption utility
$$m (c) = m_1 (c_1) + m_2(c_2)$$
with $m_1 (c_1) = v c_1$, i.e., if you have the good you garner $v$ and otherwise zero.
The money just enters linearly $m_2 (c_2) = c_2$. Gain-loss utility is always evaluated with respect to consumption utility, see the paper. That is,
actually
$$n_i (c_i|r_i)  = \mu [m_i (c_i) - m_i(r_i)]$$
with the given "universal gain-loss function".

EDIT: To make this useful for all, let me mention the paper corresponding to this model: Heidhues and Kőszegi (TE, 2014). See how they define the product and the money dimension, $k^v =v b$, where $b$ is the $c_1$ of your model (buying or not buying), and $k^p=-bp$. This paper has interesting insights on the impact of consumer loss aversion on pricing and it supersedes their earlier paper.


Source of commodity production statistics?

I work for Quandl and on our site I can recommend two free historical databases that you may want to check out:

The United Nations Industrial Commodities Database, I believe, shows production amounts for various commodities like steel, petroleum, glass etc. in metric tons for different countries: https://www.quandl.com/data/UINC

The United Nations Energy Statistics Database also shows production for other things like alcohol, gasoline etc. in metric tons: https://www.quandl.com/data/UENG

When you go to each database above, just search for "production" within each database. Hope this helps!


AA approach appears to follow two stages: first, "nature" provides which event obtains, which results in the given lottery; second, the lottery is resolved, therefore revealing the intrinsic probabilities. AA suggests to resolve by backward induction. Under usual conditions for vNM utility, agent may define a function for her utility.
I found a nice paper comparing Savage vs. AA approaches, from which I got this construction, e.g. see Fig. 1 and 2. I hope it helps.
https://link.springer.com/article/10.1007/s11166-018-9273-7


As rightly pointed out by @1muflon1@ "Panel data is nowadays quite a big field - usually you will have separate chapters for panel IV, panel logit/probit, panel time series etc".
But if you are "looking for a briefer introduction/overview", I would recommend:

Econometrics Training: Module Three Panel Data (with William Greene and John Siegfried)

Dates back to 2010, but the authors propose a theoretical part on basic models and an applied part with data and programs.


I think you may substitute it directly as mentioned?
$$v(A,k) = \max log(c) + \beta E[v(A',k')|A]$$
Applying the value function expression (note period change):
$v(A',k') = \frac{log(k')}{1-\beta} + v(A',1)$
Substituting:
$$v(A,k) = \max log(c) + \beta E\left[\frac{log(k')}{1-\beta} + v(A',1)|A\right]$$
By linearity:
$$v(A,k) = \max log(c) + \beta E\left[\frac{log(k')}{1-\beta}|A\right] + E\left[v(A',1)|A\right]$$
Since $E\left[v(A',1)|A\right] = D(A)$:
$$v(A,k) = \max log(c) + \beta \frac{log(k')}{1-\beta} + \beta D(A)$$


Find probability that payoff function is in $[10,20]$

Generally:

$P(f\in[10,20]) = P(120 \leq S_t \leq 130) = P(S_t \leq 130) - P(S_t \leq 120)$
That is, the probability that the option is between 10 and twenty is the same that the stock is between 120 and 130. The probability that the stock is between 120 and 130 is the probability the stock is less than 130 minus the probability that it is less than 120. If you are a more visual person consider this picture:

Source MathWave

If we know that $W_t$ follows a driftless-Wiener process that:

$W_t - W_0 \sim N(0, 15^2t) \rightarrow S_t \sim N(95, 15^2t)$

If $S_t \sim N(95, 15^2t)$ then $P(S_t \leq 130) = $ prob. that a normal random variable with mean 95 and std. deviation 15t which is just the cumulative distribution function (CDF) of that normal random variable.

Here, that CDF is $\Phi( (x-95) / (15 \sqrt(t)))$, where $\Phi$ is the CDF of the standard normal. So the answer is $$\Phi( (130-95) / (15 \sqrt t)) - \Phi( (120-95) / (15 \sqrt t))$$

Update:
I thought that this was a simple option payoff but this is actually a trickier problem because it is a look back option taking the maximum stock value from 0 to 2. The general idea with this more complex problem is we are studying the maximum of a Wiener process motion rather than the Wiener process itself. Stochastic Processes and Related Distributions by Daniel Herlemont, section 2 should be of some help. But I don't have a solution to this problem at this time.


Why is the labour supply independent of the wage in this case?

For some intuition, rewrite the problem as the consumption problem $\max_{(c, l)\in\mathbb{R}_{+}^{2}} (cl)^{0.5}$ subject to the constraint $c/w + l \leq 1$.
The optimal level of $l$ is then given by $l = 1/2$ as per the usual solution for Cobb-Douglas preferences.
The intuition for why $l$ does not depend on $w$ in this example is the same intuition for Cobb-Douglas consumers, who spend a fixed fraction of their income on each good.


There is a paragraph about the history of credit rating agencies that I don't understand

It’s an extremely long-winded way of saying that lending moving from bank lending to bond/money markets. The fact that depositors did not take much direct credit risk is a red herring.
I don’t see the financial logic, but yes, the banking sector moved from being lenders to underwriters of securities.
Bond and money markets are decentralised: instead of a single bank making a loan, there is a group of investors buying a new bond or money market instrument.

The passage is inherently confusing, as it is based on a couple of questionable premises.


To begin with, I think the question is wrongly stated. For if the defininition of a thin indifference curve is such that continuity of a consumer's preferences implies thin indifference curves, then, surely, continuity implies thin indifference curves... This answers your question.

However, if we are to make a suitable definition of a thin indifference curve, we may firstly say that $$[q]=\{p\in\Delta|p\sim q\}$$ is a thick indifference curve, where $\Delta$ is the set of possible bundles, and where $\sim$ denotes indifference, whenever there exists a $q'\in [q]$ and a $\epsilon>0$ such that $p\in N_{\epsilon}(q')$ implies $p\sim q'$, where $N_{\epsilon}(q')$ is some epsilon-neighbourhood around $q'$; and secondly say that $[q]$ is a thin indifference curve if it is not thick. Colloquially this means that there is some bump on a thick indifference curve $[q]$, but no such bump on a thin indifference curve.

Essentially, the above is a short exposition of A Geometric Approach to Expected Utility (Chatterjee & Krishna, 2006). Using the above definition of a thin indifference curve, they show in Lemma 2.3 that (i) continuity and (ii) independence implies thin indifference curves (note that they do not show that continuity alone implies thin indifference curves; cf. Ubiquitous' answer). Their definition relies on the following two topological concepts.

The assumption of continuity. All subsets $\{q|q\succ p\}$ and $\{q|p\succ q\}$ of $\Delta$, where $p\in \Delta$, are open; here, remember that an open set is a set for which each point in it has a neighbourhood lying in that set. Thus, this notion of continuity is similar to yours.
The assumption of independence. For all $p,q,r\in\Delta$, $p\succ q$ and $\lambda\in (0,1]$ implies that
$$\lambda p+(1-\lambda)r\succ \lambda
q+(1-\lambda)r;$$ this allows for some nice algebra.

Now, what they show in Lemma 2.3 is essentially that if you have an indifference curve $[q]$ and consider some epsilon-neighbourhood $N_{\epsilon}(q')$ around $q'\in [q]$, then $p\in N_{\epsilon}(q')$ will not imply that $p\sim q'$ for arbitrarily small $\epsilon>0$. I.e., however small, no epsilon-neighbourhood is such that it only contains bundles for which one is indifferent between those bundles and $q'$. Instead, every epsilon-neighborhood will include points that are strictly preferred to $q'$.

For continuous utility functions, I think it is fruitful to note that their image in e.g. $\mathbb{R}^2$ has (Lebesgue) measure 0 (cf. How to prove that the image of a continuous curve in $\mathbb{R}^2$ has measure $0$?)


Why is the short run average cost curve not a tangent to the long run average cost curve at the lowest point on the short run average cost curve?

The diagram is fine as an illustration of a possible relation between the long run average cost curve and one particular short run average cost curve.

