"Competitive equilibrium" vs. "General equilibrium"

Competitive Equilibrium

A competitive equilibrium ("Walrasian Equilibrium")'s defining characteristic is that it's competitive. It's about an equilibrium in which market forces (say, consumers, firms)' supply and demand responds to prices, and prices respond to supply and demand, and no Pareto-improving trade possibility remains in the end.

To be technical, consider a market with $I$ agents, $J$ goods, and initial endowments $E$ of shape $I\times J$. Also, each agent has rational preferences over the of goods.

A CE consists of a ($J\times 1$) vector of prices $P$ and a ($I\times j$) vector of allocations $X_i$ with two characteristics:

Feasibility: $\sum_i J_i \geq \sum_i X_i \, \forall j\in J$
Rationality: $X_i \succsim_i \, H \forall H: HP \leq E_iP, \forall i$

General Equilibrium

The general equilibrium's defining characteristic is that it is an equilibrium on more than one market; as opposed to the partial equilibrium in which we hold at least one price fixed and analyze the response of other markets/prices only.

So, what's the difference?

It's about the emphasis. Any GE is a CE, but not any CE is necessarily a GE. We could look at a CE of consumer goods, but not analyze labor supply (i.e., not even model labor). Would this then really be a general equilibrium? Mostly, it is about the field.

In macroeconomics, it is a standard procedure to shut off several general equilibrium response mechanisms (for example, fix labor supply) and first look at a toy model in which only one margin is allowed to vary, and understand the mechanism - the partial equilibrium. Then, after that was understood, understand to which extent the mechanism is valid and relevant once one allows other margins to adjust. Therefore, here, it is important to be able to emphasize the difference - i.e. partial versus general equilibrium.

In other fields, one may not care as much about "completely different" markets. The distinction is for example not as important in many IO topics, and hence many there use the notion of the competitive equilibrium instead.


An increase in Japan's demand for US goods would cause the value of dollar to appreciate?

You're just intermediating. The US companies would still have to pay their workers in USD, therefor, instead of the Japanese companies buying dollars in your scenario, the exporters are using the importers' Yen to buy dollars.

It's the same net effect.


How do low interest rates negatively impact bank earnings?

Unless someone can get a bank analyst to weigh in, it will be hard to get a definitive answer on this one.
The first thing to keep in mind is that bank regulations and hedging practices are radically different now than in the pre-1994 era. The Savings and Loan industry was compromised by the Volcker shock (early 1980s), and many people base their views on that episode. However, regulatory practices were overhauled to prevent a repeat.
In any developed country, bank regulators monitor the interest rate risks of banks, as do the banks themselves. Expecting interest rates to rise has been a consensus view for decades, and bankers were not outside that consensus. If the interest rate risk is (largely) hedged, then yes, bank earnings are largely insulated from interest rate movements.
Some people look at yield curve slopes, and claim that they are important for bank earnings. However, they are often working with pre-1994 models. If interest rate risks are roughly hedged, then the effect of the slope is minor.
The general absence of banks facing difficulties during the few interest rate rises are evidence that the regulators are doing what they say they are doing.
One can argue that deposits paying 0% are no longer cheap sources of funding, but this would likely only be material if interest rates were very negative. Banks generate fees off those deposit accounts, which offsets this drag.


Gross interest rate ($R$) v. Net interest rate ($R-1$)

It is often conventional. R is the amount of the loan plus the interest and r is just the interest rate. So R=1+r.

Suppose you borrow 100€ at a 10% interest rate. The interest you pay is 10€, since 10% of 100 is 10. That is where r comes in, with an interest rate of r=10%=0.1.

On the other hand, R is the rate implied by that interest rate r plus the original amount, so it is relevant for the total you pay back. Before adding interest payments, you must pay back 100% of the original loan or 1x the original loan, so R=1+r=110%=1.1.

So, in our example, with R you pay back 100×1.1= 110€, while with r we have a payment of 100×0.1=10€.


Book for Bretton Woods conferences and gold standard

Covering the historical part, you may want to look at:

1) The Battle of Bretton Woods: John Maynard Keynes, Harry Dexter White, and the Making of a New World Order

which appears to be written in a "non-fiction thriller" style, revolving around the argument that

  "(Bretton Woods) was in reality part of a much more ambitious geopolitical agenda hatched within President Franklin D. Roosevelt's
  Treasury and aimed at eliminating Britain as an economic and political
  rival. At the heart of the drama were the antipodal characters of John
  Maynard Keynes, the renowned and revolutionary British economist, and
  Harry Dexter White, the dogged, self-made American technocrat."

while the raw-data option would be

2) The Bretton Woods Transcripts

that

  "...offer the reader a front row seat at the conference that has shaped the international monetary system for nearly 70 years. The
  Bretton Woods Transcripts were never intended for publication, and
  give an inside perspective of what participants at this major
  international gathering said behind closed doors."


Why do all countries recognize foreign wealth?

Countries do not just stop recognizing foreign wealth because there are two kinds of wealth: real assets, and claims on the production of others; the values of both of these types of wealth are not determined by consensus, but rather by the use or pleasure one can derive from them.

To the first type— real assets are stuff like machines and cars and homes and all sorts of things that you can touch and which we value for one reason or another. The answer to your question as pertains this category is easy: you can "not recognize" my car as wealth all day long, but that won't affect its value to me or anyone else one bit.

To the second type— claims on the production of others come primarily in the form of money, but also in the form of non-money debt and equity. I will skip over non-money debt and equity, as they both provide a claim on a future stream of money, so their value hinges on the value of money. Now, rephrasing your question slightly, we arrive at: why is a foreign country's money valuable? Or, more specifically, why is a foreign country's money valuable in a way that is not subject to one's recognition of it?

The answer to this is simple (and a fundamental concept in international economics): a country's money is valuable to the extent that you want to buy that country's stuff (or buy claims to their production, i.e., debt and equity). This is why countries with economies based around commodity exports see their currencies fluctuate with the value of those commodities (so-called "commodity currencies")— because when demand for those countries' production increases, the values of their currencies increase. So— one can go all day not recognizing the value of another country's money, so long as one doesn't want to buy that country's stuff.

