The claim is definitely not trivial, otherwise we would not observe frequent draughts due to government subsidies (like drought in California that is at least partially caused by bad water and farming subsidies), environmental degradation and overuse due to subsidies to coal mining and oil production (see this IMF explainer), not even mentioning that often these subsidies perversely redistribute resources from poor to rich. Overfishing, is not just result of tragedy of commons but also prevalent bad fishing subsidies (see this article in The Economist), and so on.
Furthermore, your proposed solution of:

Can't this be easily avoided if, let's say, we let the said farmers consume the resources they want initially. Then, the government only releases subsidies if they deem the amount of resources used as appropriate and necessary.

would not work, because in repeated interactions people will expect the subsidy. In economics, subsidies are typically considered to be tied to some specific economic activity, more specifically some production (i.e. it is not the same as redistribution where you just transfer resources). Hence, farmers would essentially figure out how the subsidy varies with economic activity (unless you want to propose completely random normally distributed subsidy with mean zero and what would be the point of that?), and eventually realize that if they produce x the subsidy will be y. Furthermore, such arrangement would defeat the purpose of subsidy. As mentioned above subsidy is used to subsidize some economic activity, if you just want to redistribute resources you can give them regular transfers. If you would first let people make their choices and then subsidize the activity, assuming people would be completely myopic and not realize post hoc subsidy was connected to the economic activity, you just created convoluted welfare transfer, for which we already have better systems.
This is not to say that subsidies can't be useful tool for government in some situations. However, in most of the cases those situations occur when the price mechanism does not work properly (e.g. there are some positive externalities meaning the price does not reflect all important information). However, if price system is working properly distorting it often leads to either shortages or inefficient overuse.
Of course, if government would only use subsidies when appropriate there would not be any issue. I mean this is obvious, that is like saying homelessness can be solved by people getting houses, or opioid pandemic by doctors stopping to overprescribe opioids and patients taking them responsibly, or solving police shootings by having them just shoot when arresting dangerous criminals with guns. But neither getting right subsidies or solving those other issues is as simple as that, otherwise our societies would not have the issue.
When it comes to subsidies, the issue is that it is very hard to determine what optimal subsidy is in a field. Next, even once you manage to identify problems which require subsidies and what the value of subsidy is there are still political problems as alluded to by Dayne's +1 comment.
Moreover, the point of the box in your question, which is often mentioned in one way or another in almost every single textbook is to explain how price system functions to distribute information and give incentives to people to act on that information. This is something that most non-economists do not understand.
Consequently, the information in the box is both non-trivial and very relevant. It is relevant and non-trivial because most people do not understand how price system works and what happens when it is distorted. Moreover, we can empirically often see subsidies being misused and often even in areas connected to climate change (as mentioned above), and given that climate change is likely one of the defining issues of our 21st century, I would say this makes this issue as relevant as ever.


Let us prove it by contradiction. Suppose that $x^{*}$ is optimal for the first problem but not for the second. Since $x^{*}$ is not optimal for the expenditure minimization problem, there exists a bundle $x$ such that
\begin{equation*}
u(x) \geq u(x^{*}) \text{ and } p \cdot x < p \cdot x^{*}
\end{equation*}

Since the function $y \rightarrow p.y$ is continuous, and $p \cdot x < p \cdot x^{*}$, there exists $\epsilon>0$ such that $\|y-x\|<\epsilon \Rightarrow p \cdot y < p \cdot x^{*}$. In addition, since preferences are locally nonsatiated, there exists $y$ such that $\|y-x\|<\epsilon$ and $u(y)>u(x)$. Take such a $y$. We have \begin{equation*}
u(y) > u(x) \geq u(x^{*}) \text{ and } p \cdot y < p \cdot x^{*} \leq w
\end{equation*}

Or, in other words,
\begin{equation*}
u(y)>u(x^{*}) \text{ and } p.y < w
\end{equation*}
which contradicts the assumption that $x^{*}$ is a solution of the utility maximization problem.


I give here the procedure but with price $p=1$ you can do it yourself without that simplification.
Set up Lagrange
$$\mathcal L(c,l,\lambda) = u(c,l) - \lambda (c-\bar w(1-t)(24-l)) $$
clearly
$$\frac{\partial \mathcal L }{\partial c} = \frac{\partial u}{\partial c} - \lambda = 1- \lambda$$
so $\lambda=1$ and constraint is binding. Therefore
$$c^\star = \bar w(1-t)(24-l^\star)$$
Furthermore
$$\frac{\partial L}{\partial l} = (24-l)^{1/\eta} - \lambda \bar w (1-t) = 0$$
since $\lambda = 1$ it follows that
$$l^\star = 24 - (\bar w(1-t))^\eta$$
plugging $l^\star$ and $c^\star$ into utility function, starting with $c^\star$ you get
$$\bar w(1-t)(24 - l^\star) - \frac{\eta}{\eta + 1}(24 - l^\star)^{\frac{\eta + 1}{\eta}}$$
then $l^\star$ to get
$$\bar w(1-t)[\bar w(1-t)]^{\eta} -  \frac{\eta}{\eta + 1}(\bar w(1-t))^{\frac{\eta(\eta + 1)}{\eta}},$$
reduce this to get
$$(\bar w (1-t))^{\eta +1}[1/(\eta + 1)]$$
insert optimal tax and get
$$\left(\bar w \frac{\eta}{\eta + 1}\right)^{\eta +1}[1/(\eta + 1)]$$


Relationship between Nash and Coasian bargaining solutions

There is no such thing as the "Coasian bargaining solution". This is a simple principle according to which parties find an agreement somewhere on the Pareto frontier when they bargain, which means that the outcome of the bargaining process is socially efficient (abstracting from equity issues).

The Nash bargaining solution refines our predictions by specifying where the solution is likely to be located on the Pareto frontier. In some sense, it is a subset of the Coasian bargaining outcome, which can be anywhere on the Pareto frontier. In contrast to the Coase principle, it is a theorem that rests on an axiomatic characterization.


How can an outcome be Pareto efficient but not Kaldor-Hicks efficient?

Example. Each month, God gives Adam $60$ apples and Eve $40$ (for a total of $100$ apples). Let's write this allocation as $X=(60,40)$.

The Devil now comes along and offers to increase their total monthly allotment of apples to $101$, but on the condition that the allocation must be $Y=(59,42)$.

Observe:

$X$ is Pareto efficient but not Kaldor-Hicks efficient.
$Y$ is both Pareto efficient and Kaldor-Hicks efficient.
$Y$ is a Kaldor-Hicks, but not a Pareto improvement over $X$.
Through imaginary redistribution, we could get from $Y=(59,42)$ to $Z=(60,41)$. And $Z$ would then be a Pareto improvement over $X$. But the problem is that the option of making the redistribution $Y\rightarrow Z$ doesn't actually exist. And so, while $X \rightarrow Z$ would indeed be a Pareto improvement, the problem is that it does not exist and is not a possibility. It is merely something we or Adam and Eve may have imagined.

So let's see where you went wrong in your argument:

  But then that Kaldor-Hicks improvement together with that redistribution is a Pareto improvement

This is correct. Using the above example, $X \rightarrow Y$ is the Kaldor-Hicks improvement, $Y \rightarrow Z$ is the imaginary redistribution, and $X \rightarrow Z$ is the Pareto improvement.

  so there exists a possible Pareto improvement of X

The error is here. The redistribution $Y\rightarrow Z$ is imaginary and does not exist. So, the reallocation $X \rightarrow Z$ is also imaginary and does not exist.

(In this case the redistribution  $Y\rightarrow Z$ isn't possible due to arbitrary constraints set by the Devil. But in the real world there will be other constraints.)

Edit: Another example

Suppose you and I are neighbors. I really like practicing the drums at 9 am on a Saturday. You really, really, like sleeping until 10 am on Saturdays, which is, of course, significantly disrupted by my drumming. Suppose I value drumming at \$10, and you value sleeping at \$20. What are the efficient outcomes?

The clear Kaldor-Hicks efficient outcome is for me to not drum. Sure, I lose (the equivalent utility of \$10 to be precise), but I lose less than you gain. If desired, you could compensate my loss, and still be better off than if I drum.

The set of Pareto efficient outcomes is bigger. It's Pareto efficient for me to either not drum (letting you sleep), or drum away at 9 am!

Of course, we could come to a mutually agreeable resolution where I don't drum and you pay me some amount between \$10 and \$20. However this adds another layer of complexity that we didn't include: that enforceable agreements and transfers are possible (and costless). In the real world, where there are many other pragmatic issues (such as enforcement, positive transaction costs, lack of information about who the "gainers" and "losers" are, etc.), these payments might not be possible, and hence, we're reduced to considering the initial problem.


2010 flash crash: cause and rationale for illegality

What exactly is it that the trader is alleged to have done, how did this allow him to make irregular profits, and what is the mechanism by which he was able to single-handedly move the entire equities index?

  According to the Complaint, for over five years and continuing as recently as at least April 6, 2015, Defendants have engaged in a massive effort to manipulate the price of the E-mini S&P by utilizing a variety of exceptionally large, aggressive, and persistent spoofing tactics.  In particular, according to the Complaint, in or about June 2009, Defendants modified a commonly used off-the-shelf trading platform to automatically simultaneously “layer” four to six exceptionally large sell orders into the visible E-mini S&P central limit order book (the Layering Algorithm), with each sell order one price level from the other.  As the E-mini S&P futures price moved, the Layering Algorithm allegedly modified the price of the sell orders to ensure that they remained at least three or four price levels from the best asking price; thus, remaining visible to other traders, but staying safely away from the best asking price.
  Eventually, the vast majority of the Layering Algorithm orders were canceled without resulting in any transactions.  According to the Complaint, between April 2010 and April 2015, Defendants utilized the Layering Algorithm on over 400 trading days.
  The Complaint alleges that Defendants often cycled the Layering Algorithm on and off several times during a typical trading day to create large imbalances in the E-mini S&P visible order book to affect the prevailing E-mini S&P price.  Defendants then allegedly traded in a manner designed to profit from this temporary artificial volatility.
  (http://www.cftc.gov/PressRoom/PressReleases/pr7156-15#PrRoWMBL)

The offical verdict has a step-by-step walkthrough

If the trader participated only in legitimate voluntary trades via the normal market mechanism, what exactly is the behaviour that is being considered as potentially illegal here, and what is the rationale for this illegality (i.e. how can the authorities distinguish this seemingly illegal behaviour from normal market trading activity)?