Long run in the context of a firm's cost functions means that all inputs are free to vary, so it makes sense to refer to the long run cost curve.  Short run means that one or more inputs (eg capital equipment) are fixed.  Since these inputs could be fixed at different levels, there are many different short run cost curves. The long run cost curve is the envelope of these curves. Unless it has been specified at what level they are considered fixed (which could implicitly be whatever is their current level), it makes no sense to refer to the short run average cost curve.

In most cases, the minimum point of a short run cost curve will be above the long run cost curve.  This should not be surprising: it just means that, for the relevant output, it's possible to obtain lower costs if all inputs are free to vary than if only some are free to vary.

There will however be one short run cost curve corresponding to the levels of fixed inputs at which the long run cost curve is at its minimum.  The lowest point of that particular short run cost curve will be tangent to the long run cost curve (and incidentally the short and long run marginal cost curves will also pass through the same point).

A diagram showing multiple short run average cost curves, with one having its lowest point tangent to the lowest point of the long run cost curve may be found in Nicholson W (9th edn 2005) Microeconomic Theory.  For an online source see here.


Applying ensemble modelling to VAR models

Emsemble learning is beneficial in forecasting where statistical adequacy of any model in the ensemble is of limited importance. However, when models are used for inference, statistical adequacy is quite important. The correctnes of the assumed null distribution of the test statistic depends (to a larger or smaller degree) on the statistical adequacy of the model. Violations of some modelling assumptions may lead to distortions of the critical values and thus the test size, making inference unrealiable. This is a common problem known from the model averaging literature. Only statistically adequate models may be averaged when the goal is inference (rather than forecasting), as otherwise the inference is unreliable. My explanation is a bit simplistic, but I hope it conveys the main idea.


How to predict income n years after graduation using income dataset with age, but not graduation year?

I think you're looking for false precision, here.  "Years since graduation" is already a step function with an essentially arbitrary cutoff (should it really matter to your model that much if somebody is one day shy of being at the end of +1 years, versus one day into +2 years?  the actual difference is a few days.)

Just use age minus 23, or just use age in your model.  It shouldn't impact things that much either way.


Apply Ito's Lemma to exponential martingale

$\newcommand{\dd}{\, \mathrm{d}}$
If we apply Ito's lemma,
then
\begin{align*}
\dd \xi_t &= -\xi_t \dd X_t + \frac 12 \xi_t (\dd X_t)^2\\
  &= -\xi_t \left(\frac 12 \lambda_t^2 \dd t + \lambda_t \dd z_t\right) + \frac 12 \xi_t \lambda_t^2 \dd t \\
  &= -\xi_t \lambda \dd z_t.
\end{align*}


Since $a + b=1$ the equations are exactly the same. Substituting in for $a+b$ with $1$ in the third and fourth equations gives the first and second equations.


What are some non-von-Neumann-Morgenstern preferences used in economics?

The von Neumann-Morgenstern (vNM) utility function takes the form
\begin{equation}
U(p,x)=\sum_{i=1}^np_iu(x_i)
\end{equation}
where $x=(x_1,\dots,x_n)$ with $x_i$ being the (monetary) payoff associated with outcome $i$ and $p=(p_1,\dots,p_n)$ with $p_i$ being the probability that $i$ occurs.

In behavioral economics, generalizations of the vNM utility usually happen in either (or both) of the following two channels:

Non-linear probability weighting: instead of using $p_i$'s, which can be considered objective probabilities, a model may use decision weights $w_i$'s which map the objective probability distribution into a new distribution.
Reference dependent utility function: instead of $u(x_i)$, which depends only on the payoff in outcome $i$, a model may consider a utility function $u(x_i,r)$ that depends on both $x_i$ and some reference payoff $r$.

Modifications made through either of these will give rise to a non-expected utility function, which is supposed to improve the model's descriptive accuracy of people's decision under risk.

Example of 1: Rank-Dependent Utility

Suppose $x_1<x_2<\cdots<x_n$, and calculate decision weights ($w_i$'s) as follows:
\begin{equation}
w_i=\pi\left(\sum_{j=i}^np_j\right)-\pi\left(\sum_{j=i+1}^np_j\right),
\end{equation}
where $\pi(\cdot)$ is called a probability weighting function (PWF).
A common PWF is the Tversky-Kahneman PWF:
\begin{equation}
\pi(t)=\frac{s^\gamma}{(s^\gamma+(1-s)^\gamma)^{1/\gamma}}.
\end{equation}
Then the rank-dependent utility with T-K PWF is
\begin{equation}
RDU(p,x;\gamma)=\sum_{i=1}^nw_iu(x_i).
\end{equation}
Note that $w_i=p_i$ if $\gamma=1$, so that vNM EU is a special case of RDU.

Example of 2: Disappointment Aversion

\begin{equation}
DAU(p,x;\overline U)=\sum_{i=1}^np_i[u(x_i)-D(u(x_i)-\overline U)],
\end{equation}
where $D(\cdot)$ is a function that captures how disappointment ($u(x_i)<\overline U$) or elation ($u(x_i)>\overline U$) affects an individual's evaluation of a prospect. Here, the reference utility level $\overline U$ can be something like the certainty equivalent level of utility. EU can also be derived as a special case from DAU by requiring that $D(\cdot)$ be a constant function.

Example of 1+2: Prospect Theory

Prospect theory (PT) incorporates both non-linear probability weighting and reference dependence. Again, assume $x_1<\cdots<x_n$. PT distinguishes between gains ($x_i>r$) and losses ($x_i<r$). For gains, decision weights are given by
\begin{equation}
w_i=\pi^+(p_i+\cdots+p_n)-\pi^+(p_{i+1}+\cdots+p_n),
\end{equation}
while for losses the decision weights are
\begin{equation}
w_i=\pi^-(p_i+\cdots+p_n)-\pi^-(p_{i+1}+\cdots+p_n),
\end{equation}
where $\pi^+(\cdot)$ and $\pi^-(\cdot)$ are both PWFs. For instance, one can have both PWFs be the Tversky-Kahneman form, but with different parameters. In addition, the utility function also takes a reference dependent form:
\begin{equation}
u(x_i,r)=
\begin{cases}
(x_i-r)^\alpha &\text{if }x_i\ge r\\
-\lambda(r-x_i)^\beta &\text{if }x_i<r
\end{cases}
\end{equation}
where $\alpha,\beta\in(0,1)$ are parameters of risk aversion (differentiated between gains and losses) and $\lambda>0$ is the coefficient of loss aversion.
Thus, the non-expected utility function under PT is
\begin{equation}
V(p,x;\text{parameters})=\sum_{i=1}^nw_iu(x_i,r)
\end{equation}


What books to read to learn about geography and how it affects economic development?

A good starting point which should be accessible to people at all levels is the book "Guns, Germs, and Steel" by Jared Diamond.

I believe this is one of the first and main seminal works in this area.

That being said, it is not settled science that geography (alone) can doom a country's economy.


You correctly derived the Marshallian demand function for Cobb-Douglas utility, you notice that the optimal level of consumption of $x$ or $y$ is a function only of the individual's income and the price of said good.  This is an interesting feature of CD-utility, that when the price of good $y$ changes the demand for $x$ doesn't change.  This means that $x$ and $y$ are neither substitutes nor complements to one another. Econport has a nice figure of this:

$\hskip2in$

The first figure shows that as the price of good $x$ changes the quantity of $x$ changes but the quantity of $y$ does not change.  The second figure shows that as price increases the amount demanded decreases and vice-versa when price decreases.

As a side note, CD-utility further implies strict quasi-concave utility so that the indifference set is strictly convex, hence $\vec{x}^* (\vec{p},I)$ is single-valued.  With constant prices for $y$ and prices $p_a, p_b, p_c$ for $x,$ we choose the optimal consumption level of each commodity at the points $a = (x_a, y_a) ,b = (x_b, y_b) ,c = (x_c, y_c)$, such that the slope of the budget hyperplane and the tangent slope of the indifference curve are equal.