I will confess to not being terribly familiar with the situation you describe in Tanzania, but I would suggest simply that the locals who choose to sell their fish rather than eat them are likely to have a much better understanding of the implications of doing so than you or I. I would suppose that they're selling their fish because they receive something else in exchange (money), which they turn into something of greater value to them than the fish they sold. Let's say that what they receive in return is gasoline, for use in boat motors (which are essential to catching fish), generators that power lights and pumps to provide clean water, and inefficient and dirty cooking devices (that are nonetheless better than the alternative, which would be attempting to scavenge firewood). Are they better off with fewer fish and more gasoline? Yes, otherwise they wouldn't make that trade. Would they be better off if they didn't sell most of the fish and get gasoline in return, or would they be more likely to "build up important things"? No, almost certainly not— otherwise they would not sell their fish. Unless the Tanzanians you describe are being forced to trade, it's a safe bet that they're trading because it is beneficial to them. They're poor, yes— but that doesn't mean they're stupid.


I find that the essay "The New Astrology" by Alan Jay Levinovitz (an assistant professor of philosophy and religion, not an economist) makes some good points.

  ...the ubiquity of mathematical theory in economics also has serious downsides: it creates a high barrier to entry for those who want to participate in the professional dialogue, and makes checking someone’s work excessively laborious. Worst of all, it imbues economic theory with unearned empirical authority.

  ‘I’ve come to the position that there should be a stronger bias
  against the use of math,’ Romer explained to me. ‘If somebody came and
  said: “Look, I have this Earth-changing insight about economics, but
  the only way I can express it is by making use of the quirks of the
  Latin language”, we’d say go to hell, unless they could convince us it
  was really essential. The burden of proof is on them.’

The essay also makes a (more or less adequate—which, I leave up to you) comparison with astrology in ancient China to show that excellent math can be used to prop up ridiculous science and grant status for its practitioners.


Difference between direct and indirect utility

Something that may help with the intuition:

U <-  Goods <- Income Prices

The direct utility is derived from the consumption of goods. Said it simply, money, on its own, is almost worthless in terms of utility (setting aside cases where people simply like having money). Goods, on the other hand, generate utility because they can be used or consumed directly.

Now, Goods can be obtained only with money, and based on their prices (how much you can buy). So, indirectly (notice the framework i started with), income does not generate utility, but it does generate utility "indirectly", because it allows us to buy goods.

HTH


Would a sudden increase in population, increase inflation?

It would lead to demand pull inflation as the goods in the said economy would not match the demand. But this depends on the time frame and how the producers in the said economy react.
Let me give you an example of immigration. Let's say large numbers of people from a country leave their country for the said country. Ignoring all social issues let's see what would happen. On one hand inflation would increase as the immigrants would cause high demand for goods and services which would drive the prices up. On the other hand, the immigrants would bring in supply of labour which  lead to a drop in real wages and decrease the prices of goods thereby reducing prices. So an increase in population may or may not lead to inflation


What is the difference between knowledge and information?

In this paper (pdf), Peter Boettke goes into great depth explaining the difference between the two concepts in the Austrian school.

Essentially information is any data that might influence an act (or specifically the perceived utility or cost of a choice), and knowledge is the information that the actor has already collected prior to the time they made their decision and/or engaged in their behavior.

This helps to explain seemingly irrational behavior that is merely a manifestation of imperfect or asymmetric information (though it doesn't necessarily preclude or eliminate irrationality by any means).

There is also some room for "false" (or conflicting) knowledge, to provide for further irrationality (in the sense that $A$ knows $U(x)>U(y)$ and $B$ knows
$U(y)>U(x)$ where $U(x)$ is the average perceived utility of $x$ for all actors in the economy.

He of course does a much better job explaining it than I do.


What are the necessary and sufficient conditions on a utility function for gross substitutes?

The paper @Henry referred to in comments pretty much answers this question. For closure, and to summarize the jist, the paper opens:

  As is very well known, the case in which all excess demands have the gross substitute property is one in which very strong results can be obtained concerning the uniqueness and stability of general equilibrium. Considering how long this has been known it is perhaps remarkable that we apparently do not possess a convenient characterization of the class of utility functions which yield individual demand functions with the gross substitute property. ... [This] note provides a characterization of the entire class of utility functions having the gross substitute property. Since the primary interest in that property is in the analysis of general equilibrium, we shall mainly concern ourselves with the demand functions which arise in a condition of exchange rather than with those that arise when income is fixed, independent of prices. The extension of the results to the latter case being given at the end of the paper.

The main result is, in an exchange market, for any initial endowments (quoting directly):

A necessary and sufficient condition for $U(x)$ to have GS is that for every $i, j = 1,...,n, j \ne i$, positive income $Y$, and strictly positive price vector $p$:

$$
  \eta_{ij} > max(e_i, e_j, e_i(1 - \frac{1}{\alpha_j}), e_j(1 - \frac{1}{\alpha_i}))
$$

Where:

$e_i$ is the income elasticity of the i-th commodity, $\frac{\partial x_i}{\partial Y}/\frac{Y}{x_i}$.
$\alpha_i$ is the proportion of expenditure devoted to the i-th commodity, $\alpha_i = \frac{p_ix_i}{Y}$.
$\eta_{ij}$ is the elasticity of substitution i-th to j-th of the so called "Allen-Uzara" kind (what ever that is - see paper).

There are some corollaries.

The main complication with all this is you have to take income or rather income elasticity, into consideration. Some broad classes of utility functions that are sufficient for GS regardless, are only very briefly mentioned in the intro of paper.


Can an Out the Money put option's price $>$ its Strike Price?

As happened to crude oil futures in 2020, prices of certain traded instruments can go negative. In such a case, the strike can be at zero, and the put has positive value, even if the spot price is still positive.
Otherwise, it is only possible if:

interest rates are negative, and so one is willing to pay money now for less money in the future, or
somebody hit the wrong keys when trading, and it was not overridden by automatic controls.

In a positive interest rate environment, fair value is always less than the strike price if the price is floored at zero, since the maximal payout is the strike. Increasing volatility cannot affect that.


Contract theory: Incentive contracts (when agents have multiple tasks) models by G. Baker and Holmstrom & Milgrom

Holmström and Milgrom assume that the agent exhibits constant absolute risk aversion. This implies that if you change the total wage of the agent with a lump sum transfer (that does not depend on effort), you will not change the incentives. Hence, to find the optimal contract, you can find the contract that maximizes total surplus subject to incentive compatibility, and then subtract a lump sum amount to make the agent indifferent between accepting and not.


Break even is when your [economic] profits equals to zero:

\begin{align*}
\text{Cost} &= \text{Revenue}\\
N \cdot w &= Q \cdot P
\end{align*}

where $N$ is the number of workers, $w$ is wages, $Q$ is quantity produced, and $P$ is price.