  Sarao was charged in a federal criminal complaint in the Northern District of Illinois on Feb. 11, 2015,  with one count of wire fraud, 10 counts of commodities fraud, 10 counts of commodities manipulation, and one count of “spoofing,” a practice of bidding or offering with the intent to cancel the bid or offer before execution.
  (http://www.justice.gov/opa/pr/futures-trader-charged-illegally-manipulating-stock-market-contributing-may-2010-market-flash)

The relevant articles for spoofing are: Title 7, United States Code, Sections 6c(a)(5)(C) and 13(a)(2)

  (5) Disruptive practices
  It shall be unlawful for any person to engage in any trading, practice, or conduct on or subject to the rules of a registered entity that-
  (A) violates bids or offers;
  (B) demonstrates intentional or reckless disregard for the orderly execution of transactions during the closing period; or
  (C) is, is of the character of, or is commonly known to the trade as, "spoofing" (bidding or offering with the intent to cancel the bid or offer before execution).


Why does the Loanable Funds Market model use the real interest rate instead of the nominal interest rate?

As Brian mentions in his comments this is because in standard models when people make intertemporal decisions they take inflation into the account. Take the following example:
You have a rational utility maximizing person who makes decision between consuming $\\\$100$ today or saving it for later consumption. For simplicity lets assume discount factor is exactly 1 (this is unrealistic as clearly consumption in the future should be valued less than in present but it just simplifies the math). Now let us suppose the nominal interest rate $i$ is $10\%$ and the question is should you save in this example or not?
Well the correct answer here is we dont have enough information to say yes or no. If inflation is $5\%$ the person should save those $\\\$100$ if inflation rate is $15\%$ the person should not do that because in the former case you will increase your resources in real terms after accounting for inflation and in the latter you will have less of them. Hence nominal interest rate can be any arbitrary number $x$ between $[0,\infty)$, but  without knowing what inflation rate is we cannot say whether you should consume today or tomorrow (i.e. whether you should supply loanable funds to the market or not).
What matters is the real interest rate which is the nominal interest rate less the inflation rate since by Fisher equation: $r \approx i - \pi$ where $r$ is the real interest rate, $i$ nominal interest rate and $\pi$ inflation.
This covered just the supply side of loanable funds but the demand side would work in similar way. A business person would want to take loan for projects should analogously work with real returns and interest rates when evaluating business proposals.
I would not call this handwaving as Brian does which is commonly used in science to refer to addition to the model that are ad hoc or do not follow from assumptions of the model in consistent fashion but Brian is correct in saying that it is not necessarily exactly how reality works.
For example, it is documented that people can suffer from behavioral bias 'money illusion' which is cognitive bias to think of money in nominal, rather than real, terms. Under a 'money illusion' what the nominal rate is also matters in non-trivial ways. However, in simple macro 101 model which presents the classical view of  loanable funds market  where agents are rational forward looking and having rational expectations such money illusion does not exist.


How is the ARIMA model a valid approach for forecasting Economic Variables?

So your question is basically asking why a purely statistical model would be better at forecasting than a model based on theoretical relationships. For example, think about a simple form of the ARIMA model i.e. an AR model where you're just using lags of the process to explain the process itself. Now think about what is contained in the lags of the process... If the true process (i.e. the DGP) is determined by theoretical relationships between other variables then these will automatically be included in the lag. So the ARIMA model is a statistical way of modeling the process to make sure you capture the statistical properties of the underlying relationship but does not necessarily provide an explanation for what is going on. In forecasting, especially when series are volatile and erratic, you often find that simple statistical models such as these do a better job since the underlying relationships may not be very stable or may be more complicated than any theory we can come up with. This is related to a recent article  which you may find interesting: http://www.sciencedirect.com/science/article/pii/S0169207017300997


Is the shareholder-creditor conflict the same as debt-equity conflict?

No. Creditor and debt holders are not necessarily the same. The firm owes money to both. You can have debt holder vs other creditor conflict, who has priority and who has what charge to which asset.


Impact of auction systems that allow 'sniping'

Firstly, it's right to say that the hard ending rule on ebay seems to be behind sniping. Here's a figure from Roth & Ockenfels' AER paper:

On eBay (fixed end time) bids arrive much later than on the now defunct Amazon auction platform (which used an extendable end time).

One explanation (see here and here) for this is that people want to hide their private information. If you think that you discovered a 'hidden gem' then the last thing you want to do is start bidding and let everyone else know that it's valuable! Note, from the figure, that sniping seems to be more acute in antiques auctions, where private information is likely to be more important.

The other leading explanation is that some bidders do not understand that they can use the automatic proxy system to take care of the bidding, and 'naively' sit incrementing their bid manually. Sniping is then a way to take advantage of such bidders' poor reaction speed. An experiment by Ely & Hossain that appeared in AEJ Micro verified that sniping indeed gives you an advantage over such naive bidders. This marketing Science paper by Zeithammer and Adams also provides evidence that manual incremental bidding is common and that it is therefore wrong to think of eBay as a simple implementation of a second price auction.

So, two perspectives on what is going on here: concealment of private information and exploitation of naive bidders. Both of these have one thing in common: they imply that Sniping leads to lower prices, not higher.

So why does eBay persist in the use of such a mechanism? Only they know. But here is what I suspect:

eBay is a two-sided market. It must attract both sellers and buyers. Usually, optimal pricing in a two-sided market involves subsidizing one side of the market to get them onto the platform before milking the other side. But buyers already pay $0 to eBay; what if a bigger subsidy is needed? One way to implicitly subsidize buyers and attract them to the platform is to choose a mechanism that results in a lower selling price. In the end, if the result is indeed to attract more bidders, this might not even be that bad for eBay. Bulow and Klemperer have shown that adding bidders to an auction is almost always more profitable for the seller than redesigning the auction but keeping the number of bidders the same.


In your context, Slutsky Equation says, after $p_x$ increases from 1 to 4, the following is true:

\begin{align*}
\text{total demand change in $x$} & \\
= \text{demand change in $x$, keeping $U$ fixed at 2} & \\
+ \text{demand change in $x$, accounting for the income change if we do not fix $U$ at 2.} &
\end{align*}

In the example, the substitution and income effects are of the same sign, so I use absolute values for the demand changes in the equation above. Thus the plus sign rather than the minus sign in Slutsky Equation.

The total demand decrease in $x$ is $3$, that is, $$x_0 - x_1 = 4 - 1 = 3.$$

The demand change in $x$, keeping $U$ fixed at 2 is: $$x^{c}_0 - x^{c}_1 = 4 - 2 = 2.$$

To fix $U$ at 2 under the new price $p_x = 4$, the consumer needs the new income to be $I_1 = 16$ instead of 8. With \$16, the consumer buys 2 units for both $x$ and $y$. If we do not fix $U$ at 2 when $p_x$ increases, which means we allow income to decrease from 16 to 8. The demand reduction in $x$ induced by this \$8 income decrease is: $$0.5 \times 16 \div 4 - 0.5 \times 8 \div 4 = 2 - 1 = 1.$$

Therefore we have $3 = 2 + 1$, as Slutsky Equation tells us.


How much can we trust macroeconometric analysis?

I do not think that macroeconomic analysis would be 'less trust worthy'. In the same ways as you can solve the issue of omitted variables and reverse causality in microeconomics you can do it macroeconomics as well. Macroeconomics, is not just vector autoregressions (VAR - which by the way corrects for endogeneity). Simultaneous equation techniques, even difference-in-difference (DiD) and regression discontinuity (RD) etc are used even in macro literature even if they are less common (see this recent paper on identification in macroeconomics Nakamura & Steinsson, 2018).
In addition I think you are actually exaggerating quality of quasi-experimental methods such as IV or DiD. For example, this recent paper shows that large portion of IV papers uses weak instruments as the rule of thumb that $F$-stat. should be above 10 is invalid and  true threshold is around $F>105$ (see here Lee McCrary Moreira & Porter 2020). In addintion DiD are notorious for $p$-hacking and other issues,  Duflo & Mullainathan (2004) literally have paper titled: "How much should we trust differences-in-differences estimates?" Spoiler alert their answer is not as much as people usually do.
I think it would be fair to say that a reasonable person could defend saying that typical VAR has probably on average less issues that let's say DiD (but to be clear I am not claiming that as  even this lacks nuance as the model selection and specification is always case dependent there is no one model uber ales - even RCTs have a problem when it comes to generalization of results).
When it comes to just empirics in general I could not find any paper that would show that empirical research in macroeconomics is less replicable than in microeconomics. I would also take an issue with claim that macroeconomic models cannot control for all relevant variables. There are macro models (e.g. dynamic stochastic general equilibrium  (DSGE)) that include scores of different equations and even more variables. Next, even despite of this when it comes to omitted variable bias you might have a valid point although a lot of attention is being paid to the issue it might sometimes be hard to solve, but with the reverse causality your accusation that macroeconomics does not pay enough attention is unfounded. Most published research in macroeconomics pays very large attention to reverse causality (especially in present day, maybe 50-60 years ago that would be valid point as well). In fact that is why models and estimation techniques like VAR, DSGE, IV, GMM and many other simultaneous equations approaches are so popular and dominate macroeconomics, so this second charge is simply unfounded.
However, when it comes to forecasts I would agree that macroeconomic forecasting is for sure less accurate then microeconomic forecasting (e.g. forecasting aggregate output vs firm forecasting demand for its onw products). However, there the fault would not be in the models themselves necessary but rather with the fact that macroeconomic aggregates contain more noise, are harder to measure, and are reported on lower frequency and of course with less data it is harder to build good forecasting model.
Lastly, it is not really easy to qualify how much you should trust a model in any field. You should approach any model and set of results with healthy doze of skepticism, be they from VAR or RTC or any other approach. Different situations will require different identification strategies. Furthermore, you should not put all faith into single paper but wait for replications/put the paper into larger context of pre-existing literature. I also tried to find some work that would compare replicability of microeconomics vs macroeconomics, but unfortunately there does not seem to be such paper but I would not expect macroeconomics having much worse replicability rates then microeconomics per se.


Utility Theory/Marginal Rate of Substitution: Can the marginal rate of substitution be calculated for a point of the budget line?

Your claim that "MRS can only be calculated on for a point on the indifference curve and not for a point on the budget line" reveals a misunderstanding. Note that every point lies on some indifference curve. So each point on the budget line also lies on some indifference curve. We also know that all indifference curves are convex, since the utility function has Cobb-Douglas form.