Strict quasiconcavity implies single-peakedness, i.e. any strictly quasiconcave function has a unique supremum (or maximum if the domain is compact). Hence, any strictly increase convex function is also strictly quasiconcave.

Here are a couple figures to illustrate the difference. The function on the right is not quasiconcave because it has two local maxima.


own and cross elasticity for many products

this comes from a standard cob-douglas utilty function such as $U=A^\alpha\cdot B^\beta$ w.r.t a budget constraint. If you take a monotonically increasing function of U such as a log which leads to $ \ln (U) = \ln (A^\alpha\cdot B^\beta) -> \alpha \cdot \ln (A) + \beta \cdot \ln (B)$ by solving this via a method like subbing in the budget constraint to get the indirect utility form and adding some dummy and interactions to control for the promotions you get the form above. You can see that this is founded purely from first principals but runs into the "too many parameters" problem when you have many products as you correctly anticipated. Imagine we have 100 products and we need to calculate the elasticity for every product pair. Well then we would have 100 equations with 100 elasticity parameters + 100 intercepts and whatever promotional dummies = $ 100 \cdot 100 + 100 10,100$ minimum parameters. As you might not even have this many data points and not enough to measure efficiently you run into problems and need to use other methods that impose more assumptions on the data.


Because of the recession some members of the household may have lost their jobs. So maybe they don't have enough money to pay a utility bill? To pay for urgent repairs? To buy a Christmas present? There are a variety of possible reasons.


Relationship between the Tragedy of the Commons and negative externalities?

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

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

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

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


Are services included in the calculation of a trade deficit?

The standard is that they are. For example, see the current report on the trade in goods and services for the United States: link to BEA website; latest report.


There is a lot of literature on this question.

This review looks like a good place to start although it is from 2013. It looks at a wide range of both qualitative and quantitative approaches.

  Among them, the most frequently used technique is the time series econometrics in order to forecast the
  volatility of oil prices, the second frequently used is the financial method, the third frequently
  used methods are based on structural models and non standard computational models, and the
  least used technique is the qualitative knowledge based method


How do economists explain why people contribute to Wikipedia?

I wouldn't underestimate the role of learning by answering.
Drafting a significant text typically forces a person to put their thoughts in order, to engage in research, and then to structure the information for the purpose of recording and conveying it. It is not unusual that further insights or questions emerge during this process, the answerer certainly becomes more familiar with the subject, and good communication is itself a skill that requires significant attention and practice to develop.
Moreover, publicising one's thinking (even to a very small audience) typically invites challenge and puts it to the test of what others think of it, which again tends to flush out all kinds of faults and oversights - either faults in the thinking itself, or faults in the way it has been articulated and formulated into words.
Clearly, the assumption embedded in this question is that communication is done purely for the benefit of the listener, and that knowledge transfer is done in a "jug and mug" style, but there is more truth than you might think in that hoary old claim that academics have much to learn from their students.
So part of the answer to why people freely labour to communicate on sites like Wikipedia (not to mention here at StackExchange) is therefore bound up in the question of what stake they have, not just in developing the knowledge they appear to possess, but also in developing and rehearsing all the broadly intellectual skills associated with the development, retention, and communication of knowledge.


Empirical ranking of firms based on productivity

There is a scientific tradition of decades that occupies itself with the measurement/estimation of the productivity/efficiency of firms. The three strands of the literature are Data Envelopment Analysis (DEA), Discriminant Analysis (DA), and Stochastic Frontier Analysis (SFA).

I am familiar with the third one. Stochastic Frontier Analysis starts with the observation that firms do not operate all the time on their efficiency frontier, i.e at maximum efficiency, either due to unanticipated shocks, or because, while competitive market forces may push firms to be efficient, they nevertheless are not that strong or that perfect in their effects in order to make firms to be fully efficient, as it is usually assumed in theoretical models. Therefore, inefficiencies due to organizational problems and the like, may persist.

"Efficiency" in the context of SFA, has many facets: output-oriented technical efficiency, input-oriented technical efficiency, cost-efficiency, revenue efficiency, profit efficiency. All have been developed in the literature. One can choose the approach  or approaches most suited to the purpose at hand, and to data availability.

To consider the case of output-oriented technical efficiency, SFA modifies/augments the production function of a firm as

$$Q = F(\mathbf x) + u -v$$

Where $u$ is a zero-mean normal random variable and $u$ is a non-negative random variable (usually specified as a half-normal or as an exponential r.v.). The $v$ component captures the inefficiency (measured in terms of output), while the $u$ component captures stochastic disturbances that may affect production (either positively or negatively).  $F(\mathbf x)$ represents the full-efficiency level of output.

Econometrically, this is estimated by using Maximum Likelihood (the least-squares method cannot decompose the error term in its two components), on a data set that contains data on output, and on quantities of input factors (in other words, no more than the usual data set required to estimate a production function).
The estimation procedure itself will provide of course estimates that are averages over the data set. If one wants to rank the firms present in the sample, one can implement the approach developed in Jondrow, J., Knox Lovell, C. A., Materov, I. S., & Schmidt, P. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of econometrics, 19(2), 233-238.

A comprehensive book on Stochastic Frontier Analysis is Kumbhakar, S. C., & Lovell, C. K. (2003). Stochastic frontier analysis. Cambridge University Press.


I did some napkin math based on your data. At 4 tx/s and 8GW, that is 2GWs per transaction. 0.5kg/kWh is around 139kg/GWs. Thus each transaction is around 278kg. Looks like we reached the same answer.

But is this the carbon footprint of one Bitcoin transaction? To put it differently, if there was a global carbon tax, would it makes sense to charge for 278kg per transaction? Probably not. In fact, almost certainly most of the tax would just apply to the electricity bill of Bitcoin miners, which is split between hashing for the block reward and processing transactions.

There are roughly 2000 transactions per block. Each transaction costs roughly \$1. The block reward is 12.5 Bitcoins as of now. At \$8200 per Bitcoin, roughly $\$2000/(12.5\space\text{BTC} \times \$8200/\text{BTC} + \$2000)=0.0191$ or 2% of a miner's electricity bill goes to transaction processing. So perhaps it makes more sense to say that each transaction costs around $278\space\text{kg} \times 0.02=5.56$kg of carbon.

So what about the rest of the carbon? In some sense, the main job that PoW does is preserving the integrity of existing token balances. The block reward is seniorage. This a similar principle to how central banks print more money and thus reduce the value of existing bank notes and coins. As of now there are close to 18 million Bitcoin in existence. Continuing with your carbon emission numbers, each Bitcoin holder that isn't transacting is then responsible for $((8/(18 \times 10^6)) \times 139) \times 0.98=0.000060542$kg of carbon per second per Bitcoin or 5.23kg of carbon per day per Bitcoin.


Why would a cash-rich company borrow money?

You are right that it seems strange why a cash-rich company is borrowing. In the case of Apple, the money that they are borrowing is being used to pay dividends to shareholders. The reason why they aren't using their \$200 billion is because doing so would cost them tens of billions of dollars in taxes. The current US tax code taxes corporations at 35% when they bring money they made overseas back to the US (this is called repatriation). So while, Apple has \$200 billion on the surface, \$180 billion of that is sitting overseas and can't be used to pay shareholders. It is cheaper for them to borrow money to pay dividends, than incur the huge tax costs associated with repatriation.

In general, however, borrowing is also attractive to firms today since interest rates are so low. If you can borrow at 4%, and expect to earn a return of 8% on that capital, taking on debt seems like a good deal. Therefore firms flush with cash still may borrow if they feel the return they can earn on the borrowed money is greater than the cost of interest.

Check out this article from Bloomberg for more information on the Apple case: Bloomberg Article


Why does marginal private cost increase with quantity?

What doesn't make sense to me is that the supply curve is upward sloping because marginal costs increase. Why is it that it costs more to make the next toy than it did the last?

The supply curve depicts the short time supply curve.

If resources are abundant, low cost producers can easily increase production by building another factory that is at least as efficient as the exisiting ones.
However, building a new factory takes time. In the mean time the slack will be met by increased production from higher-cost producers and overtime work, both of which have higher costs.