An $x$% increase in productivity is the ability to hire the same amount of workers and get $x$% more output.

Assume that $N$ and $P$ remains unchanged, a 20% increase in wages would lead to the LHS's being $L \cdot 1.2w$ instead. How would the RHS need to change to maintain equality?


If there is a tax to be paid for every income event, doesn't that imply most money in circulation belongs to the goverment it circulates in?

No there are several flaws in your argument:

Starting with the most obvious problem. Just because something will be eventually owned by someone does not mean it is correct to say that the thing is owned by that entity already. This is equivalent of stating: "My house will be once inherited by my posterity so I don't own it but they do."  This is flawed from economic perspective. Ownership (property right) is defined as (see Mankiw Principles of Economics 8ed pp 11):

the ability of an individual to own and exercise control over scarce
resources.

The definition might be slightly different in different strands of research, but generally ownership in economic sense is determined by who has exercise/control over something. Until government actually seizes the ownership of the thing it from economic perspective does not own it. Furthermore, I am not a lawyer but I am going on a limb here to say I doubt this would even hold in legal sense, so the assertion is flawed prima facie.

Next, typically government does not just hoard resources it gets (in your example currency), but also spends it. Since you are building theoretical model you are free to make assumption that government never spends its resources but that assumption does not hold in real world so you cant automatically claim conclusions from your model carry there. Models do not have to be 100% realistic (what even more they should not even attempt to do that - they are models) but in your case assumption of 0 government spending is the primary assumption making the argument, but empirically it is clearly invalid - that is serious flaw in this case.

Even if we forget about the point 1 and 2, you are making claims that go way beyond the model you use. In your model government taxes currency. It would be true that if there is fixed amount of currency and government taxes it at each point when it is through spending turned into income, then eventually in the limit government would own all currency.

However, currency, or money more broadly,  in itself is neither income nor wealth - it is way how we measure income or wealth. Income is generated by production. If you produce two widgets, value those widgets are your income. Money that you will get from selling those widgets measure (and store) value of those widgets. If government would tax away all currency people would just revert to barter economy where they would exchange goods and services for another goods and services and those would be peoples' incomes. Government would own all currency but not peoples' incomes.
Now this is not just an attempt at  'gotcha' - this is important distinction. If government would be taxing goods and services in-kind, then government might never get hold of all of them as people can always produce more and more goods and services ad infinitum.
In addition, you have to be clear with your terminology. Income is not wealth. Wealth is defined as net value of your total assets which are accumulated by saving. If you spend your income it is not wealth and consequently saying: " most wealth in circulation belongs to the goverment it circulates in, as long as it keeps circulating?" Is incorrect. Because what is circulating in your example is income not wealth.
Lastly,  the same caveat that I mentioned about income applies to wealth. Wealth is not simply money. Person with no money but ownership of billion dollar company has more wealth than a person with full wallet of banknotes.


Turns out I was looking for median net worth in the US over time. For some reason, I thought it was more complicated than that.


How does stock market drop affect the economy if it doesn't affect the corporations?

Companies don’t issue stocks once and for all. It’s one of their sources of financing. Even if a majority of stocks is traded on secondary market companies still routinely issue new stocks when they are in need of cash.
Stock owners may feel less wealthy if the stock values fall and hence they might spend less or postpone their consumption. People who were just to cash out, for example due to retirement, might decide to postpone that and lower their consumption until the market recovers. This is negative demand shock and it’s bad for the economy.
There is also reverse relationship. A stock price is basically derived from the discounted expected value of future profits that the company will earn. If the expected future profits are lower due to some economy wide problems stock market will pick on that. The causation there is exactly opposite - it’s not stock market that affects the economy it’s economy that affects the stock market. Often when policy makers talk about improving the stock market they actually talk about policies that affect companies profitability not about policies that target sellers and buyers on secondary market.

The above list is not exhaustive but it should give you some idea why there might be some relationship between how the economy and how the stock market is doing.


Which institution (government or private) provides the complete data on HS (Harmonized System Code), tariff schedules for India, China and US?

The best place for this information is WTO TAO. The data does require a little cleaning but you have information on a countries' mfn


Clarification about demand elasticity and monopoly

You are correct in saying that there is an elastic portion within the inelastic demand. The concept is much easier explained when using a simple demand curve diagram. From the diagram given below, we can clearly see the varying elasticities in different parts of the curve. You can even try it yourself, using 2 points on each part and comparing the elasticity.


Why is the tat-for-tat strategy a Nash equilibrium in infinitely repeated games?

(i) In the 1 round case, tit-for-tat is not a NE. To see this notice that the tit-for-tat strategy, as you describe, dictates that the players play $(H,H)$ in the first (and only) round---as you point out, this is clearly not a NE, since either player can increase her payoff by changing her strategy from $H$ to $C$. Perhaps what you missed is that the strategy includes proscription in first round, which does not cohere from the 1-shot Nash behavior.

(ii) In the $N$-round case, again tit-for-tat is not a NE. This is a little more subtle that point (i) but not much. If both players play according to the strategy, then they will make it to the $N-1$ round playing $H$. At this point, the strategy dictates they play $H$ in the $N^{th}$, and final, round. For the same reason as in (i) this is not a best response, hence not an equilibrium (note that forward looking agents would anticipate this, so the strategy would break down immediately, but analyzing the last round is sufficient to see it is not an equilibrium).

(iii) In the infinitely-repeated case, tit-for-tat can persist, but it depends on how agents discount future utility in comparison with current utility. The general logic is that since there is no final period where things begin to unravel, players are always willing to forgo current utility to maintain good standing (the tit part of the tit-for-tat?) and therefore a higher future (continuation) payoff. Of course, if the players care about today's payoff far more than tomorrow's, they will defect and play $C$. See here for more about NE in infinitely-repeated games.


General price level is defined by the price that you pay for a basket of goods. This basket of goods is decided on the basis of general consumption patterns in the economy and includes a number of sectors (with a number of items) like food, transport, medical care, etc. Such baskets can be defined differently to arrive at different measures of general price levels such as the one faced by end consumers or wholesale buyers.

In a nutshell, it gives an idea of how the prices in the economy are moving. So, price of a good A might increase while price of good B might decrease but it may so happen that the general price level may increase or decrease depending upon the defined basket and the weights assigned to the items in basket.