At $C^*$, the optimal bundle, the indifference curve has to be tangent to the budget line, so it has the same slope as the budget line. At point $a$ the indifference curve (by convexity) intersects the budget line from above and therefore must be steeper than the budget line. Thus the MRS at $a$ is larger than the MRS at $C^*$.


You can't apply it to the national income identity directly because its components, namely consumption, investment and imports are functions of national income (output) and hence, they are not autonomous. In fact, in simple undergraduate level model, following Blanchard et al:

$$ Y = C(Y-T) + I(Y,i) + G  + X(Y^*, \epsilon - M(Y, \epsilon)/ \epsilon  $$

Where in addition to variables already described in your post $T$ are taxes, $i$ is interest rate $Y^*$ foreign output and $\epsilon$ is the exchange rate.

So you cant simply apply the multiplayer just to the variables itself as you would apply them to output multiple times. Rather you first need to solve the equation above for output. To do that I will assume two simplifications - $I$ will be fixed (that is $I = \bar{I}$ and consequently $I$ is no longer function of $Y$, and autraky to get rid of $X$ and $M$ - this is to simplify the math as now only $C$ is a function of $Y$ making solution easier (not doing so would only cause multiplier to be more complex and derivations longer). Moreover, assuming that $C$ is given by $C = c_0 + c_1(Y-T)$, the solution to the goods market equilibrium will be given by:

$$Y  = \frac{1}{1-c_1} \left( c_0 + \bar{I} + G - c_1T\right)$$

where the term $\frac{1}{1-c_1}$ is the multiplier (which you denote by $k$). Applying multiplier makes sense only at this step because only now Y was eliminated from the right hand side of the equation. Previously, you were applying the same multiplier to Y over and over again without noticing it.

Also this is completely correct:

  multiplier effect tells us that an autonomous injection into the economy will result in a multiplied increase in the real national income due to rounds of induced consumption.

But no part of the original accounting formula contains autonomous spending aside form $G$. In fact the solution to the goods market equilibrium given by the equation where we eliminate $Y$ from right hand side gives you effect of autonomous injections as in that solution $c_0$ is the autonomous consumption, $I$ was assumed away to be autonomous by assuming its fixed (admittedly that was bit sloppy from me but it simplifies math and shortens the explanations) and $G$ and $T$ are arguably autonomous by themselves.


Why the source profit is not only trade markups?

Because an extraordinary profit can also be derived from preferences, and brand. Why would you pay 4x more on an Iphone? Apple's ability to raise its price is not due to the market power it has, but rather to consumer preference, brand preference. Just answered only what was in the title and not on the basis of Marx's theories


What's a « 1-Ratio» ? From a text on Capital's share of GDP

I'm pretty sure he means "1 minus the labour share percentage", i.e. he's estimating the capital share of GDP as the proportion of GDP not going to labour.  It's not typeset well, but he has used an em-dash (longer) after "GDP" and a minus sign (shorter) after "1".


Find value of $\beta$ for which there is a strictly dominant strategy

Hint
Let $h_i^*(h_{-i}$) be firm $i$'s best response to the other $N-1$ firms' strategy profile $h_{-i}$. If $h_i^*(\cdot)$ is a dominant strategy, then it must be independent of the other firms' strategies, i.e. $h_i^*(h_{-i})=h_i^*$ for all $h_{-i}$.


Does people paying back their debts cause deflation?

It is true that paying back loans causes contraction of money supply (if not offset by faster creation of new loans). However, it is not correct to say that this generally happen when debt is forgiven and it does not need to lead to deflation.
First, debt forgiveness can actually be thought of as a permanent expansion of money supply not contraction. An example: central bank buys $\\\$100$ of government bonds that government then gets to spend. Afterwards, central bank decides that the bond will be destroyed without asking for government to pay back the $\\\$100$. The $\\\$100$ still exists and still can be used to purchase goods and services and circulate in the economy. Moreover, since the debt which originally created it was scrapped that $\\\$100$ can continue to exist forever leading to permanent expansion in money supply.
Second, for money supply to contract it is not enough that one loan gets repaid if new loans are issued at the same time - money supply is aggregate quantity. Furthermore, money supply can be expanded even by different ways than just by loans (see this past question on Economics.SE), so also in principle if central bank intervened money supply could expand or stay constant even when borrowing drops. However, lets assume that that there will be on net less loans in economy and central banks will just do nothing and so money supply actually indeed contracts. That is still in itself not necessary enough to cause deflation.
For deflation to happen the price level has to drop, and the price level $P$ is by standard textbook monetary equation given as $P = MV/Y$. Where $M$ is the money supply, $V$ velocity of money, $Y$ real output. Thus for decrease in $M$ to cause deflation we also have to additionally assume that such decrease won't be offset by changes in velocity or real output. That is not always realistic. Usually, credit drops during recessions for various reasons (for example as argued by Bernanke in his research during recessions it might be hard to distinguish good and bad borrowers which would lead to credit rationing and consequently drop in borrowing). More generally, the amount of credit in economy is very pro-cyclical (see for example Gaiotti (2013) and sources cited therein). Hence, often when $M$ contracts due to lower amount of loans $Y$ contracts at the same time and the two can in principle cancel each other. $V$ also does not stay constant across business cycle generally decreasing during the recessions (see for example Anderson, Bordo & Duca (2017)). Thus while ceteris paribus decrease in credit and contraction of money supply would lead to deflation in real world you might not observe deflation whenever credit drops due to effects of other factors that are changing at the same time.


intuition behind the blanchard kahn conditions?

The condition that unstable eigenvalues equal in number the control/decision/non-predetermined variables is equivalent to the requirement that a model possess the "saddle point property".

Of more interest is why economists generally want their models to possess such a property, something that holds for the DSGE models.

In Economics we call models with the saddle point property as "saddle path stable"; a mathematician would disagree. From a mathematical point of view these models are unstable, because there is a unique path to the fixed point/equilibrium. It should then be evident why such models are characterized as unstable: the slightest perturbation will push the dynamics off the unique path to equilibrium, never to return... enter human will and purposeful action by economic agents: we keep the model on the unique path on purpose, in order to fulfill the optimization conditions that describe our will and desires. In other words, going to the fixed point is the optimal thing to do from a utility-maximization point of view. And if a shock happens we forcefully "jump" back on the saddle path (that may have changed or stayed the same due to the shock), correcting the course of the economic system by will and decision.

Consider now a model that is mathematically stable proper. It means that it does not matter where we start, and it does not matter what we do, we will end up in the long-term equilibrium. Hardly an appropriate model to reflect the observed human affairs, or decision-making.

And decision-making is structurally an unstable phenomenon, mathematically speaking. This may help glean a bit more intuition: to possess "as much decision-making as needed" in order to have a unique way to go to the fixed point, we need the model to allow us to actually decide optimally on the number of variables the model premises say that we can decide upon, no less and no more: so, as many unstable roots as "unstable"(decision) variables.

If the unstable roots are less than the unstable/decision variables, the model does not give us the "degrees of freedom" we need - it is "too stable", hence the many solutions: it is mathematically stable. Boring.

If the unstable roots are more than the "unstable" variables, we cannot control the model through our decision making, and it will explode/implode.


Let me begin with noting that models such as the CAPM have been extensively falsified, beginning with Mandelbrot in 1963 and ending with the Fama-MacBeth testing in 1973.  Other falsifications followed, but really, it has been a zombie theory since the early seventies.  The difficulty is that the falsification has been like the Michaelson-Morley experiments in the 1880s.  Once they were done, classical physics was falsified, but Plank and Einstein were not around yet.

I have a paper in peer review proposing a new stochastic calculus for options pricing and portfolio construction, but there is nothing resembling a consensus on a replacement.  The math is very different.

The core of your problem can understood in two equations.  The first is $x_{t+1}=\mu{x}_t+\epsilon_{t+1}$.  The second is $r_t=\frac{p_{t+1}q_{t+1}}{p_tq_t}-1$.

For the first equation, for someone to be willing to invest, $\mu>1$.  It was proven in 1958 that this problem has no meaningful solution in Frequentist statistics.  The CAPM is a Frequentist model.  For the CAPM, this means that $\tilde{w}=R\bar{w}+\varepsilon$ only has a solution when $R$ is known, which is an assumption of the math underlying the model.  In other words, models such as the CAPM and Black-Scholes depend on it being true that people know the true values of the parameters.  If they do not, it is known that these models cannot be solved.  The argument has been that the market behaves as if it knew the parameters.  A Bayesian derivation of the CAPM results in a Cauchy likelihood not a normal one.

The second equation makes returns a function of data rather than a known parameter.  As such, it must be derived.  I have a paper deriving the distribution of returns.  The distribution is the product of the ratio of prices and the ratio of volumes if dividends are ignored.  Dividends create their own complications.

However, from auction theory, it can be determined that the dominant element of the resulting mixture distribution is the truncated Cauchy distribution.  It has no first moment, so $\beta$ cannot exist as described in the CAPM.  That is different from saying that it cannot be found.  Such a thing implies the non-existence of the population parameter as the model describes it.

I left out the logarithmic models for two reasons.  First, the CAPM has additive errors.  Second, the distribution created by taking the log of Cauchy distributed variables is the hyperbolic secant distribution. It has no covariance structure in the multivariate form, so the CAPM is defeated anyway.

A short proof that the CAPM cannot function would be to note that if $q_t=q_{t+1}$ which rules out mergers and bankruptcies and $\delta_t=0,\forall{t}$ and there are no dividends, then return is $\frac{p_{t+1}}{p_1}$.  Because stocks are sold in a double auction, there is no winner’s curse.  The rational behavior is to bid your expectation.  Using the assumption of many buyers and sellers from the CAPM, the limiting distribution of the limit book must be normal.

If you center the distribution of prices around the equilibrium prices and assume the market is approximately in equilibrium, ruling out things such as a liquidity crisis, then you end up with a bivariate normal distribution.  The equilibrium return $r^*=\frac{p_{t+1}^*}{p_t^*}$.  Errors could be thought of as excess return, plus or minus.

Noting that the slope is the same as the tangent of the angle, you quickly get very close to the Cauchy distribution by observing that $$\theta=\tan^{-1}(r).$$  The arctangent is the kernel of the cumulative density function of the Cauchy distribution.  The angle is, minimally, a transform of returns via the Cauchy distribution.