If there is a lasting increase in demand, the most efficient manufacturers will build additional factories that can produce at a low cost and thereby increasing supply, shifting the supply curve to the right.

If resources are scarce, then increasing production will mean that you have to use resources with higher cost. Higher wages for workers, using farm land that yields smaller harvests, mine lower quality ore and so on.

The cost increase can be offset by technological advances or lowering of other factor costs. Take the shale oil industry, where improved drilling technology has greatly increased the production per drilling rig. Also, the factor cost has fallen for labor and drilling services. The combined effect has reduced the cost from ca \$70 per barrel to ca \$40 per barrel. This has allowed US shale oil producers to increase production despite oil prices dropping from \$120 to \$50 per barrel. However, there is no guarantee that this can offset the entire cost increase; increased demand can result in permanently higher prices.


What is the economic strategy of the UK?

You are correct in saying that a household is not comparable to the U.K. or any other country. A household does not issue currency and bonds and typically cannot issue debt obligations that are good beyond, say, approximately 30 years. A person in a household can borrow for approximately 30 years to buy real estate but it would be difficult for that person to borrow for 100 years. Contrast this to the U.K. government which can easily borrow for 30 years and even beyond 100 years. I am reasonably sure the U.K. will collect taxes from people that haven't yet been born and it will collect taxes from companies that have not yet been founded so the value of a long maturity bond appears to be supportable. Likewise some existing U.K. companies and some that will exist in the future can sell long dated bonds.  Existing U.K. companies and those that will exist in the future will also be able to sell shares in their equity and the buyer usually has no right to sell them back to the company, ever. That could mean a long time. If the equity being sold to foreigners is land then that is sustainable only until the supply of land on the islands of the U.K. has been exhausted.

The money raised by Britons working to produce exports pays for most of the imports. Additional to that, the money raised by the U.K. government and U.K. companies selling bonds and shares can be used to buy imports as long as outsiders want to buy bonds and shares. That might be many years so it might be sustainable for a long time. I don't know if this is as much a directed or planned strategy as it is a result that spontaneously emerges from a multitude of foreigners simply wanting to own U.K. real estate and bonds and shares and the U.K. willing to sell those assets. Additional to that, the U.K. receives interest, principal repayment, and dividends from abroad. The sustainability of these depends upon the particulars.


Can there be too little unemployment for the health of the economy?

Let me answer a simpler question first. Is it possible for there to be too little orange juice in the grocery store? Definitely.

Let's say that the price of OJ is set too low (\$1 per liter) and customers who arrive early in the morning buy all the OJ. Assume that those customers think buying all the OJ is a good deal and they figure they'll enjoy drinking it, but that at regular price (\$4 per liter) they'd buy much less, they wouldn't want any more at those prices, and there would be lots left on the shelves.

People who arrive later in the day want some OJ at \$4 per liter. If they could find them, the early OJ buyers would happily sell them the OJ at that price and pocket the profit (that follows by the demand schedule I sketched out in the second sentence of the last paragraph). That means that there are deals to be done that would improve the allocation of OJ (there are welfare increasing, Pareto-improving, trades to be made). But the early customers and the late customers have trouble finding each other and so the OJ stays in the early shoppers' refrigerators.

Just about everything I just said about OJ holds for worker labor. Surprise! If the price of labor is set below the equilibrium price then early buyers purchase an inefficient quantity. Later buyers can't find the workers they need even though the marginal value of those workers is higher than the price at which the early employers bought them. Because (or perhaps I should say if) it is less efficient to look for a job while you have a job, when unemployment is too low workers ended up employed by firms that do not employ them at their highest marginal product. If only alternative employers could be found output and welfare could be improved. In fact, using a Kaldor-Hicks mechanism it is possible to make the new employer, the old employer, and the employee all better off under such circumstances. Thus it is not efficient under production efficiency or welfare efficiency criteria.


Calculating rate of growth of per capita income

Consider: If national income is increasing at a slower rate than population growth, then intuitively per capita income will be falling. Here is a set-up for the rate of decline in per capital income.

$$\text{per capita income}_t = \frac{\text{GDP}(1.015)^t}{\text{population}(1.025)^t} \text{per capita income}_{t-1}$$


Capitalism works best when there is elasticity- the price can go up or down by a marginal unit without running into the problem of plateauing supply or demand.

In extremely wealthy or extremely poor places, the market can experience inelasticity- where a change in the price will not affect demand.

Cheap item inelasticity:
E.g. The water is free at restaurants but we don't see people drinking insane quantities of water, though supply/$0 should equal infinite demand.

Expensive item inelasticity:
Someone is stranded in the desert and has no water. A vending machine offers him water for 100 gold coins. Even though the price is very high, the man still needs water. To save his life, the man would pay 100 or even 200 coins, doubling the price without reducing the demand. As it happens, the man has only one coin and dies because the vending machine was unable to adjust its price to make a sale.

Cheap item inelasticity is rarely a problem because if a country is stuck with undesirable surplus, it could just burn it or throw it in the sea.

Expensive item inelasticity is more prevalent in poorer places where more of the population is unable to afford important goods. A country could A) allow its people to starve B) subsidize goods for the poor C) set a maximum price for the item.

B and C are not free-market options.

A poorer economy is more likely to run into the problem of Expensive Item Inelasticity and is thus more likely to attempt to resolve it.


Does anyone here have experience with GARCH-MIDAS forecasting?

Sean Becketti has a very readable book called Introduction to Time Series Using Stata that has a chapter on (G)ARCH models. Unfortunately, it does not discuss mixed-data sampling (MIDAS), as that is a more advanced topic. I am not aware of any introductory treatment  of that material.


The tangency condition itself is the condition that the optimal point, for an interior optimum, is the point where the MRS must equal the slope of the budget line. So the second part of your question is true. It is at the tangent point where MRS equals the slope of the budget line. You've confused yourself with the second (sufficient) condition which, on the other hand, states that the utility function must be strictly quasi-concave in order for an interior optimum to exist.
Hope this clarifies.


As often with models embodying some form of "irrationality" (whatever that means), HD does a great job at matching a whole lot of behaviors, but leaves room for rather annoying Dutch Book situations (also know as "money pump" situations). These suggest that HD might generate some inaccurate predictions, and induce undesirable behaviors when included in models.

Here is an example. Suppose today is $t=0$ and I owe you a dollar one periods from now at $t=1$. I offer you the following sequence of deals:

In $t=0$, I offer to pay you some fee $f_0$ in $t=2$ in order to postpone my payment from $t=1$ to $t=2$.
In $t=1$, I give you the possibility to pay me some fee $f_1$ in $t=2$ in order to get the dollar back in period $t=1$ instead of $t=2$ (assuming you accepted the deal in $t=0$).

Case 1 : you have a classical exponential discount factor $\frac{1}{(1+\delta)^t}$.

Period $t=0$ : what is the minimal additional $f_0^*$ I can offer to pay in $t=2$ for you to let me postpone my payment to $t=2$?

$$ \begin{align} f_0^* & = (1+\delta)^2 \left[ \frac{1}{(1+\delta)} - \frac{1}{(1+\delta)^2} \right] \\
                       & = \delta \end{align} $$

Period $t=1$ : what is the maximal additional $f_1^*$ I can ask you to pay me in $t=2$ in order for you to get your one dollar in $t=1$ instead of $t=2$ ?

$$ \begin{align} f_1^* & = (1+\delta)  \left[ 1 - \frac{1}{(1+\delta)} \right] \\
                       & = \delta \end{align} $$

So summing up the two deals : in period $t=0$ I offer to pay you $\delta$ more in $t=2$ to postpone the payment, but then in $t=1$ you promise to pay me $\delta$ more in $t=2$ to get the money earlier. Overall the deals cancel out, I still give you the dollar in $t=1$ and no one owes the other anything in $t=2$.

Case 2 : you have HD with discount factor $\frac{1}{(1+\delta t)}$.