Quadratic utility: monotonicity and risk aversion

Quadratic utility is given by
$$u(w) = w - b w^2$$
which has derivative
$$u'(w) = 1- 2b w$$
such that for high levels of $w, u'(w)<0$. That is, the utility is not everywhere increasing. This may be weird because even people with high wealth should prefer more to less.
The second derivative is
$$u'(w) = -2b$$
such that absolute risk aversion is
$$\frac{- u''(w)}{u'(w)} = \frac{ 2b}{1- 2b w},$$
which is increasing in wealth. This contradicts evidence that wealthier people take more financial risks instead of less.


How does the self-corecting mechanism put the economy back to long run equilibrium following a negative shock on the stick-wage SRAS?

The SRAS wage price being bumped up temporarily means that employers are forced to pay more for labour. From the graph, you can see aggregate demand is much lower at the higher wage price (SRAS1) however the stickiness of wages & employment means that employers have been forced to pay more in wages but cannot immediately adjust the 'supply' by firing employees. Likewise workers will not likely be willing to accept pay cuts, so in the short run the market will be pushed off equilibrium. However, given a little more time, the firms will find ways to let go of employees, bringing the market towards point Y1. This is 'automatic' in the sense that workers are expecting wages of SRAS1 and firms only want to pay for Y1 amount of labour. Once the employees have been laid off to reach Y1, there will be unemployed workers who are willing to work for less (since otherwise they get nothing and we know the position of the LRAS of labour implies a larger available work force than point Y1) and their negociation with firms will push the market back to equilibrium at the lower wage price.

To give a real life example of this, (I know it's micro and this is a macro effect but it helps to build an intuitive sense of how this works) I know of a factory that had a strong union that pushed continuosly for wage increases despite the factory being the least efficient and cost-effective in the firm. So when they threatened to strike, the firm gave in to their wage demands however the firm also invested to build capacity in the other more efficient factories. Doing so took about 2 years.

Finally, once the firm was sure it could handle losing the output from the 'bad' factory, it gave an ultimatum, the workers would have to be more efficient at a lower wage or it would shut the factory down. The workers refused, and the factory closed. Over the next year, the workers realized that nobody was hiring for the wages they wanted and after a little over 12 months most of the workers were hired back at the lower wages the firm wanted in the beginning and the factory re-started. From start to finish it took 3 years for the wage to 'equilibrate' at this firm.


Why is Pareto efficiency not always equitable or equilibrium?

You seem to be confusing concepts from partial and general equilibrium.

Partial equilibrum

Supply and demand functions are usually mapped in such a way that quantity is on the $x$-axis and price is on the $y$-axis. Competitive equilibrium is where the supply and demand functions intersect.$^1$ It is called partial equilibrium because only the market for one good was analysed. Slopes play no role in determining whether a point is an equilibrium or not.

General equilibrum in pure exchange economies

General competitive equilibrium considers all goods. Lectures usually restrict themselves to two types of goods and two consumers, as that scenario is easier to understand but gives the same insights.

The most frequently used display method in pure exchange economies is the Edgeworth box. It uses the fact that the total amount of goods is given, an allocation just distributes these among the two consumers. Quantity of good $x$ is on the $x$-axis and quantity of good $y$ is on the $y$-axis. Distance from the lower left corner shows the first consumers basket of goods, distance from the upper right corner shows the second consumers basket of goods. Given utility functions one can analyse Pareto-optimality in this setting. An allocation is Pareto-optimal if the slopes of the indifference curves running through the allocation are identical.$^2$

Also given an initial allocation, which denotes the property of the consumers, one can derive the general competitive equilibrium. The equilibrium price ratio is where the price vector going through the initial bundle is tangential to an indifference curve of each consumer and the point of tangency is the same. The equilibrium good allocation is the point of tangency. As a result, here, the slopes of the indifference curves are identical, hence the equilibrium good allocation is Pareto-optimal.$^3$
Intersection plays no role in determening whether a point is an equilibrium or not. Since we draw the indifference curves that run through the same point of the Edgeworth box, they will intersect (run through the same point) for sure.

$^1$
There are some exceptions when $p = 0$ but that is a special case.

$^2$
There are some exceptions where the indifference curves are non-differentiable at the allocation and hence the slopes do not exist. The allocation may still be Pareto-efficient. In case the allocation is on the side of the Edgeworth box there are further exceptions.

$^3$
Again, this is only true if the allocation is in the interior of the Edgeworth box and both indifference curves are differentiable.


The gravity model of migration, like the gravity model of international trade, is a theoretical model. When you try to estimate the model, there isn't a predetermined cap to what kind of variables or how many of them you can include in your regressions as controls in the reduced form econometric specification. The controls aren't just limited to dummies. Those estimated coefficients are often interesting in their own right.

As Bunea (2012) says (emphasis mine):

  Since Lowry (1966, pp. 1-118), the basic gravity model has been
  extended to the following form:

  $$
\begin{align*}
M_{ij} = &\beta_0 \times log(g) + \beta_1 \times log(P_i) + \beta_2 \times log(P_j) + \beta_3 \times log(X_i) + \\
&\beta_4 \times log(X_j) + \beta_5 \times log(D_{ij}) + \varepsilon_{ij}
\end{align*}
$$

  where $X_i$ is a vector of explanatory variables describing different features of the origin (i.e. push factors) and $X_j$ is a vector of explanatory variables describing features of the destination (i.e. pull factors). Push factors are those characteristics of the origin place that encourage (discourage) out-migration (in-migration), such as low incomes, high unemployment, high prices, in general few opportunities for development.

Whether some of these explanatory variables should be included in your regressions warrants a separate question and is dependent on the research context.


Substitute a continuos variable with a categorical one in Linear regression

You can use the continuous variable "Assets" as stand-alone, and use its categorical incarnation for the interaction term.
While we may be accustomed to use "automatically generated" interaction terms as part of ready-made functional forms like the translog, nothing forbids us to introduce selectively interaction terms in a regression setting, when we have an economic, structural argument as to why this specific interaction term is meaningful and why it belongs to the regression.
Therefore, using two different versions of the same variable is in principle acceptable as long as a solid argument can justify it.
From a technical point of view, it does not create any issues.


Real wages fluctuation as per classical economics

Classical economics is actually not taught at universities anymore (not since 19-20 century at least). You probably have in mind some Neoclassical model. I will presume that since you say you study macroeconomics and not only classical economics is now just part of history of economics, it for the most part did not dealt with macroeconomics.

You don’t mention in which model you observed this, but in general this has nothing to do with whether model is classical or neoclassical. For example, many business cycle models on purpose ‘turn off economic growth’ (which is what in long run drives also increases in real wage), implication of which is that also real wages remain same, and this holds for both Neoclassical or New Keynesian models.