Solving for the ratio of two normal distributions by integrating around the equilibrium rather than (0,0), in other words treating the equilibrium as the location of no error, or conceptually by operating in the error space rather than the price space, give you a Cauchy distribution.  It is well known in statistics that the ratio of two normal distributions centered around zero is a Cauchy.  By treating the equilibrium as zero, it still comes out a Cauchy distribution truncated at -100%.  If there exists just one stock that didn't pay a dividend, then the CAPM is intrinsically falsified.

So the answer to your question is, there isn’t a solution.

If you want to optimize a portfolio, use the Kelly bet instead.

Visually, I took the returns for Carnival Cruises, I didn't subtract one, I just took the ratio.  I performed a kernel density estimate having removed the return from dividends to make it consistent with the above.  I then mapped the truncated Cauchy distribution from the maximum likelihood estimator.  As you can see, even if everything I wrote above is false, there cannot be a $\beta$ as described in the CAPM.

There are actually three ways to improve the fit, but I used the method most quants would use instead.


The three critical exogenous variables that drives the demand for and supply of money, according to Investopedia, are liquidity, investment, and consumption.

According to theory, liquidity is determined by the size and velocity of the money supply. The levels of investing and consumption are determined by the marginal decisions of individual actors.

All of this is depicted in the IS-LM model which stands for "investment-savings" (IS) and "liquidity preference-money supply" (LM).   This was used to explain the economics ideas by John Maynard Keynes in the 1930s.  Developed by economist John Hicks in 1937 after Dr. Keynes published his book "The General Theory of Employment, Interest and Money" (1936).


The EU passporting system for banks and financial services companies enables firms that are authorised in any EU or EEA state to trade freely in any other with minimal additional authorisation. These passports are the foundation of the EU single market for financial services.


There can be civil or criminal penalties applied for non-compliance.

See for example:
https://www.gov.uk/government/publications/environment-agency-enforcement-and-sanctions-policy/annex-2-climate-change-schemes-the-environment-agencys-approach-to-applying-civil-penalties

https://www.daera-ni.gov.uk/articles/euets-fees-charges-and-civil-penalties

International trading schemes depend on international law. Membership of such schemes will depend on accepting an adjudication body to rule on breaches, as with any other international contractual agreement.


Are the primary dealers obliged to buy treasuries no matter what?

I assume this refers to the U.S.
(Also, see this question/answer: link to question.)

If so is the reason it is said that the government can always pay their debt because the primary dealers are obliged to always loan to the government?

That’s one reason, but most people are unaware of this angle. I would argue that the usual reason given is that the central bank can buy government bonds in “unlimited” size.
There are limitations on this, and government debt issuance, but they can be bypassed at any time by issuing a new law. Another thing to keep in mind that jurisprudence around Treasury default is not settled, there are arguments that a Treasury default is a “more illegal” option than the Treasury not paying for spending that was authorised by Congress.
From the perspective of underlying economics, the reality that there is an open-ended buying capacity at the central bank is why people refer to currency sovereign debt as default risk free.

Is there a case in which the primary dealers could refuse to buy treasuries?

They submitted to an agreement to bid, so not really. At most, the bids might not cover the auction.

In general, are the primary dealers incentivized or compelled under the law to always bid for the treasuries?

Incentivised - certainly. They get first chance to bid on Treasuries, and their job is to have a sales force that is capable of finding bidders who will pay a higher price in the secondary market. This is why firms become primary dealers in the first place.
“Compelled under law” is a strong phrase; they have a binding contract to bid. Since primary dealers are financial entities whose overall activities are regulated by the Federal government, they would put themselves in a very awkward situation if they tried to break a legal agreement with the government.


Is $\lim_{t \rightarrow \infty} B_t = 0$ at equilibrium in classical monetary model, where $B_t$ represents bond holding?

In general, no.

As you correctly say, No-Ponzi and Transversality imply that the NPV of real bond holdings go to zero. Since we (in general) have not pinned down inflation paths, this does not imply $\lim_t B_t = 0$, as you correctly suspect.

If you can provide more information about what model exactly you work on or the situation you're looking at, I could update my answer.


Removing a degree of freedom from relative utilitarianism

One of the major criticisms you hear about classical economic frameworks is that ordinal utility is the only valid form of utility, because cardinal utility is just putting arbitrary numbers onto people's preferences. The thing is, cardinal utility is really not as fraught as heterodox schools (or even Austrian economists) might expect. Cardinal utility is only an expression of preference up to positive affine transformations, so as long as a utility function maintains the order of all the preferences, the utility functions represent the same preferences; cardinal utility just allows for us to express convexity/concavity along with it.

So when I see a system of utility such as this, it just looks like a normal monotonic transformation into the range $[0,1]$. The only problem with it is that it will normalize all utility functions considered into that range, and you might lose some information about the strength of preferences relative to other agents to each other. I'm not exactly sure what it would be used for.


Are savings necessary for economic growth?

I don't know if you're arguing a theoretical framework or whether saving is important for real economic growth. In theory a special case where all consumers would spend 100 % (MPC=1) of their income is possible to argue - the framework would be loaded with questions - it might, for example, make banks redundant.

In basic economic models savings is often considered equal to investment (you see a variation of S=I in many macroeconomic models) which means that all saved income is used for investment and therefore expected to expand the economy for future periods. In real life the relationship isn't quite this straightforward, but the basic idea still holds.


What impact would falling oil prices have on the natural rate of unemployment?

We need to distinguish between theory and the real world.

In theory, anything can happen. You would need a model that incorporates something that resembles an oil price (many standard models just have a single aggregated good). What then happens depends upon what other assumptions you stick into the model. Whether any of these models have any relationship to the real world is unclear. In any event, you would need to fix a particular model, and as a new question about its behaviour. (E.g., “What is the effect of an oil price rise in {Model X}?”)

In the real world, we need to distinguish the measured unemployment rate, and the “natural rate.” There are a number of ways of estimating the natural rate of unemployment, and what happens to them depends on all of the inputs into the estimation procedure.

What really matters in the real world is what happens to the measured unemployment rate (which may flow into the estimates of the “natural unemployment rate”, as many of the estimation procedures resemble low pass filters). I think the answer is a definite “it depends.”

Firstly, it depends on what country you are talking about. For an oil producer, falling oil prices can easily be a disaster for employment. Many oil producing countries have government revenues that are highly sensitive to oil prices, and so they may be forced to cut back spending. However, they generally have financial reserves, and so can handle limited price falls with limited disruption. Therefore, you need to look at each involved country separately.

For an oil consumer, a rapid rise in oil prices is disruptive; the 1970s experience could be used as an example. Consumers have to spend more on energy, making some products and services unviable. Meanwhile, the increased income is flowing to overseas producers. There is a “terms of trade” shock. The economy will eventually adjust to the new pattern of activity that incorporates higher oil prices, but in practice, the adjustment implies higher unemployment in the near run.

If the fall in oil prices is reversing a previous spike, this will presumably undo the previous disruption. However, if prices were previously stable, effects may be less dramatic. The effects on the economy will depend on how consumers react to the fall in energy prices. If they use the energy savings to buy domestically-produced goods and services, the total volume of domestic production rises, and so firms would presumably need to hire extra workers to produce the greater volume of output. However, the energy savings could just lead to higher savings, leading to no change in domestic production, and presumably employment (in the near run, at least).

The key is that falling input prices are generally not enough to cause increased production by itself; the firm needs to sell a greater quantity of goods, or else the extra production would just represent an undesired increase in inventories. (Since firms have to project demand, they could ramp up production (and hence, employment) to meet projected demand, but if that demand is not realised, they would have to reverse that decision.

For a country that is both a consumer and importer of oil (such as the United States) there is a trade-off between the benefit to consumers versus the potential loss of fixed investment in energy production. Therefore, it could go either way; you would need to do a fairly detailed model to get an estimate.


Interpretation of Nash equilibrium as a potential stable point of a dynamic process

I am not a big fan of any "dynamic adjustment" ideas in static games to justify Nash equilibrium, but for some people it is helpful. I would see it more as an inner monologue with many "what if"-questions.
As an example, consider Cournot competition. Supposse, two firms compete in quantities. The figure below (also from the wikipedia page) depicts the reaction functions (or best-response functions). If firm 2 sets quantity $q_2$, the best response by firm 1 is to set $q_1= R1(q_2)$. We have a Nash equilibrium where these two functions intersect, i.e., when all firms play a best response against each other. The NE is at $(q1,q2)$ in the figure.

Suppose firm 1 thinks: "I believe firm 2 sets quantity $q'_2<q2$. Hence, I will respond with $q'_1=R1(q'_2)$." Next firm 1 would think: "But wait, if I set $q'_1$, then firm 2 would not set $q'_2$, but $q''_2=R2(q'_1)$. This means I should set $q''_1=R1(q''_2)$." Next: "But wait, then firm 2 would set $q'''_2=R2(q''_1)$..." and so on. This though process converges to the NE $(q1,q2)$. Similarly, we arrive at the same NE when starting with $q'_2>q2$. If you want to, you can also think about the firms actually setting these quantities in repeated interactions, making only one of the steps of the thought experiment, and thereby they would also arrive at the NE and stay there.
In this sense,  "a Nash equilibrium can also be interpreted as a potential stable point of a dynamic adjustment process in which individuals adjust their behavior to that of the other players in the game, searching for strategy choices that will give them better results."


Value Function For Durable-Good Monopolist with General Distribution

You probably want to say that the optimal profit is $\pi=\frac{[1-F(p^*)]^2}{f(p^*)}$ where $F(x)$ is a given probability distribution, $f(x)$ is its density and $p^*$ satisfies $p^*=\frac{1-F(p^*)}{f(p^*)}$.

If you are dealing with a general $F$ function, you may want to state the conditions that guarantee that $p^*$ exists and it is unique. If $F$ is uniform or some other well-known distribution, however, you should probably find in closed form the value of $p^*$ and give an actual number as optimal profit.


Graduate level texts/notes that cover the Short Run and Long Run Costs of firms' production

Textbooks:

Mas-Colell, Whinston, and Green (1995). Microeconomic Theory. Chapter 5
Geoffrey Reny. Advanced Microeconomic Theory, 3rd edition. Chapter 3
Kreps (1990). A Course in Microeconomic Theory. Chapter 7
Varian (1992). Microeconomic Analysis, 3rd edition. Chapter 5

Lecture notes: I think undergraduate notes are more useful on this respect. For instance:

Chapter 6 to Chapter 8 here.
Set 6 and 7 here (go to downloads to get slides).