Period $t=0$ :

$$ \begin{align} f_0^*(HD) & = (1+ 2\delta) \left[ \frac{1}{(1+\delta)} - \frac{1}{(1+2\delta)} \right] \\
                       & = \frac{\delta}{1+\delta} \end{align} $$

Period $t=1$ :

$$ \begin{align} f_1^*(HD) & = (1+\delta)  \left[ 1 - \frac{1}{(1+\delta)} \right] \\
                       & = \delta \end{align} $$

Summing up the two deals, I still give you the dollar in $t=1$, but now you owe me an additional $\left[\delta - \frac{\delta}{1+\delta}\right]$ in $t=2$ which is strictly larger than zero for $\delta > 0$. Thus in a sense, I made money out of "nothing" (or some would say I made money out of your time-inconsistent preferences).

Whether this is bothersome for the HD model depends on whether you believe that these kinds of money pumps are likely or unlikely to occur.

==================

In the comments, the OP also asks whether HD would have any influence on risk behavior. I do not think it would. HD denotes a specific way to discount utility but does not impose restrictions on the form of the instantaneous utility function $u(\cdot)$ which determines risk aversion in uncertain environments.


Has the Nash Equilibrium led to any significant economic discoveries?

Two areas that have been profoundly affected by game theoretic research stemming from Nash's contribution are

Oligopoly theory

There are actually a few examples of what would come to be known as Nash equilibrium in the industrial organization literature that predate Nash's work (for example, Cournot's 1838 analysis of oligopoly competition). However, until Nash (and Selten, Harsanyi, and others) made game theory a general purpose tool, industrial economics was primarily focused on relatively naive models of competition. In the last 30-40 years there has been a revolution in industrial organisation as economists have used game theory to essentially reinvent the study of market competition around oligopoly theory and the study of strategic interaction. Our modern understanding of consumer search, limit pricing, strategic entry and entry deterrance, predatory pricing, strategic advertising, switching costs, product differentiation, platform competition, horizontal and vertical integration, etc. are all predicated on models that rely mostly on Nash equilibrium (or a refinement thereof) as the solution concept. Jean Tirole was recently awarded the Nobel prize largely for work in this area.

This work has also found great practical application in areas such as antitrust policy. Prior to the 1960s, antitrust enforcement in the US (and, to a large extent, elsewhere) was inconsistent and based on unsound economic principles. A combination of the insistence by scholars (especially those based in Chicago) on more careful analysis, and the new tools of oligopoly theory have lead to a much more robust and well-grounded approach to regulating competition.

Auction theory

The study of auctions is game theoretic by its very nature: most auctions involve very direct strategic interaction between a relatively small number of bidders. It should come as little surprise, then, that auction theory essentially did not exist prior to the work of Nash (the formal study of auctions can be traced to W. Vickrey (1961) "Counterspeculation, Auctions, and Competitive Sealed Tenders," Journal of Finance 16(1); also the recipient of a Nobel prize).

None of the cornerstones of auction theory (revenue equivalence, the linkage principle, optimal auctions—source of yet another Nobel prize, etc.) would exist without the solution apparatus that can be traced to Nash. This work, too, has been of great practical importance. From radio spectrum licenses to carbon emissions permits, and from public procurement to Google ad auctions, auction theory has had a significant effect on informing good auction design. See Klemperer (2004) Auctions: Theory and Practice, Princeton University Press for an accessible summary of the theory and its applications.


What caused the stagflation in the early 1970s USA?

The 19702-73 inflation was a supply side shock, a negative supply shock to be specific. Because of the high oil prices, production cost of almost every rose sharply.

Since, this was the first time that such a shock was seen at such large scale it was mostly misunderstood and traditional short term policy tools i.e. easy monetary policy and fiscal stimulus were deployed. What had actually happened was since oil is such an essential part of production, not just the short term but the long term output or the potential output itself was affected and should have been revised. Because of the incorrect diagnosis and policy response, inflation got embedded into the long term expectations and hence it just went into a spiral.


Is there fundamental economical reasoning for patriotism?

I think the purpose of patriotism is to create incentives for actions with positive externalities.

Your example of joining the army is a good one. The opportunity cost of joining the army is huge. You are risking your life for a relatively meager salary and are not gaining skills in the workplace which you could outside of the army. There is however a very strong positive externality of having a large army with willing participants.

Patriotism creates an additional incentive for individuals to perform these types of actions which otherwise might not be performed. Actions such as voting, community building, paying taxes, and working in certain industries for lower pay (think ACLU lawyers) are in large part undertaken due to a feeling of community that people within a country feel. This social incentive promotes positive externalities and benefits the society as a whole which is why patriotism is likely such a desirable attribute to be fostered within a country.


Macroeconomic policies and trade balance

In a small open economy specifically (as opposed to a closed economy, which does not trade with other countries, so $NX$ is not considered) , the the real world interest rate is not effected by the economy increasing its internal interest rate. As consumers can simply turn to the world market and get funds at a lower interest rate if the internal interest rate increases greater than the world interest rate. However an increase in government expenditure will increase the trade deficit.

Note that Net Exports equals Net Capital Outflow. This can be visualized mathematically:

$$NX=S-I$$

Where: $S=$ National Savings $= Y-C-G$.

This means that as Government expenditure $(G)$ increases National Savings $(S)$ will decrease. Thus resulting in a greater trade deficit.

Therefore, It is of my humble opinion, based on the question, it seems that an increase in government expenditure will not assist in lowering the trade deficit.

Hope this is helpful.


Here is a simple explanation for a single input and output technology represented by a production function $f:\mathbb{R} \to \mathbb{R}$.

Note that Average Product (AP) is defined as
$$
AP(x) = \frac{f(x)}{x}
$$
, and Marginal Product (MP) is defined as
$$
MP(x) = \frac{\partial f(x)}{\partial x} = f'(x)
$$

Now, we take the derivative of the function $AP(x)$, and then we have
$$
\frac{\partial AP(x)}{\partial x} = \frac{f'(x)x-f(x)}{x^2}
\\
= \frac{1}{x}\bigg[f'(x)-\frac{f(x)}{x}\bigg]
\\
= \frac{1}{x}[MP(x)-AP(x)]
$$

Since $x$ indicates the level of the input, $x>0$, and thus we have,
$$
\frac{\partial AP(x)}{\partial x} > 0 \iff MP(x)>AP(x)
$$
, or
$$
\frac{\partial AP(x)}{\partial x} < 0 \iff MP(x)<AP(x)
$$


Why do banks loan at APR < 6%, when they can invest that principal in ETFs?

XSP is riskier than the preferential rate personal loan. The Standard and Poors 500 is a large composite of U.S. equities, hedged (short USD, long CAD). XSP combines the equity market volatility and the USD / CAD volatility but it tries to offset currency value change by holding a hedge. Some of the volatility is offsetting; some is additive. The equity composite risk is acceptable for many investors if they intend a long investment period, for example, 30 years. The USD / CAD risk is acceptable for some investors if both the Federal Reserve and the Bank of Canada manage to achieve roughly equal inflation rates over the long investment period, but XSP's manager aims to minimize this risk. For many investors, the risk of XSP is only acceptable if a long investment period is intended. However, the preferential rate personal loan is likely for a shorter period. Over that shorter period XSP is expected to be riskier than the personal loan. The preferential rate personal loan is made after checking employment history, income, assets, and other indications of ability to meet obligations. A bank's business model is to own loans; not huge amounts of an equity index. Bank regulators force banks to keep risk below a certain level.

Incidentally...

If XSP is held in the investor's taxable account, keep in mind that the XSP manager sometimes returns capital to the investor which lowers the investor's average cost. The XSP manager sometimes reinvests cash into more equity which effectively means it raises the investor's average cost. Unless you plan to invest extremely large amounts, you might find keeping track of these things to be not worth the effort.

Addendum:

There was a request for information about XUS. You avoid the "currency hedging risk" inherent in XSP by choosing XUS instead. Currency hedging risk is the risk that the fund manager's hedging activity imperfectly eliminates your exposure to the USD which is inherent in the underlying asset which is based on the S&P 500. By choosing XUS instead, you are accepting "currency risk". That is the risk created by exposure to the USD which is inherent in the underlying asset which is based on the S&P 500.

In this risk chart they show that XSP has both kinds of risks, because the hedging is imperfect so XSP still has currency risk. By implementing hedges, the manager aims to make that currency risk less than what is in XUS.