This usually done on purpose so scientists and students can examine how economy behaves, for example during the business cycle, without having to track extra variables/equations and to also make math easier.

Going back to your question there are actually many Neoclassical models of economic growth where real wages increase. For example, in famous Solow-Swan  technological growth leads to increases in productivity and real output per worker and hence consequently also real wages.


If you have an estimate of the probabilities of each scenario, say with probability $p\in[0,1]$ the loan is repaid (assuming no other scenario exists), then you can calculate the expected value of making the loan of size $L$:

In scenario 1, payoff is $-L+(1+0.05)L=0.05L$ (giving out $L$ and getting back the principal plus interest)
In scenario 2, payoff is $-L$ (giving out $L$ and getting nothing back)

The expected payoff from making the loan would be
\begin{equation}
EV=p(0.05)L+(1-p)(-L)=1.05pL-L.
\end{equation}


Does national debt and its repayment assume population increase?

tl;dr:  No, repaying national debt does not assume population increase although depending on the parameters of economy population increase can sometimes help with repaying the debt and also help with reducing the ratio of debt to GDP, but it is neither required nor assumed. Moreover, depending on parameters population growth can even be a hindrance as well.
Full Answer: No the statement in the question is not accurate for several reasons. It is true that GDP depends on population because if every person can produce $\\\$100$ worth of GDP then 10 people will be able to produce $\\\$1000$ of GDP. However, you are incorrect in saying:

decreasing population would mean both a decrease in GDP per capita

because GDP per capita is already calculated as GDP per person. If every person can produce $\\\$100$ then GDP per capita will be $\\\$100$ whether country's population would be ten people or thousands, because GDP per capita is by definition total GDP of a country divided by population.
Furthermore, you seem to be confusing concept of repaying debt with growing out of debt.
From economic perspective what matters the most is the size of debt relative to national income. If a poor person who earns $\\\$200$ a month has debt of $\\\$10000$ that is a problem, but if rich person who earns $\\\$2,000,000$ a month has $\\\$10000$ that is not a problem at all (at least not from economic perspective).
Hence there is a concept of growing out of the debt which says that provided that $GDP$ grows at faster rate than debt the debt to GDP ratio will become smaller and smaller over time. However, this has nothing to do with paying down that debt in principle as the debt is still there and just becomes less economically significant.
From this perspective what matters is what is total GDP and total debt not their per capita counterparts. GDP can grow thanks to population growth but population growth is only one of the factors that can cause GDP to grow. In fact most of GDP growth comes from advancement in technology which makes economies more productive (see Romer's Advanced Macroeconomics). However, at the same time debt can grow with population as well if government borrows to fund policies that depend on size of population (such as healthcare for example) rather ones that have mainly fixed cost such as many public goods like water filtration. Provided that total GDP increases at higher rate as a response to population ($Pop$) growth than total debt $D$ (that is $\partial GDP/ \partial Pop > \partial D /\partial Pop \quad |  \partial GDP/ \partial Pop > 0$) it can help to decrease the debt to GDP, but that is not the same as saying it helps to repay debt and even if it helps to reduce debt to GDP ratio it does not mean at all that this ratio cannot be reduced without any population increase. In fact empirically in recent years in developed countries most growth in total GDP comes just from technology/productivity increase as in many developed countries population more or less stagnates but most of them still experience some growth of GDP.  Furthermore,  note that if $\partial GDP/ \partial Pop > \partial D /\partial Pop \quad |  \partial GDP/ \partial Pop > 0$ does not hold population growth can even make the debt to GDP worse.
When we talk about repaying government debt we have to look at government budget constraint. The government budget constrain is given as:
$$G-T=\theta + \beta$$
where $G$ is government spending, $T$ is the net tax revenue after transfers and interest payments, $\theta$ is government financing by high powered money and $\beta$ is government financing by bonds (see for example Blinder & Solow (1973); Christ (1968); Tobin & Buiter (1976).
Government debt is accrued when government issues bonds $\beta>0$ and conversely government debt is repaid when  $\beta<0$. Hence in order to see what needs to happen to start repaying the debt we can just solve the budget constraint for $\beta$:
$$G - T- \theta = \beta$$
which tells us that $\beta<0$ when government spending $G$ will be smaller than the amount of taxes $T$ and high powered money $\theta$ government issues (so when $G<T+\theta$). Hence population growth is not necessary for repayment of debt or even assumed. Government will start repaying its debt if its spending is lower than net taxes plus high powered money it issues. Sure if population growth can increase net tax revenue $T$ while not causing government spending $G$ to increase it can help with repaying the debt but it is in no way necessary to assume it will happen for debt to be repaid (and it is also possible that increase in population could lead to more government spending than the increase in tax revenue where population increase would make situation worse).


Question about an ergodicity in economics paper

OP's Python code is computing one path in time and is not averaging over the paths. So it is not the value shown in the plot. In fact what the OP's Python code computes is $(1+\Delta x_H)^h(1-\Delta x_T)^t$ where $h$ denotes the number of heads and $t$ the number of tails tosses. It is closer to the red line which is the most likely path where $h=t$.
$$\mathbf E[x_{t+1}|x_t] = \big[(1+\Delta x_H)p_H+(1-\Delta x_T)p_L\big]x_t=(1+p_H\Delta x_H-p_L\Delta x_T)x_t=:ex_t,$$
and
$$\mathbf E[x_{t+1}|x_{t-1}]=\mathbf E[\mathbf E[x_{t+1}|x_t]|x_{t-1}]=e^2x_{t-1}.$$
So $\mathbf E[x_t|x_t]=e^tx_0$ exactly as shown in the paper plot. This can also be derived directly through the generating function of the expected $\frac{x_t}{x_0}$ which is, due to the independence of each toss, simply the product of all the dot product of payoff and its associated probability, i.e., $e^t$.


Why does strictly Walrasian demand with quasi-concave utility function mean that the walrasian demand having only one single consumption bundle?

For case 1, you can argue $z$ will be unique by contradiction:

Suppose ad absurdum there is another $z'$ that is feasible (i.e. $p^Tz' =w$) optimal and $z'\neq z$. Then you can consider a convex combination of $z$ and $z'$: $\bar z = \beta z + (1-\beta) z'$, for $\beta\in(0,1)$. Notice that $\bar z$ is still feasible (because it is a combination of two feasible bundles) and, because of strict quasi-concavity, $u(\bar z) > u(z')$ so that $z'$ cannot be optimal, a contradiction.