In my experience, graduate notes deal with deeper issues. For instance this, this, or this one dig much deeper, skipping SR/LR cost functions altogether.

In any case, here Google is your friend. The trick (imo) is to add "pdf" to the search, to get lecture slides. For example:

http://google.com/#q=microeconomics+cost+function+short+run+long+run+pdf


What is the best way to compare the price of a GB of internet across countries

Purchasing Power Parity (PPP) is probably the most convenient way of doing such comparisons so you are on right track. As mentioned in the comments there are other ways how to do international price comparisons but PPP is probably one of the few ways that do not require much auxiliary estimation/research as it is already readily avaiable to public.
PPP works in a very similar way to an exchange rate. In fact PPP is sort of an exchange rate built under the assumption that the law of one price holds (Krugman et al (2012). International Economics: Theory and Policy). Consequently PPP is an alternative to market exchange not another factor you use on top of it (so the calculations in question are not appropriate).
For example, if in China 1 GB of data costs $¥10$ and PPP is $4.15 \frac{¥}{\\\$}$, the adjustment would be made as: $¥10/(4.15 \frac{¥}{\\\$})\approx {\\\$}2.41$. Afterwards, the prices can be compared as apples to apples so in this case 1GB of data in China would be more expensive than 1GB of data in US (which according to your data costs ${\\\$}1.37$ ), once adjusted for PPP (although I just made the $¥10$ price up you should use your prices).
Note, even tough it is not always stated PPP is implicitely expressed in $\frac{\text{local currency}}{USD}$ since it is based on comparison of price levels of two countries and by convention US is always in denominator. In fact most datasets will even warn you about this. For example, OECD dataset reports its PPP as:

Purchasing power parities (PPP)Total, National currency units/US dollar,
[emphasis is mine]

You can read more about PPP in Krugman et al. International Economics: Theory and Policy 9th ed. Chapter 16. It is an undergraduate textbook so it contains some worked simple examples.


I have only read the abstracts, but the two statements aren't conflicting.

From Wikipedia, a production function gives the technological relation between quantities of physical inputs and quantities of output of goods. A household production function is a form of that idea that looks out how households combine inputs to get outputs that they consume such as water.

Under the HPF model, water is considered as an output that households consume. However, there are many ways to combine inputs to obtain water: you can use utility based water if the infrastructure for that exists or non-utility based water (involving personal tanks, pumps, etc). The assumption is that households will be willing to pay for the utility based water infrastructure at least the amount that it takes to upkeep their non-utility based water that they currently own accounting for the sunk costs of the upfront purchase of the tanks and pumps. And hence that is the "lower bound to WTP". But this assumes that the utility based water is higher quality than what households already have. As noted in the abstract of the latter paper, "[w]e attribute this departure from the traditional relationship between averting expenditures and contingent valuation to the lack of household confidence in the quality of utility-provided water." Hence, current coping costs become an upper bound to WTP. To put it differently, if households believed utility based water is exactly equivalent to what they currently have, then the WTP would be exactly equal to current coping costs.


Homothetic preferences and utility functions

As noted in the comments, it is not true that homothetic preferences must have constant marginal rates of substitution.

To see this, recall that preferences given by the utility function

$$ u(x,y) = x^\alpha y^{1-\alpha} $$

are homothetic. (More generally, Cobb-Douglas preferences are homothetic.) However, the marginal rate of substitution is

$$ \text{MRS}(x,y) = \frac{\alpha}{1-\alpha}\frac{y}{x}, $$

which is not constant. However, the MRS is homogeneous of degree zero, since

$$ \text{MRS}(\lambda x, \lambda y) = \text{MRS}(x,y). $$

Homogeneity of degree zero of the MRS is a general property of homothetic preferences. This follows from the fact that (continuous) homothetic preferences have a utility representation that is homogeneous of degree one.

Conversely, when the MRS is homogeneous of degree zero, preferences are homothetic. Hence, preferences that exhibit constant MRS are also homothetic. The proof is a little involved. For this, I refer to you lemma $1$ of "Duality and the Structure of Utility Functions" by Lau (1970). (Note that Lau states a different definition of homotheticity than you do. However, the Lau's definition and yours are equivalent when preferences are continuous -- which they must be for the MRS to be well-defined.)


I would begin my search by finding related papers in the Journal of Applied Econometrics that contains currency as a key word.

After a related paper is identified, I would to go to the data archive URL: http://qed.econ.queensu.ca/jae/ to see if the data in the paper were uploaded there.

Two papers I found that are related to financial contagion (and possibly leading to a relevant data set for your study):

Eichengreen, B., Rose, A.K. and Wyplosz, C., 1996. Contagious currency crises (No. w5681). National Bureau of Economic Research.
Dungey, M. and Renault, E., 2018. Identifying contagion. Journal of Applied  Econometrics, 33(2), pp.227-250.

You can also use the references therein to find more related papers. I hope it helps so far.

P.S. If your school has a subscription to Bloomberg Terminal, I believe those currency data can be found in the Terminal.


How should I adjust data for both inflation and foreign exchange rate?

NO, it is not redundant. Controlling for nominal effects gives you a better picture, and makes more sense on a theoretical level. To transform assets into USD use

$\textit{asset}_{USD}=\frac{s_t P_{t,JPY}}{P_{t,USD}} \textit{asset}_{JPY}$

where the fraction is the real exchange rate, $P_t$ is the respective price level and $s_t$ the nominal exchange rate.

Alternatively, you can work with differences

$\Delta rer =\frac{\Delta s_t \pi_{t,JPY}}{\pi_{t,USD}}$.

Note that the real exchange rate is far from perfect, but it is common practice in macroeconomics. Also, it does not matter which transformation you do first, as its purely multiplicative.


Gelman and Hill's Data on Effects of Child Support Enforcement

I just faced the same problem and found the solution:

Use this code in R:

input Stata file

library(foreign)
child <- read.dta("C:\child.iq.dta")

Code found here:(https://www.statmethods.net/input/importingdata.html)

You need the double " \ " if you're using R.
read.dta("    ") Type the exact folder with data ending. Be careful to use common characters, otherwise R could have problems finding the folder. In my case I just saved the files on C:\.

This way you can access all Data.

I'm using the latest R-Studio version.

I hope I could help you!


Differences between best response, dominant strategy and Nash equilibrium

Consider the following game between P1 (row player) and P2 (column player):
\begin{array}{|c|c|c|}\hline
& L & R \\\hline
T& 1,1 & 2,0 \\\hline
B& 0,0 & 1,1 \\\hline
\end{array}

$T$ is P1's dominant strategy
$T$ is P1's best response to both of P2's strategies $L$ and $R$
$L$ is P2's best response to P1's strategy $T$
$R$ is P2's best response to P1's strategy $B$
$(T,L)$ is the only Nash equilibrium

Generalizing from the above observations:

A strategy is dominant if and only if it is a best response to each of the other player's strategies, e.g. P1's $T$.
A strategy that is a best response to some but not all of the other player's strategies cannot be a dominant strategy, e.g. P2's $L$ and $R$.
A Nash equilibrium is a pair of mutually best responding strategies, e.g. $(T,L)$.


Compute the average income and the average utility

These are not two densities, but one density defined on the interval $[0,1.2]$, taking two different values. The average income is then the integral of the density function, i.e.

$$
\int_0^{0.5} 1 x \, dx + \int_{0.5}^{1.25} \frac{2}{3} x \, dx = \frac{9}{16} = 0.5625
$$

In order to obtain the average income, you do the same with the Utility and $\bar{z} = \frac{9}{16}$.


The Dynamic Programming ("Bellman' Equation") formulation incorporates the terminal boundary condition ("transversality conditions") needed in case we use the Lagrangian/Euler equation formulation. The initial conditions are still needed in both approaches.

To see why, consider the problem

$$\text{max}_{\{x_t\}} \sum_{t=0}^{\infty} \beta^t U(c_t)$$

$$s.t.\;\;\; a_{t+1}= (1-r)a_t + w - c_t, \;\;\; a_0 \; \text{given}$$

Solving the budget constraint for $c_t$ and inserting into the objective function, we have compactly

$$\text{max}_{\{a_{t}\}} \sum_{t=0}^{\infty} \beta^t U(a_t, a_{t+1}),\;\;\;\; a_0 \; \text{given}$$

where we treat the stock variable next period as our decision variable.
Now for the optimal sequence, $a^*_{t+1}$ must solve the following problem:

$$\max_y \big[U(a^*_t, y) + \beta U(y, a^*_{t+2})\big],\;\;\; y\;\; \text{feasible given}\;\; a^*_t$$

In the words of Stokey and Lucas "a feasible variation on the sequence $\{a^*_t\}$ cannot lead to an improvement on an optimal policy".

Then we get the first order conditions (differentiating with respect to $y$ essentially)

$$U_2(a^*_t, a^*_{t+1}) + \beta U_1(a^*_{t+1}, a^*_{t+2}) =0$$

where the subscripts $1,2$ denote partial derivatives. This is a second-order difference equation, and so it requires two boundary conditions. We have already one of them, the given initial value of wealth $a_0$. We need one more, hence the terminal, "transversality" condition.

In contrast, using the Dynamic Programming approach we arrive at a first-order difference equation, and we do not need an additional boundary condition.

For the full exposition, see Stokey & Lucas p. 97-100.


According to the OECD: Israel's spending per-student is low relative to other OECD countries. Given that countries like the US have both higher spending per-student and higher enrolment rates, it is not clear what a switch to heavier state subsidisation (both the UK and US already heavily subsidise universities) would achieve. Bear in mind that most of the best US universities privately subsidise talented students from poor backgrounds so that the highest fees are mostly bourne by the wealthy.

It seems that implicit in your question is the idea that Israel rations its heavily subsidised tertiary education by imposing more demanding entrance requirements, but it is not clear to me that this is true. The entrance requirements for elite universities such as Harvard, MIT, Oxford, or Cambridge are among the most demanding in the world. There are 4599 higher education institutions in the US that cater to a very broad spectrum of student types.


Stone-Geary preferences and competitive equilibrium

This is a paper using a competitive monopolistic framework (in GE). It is an old paper by Stratz (1989). Recent work with Stone-Geary preferences relates to the issue of structural transformation following the work of Herrendorf, Rogerson and Valentinyi (2013), although there is considerable debate on whether these preferences appropriately capture the data. All these papers have a representative consumer, with expenditure shares changing over time due to growth.