What is the likely result of rent control in Berlin?

Rent control will over time decrease the supply of housing while increasing demand causing a housing shortage. Moreover, there are also studies that show that under rent control there are not just shortages of houses but also misallocation, that is the houses are no longer allocated to people who have highest utility/consumer surplus from having them (Glaeser and Luttmer, 2003).

A recent literature review on rent control concluded (Jerkins, 2009):

  I find that the preponderance of the literature points toward the conclusion that rent control introduces inefficiencies in housing markets. Moreover, the literature on the whole does not sustain any plausible redemption in terms of redistribution.

Furthermore, the IGM forum, a platform that surveys the top policy economists, shows that virtually all of them think that rent control (at least as applied in US) had a negative effect on availability and quality of housing (see here).

However, note an important caveat is that as any policy also rent control is not always homogeneously applied. I saw some studies showing net positive redistributional effects of rent control but it’s only small minority of all studies and usually the positive results come from rent controls that were applied only to special subsection of housing market for example government owned social housing. Those studies to my best knowledge do not really apply to the Berlin case, which is going more or less the similar route as San Francisco or New York where the effects are shown to be significantly negative.


There are two assumptions in your explanation that require change

1st of all, regading the seller

  The seller can sell some at a profit, and some at a loss, and as long
  as the loss and profit cancel out, he's on the supply curve.

The supply curve theoretical logic is that the seller will produce as much products as possible, at a rising cost, as long as the market price that he sees is higher than the last product he produced - the marginal product
Based on that, the seller will always sell at market price. the profit comes from the gap between the market price and the entire cost of production, which is cheaper than the marginal cost. he's initial products cost less

The supply curve is the average MC of all firms, which, in a competitive market model, share the same technology, since open information is available, so the average should be of identical firms


Under most capitalism-like systems, companies are funded in two ways.  One is debt with positive interest, the other is by selling equity to shareholders.  If you could effectively prohibit debt, then companies could conceivably adapt by switching to a 100% equity model, in which individuals would shift all of their interest-bearing savings into shares.  This would create various inefficiencies (and create a lot of problems for consumers who would be unable to obtain mortgages), but wouldn't fundamentally destroy the incentive to produce.


How to find $\phi$, that denotes the correlation of signals among informed traders?

A degenerate joint normal is distribution is one in which you cannot find a PDF for the distribution. They assume you can. (The covariance matrix is invertible).

Let $f(s_1,s_2\dots,s_n,v)$ be the distribution.
If I was to exchange $s_1$ for $s_2$, $f(s_2,s_1,\dots,s_n,v) = f(s_1,s_2\dots,s_n,v)$, the distribution does not change. And you can exchange as many indices (signals) as you'd like.

The assumption that the distribution is jointly normal implies $\tilde{v}$ is an affine function of $\tilde{s}_i$, which then implies the sum of signals.

Regress $\tilde{v}$ on $\tilde{s}_i$ and calculate $R^2$ (the Coefficient of determination).

This is something I hope someone else can answer.


Is Ireland setting itself up for a debt crisis?

Your figures seem to come from a European Central Bank analysis published in September 2016 for the position at the end of 2015

Different people get different numbers, but the order of magnitude is probably credible

But this sort of number has been coming down compared with previous years.  For example IMF publishes the following graph


When someone says two things are equivalent, what that means is that they give the same result for some test; they are equivalent with respect to that test. For instance, in Texas Hold 'Em, getting dealt the ace of spades, then the ace of diamonds, is equivalent to getting dealt the ace of diamonds and then the ace of spades, because strength of hands doesn't depend on the order that you received your cards. So to answer the question "How are these functions equivalent?", we have to know what test they're equivalent with respect to.
A utility function is a tool that's used to determine, given two options, which one someone would take. The idea is that we look at what utility each option has, and the person will take the one with the higher utility. For this test, we only look at which is larger, not the absolute size. So if you have two functions $f$ and $g$ that always give the same order, they are equivalent with respect to this test. That is, given any two options $a$ and $b$, if $f(a)<f(b)$, then $g(a)<g(b)$.
Now, if we set $f$ to $(x,y) \rightarrow xy$ and $g$ to $(x,y) \rightarrow (xy)^2$, we can introduce $h: u \rightarrow u^2$. Then $g(x,y) = h(f(x,y)$. In other words, $g$ is $h$ composed with $f$. If we assume that $x$ and $y$ are positive, then $h$ is monotonically increasing, and thus composing it with any function doesn't change ordering; if $n<m$, then $n^2<m^2$ (again, for positive numbers). Any time two functions are such that one can be written as a monotonically increasing function composed with the other, the two functions are equivalent with respect to ordering.
However, it is important to note that utility functions are also used for evaluating a concept called "lotteries". This is where someone chooses between options that involve different probabilities of different outcomes. For instance, someone might have a choice between "1% chance of getting \$1m and 99% of getting nothing" versus "100% chance of getting \$100k". When evaluating lotteries, the functions that you list are not equivalent when applied to the outcomes.


The Fed’s liabilities (technically broader than the true monetary base but arguably more relevant depending on your definition of “money printing”) are released weekly in their H.4.1 release. They appear in Table 4. Right now they are about 6.3 trillion dollars, up almost 2.4 trillion from a year ago.

They’re “validated” in the sense that the Fed has internal controls, external third-party auditors, and is subject to regular Congressional oversight.

Yes, you can find a time series from the St. Louis Fed’s FRED service.


Can demand side restrictions explain the productivity paradox (Solow paradox)?

Capital accumulation would still appear as investment GDP. Its possible theres other applications for this spending that would result in higher gdp. For example, GDP spiked in ww2 because military spending happens to be very efficient at inflating GDP.
So it is intuitively plausible that potential output is hidden by rising investment- the closest equivalent in economics is baumol cost disease, where the low productivity sectors gain more wages as growth progresses. However, the example you are asking about, in technology, is not that related to macroeconomic investment. The overall infrastructure level in energy production and distribution drives the output of everything- so there isnt much tradeoff there, consumption is made possible by shared infrastructure used for both consumption and investment.
Technology likewise is shared infrastructure- you could use a semiconductor plant for either consumer or business goods- so theres only a limited extent to which it would matter in practice. But there could indeed be Baumol like factors which cause resources to be allocated in a way that results in lower output. Baumol phenomena are almost the opposite of what you are describing but they are the closest thing in economics to the idea that growth may be "hidden" through factor reallocation.


The relationship between indirect utility and expenditure functions

Even if $u^b$ is finite, it can never be achieved. This is what is meant by "does not attain a maximum". Rather, $u(x)$ approaches $u^b$ from below as $x \to \infty$. This is because $u$ is strictly increasing. If we had $u(x_*) = u^b$ for some $x_*$, then we would have $u(x_* + 1) > u^b$ and $u^b$ could not be a bound. This is why $U$ is written as the half-open interval $[u(0), u^b)$.


There are three big sources for data on inflation expectations in the US:

Market implied expectations from the TIPS spread. TIPS securities provide inflation protection but are otherwise roughly comparable to normal treasuries, so the difference in yields between these two is a measure of expected inflation.
Consumer expectations from the University of Michigan Survey of Consumers, which you can find here.
Surveys of professional forecasters, such as this survey.

Which of these measures is most useful is not clear, and I've seen all three used at different times and in different places. This speech by Janet Yellen has some discussion of the different measures, as does this paper by Carola Binder.


Is there a class of demand functions that deliver equal surplus to consumers and a monopolist?