MLE using multivariate normal distribution

The "trick" you are referring to is a property of the trace of a product of matrices, namely

$${\rm tr}(ABC) = {\rm tr}(BCA)$$

assuming the dimensions are conformable of course.

Now, note that the dimension of $(x_n-\mu)^T\Sigma^{-1} (x_n-\mu)$, for each observation, is $1 \times 1$. So trivially,

$${\rm tr}\Big[(x_n-\mu)^T\Sigma^{-1} (x_n-\mu)\Big] = (x_n-\mu)^T\Sigma^{-1} (x_n-\mu) $$

But since also, from the mentioned property of the trace,

$${\rm tr}\Big[(x_n-\mu)^T\Sigma^{-1} (x_n-\mu)\Big] = {\rm tr}\Big[\Sigma^{-1} (x_n-\mu)(x_n-\mu)^T\Big]$$

combining one gets the alternative expression for the mutlivariate normal log-likelihood.


(1) Since the RD design identifies an effect only at the cutoff (in your case, at precisely 12am on the last day of the year), I don't think it's an issue of data manipulation for you to be removing the tails. Your estimates really shouldn't be sensitive to observations far away from the cutoff, but this depends somewhat on how granular your data is and how many observations you have (a lot of birth data is quarterly, which may make this strategy difficult).

(2) Sharp vs. fuzzy design refers to the assignment of the treatment. If your treatment of interest is being born December 31st vs. being born January 1st, then this is a sharp design because the running variable deterministically assigns treatment. If there is noncompliance with treatment, (i.e you were born December 30 but you somehow end up getting "treated" as though you were born in January the following year) this is when you would use the fuzzy design.

(3) Sharp RD is just a special case of fuzzy RD. Say $Y$ is your outcome of interest (in this case, wages), $X$ is your running variable (day of the year), $D$ is a dummy variable for treatment assignment where $D=1$ if $X>c$ and $D=0$ if $X\leq c$, and $c$ is the cutoff (December 31). Then the treatment effect for the fuzzy design is (from Lee and Lemieux 2010):

$$
\tau_{fuzzy} = \dfrac{\lim_{\varepsilon\downarrow0} \mathbb{E} \left[ Y | X = c + \varepsilon \right] - \lim_{\varepsilon\uparrow0} \mathbb{E} \left[ Y | X = c + \varepsilon  \right]}{\lim_{\varepsilon\downarrow0} \mathbb{E} \left[ D | X = c + \varepsilon  \right] - \lim_{\varepsilon\uparrow0} \mathbb{E} \left[ D | X = c + \varepsilon  \right]}
$$

Because $X>c$ means by definition $D=1$, the denominator reduces to $1$, leaving us with the sharp treatment effect.


The answer from the former Chair of the Federal Reserve is in a word: tradition.

Chair Ben Bernanke testifying to the United States Senate.


Is there a name for this type of CES look-alike utility function?

I believe it can be found as "nested CES"
See for example:
Nested CES


Hicksian demand is the consumption bundle that minimizes the expenditure of the consumer subject to the constraint that he attains some target level of satisfaction in equilibrium. In the problem, the expenditure on any bundle $(x, y)$ is given by $p_Xx + p_Yy$ and the target level of satisfaction is $\mu$. Given that the utility function is $u(x, y) = \min(x, y)$, the expenditure minimization problem is formulated as:

\begin{eqnarray*} \min_{x, y} \ \ & p_Xx+p_Yy \\ \text{s.t.} \ \ &  \min(x, y) \geq \mu\end{eqnarray*}

Solution to this problem is a function known as Hicksian demand function :

$x^h (p_X, p_Y, \mu) = \mu $

$y^h (p_X, p_Y, \mu) = \mu $


How can we estimate the tax incidence from a 20% tariff on Mexican goods?

Due to the tariff, the supply of any product being imported from Mexico to the U.S will shift back. This would mean that prices of goods will increase in the U.S itself and most of the tariff will eventually be paid by U.S citizens who buy the goods. As the price increases, consumer surplus decreases and the market will not be at equilibrium, therefore a deadweight loss will be present.If the selling price of a product is 10.5$.The new selling price is 12. There will also be a deadweight loss as the society will not receive the quantity it demands.


Check out this link from the United States Department of Agriculture.

This data set contains annual and monthly data for exchange rates. It includes both bilateral nominal and real exchange rates for 79 countries, plus the European Union, as well as real trade-weighted exchange rate indexes for many commodities and aggregations. All series are updated quarterly. Data series start at the beginning of 1970 and run to the last available data point.

As pointed out by @luchonacho, real exchange rates here are derived by multiplying the nominal exchange rate by the ratio of the U.S. to local currency Consumer Price Index


How does fuel tankering save airlines money

Airlines typically have a "good" contract for fuel with some supplier for their base airports (they buy a LOT of fuel and hence, they are able to negotiate higher discount). When a plane flies to a small(er) airport (e.g. where the airline goes 2-3 times a week), there they won't have a discount, so they would have to pay more. Therefore, it might be a case that it is more efficient (or profitable) to take on board more fuel (even if it means that the plane will burn more fuel) than to buy fuel for a higher price, i.e. they might prefer to burn more of cheaper fuel than burn less but of more expensive one. I am talking about the case of domestic flights: the base price of fuel might vary quite a bit (you can easily google fuel prices for different airports in various countries). So if it is a case for domestic flight, a similar observation could possibly occur for international flights.

In general, airlines do not produce a lot of economic profit. That is why, in order to maximize their profits, airlines do everything they can (one of these actions is fuel-tankering). They of course do not take into account the negative externality they create by burning more fuel (the extra social cost). So that they end up providing access amount of the activity (more than social optimum).

They could stop doing so but their profits (if occurring) would be lower. Next question could be - whether passengers would like to pay more so that airlines stop doing it? You can probably guess the answer to that.

Oh and in the second link provided by @E.Sommer, this, you have someone who actually has some real world experience on that matter:

"I only saw this happen operationally when we were going to be very light and the outstation fuel was very expensive. Usually our loads were high enough that we were struggling to get all 50 passengers, bags, and especially jumpseaters on board with the required fuel load. In that case it would not be economical to take more fuel because we'd have to take fewer passengers." ~ @casey


Monetary policy: increasing interest rate

so admittedly the question as a whole seems slightly confusing. BUT taking the first part: When the Federal Reserve wants to increase the inter-bank lending rates (The "Fed Funds" rate) -- it SELLS its own Treasury Bills through something called "Open Market Operations." By selling its T-bills, it takes money OUT of the system. Less money in the "system" means the inter-bank lending rate will go up. By selling its securities, it is taking money OUT of the system. Decent video here.