"Elasticity of marginal utility of consumption ( μ ) with respect to utility." (Green Book quote)?

Mere googling leads me to find a bunch of references about elasticity of marginal utility.

Here Professor Acemoglu defines the elasticity of marginal utility as the inverse of the intertemporal elasticity of substitution (pagg. 17-18).

Here you can find a question analogous to yours together with an answer explained in an easier way than Acemoglu's lecture.

If you are interested in something more empirical, have a look here: it is a paper by David Evans about the empirical estimation of elasticity of marginal utility in OECD countries.

Hope this is enough. If you have other questions, please ask


Lagrangian multiplier and optimal bundle

Your steps look okay, and the solutions are correct. You can rule out corner solutions by evaluating the utility function at the "corners" and compare those values to the optimum you found. You should be able to verify that $U(50,20)>\max\{U(0,120),\,U(60,0)\}$.


What is the characteristics of economic downturn and which countries experience economic downturn from 2010 to 2018?

A downturn is characterized by a time period of lower economic growth or economic contraction. The term economic downturn has no formal definition and can mean many things including a recession. An economic downturn might also be used to describe periods of lower economic growth. On the other hand a recession is a specific term that is often used to describe two consecutive quarters of economic contraction.
For example, Australia has experienced near continuous growth since the early 1990s. In that three decade span Australia has experienced individual quarters of contraction but never two consecutive quarters of contraction. So it can be said that Australia has experience brief economic downturns but no recessions in the past decades.
Not completely the same as a list of countries that have experience economic downturns, but Wikipedia has a list of economic crisis by decade. A few notable examples in the 2010 to 2018 time frame are Brazil, Greece, and Venezuela.
Here is a chart from a World Bank research paper that shows the number of countries in recession by year.

This definition comes from the site Market Business News and offers a more precise definition of economic downturn.

An economic downturn, or a downturn, occurs when the value of stocks, property, and commodities fall, productivity either grows more slowly or declines, and GDP (gross domestic product) shrinks, stands still or expands more slowly.


Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation

This is more of a calculus question. Recall the total differential of a function $f(z_1,z_2,z_3)$:
\begin{equation}
\mathrm df(z_1,z_2,z_3)=\frac{\partial f(z_1,z_2,z_3)}{\partial z_1}\mathrm dz_1 + \frac{\partial f(z_1,z_2,z_3)}{\partial z_2}\mathrm dz_2+\frac{\partial f(z_1,z_2,z_3)}{\partial z_3}\mathrm dz_3.
\end{equation}
Hence,
\begin{equation}
\frac{\mathrm df(z_1,z_2,z_3)}{\mathrm dz_1}=\frac{\partial f(z_1,z_2,z_3)}{\partial z_1}\frac{\mathrm dz_1}{\mathrm dz_1} + \frac{\partial f(z_1,z_2,z_3)}{\partial z_2}\frac{\mathrm dz_2}{\mathrm dz_1} + \frac{\partial f(z_1,z_2,z_3)}{\partial z_3}\frac{\mathrm dz_3}{\mathrm dz_1}
\end{equation}
Applying to your case, we substitute $p_1$ for $z_1$, $p_2$ for $z_2$, and $\overline m$ for $z_3$ (noting that $\overline m(p_1,p_2)$ is a function of the prices):
\begin{align}\require{cancel}
\frac{\mathrm dx_1(p_1,p_2,\overline m)}{\mathrm dp_1}&=\frac{\partial x_1(p_1,p_2,\overline m)}{\partial p_1}\cancelto{1}{\frac{\mathrm dp_1}{\mathrm dp_1}} + \frac{\partial x_1(p_1,p_2,\overline m)}{\partial p_2}\cancelto{0}{\frac{\mathrm dp_2}{\mathrm dp_1}} + \frac{\partial x_1(p_1,p_2,\overline m)}{\partial \overline m}\frac{\mathrm d\overline m}{\mathrm dp_1}\\
&=\frac{\partial x_1(p_1,p_2,\overline m)}{\partial p_1} + \frac{\partial x_1(p_1,p_2,\overline m)}{\partial \overline m}\overline x_1
\end{align}


Inelastic offer, tax paid by seller, who supports the charges

If "supply is perfectly inelastic" it cannot be the case that the supplier can "just lower his production". The point of "perfectly inelastic supply", is exactly to represent the case, where the supplier will offer a specific quantity at whatever price, even zero.  The classic case here is a good that is it deteriorates quickly in terms of quality or even consumption safety (say fresh foods).

The equilibrium price is then determined by demand. If the state appears and wants to take a chunk out of the price by imposing a tax, the tax will fully burden the supplier.

Of course this is the static approach. In a dynamic setting, such a situation may for example create incentives for an unofficial market, where the supplier tries to hide sales from the state in order to reduce the tax burden.


Deriving demand function in case of multivariable utility functions with min and max structures

It is possible to use a Lagrangian to obtain your Marshallian demands, provided you break each min function up into two different pieces and remain wary of boundary solutions. So for example, if you impose the condition $x_1<\frac{a}{2}, x_2<\frac{b}{2}$ you can simplify your utility function to $x_1 x_2 + x_3$, and then solve for Marshallian demands that are valid when this condition holds. Once you've obtained your demand for this piece it's good practice to re-state your condition as a function of the parameters (a, b, w, and $\textbf{p}$) Then go back to your original utility function, impose an alternative condition and repeat to get a different piece of the demand. The demand function will be piecewise (and in this case it seems like it'll consist of quite a few different pieces). Good luck!


When people talk about 'elasticity of demand' without further qualification they normally mean 'price elasticity of demand':
$$\text{E}_p=\frac{\partial Q_t}{\partial P_t}\frac{P_t}{Q_t}$$
However, note your calculations are not entirely correct as in this case the elasticity should be:
$$\text{E}_p=-\frac{1}{\gamma}\frac{P_t}{(X_t-P_t)/ \gamma} = - \frac{P_t}{X_t-P_t}$$
However, the paper never claims $\gamma$ is elasticity and that the demand has constant elasticity in this case. Based on discussion in the comments which mentions that the claim was actually not made by the paper but by some student I assume it was a mistake (confusing slope of a demand with elasticity is actually surprisingly common among students).


Why U.S Import from China is a big deal?

You are right. There is nothing in "importing" which is intrinsically related to "borrowing". If economics books often quotes this, it is because they make an accounting-like shortcut (under assumptions of balanced public accounts) that is representative of the USA-China case.

On the one hand, USA has a net negative trade balance with China, i.e. USA is "net-importing" from China.
On the other hand, the "U.S. debt to China is $1.2 trillion as of August 2017".

The accounting-like shortcut consists of saying that USA debt to China is actually used to import goods from China. This is not the factual reality, but an accounting one. The real story behind is that actually, when importing goods from another country, a U.S. private company is not doing so from a local one who would pays taxes and thus generates tax income for the U.S. government, which would in turn allows it to contract less debt and so on...


The Frisch-Waugh-Lovell Theorem: an exercise

What we know from FWL theorem, is that the regression

$$M_1y = M_1X_2\beta_2 + M_1u \tag{1}$$

will give the same estimates for $\beta_2$ as the full regression

$$y = X_1\beta_1 +X_2\beta_2 + u \tag{2}$$

where

$$M_1 = I - P_1 = I - X_1(X_1'X_1)^{-1}X_1'$$

is the so-called annihilator or residual-maker matrix.  The estimator from $(1)$ is

$$\hat \beta_2 = (X_2'M_1X_2)^{-1}X_2'M_1y \tag{3}$$

So it boils down to examine whether the estimator from the specification

$$P_1y = P_1X_2\beta_2 + w \tag{4}$$

which is

$$\tilde \beta_2 = (X_2'P_1X_2)^{-1}X_2'P_1y \tag{5} $$

will be the same as $\hat \beta_2$.

Well,

$$(2),(3) \implies \hat \beta_2 - \beta_2 = (X_2'M_1X_2)^{-1}M_1u \tag{6}$$

while

$$ (2), (5) \implies \tilde \beta_2 -\beta_2 = (X_2'P_1X_2)^{-1}X_2'X_1\beta_1+ (X_2'P_1X_2)^{-1}X_2'P_1u \tag{7}$$

Given that $(6)$ and $(7)$ involve arbitrary exogenous quantities ($u, \beta_1$) I don't see how they could be equal, except by zero-probability chance.

Even if in our sample $X_1$ and $X_2$ are orthogonal (which would eliminate the first term in $(7)$ but which, with observational data, is a joke to even mention), then the two would be unbiased under strict exogeneity -but this is as far as similarities appear to go here.


How to show that the income elasticity of Marshallian demand is equal to unity?

Here's my attempt at a hint, though I appreciate feedback, as I am not sure how rigorous this is. As per the comment I gave with the resource, your question seems to require a previous question in order to do this.

So start by showing that the share of income spent on good $x_i$ can always be measured by the elasticity of expenditure function with respect to $p_i$ at $(p, u^*)$ where $u^* = v(p,w)$

$$\mid \eta^ {e_{x_i, p_i}}\mid \ = \frac{\frac{\Delta x_i}{x_i}}{\frac{\Delta p_i}{p_i}} = \frac{\Delta x_i}{\Delta p_i} \cdot \frac{p_i}{x_i} = \frac{\partial x_i}{\partial p_i} \cdot \frac{p_i}{x_i}$$

We know that,

$$e(p,u^*) = p \cdot \tilde x, \forall \ \tilde x ∈ x^h (p, u^*) = x(p, e(p, u^*))$$

by duality, where $x^h(p, u^*)$ denotes Hicksian demand. So,

$$\frac{\partial e(p_i,u^*)}{\partial p_i} = x_i$$
$$\frac{\partial x_i}{\partial e(p_i, u^*)} = \frac{x_i}{w}$$

$$\implies \frac{\partial x_i}{\partial p_i} \cdot \frac{p_i}{x_i} = \frac{\partial e}{\partial p_i} \cdot \frac{\partial x_i}{\partial e}\cdot \frac{p_i}{x_i} = \frac {x_i^2}{w} \cdot \frac{p_i}{x_i} = \frac{p_i x_i}{w}$$

Which is the share of income spent on good $x_i$


Fair value that a risk averse individual would pay to enter a gamble

Yes.
In general not.