We have that

$$D(p^*,\mathbf{a}) = -\frac {d}{dp^*}\int_{p^*}^\infty\!D(p;\mathbf{a})\,dp,$$

$$\Rightarrow \text{PS}(p^*) = -\text{CS}'(p^*)p^* \tag{1}$$

So

$$\text{PS}(p^*)= \text{CS}(p^*) \Rightarrow -\text{CS}'(p^*)p^* = \text{CS}(p^*)$$

or

$$\text{CS}'(p^*) + \frac 1{p^*}\text{CS}(p^*)=0 \tag{2}$$

which is a first-order linear homogeneous differential equation in $p^*$ with variable coefficent. Its solution is

$$\text{CS}(p^*) = B\exp\left\{-\int \frac 1{p^*}dp^*\right\} = B\exp\left\{-\ln p^*\right\}=B\frac 1{p^*},\;\; B>0 \tag{3}$$

So we have that the demand function the OP seeks must satisfy

$$\int_{p^*}^\infty\!D(p;\mathbf{a})\,dp = B\frac 1{p^*} \tag{4}$$

Since it should hold $\forall p^*$ we can consider the derivative w.r.t to $p^*$ on both sides, to obtain

$$D(p^*;\mathbf{a}) = B\frac 1{[p^*]^2} \tag{5}$$

But since, again, it should hold $\forall p^*$, it holds $\forall p$. So

$$\text{PS} = \text{CS} \Rightarrow D(p;\mathbf{a}) = B\frac 1{p^2} \tag{6}$$
Verification of $(6)$ is straightforward.


In 2011, Tom Sargent and Chris Sims were jointly awarded the Nobel Memorial prize for empirical work.

  The Royal Swedish Academy of Sciences has decided to award The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for 2011 to Thomas J. Sargent and Christopher A. Sims "for their empirical research on cause and effect in the macroeconomy."

Dr. Sargent's contribution was related to the use of structural macroeconometrics in policy and analysis and Dr. Sims' contribution was to the use of vector autoregressions (VAR) to analyze temporary changes in policy and other factors.

Source: Nobel Prize Website


In Mankiw's Macreoconomics, how come capital is assumed to be fixed while investment is assumed to be variable?

It seems that Mankiw has implicitly assumed that all the investment is used to replace the depreciated capital. See the second sentence in the Investment section of Chapter 3-3:"Firms buy investment goods to add to their stock of capital and to replace existing capital as it wears out. "

Usually, the law of motion of capital is written as
\begin{equation}
K_{t+1}=I_{t+1}+(1-\delta)K_{t}
\end{equation}
where $\delta$ is the depreciation rate of capital. By assuming capital to remain at a fixed level $\overline{K}$, I believe that Mankiw is trying to only discuss the steady state in which capital is remained at a constant level, while avoiding introducing any more details. Since this is just the beginning part of textbook, everything is made as simple as possible. There is even no time subscripts for variables!


Since the US-China Trade Deficit grew, would the USD be valued more now compared to the RMB?

The "US-China trade deficit" isn't a real thing. Yes, there are some transactions classified as "exports from US to China" and others classified as "exports from China to the US", and you can subtract the latter from the former and get a negative number, but that doesn't represent anything fundamental about the world economy. Suppose that the US were to stop buying widgets from China and buy them from Taiwan instead, and the country that was buying them from Taiwan were to start buying them from China. Everyone would end up buying/selling the exact same amount of widgets, yet the "US-China trade deficit" would go down despite absolutely nothing fundamental about the world economy changing.
The overall trade deficit of the US does have an effect on the USD, but higher trade deficits make a currency go down in value, not up. Of course, a decrease in currency value tends to decrease trade deficits, which means that this effect tends to be cancelled out.


If you aren't interested in learning from a game and decision theoretic perspective, I'm not exactly sure why you're posting on an economics forum. Because that's what learning really is, from an economics perspective. AI really breaks down into three subfields: logical, behavioral, and machine learning. The logical subfield deals with logical reasoning, automated proof-writing, automated conjecture making, and such. Behavioral AI is really more in line with theoretical economics- game theory, decision theory, mechanism design, etc.

Machine learning is really what constitutes mainstream AI research nowadays. This is really due to the fact that we now have the resources and tools to better deal with big data, rather than a philosophical revelation or technical breakthrough. Hot topics in computer science are very industry and money driven (as a theorist, I would argue too much so). Machine Learning really boils down to applying a stochastic process and refining a model. There isn't so much learning going on, just enhanced stupidity that works well sometimes. That's not to dismiss Machine Learning, but we should call it what it is.

I would definitely recommend AI, Machine Learning, and Evolutionary Game Theory, though. Russell and Norvig is the established classic AI text, and it has sections on Machine Learning as well. Link: http://aima.cs.berkeley.edu/

Evolutionary Game Theory uses similar techniques as Machine Learning. It relaxes the assumptions of Neoclassical Game Theory. Agents need not be perfectly rational. They can have imperfect information and adjust their strategies myopically. The game is played repeatedly. We then see how "mutation" (such as human error or experimentation) in enough agents drives changes in equilibrium. So we have a dynamical process to select equilibria in games. We can apply dynamics such as the imitation dynamic, the best response dynamic, etc. Weibull (https://mitpress.mit.edu/books/evolutionary-game-theory) and H. Peyton Young are both good introductions (https://www.amazon.com/Individual-Strategy-Social-Structure-Evolutionary/dp/0691086877/).

I took a seminar in Economics this past spring, the first half of which was Evolutionary Game Theory. We went through a bunch of papers as well; a subset of the following. One paper I enjoyed was Competitive Behavior in Market Games: Evidence and Theory. It showed that as the number of agents was made sufficiently large, that evolutionary forces drove the Nash equilibrium to the Walrasian equilibrium (under certain assumptions). This provides a behavioral motivation for the study of r-fold replica economies in the general equilibrium setting.

Mark E. Schaffer (1989): “Are Profit-Maximisers the Best Survivors?” Journal of Economic Behavior and Organization, 12, 29-45.

Mark E. Schaffer (1988): “Evolutionarily Stable Strategies for a Finite Population and a Variable Contest Size,” Journal of Theoretical Biology, Vol. 132, No. 4, 469-478.

Hehenkamp, B., W. Leininger, and A. Possajennikov (2004): “Evolutionary equilibrium in Tullock contests: spite and overdissipation,” European Journal of Political Economy, Vol. 20, 1045–1057.

Duffy, J., A. Matros, and T. Temzelides (2011): “Competitive Behavior in Market Games: Evidence and Theory,” Journal of Economic Theory 146, 1437-1463.

Kandori, M., G. Mailath, and R. Rob (1993): “Learning, Mutation and Long Run Equilibria in Games,” Econometrica, 61, 29-56.

P. Rhode, and M. Stegeman (1996): “A Comment on ‘Learning, Mutation, and Long-Run Equilibria in Games’,” Econometrica, 64, 443-449.

W. Sandholm (1998): “Simple and clever decision rules for a model of evolution,” Economics Letters, 61, 165-170.

Young, P. (1993): “The evolution of conventions,” Econometrica, 61, 57-84.

Young, P. (1993): “An Evolutionary Model of Bargaining,” Journal of Economic Theory 59, 145-168.

M. Saez-Marti and J. Weibull. (1999): “Clever agents in Young's evolutionary bargaining model,” Journal of Economic Theory 86, 268-279.

Matros, A. (2003): “Clever Agents in Adaptive Learning”, Journal of Economic Theory, 111, 110-124.

Ellison, G. (1993): “Learning, local interaction and coordination,” Econometrica, 61, 1047-1072.

Glenn Ellison (2000): “Basins of Attraction, Long Run Equilibria, and the Speed of Step-by-Step Evolution,” Review of Economic Studies, 67 (1), 17-45.

Bergstrom, T. and Stark, O. “How Altruism Can Prevail in an Evolutionary Environment.”

American Economic Review, May 1993 (Papers and Proceedings), 83(2), 149-55.
Eshel I., L. Samuelson and A. Shaked (1998): “Altruists, Egoists, and Hooligans in a Local Interaction Model,” The American Economic Review 88(1), 157-179.

Matros, A. (2012): “Altruistic Versus Egoistic Behavior in a Public Good Game,” Journal of Economic Dynamics and Control 36, 642-656.

Robson, A., and F. Vega-Redondo (1996): “Efficient Equilibrium Selection in Evolutionary Games with Random Matching,” Journal of Economic Theory, 70, 65-92.

Josephson, J., and A. Matros (2004): “Stochastic Imitation in Finite Games,” Games and Economic Behavior, Volume 49, Issue 2, 244-259.