I'm not sure why your teacher asked about common stocks, or longer-term bonds, etc. The Fed lowers/raises the Fed Funds Rate only through buying & selling short-term Treasury Bonds.


A confusion regarding search and matching model in Pissarides's "Equilibrium Unemployment Theory" book

$q(\theta)$ is defined as the job-filling rate. Note that market tightness $\theta$ is not necessarily constant over time (Pissarides makes a dynamic analysis at some point). It may help to denote it $\theta_t$.
As an approximation, $q(\theta_t)\delta t$ is a probability for a firm to meet a worker between $t$ and  $t+\delta t$ for $\delta t$ small enough.

1) If you choose a large $\delta t$, this approximation is not valid anymore. In other words, assuming a large $\delta t$ prevent you from interpreting $q(\theta_t)\delta t$ as a probability. To define an equilibrium, Pissarides will anyway take the limit $\delta t\to 0$.

2) $q(\theta_t)$ is a rate (that is not constrained to be lower than 1), whereas $q(\theta_t)\delta t$ is a probability. Thus, the probability of a firm not meeting a worker between time $t$ and $t+\delta t$  is $1-q(\theta_t)\delta_t$.

$1-q(\theta_t)$ has no clear interpretation (it can even be negative). I guess (but I would like confirmation) that the rate of a firm not finding a worker cannot be defined in this case (or it would be $+\infty$).


Is Marginal Rate of Substitution a multivariable function?

$\frac{dy}{dx}$ is written as a function of a single variable right?

I don't think so. Your shorthand notation should be standing for

$$\frac{dy}{dx} = -\frac{U_x(x, y)}{U_y(x,y} $$

and hence is a function of both variables ${x,y}$. That makes sense, as your MRS could depend on the locus you're at.


Prices changing so frequently is simply the result of an adjustment between demand and supply in the market. Demand and supply change all the time, because market venues allow them to change very frequently, and so does the prices. This does not mean that the fundamentals of the underlying assets are also changing, this is just the way market process (what it perceives as) new information.

Say the price of a stock is $x_0$ and I'm about to buy 1,000 units of that stock. Effectively, I will buy those 1,000 units at a price $x_1>x_0$ because at a given point in time demand increases so the price adjusts. However, if there is no new information, it's likely that somebody else would want to sell 1,000 units after that, and then the price would adjust downward at $x_2<x_1$. Note that we do not necessarily have $x_1=x_0$ though. It depends on much more factors that in my simple example, but the idea is there.

The price changing a lot, also means that you, as an investor, are able to buy/sell at any point in time. If, as you said, prices were updated once a day, that means that you would be able to make a transaction only once a day. Actually this exists on some market, and in general the price is set through an auction process. But obviously, if possible you want to be able to buy/sell at the moment you take the decision, and in general you would dislike to wait until the daily batch processed.

Regarding, the high frequency that the most liquid markets have reached now, this is the result of the competition between market venues. Indeed, in current days, there are often several places where you can buy/sell a particular stock for instance. Since market venues are seeking to attract the largest possible amount of transaction on their market, for liquidity reasons, this results in market competing on the frequency they offer to market participants.

Actually, this is a bit more complicated, let me just sketch up some words. Algorithmic traders are the type of market participants that provide a lot of liquidity because their are able to buy/sell extremely fast, there are the new market makers in a sense. The people who set up those algorithms (large banks mostly) are also seeking for profit. They know that high-frequency will make them more efficient than classic human investor, so they are looking for the fastest possible way to make transaction on a market. And market platforms, wanted to attract those liquidity traders (the algorithmic traders), have increased (a lot) the frequency of their market. This is not necessarily bad, actually if you buy/sell something on a exchange-market, it's likely that your counterparty will be an algorithm. The question of whether it's efficient or not, especially in time of crisis, is more opinion-based and there are some research on that issue.


Is the opportunity cost under the supply curve?

Opportunity costs occur for all suppliers. The lowest price at which supply occurs (agents willing to sell) is just above the lowest opportunity cost of the suppliers.

I would not describe it as a point on the supply curve. Because you will not offer something for sale unless it is greater than you opportunity cost. It is important to note that opportunity costs dictate the starting point and slope of the supply curve.

So presuming your opportunity cost for 1 unit is 10\$ you will only sell at 11\$ (opportunity cost + 1), another persons opportunity cost may be 12\$ and so they are only willing to sell at 13\$ hence the increase in quantity supplied as price rises, more and more people are willing to sell as their opportunity costs are covered and they can make a profit.


Is the world economy highly-dependent on the United States of America?

During 2017 US GDP made up 24.03% of global GDP, so yes, the world economy is heavily dependent on the US.

Specific effects on individual countries depend on current levels of trade.  The one country that would be most negatively affected (especially given news about the NAFTA negotiations), would be Canada (582 billion traded with a GDP of 1.653 trillion).  Most other countries probably wouldn't experience that level of total economic collapse, but depending on what scenario you're suggesting things aren't going to go well regardless since the US is also instrumental in doing things like the dollar being the global reserve currency and being the basis of the petro trade, as well as subsidizing global security (mostly in regards to international shipping and piracy).


What is it about the money market safeguards that increase volatility?

I don't know much about repo markets, but in dynamic systems in general, two things are likely to generate volatility:

Large shocks of any kind, corrective or not, especially when they are reactive (and therefore delayed and possibly out of phase with underlying cycles - think about pushing a child on a swing while standing at the edge, versus standing in the middle, of the arc).
Reducing the inertial mass of the system.  In this case, reducing the volume of trading.

You have both here. The large shock is the corrective policy (post-2008 actions like TARP), coming potentially years after the initial cause of the financial crisis. The reduced inertial mass can be partly explained by traders reacting to the disconnect between asset values and fundamentals due to actions like TARP, which was mainly about buying up worthless assets to keep banks afloat.