Let's say the individual has initial wealth $W$ and the gamble $g$ has payouts $0$ and $G$, each with probability $1/2$. As you say, the certainty equivalent $C$ of the gamble is the amount $C$ with $$u(W+C)=(u(W)+u(W+G))/2.$$ Now the same individual would be willing to pay at most $P$ to enter the gamble, where $$u(W)=(u(W-P)+u(W+G-P))/2.$$ So if $C$ is the certainty equivalent of $g$ at wealth level $W$, then $P$ is the certainty equivalent of $g$ at wealth level $W-P$. If $u$ is linear, then $P=C=G/2$ follows, but in general $C$ will differ from $P$.


No, there is no such evidence, because Russia does export gold, though it also adds to its reserves

For example Sputnik News (established by the Russian government-controlled news agency Rossiya Segodnya) reported

  Exports of fine gold from Russia increased 2,5 times to 56,6 tons (1,82 million oz) last year, compared to 22,4 tons in 2016, according to the Russian State Assaying Chamber under the Ministry of Finance.

  ...

  Russia's precious metals refineries reportedly produced 306,9 tons (9,867 million oz) of gold in 2017, which is 6,4 percent more than 288,6 tons produced in 2016. 18,4 percent of all the gold produced in the country was exported, while the rest 224 tons of the metal were purchased by the Central Bank of Russia to add to the country's gold and foreign currency reserves, RIA Novosti reported.

  ...

  "The exports (of gold) in 2017 were not as high as they were in 2014 — 140 tons", the expert told RIA Novosti.


Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete?

Consider lotteries over $\{x,y,z\}$. Let $u(x)=0, u(y)=\frac{1}{2}, u(z)=1$. Consider the nonlinear transformation f(t)=t^2. Let $v:=f\circ u$, so $v(x)=0,v(y)=\frac{1}{4}, v(z)=1$.

Consider two lotteries,  $P=(0,1,0)$ and $Q=(\frac{1}{2},0,\frac{1}{2})$.

$$E_P[u]=\frac{1}{2}=E_Q[u]$$

$$E_P[v]=\frac{1}{4}<\frac{1}{2}=E_Q[v]$$

In general, let $\succeq$ be a preference over lotteries $\Delta(X)$.  Let $U$ be a utility function of $\succeq$ that has the EU form, so $U(P)=E_P[u]$ for some $u$. Take any increasing transformation $f$ and define $V(P):=f(U(P))$ then $V$ will also be a utility function for $\succeq$, that is $V(P)\geq V(Q)\iff P\succeq Q$. However, unless $f$ is a positive affine transformation, that is $f(x)=Ax+B$ where $A>0$ then $V$ will not be an expected utility function. That is, there will not exists a $v$ such that $V(p)=E_p[v]$.


Why does adding a quadratic term to a regression change unrelated coefficients?

Your errors aren't the same anymore.  For example, instead of writing $Y = \beta_1 + \beta_2 X + U$, you're actually writing  $Y = \alpha_1 + \alpha_2 X + \alpha_3 X^2 + V$.  There is no expectation that they should be the same.

In other areas, the trouble is that the error term is likely correlated with your regressors.

Fear not: running wages on education is a common specification.  Searching for something like

  wages education endogeneity

should bring up a whole slew of papers that treat the topic.


Does one include inflation when computing elasticity?

Elasticities are partial derivatives -- so to estimate them you need to hold all other factors fixed! That would include the prices of other goods.


Is it possible to sell a rival and non-excludable product?

A good is excludable if people can be prevented from using it. If one person is using any rival good then this good won't be available for others. You asked about rival and non-excludable good such as Common-pool resources. Examples of Common-pool resources is fisheries, forests, groundwater basins, oil fields and so on. Unlike pure public goods, common-pool resources face the problem of overuse (the tragedy of commons).
Let's see the case of fisheries you talked about. Generally, fishermen are free to fish in the sea. The tragedy of the commons problem tells us that each of the fishermen will try to catch more fishes as they are rival goods, unlike public goods. Therefore, this common pool resource of sea fishes will be vulnerable to get extinct or get empty due to overuse. To reduce the chances of this happening, government or any common group will be given authority to manage it and reduce the overuse of it. Nobel prize winner economist, Elinor Ostrom noticed this and talked about collective-choice arrangements and effective monitoring of common-pool resources.
Coming to your doubt, CPRs may or may not be sold. Talking about Sand in the river basin (another example of  CPR) there is an example of selling of rights to mine or excavate sand. Also, there is a prohibition of fish mining from the area where fishes are endangered species.  due to over mining or preserving the bio-diversity.
Therefore, it depends on the situation whether Common pool resources can be sold or not.


I think you are referring to Optimization, which is taught in both engineering, math, computer science, biology, and economics.   In engineering, it's taught in a general course on Linear programming, and in economics it would be taught in a class like Operations Research.   For both courses, I believe the standard introductory text these days is Winston, Wayne L. (2004), Operations Research: Applications and Algorithms (4th Edition).  You'll need to have a  background in linear algebra to digest this book.

But there is a ton of stuff on Youtube that will probably suffice.   Google "Linear Programming". Once you understand the basic principles of the Simplex Method, you can simply download some free software like LINDO or use Excel, and you'll cover 99% of the needs of most mere mortals.

You can also find good courses on Coursera.

That being said, Optimization can get very  complicated and require courses in advanced linear algebra and calculus. For example, convex optimization is taught in many universities, but at the graduate level or in pure Mathematics. See http://stanford.edu/~boyd/teaching.html for a taste of what some engineers work on when they build very complex "machines".


By stnadard OLS regression results, in the simple regression

$$y_t = \alpha + \beta z_t + v_t, \;\;\;t=1,...,T$$

we have that

$$\hat \beta = \frac {\sum_{i=1}^T (z_t - \bar z)(y_t-\bar y)}{\sum_{i=1}^T (z_t - \bar z)^2}$$

and

$$\hat \alpha = \bar y - \hat \beta \bar z$$

So the residuals are

$$\hat v_t = y_t -(\hat \alpha +\hat \beta z_t)$$

Then, substitute for your particular $y_t$ and $z_t$ in all the above.


Yes the two approaches are equivalent. However, that does not mean that the respective individual variables are equivalent. Taxes are not equivalent to government spending but the both equations equally capture all Government output. For example in the first approach:

$$GDP = C+ I + G +NX$$

Where $C$ is consumer spending, $I$ is investment and $G$ government spending, $I$ is also equal to private and public saving $I=S + T-G$, so if government spend less than what it collect in taxes the public savings and public portion of investment increases, and when it runs budget deficit vice versa, so the possibility of running either surplus or deficit or balanced budget is already accounted for there. No assumption that its all spent is necessary.

Second, any income, whether it is wage or not, can be only consumed or saved. The consumption part is explicitly included in the formula as $C$ the saving part is the $S$ which represent the private savings from which investment is created. So if a person spend less their income investment increases thanks to private saving, and if a person lives on debt investment decreases to reflect that.

Also, both formulas are just accounting formulas. By itself they have no behavioral assumptions/spending assumptions. They are national equivalent of the kind of accounting that you could see in firms book just track the sources of income and spending.


Will an increase in interest rate cause short run aggregate supply to shift?

Yes, however a supply shift as a result of interest rates can be (sticky).this is why after a stock drop, a recession can take 1 year- 18 months to occur. So when we look at economic indicators over the past year, the 10-year approaching 3% has not led to a reduction in aggregate supply. It may not be until FY 18 Q4 that we see a drop a significant drop in in supply. Supply and interest rates do not have a “flexible” relationship, but instead a “sticky” one in which supply may not drop immediately, but over time your answer is correct.


The Applied Theory of Price

by Donald N. McCloskey

McCloskey published the book (pdf) for free now.

The Chicago school's other economists also published their books on price theory (see Milton Friedman's and George Stigler's).


How much influence does the president really have on US economy?

Here is one paper that may be of interest:

  Analyses of the effects of election outcomes on the economy have been
  hampered by the problem that economic outcomes also influence
  elections. We sidestep these problems by analyzing movements in
  economic indicators caused by clearly exogenous changes in
  expectations about the likely winner during Election Day. Analyzing
  high frequency financial fluctuations following the release of flawed
  exit poll data on Election Day 2004, and then during the vote count,
  we find that markets anticipated higher equity prices, interest rates
  and oil prices and a stronger dollar under a Bush presidency than
  under Kerry. A similar Republican-Democrat differential was also
  observed for the 2000 Bush-Gore contest. Prediction market based
  analyses of all Presidential elections since 1880 also reveal a
  similar pattern of partisan impacts, suggesting that electing a
  Republican President raises equity valuations by 2-3 percent, and that
  since Reagan, Republican Presidents have tended to raise bond yields.

Partisan Impacts on the Economy: Evidence from Prediction Markets and Close Elections Snowberg, Wolfers, and Zitzewitz (2006)

This might give some indication of an upper bound on these effects since only some of the increase in stock market wealth is from an increase in aggregate wealth. The rest comes from a change in transfers and so not really an effect on the economy.

Here's a similar paper from Germany:

  Rational partisan theory suggests that firms perform better under
  right- than left-leaning governments. In the pre-election time,
  investors should anticipate these effects of government partisanship.
  This is the first study to investigate such anticipated partisan
  effects in Germany. Applying conditional volatility models we analyze
  the impact of expected government partisanship on stock market
  performance in the 2002 German federal election. Our results show that
  small-firm stock returns were positively (negatively) linked to the
  probability of a right- (left-) leaning coalition winning the
  election. Moreover, we find that volatility increased as the electoral
  prospects of right-leaning parties improved, while greater electoral
  uncertainty had a volatility-reducing effect.

Partisan politics and stock market performance: The effect of expected government partisanship on stock returns in the 2002 German federal election   (Füss, Bechtel (2002))

It also depends on the baseline way of measuring impact. A really terrible president might be able to wreck serious damage on the economy while the other branches and electorate would take time to undo that damage and remove him. Should presidential performance be measured against the very worst that an incompetent or malicious person could deliver? Or are they best compared with other likely serious contenders? These papers above are much more measures of the latter than the former.


Two Players Different Strategies in infinitely repeated game

Just so that we have a common understanding of the strategies you mentioned:

  Grim trigger: "Play $C$ unless the outcome of any previous stage is not $(C,C)$; in that case, play $D$."

  Tit-for-tat: "Start by playing $C$, and then play the action used by the other player in the previous stage."