I'm looking for a reviewed source on the amount of money in the world

If you're looking for total value of banknotes and coins in circulation, then the Bank for International Settlements provides some useful statistics. While the BIS only collects data on ~20 countries including the EU, the noted countries cover almost all of the value of banknotes and coins in circulation as of now. At the end of 2017, the total amount in USD is $6.458 trillion.


Use of the term "effective" in economics

In economics, we are mostly interested in studying how incentives shape decisions. In many situations, there is a gap between the concept that captures the incentives that a person is facing, and the name it receives in the real world. For example,  in general, wages are what provide incentives for people to work. However, most people pay taxes or have other deductions. Therefore you can define the "effective wage" as the money the person gets to keep after taxes are taken out, etc. Now, the effective wage is really what is shaping the decisions of the person.

As you can see, the use of "effective" can vary a lot from topic to topic, but it almost always refers to some adjustment in the variable so that it really captures the incentives agents are facing.


Can you prove, and with what assumptions, that a market will allocate some minimum amount of basic resources to every worker?

There is no guarantee that anyone in market economy earns some subsistence minimum. Generally, wage depends on marginal product of worker's labor and if there are some quasi-rents to be had also on the relative negotiating power of worker and employee. Of course, there is a bit more nuance to it, for that you can see Borjas: Labor Economics 5th ed, but assuming that people roughly get wage equal to their marginal product is reasonable first approximation.
There is no reason to a priori assume that marginal product of some worker will be enough to procure some basic goods and services (food, shelter, clothing are goods not resources - labor and other factors are actually resources in economics). So it might very well be that there are people for whom wages are not enough to be able to sustain themselves just on their own without some sort of subsidy/charity.


What are some famous examples of infant industries that failed?

Malaysia's Proton cars (if you want a specific example ), but overall the Malaysia Automobile industry failed. Currently, only the locals drive Malaysian cars.


What would happen if tomorrow all private and public debt was erased?

It would depend a lot on how the debt was "erased." If you are simply suggesting a transfer payment from creditor to debtor, what would force such an event? Or would it be voluntary? If it were forced, then you would have a threat to private property rights and therefore, a disincentive for further lending. Security of capital would be diminished and all investment might stop overnight.

This question is very broad. But the answer of what might happen would depend very much on the details of how all this might come about.


Link between supply of domestic assets and monetary policy

Monetary policy is conducted by the Swiss Central Bank. The Swiss Central Bank has a monopoly over the issue / production of Swiss francs.

The purpose of the Swiss Central Bank is to produce / supply Swiss francs to the Swiss public if the Swiss public wants to hold more Swiss francs and to purchase Swiss francs of the public if the Swiss public wants to hold fewer Swiss francs. If it doesn't bad things will happen but that's outside of the scope of this question.

The Swiss Central Bank does this by either purchasing domestic assets with newly created Swiss francs and selling domestic assets for previously created Swiss francs.

The reason that the Swiss Central Bank does this by purchasing and selling domestic assets is that it is often not appreciated if one country's government interferes in the economy of another country's government and the Swiss Central Bank is considered to be part of the Swiss State.

The problem the Swiss Central Bank faces is that the Swiss currency and Swiss domestic assets are considered to be good stores of value by foreigners. The function of a currency is a unit of account, store of value, and a medium of exchange. So the Swiss currency fulfills the second function, store of value, for foreigners. But this leaves fewer Swiss francs for the Swiss public to use as a medium of exchange. And if there are fewer Swiss francs but the demand of the Swiss public is the same, then this results in deflation. Swiss francs become relatively more valuable compared to other goods. The prices of other goods, in terms of Swiss francs drop. At the same time there are fewer domestic assets that can be exchanged for newly created Swiss francs because these have been purchased by foreigners.

This is highly simplified, but I hope that this answers your question.


Can a firm have a negative turnover during a period of time?

One possible circumstance relates to firms undertaking long term contracts (eg for building or engineering work). Where a contract is uncompleted at the end of a period, the firm may (depending on its accounting policies) include in its turnover an amount reflecting its assessment of the work in progress.  Sometimes unforeseen difficulties in completing a contract will subsequently come to light, and it may become necessary to include an offsetting reduction within turnover for the next period. If the contract is a large proportion of the firm's activity, then this could result in overall turnover for that period being negative.


Can the weierstrass and the Kuhn-Tucker theorems be used to obtain and characterize a solution? Why or why not?

I assume $x_i$ represents the quantity and belongs to $\mathbb R_{+}$. You can form the constraints as follows:
$$
x_i \geq0 \quad\forall i \in [3] \\
\sum_{i=1}^3p_ix_i \leq I
$$
You can simplify the objective by noting that for the utility to be the maximum, $x_2 =x_3$. Try to reason why this is true. Hence, the final problem becomes,

$$\
\max_{x_1, x_2, x_3}x_1^{1/3} +x_2 \quad s.t. \\
x_i \geq0 \quad\forall i \in [3] \\
\sum_{i=1}^3p_ix_i \leq I \\
x_2=x_3
$$
Can you now set up the lagrange multiplier function? As far as KKT conditions are concerned, I believe they should help because you are trying to maximize a concave function(in $\mathbb R_+$) subject to convex constraints and the strict inequality constraint is linear.

Edit 1: Let's eliminate $x_3$ as we know that $x_2=x_3$. The problem simplifies to
$$\
\min_{x_1,\ x_2}\ -x_1^{1/3} -x_2 \quad s.t. \\
x_1 \geq0,\ x_2 \geq 0 \\
p_1x_1 + (p_2 + p_3)x_2 \leq I
$$
$$\
\mathcal L(x_1, x_2)=-x_1^{1/3} -x_2 + \lambda_1(-x_1) + \lambda_2(-x_2) + \lambda(p_1x_1 + (p_2 + p_3)x_2 - I)
$$
Edit 2: I see solving the Lagrangian can be tough. Let's simplify, we know that all constraints cannot be active at the same time. It will yield an utility of zero.

Case-1: $x_1=0, x_2>0$
You can check algebraically, $x_2=\frac{I}{p_2+p_3}$. Hence, utility$(U)=\frac{I}{p_2+p_3}$

Case-2: $x_1>0, x_2=0$
You can check algebraically, $x_1=\frac{I}{p_1}$. Hence, utility$(U)=\left(\frac{I}{p_1}\right)^{1/3}$

Case-3 $x_1>0, x_2>0$
You can now use the Lagrangian, its much simpler than the original Lagrangian problem because $\lambda_1=\lambda_2=0$
$$\
\mathcal L(x_1, x_2)=-x_1^{1/3} -x_2 + \lambda(p_1x_1 + (p_2 + p_3)x_2 - I)\\
\frac{\partial\mathcal L}{\partial x_1} = 0 \implies x_1 = \left(\frac{1}{3\lambda p_1}\right)^{3/2}\\
\frac{\partial\mathcal L}{\partial x_2} = 0 \implies \lambda = \frac{1}{p_2+p_3}\\
\text{Use the constraint, }p_1x_1 + (p_2 + p_3)x_2 = I \text{ to find } x_2
$$
You can simply finish saying the solution is $\max$ of all three cases. As per the KKT conditions are concerned, one of the three solutions will satisfy KKT Conditions depending on $p_1, p_2, p_3 \text{ and } I$. Note that this is no different from the original problem and hence, KKT condition should be satisfied by one of the three depending on $p_1, p_2, p_3 \text{ and } I$. We could have obtained the same solution using the original Lagrangian. Even there we would have ended up with a $\max$ because of $\lambda_1, \lambda_2$ and invoking KKT.


Guess 2/3 of the average with integers - mixed strategy equilibria?

Quick note: in pure strategies for sufficiently many players, shouldn't all 1 be NE as well?

Onto mixed strategies:

To have a mixed strategy Nash equilibrium, each player needs to be indifferent between the strategies they are mixing and they must prefer all those strategies to the ones they never play.

That means players must mix only between strategies between which they have an equal probability of winning (when given all other players' strategies). I suspect you can use this to show that players must mix between 0 and 1. Then it remains to solve for whatever mixed strategies give which players indifference between 0 and 1.