Therefore, on equilibrium path, the outcome $(C,C)$ will be observed, and each player gets a discounted payoff of
\begin{equation}
3+3\delta+3\delta^2+\cdots=\frac{3}{1-\delta}.\tag{1}
\end{equation}

Suppose player 1 who adopts grim trigger deviates in the first stage only. The outcome in stage 1 would be $(D,C)$, and the outcome in all subsequent stages would be $(D,D)$ according to the strategy profile. Thus, player 1's payoff from the deviation would be
\begin{equation}
4+2\delta+2\delta^2+\cdots=4+\frac{2\delta}{1-\delta}.\tag{2}
\end{equation}
$(1)$ and $(2)$ imply that a one-stage deviation is not profitable for player 1 if $\delta\ge\frac12$.

Suppose player 2, who adopts tit-for-tat, deviates in the first stage only. The outcome in stage 1 would be $(C,D)$, and $(D,C)$ in stage 2, $(D,D)$ in all subsequent stages. Player's payoff from the deviation would be
\begin{equation}
4+0\delta+2\delta^2+2\delta^3+\cdots=4+\frac{2\delta^2}{1-\delta}.\tag{3}
\end{equation}
$(1)$ and $(3)$ imply that a one-stage deviation is not profitable for player 2 if $\delta\ge 1-\frac{\sqrt 2}{2}$.

Note that $\frac12>1-\frac{\sqrt2}2$. Hence, as long as $\delta\ge\frac12$, player 1 using grim trigger and player 2 using tit-for-tat can be sustained as a Nash equilibrium of the infinitely repeated prisoner's dilemma. However, that the strategy profile is not a subgame perfect equilibrium (for a similar reason why a symmetric tit-for-tat strategy profile is not subgame perfect).


Are the EU funds coming from EU citizen's taxes as well?

The main four sources of EU revenue are:

Custom duties and levies - EU calls this its 'Traditional own resources'. These are however not collected directly but member states collect it on the EU's behalf and are allowed to retain (currently) $20\%$ cut from these. These duties are ultimately, at least partially, payed by the EU citizens either directly or indirectly through tax burden incidence (save for special cases where the tax burden incidence might fall on non-EU citizen or company owned by non-EU citizens).
VAT - After EU harmonized the VAT collection rules among the member states a small percentage of VAT was set up to be directed towards the EU budget (between $0.15-0.30\%$ - however this rate has many asterisks and caps attached to it for complete rules see here). The VAT is again not collected directly by EU but by the member states on its behalf but it is for the most part payed by the EU citizens. Of course, part of it might be payed by people on vacation - especially for consumption of non-durable goods as with durable goods its often possible to get VAT rebate.
National contributions from member states - EU calls this 'Gross National Income-based own resource' since it is calculated from member state's GNI and is currently capped at $1.2\%$ GNI. The member states themselves decide how to raise this money - some of them might come from non-EU citizens or firms not owned by EU nationals but empirically most nations raise revenue primarily by taxing their own citizens. For example, most EU countries raise large portion of their revenue through income taxes so when EU citizens pay their income tax little bit from it is forwarded to the EU budget. Of course, most modern nations levy a plethora of different taxes to see exactly where individual members raise their revenue you have to look at their individual budgets.
Other sources - these include fees and fines EU issues, or contributions of non-EU countries to research projects, or taxes on EU staff etc. and other items. Again some of these are presumably collected from EU citizens.

Moreover, note in case of all of the above even some non-EU countries have to contribute, such as Norway for example, for accessing the common market.


Murray Rothbard gave a "natural rights" justification for an AnCap society.

David Friedman (son of Milton Friedman) discusses and gives a consequentialist defence for an Anarcho-Capitalist society. It's discussed in his book 'The Machinery of Freedom' and references 14th century Iceland for an approximation of how a society based on private laws and courts work.

Murray Rothbard, however, is still is the best known AnCap theoretician.


Can there exist something that subsidises that is not a subsidy

My answer relies on two quotes. The first one:

  A rose by any other name would smell as sweet

And the second one is from the definition of State Aid by the European Union's competition authority:

  State aid is defined as an advantage in any form whatsoever conferred on a selective basis to undertakings by national public authorities.

There is a difference between illegal state aid and subsidies, but the difference is in the "selective basis". Aid in any form that confers an advantage is aid.


How to estimate market risk using only publicly available data?

This paper on Fluctuations in Uncertainty may be helpful and relevant.

  The  volatility  of  the  stock  market  or  GDP  is  often  used  as  a  measure  of  uncertainty  because  when  a  data  series  becomes  more  volatile  it is  harder  to  forecast.

Computing the variance or standard deviation of the growth rate of a variable is quite a common procedure to get volatility figures.

The above figure shows the VIX index of 30-day implied volatility on the Standard & Poor's 500 stock market index. The  VIX  index  is  traded  on  the  Chicago Board Options Exchange. It is constructed based on the values of a range of  call  and  put  options  on  the  Standard  &  Poor's  500  index  and  represents  the  market's  expectation  of  volatility  over  the  next  30  day.

Other  common  measures  of  uncertainty  include  forecaster disagreement, mentions of "uncertainty" in news,  and the dispersion of productivity shocks  to  firms. Check Bloom's web page and his Economic Policy Uncertainty Index


The first answer of presented in the list is wrong. GDP is measure of current production not of past inherited wealth. Even though the existing capital plays a part, the lowest of deprecation rate is around 25 years IIRC, so by and large the wealth is not inherited, but created by the generation.

Advances in technology are usually assumed to spread all around the globe quickly (certainly within one generation). So that's not the answer either.

I would argue that the important values and institutions that allow for wealth creation are the primary reason. It would not be too far of stretch to say that the values that made the wealth creation possible in the first place are what allows the continuation in wealth generation.

(Of course the GDP growth in developed countries does not seem to be too persistent, and has been falling. The alternate answer is that rich nations don't remain rich.)


Why are aeroplanes not made in one place?

Short answer
Airbus is a particular case of decentralised supply chain which came from historical and political reasons. Airbus is a consortium with several European states having a stake on it, which means that each state wants a part of the production in their country.
Long answer: Why is Airbus' supply chain disperse
The aviation industry for commercial planes basically has has two large players nowadays: Boeing and Airbus. The 70's-80's saw the consolidation of American producers, with Boeing as the survivor and most successful of them (incorporating other large players such as the old McDonell Douglas).
Europe had smaller producers, such as BAC or Aerospatiale. Smaller European producers in the 70's and 80's wanted to compete with Boeing, namely with the success of the 727, but the fragmented market would be a challenge. Therefore, Airbus was a consortium created with several European manufacturers to have a large aviation player with European roots. To minimize political difficulties, the supply chain was split over several countries:

While the original partners in the company recognised that the only way to compete was to consolidate national industries on a regional European basis, consolidation required negotiation and political finesse. Most sensitive was the decision where to site the different manufacturing operations.
The easiest way to defuse tensions was to build different bits of the first plane, the A300B, in the different partner countries. The French made the cockpit, the control systems and the lower-centre section of the fuselage; the UK made the wings, and the Germans made the rest of the fuselage and a part of the centre section. The Dutch made the moving parts of the wing, the flaps and the spoilers, while the Spanish made the horizontal tailplane.

Source: Financial Times
This supply chain is unlikely to become more centralised or placed offshore, for political and economic reasons.

From the economic perspective, today's supply chain is too fixed to be able to be moved somewhere cheaper, as the regions where each part is produced developed local expertise and innovation centres around it. Another argument is that the de-centralized supply chain helps to have a faster delivery time (see FT article mentioned above).

From the political perspective, European stability (commercial and military) requires that countries depend on each other for developing aircraft. Although Airbus is mostly known from the A380s and A320s, they also produce military aircraft with their subdivision Airbus Defense and Space. Placing production outside of Europe would place aviation expertise in other countries, a strategic expertise to have for defense.


What is the percentage of free riders in public goods games?

So you are looking for a meta paper that aggregates results from other papers. What you mean by "all experimental public good games" is unclear because the setup of most public good games is different. The multiplicator of the public good, the number of rounds, the level of allowed commucination, whether there is punishment, etc., these frequently vary and have a very big impact on the course of play.

Another reason why such a meta paper is unlikely to exist is because the ratio of cooperators is context dependent. How the possible actions are labeled: 'Cooperation' and 'Defection' or 'Give money' and 'Save money' has a strong effect on behavior. So even seemingly similar, 'basic' games could be very different.

Your best shot may be trying to find a famous experiment and seeing if there have been any replications. You could then aggregate the data and calculate the desired ratio.


This is a more "practical" answer, vs a deeper theoretical one, or even a specific one.

Take it as "a broad answer to a broad question."

Also, since it is a "Bayes vs frequentist" issue, at least the last few suggestions must be taken tongue-in-cheek.

Step 1: Use simple models you understand to start. Lowering researcher error due to misapplication should always be a first-order priority.
Step 2: Learn more about each approach as much as possible. Implement the same estimator from both perspectives if at all possible, for purposes of really wrestling with what is going on at a deep level. Again, start simple. replicate things you already know work and are well established. (Can you write a basic regression from scratch using both approaches? This is much deeper than it may appear.) Get some good introductory texts. Don't be afraid of "lowly undergrad" texts for introduction. The "puppy book" on Amazon is good here, as is "Think Bayes" from Green Tea (both for initial intro to Bayes).
Step 3: Hopefully the earlier efforts will start revealing that some problems are more naturally approached in one framework vs. the other. When you start getting a good feel for this, re-examine the problem you want to address. Which approach seems appropriate to you now?
Step 4: realize that if you are using likelihood-based methods, Bayesian and frequentist are two sides of a similar coin. (Or to quote the ever-entertaining Cosma, "Bayesian estimation is a likelihood-based method in which the impact of facts and experience is blunted and smoothed by prejudice.," haha.)
Step 5: realize that there are even more varieties of estimation which don't neatly fit into previously-understood categories -- non-parametric, semi-parametric, semi-non-parametric -- and begin to despair that you will ever know or understand all there is to know about estimation, and which is the absolute best method for any one particular question.
Step 6: Enlightenment. Use the tool that you believe is best for the task, in your own honest opinion -- even if it is "best" based only on Step 1, which is simply "I use this because I understand it the best and I know I am not accidentally doing something extremely wrong."

So there you have it, "a broad answer to a broad question."

All that said, I really do like both Bayesian and frequentist approaches. A lot of things goes into deciding which to use. Some problems lend themselves well to one vs the other. Some audiences lend themselves to understanding one vs the other (recall that often effective communication of a concept can be very important). It's up to you to learn enough about both the methods and the problems you are trying to address to choose well.