Experiments contradicting the expected utility model

this paper http://else.econ.ucl.ac.uk/papers/uploaded/243.pdf (Choi 2007) has a nice state of the art experiment that deals with rationality and expected utility is a special case of it. In general only 17% of consumers are compatible with rationality ergo the remaining part cannot be expected utility maximizers.  Quah has a nice paper on the revealed preference theory of expected utility (among other models), he uses Choi dataset to test expected utility hypothesis that is going to be rejected more times than rationality https://ideas.repec.org/p/lec/leecon/13-24.html


Effects of Robotics on the overall marginal propensity to consume

If your assumption that "only a few jobs are left (primarily high-skill)" is true, then there are roughly two options:

people without jobs become redundant, meaning they will not reproduce anymore and disappear (pretty much as it happened to the horse). Here you end up with a society of a much reduced size, which will surely happen through some form of recession, or long stagnation period (kind of like a convergence to a new steady state. Naturally, this is very unlikely to happen in democracies (horses could not vote). An alternative is for many of the jobless to emigrate, but automation being a global force, this is just delaying the problem.
the few remaining jobs are shared among the people. As Keynes forecasted almost 90 years ago, technology could make a 15-hours working week possible. Thus, the fewer hours of work available can be shared among the population (which would require some re-skilling effort). Although I am skeptical this will ever happen in capitalism, at least it averts a big recession.
taxation becomes much more progressive, taxing the rich to provide subsidies to the jobless. An "extreme" form this could take could be the Universal Basic Income, or the Negative Income Tax, favourite of Friedman. Since robotics is to increase productivity and increase profits (by lowering the labour share), an UBI could be finances via taxation on profits. On the one hand, giving income to the rest of the population is likely to generate more demand for products and services, leading to more job creation and growth. On the other hand, these taxation systems could be combined with some form of "unproductive" work, like volunteering, community work, etc. There is plenty of evidence that employment is important for mental and social wellbeing (e.g. here), so simply providing income might not lead to socially desired outcomes. As Voltaire said,

  “Work keeps at bay three great evils: boredom, vice, and need.”

In all three options (explicitly and drastically in the first option), fertility is likely to endogenously adapt to these changes, just as it has done so in the past. Likewise, political ideas also adapt to technological and cultural changes, so things like UBI, which before were not feasible, might become socially accepted. The call for UBI from some of the very rich might partly reflect this (or an instinct response of those benefiting from capitalism to save it from a potential crisis/revolution).

Having said all this, I would dispute your assumption that there will be no jobs for the low/middle skilled individual. Under alternative assumptions the three options mentioned above might not be the most likely options anymore.


Comparing relative change for different base value

https://en.wikipedia.org/wiki/Relative_change_and_difference
Törnqvist, Leo; Vartia, Pentti; Vartia, Yrjö (1985), "How Should Relative Changes Be Measured?", The American Statistician, 39 (1): 43–46, doi:10.2307/2683905


What does this condition for a profit of a firm exist mean?

It means the impact of changing labour on the marginal product of capital is positive. IE if you increase labour MPK will increase and also if you increase labour MPL will increase.


"Loss leader" is a term primarily from marketing. It is occasionally used by economists, but not in a formal way because its definition is insufficiently precise.

To see why we have to be careful, it is useful to think about the economic principles underlying the three examples you mentioned. I do this below, but the ;tldr version is that the business model for selling data follows a totally different economic logic and even grocery stores vs playstations follows slightly different logic.

The grocery store example is probably the closest thing to what would commonly be understood as a loss-leader. The reason this strategy works is because consumers face some kind of friction that makes them disproportionately prefer one-stop shopping to visiting many stores (e.g. becoming informed about different stores is costly, switching stores in the middle of a shop is costly, etc.). The fact that consumers don't want to go to many stores means that once they are attracted into a store by a low price, they can be exploited with higher prices on other goods. To reiterate: note that this business model is driven by a feature of consumers' behaviour (search/shopping frictions).

The Playstation example follows a slightly different logic, similar to the razord and blades model mentioned by others. The key factors here are: (1) products are complements—we have two types of good (games consoles and games, or razors and blades) that only work if they are consumed together. (2) products are imperfectly compatible (I can't use Playstation games in an XBox).

Now, suppose I bought a Playstation and then decided the games were too expensive and I would prefer switch over to XBox. This would require that I buy a new games console, which is expensive—so I will tend to be unwilling to switch to a different platform. This is just like the grocery store example: we have a situation where consumers are unwilling to switch from one supplier to another. Just like that example, firms offer a low introductory price to initially attract consumers, only to later exploit them once they are locked-in.

But note here that the switching frictions are not an intrinsic property of consumer behavior like in the earlier examples, but rather are now driven by the properties of the products themselves (complementarity and incompatibility). We have therefore identified two distinct sets of conditions under which this kind of pricing strategy might be attractive to a firm: either consumers are intrinsically reluctant to switch or they can be made so through design and compatibility choices.

What about businesses that offer free services in return for data? Here the underlying economic logic is completely different to the other two cases. These are typically examples of so-called two-sided markets. A two-sided market is a market in which a central intermediary (called a "platform") matches people from two distinct groups. In this particular example the two sides will be consumers and marketing firms, and the job of the platform is to bring the two together so that new value can be unlocked through the exchange of data.

Two-sided platforms typically involve a chicken and egg type problem because in order for the platform to function it is necessary to make sure both groups are on board (a heterosecual dating site that attracts only men won't be very useful!). The usual solution to this problem is that one of the two groups is subsidised (e.g. allowed to join the platform for free or at reduced cost). Once that group joins, the platform becomes more attractive to the other group, who can be charged a higher price. A classic example of this is nightclubs, which would often run "ladies nights" (low price admission for females,) thus ensuring many females enter the club. Once the club is full of females, it becomes much easier for the club owner to charge a high admission fee to men. Similarly, firms like Facebook subsidise consumers (with a free service) to get as many consumers on board as possible, so that the firm is able to extract as much value as possible from the other side of the market (selling data to marketing firms).

Note that the underlying economic mechanism here is different from the other cases. Those examples were about creating frictions to lock-in consumers, so that those same consumers could be charged a high price. Two-sided pricing is about offering a low price to one group in order to get them on board so that a totally different group of consumers can be charged a high price.

Final note: games consoles are also two-sided markets (they serve both gamers and game developers and must get both on board to be successful). So a bit of the two-sided logic applies there too: Playstations are sold below cost to gamers to get lots of gamers onto the platform because this allows Sony to maximise revenues from the royalty fees paid by game developers, as well as revenues from selling games to consumers.


In the eyes of a normal citizen, what difference does it make if my country has debt or no debt?

1)  Debt matters because it smoothes (or unsmoothes) taxes over time, which matters because the deadweight loss from taxation is (roughly) proportional not to the tax rate, but to the square of the tax rate.

2)  Because family sizes are not homogeneous, government debt (which transfers the tax burden to future generations) can redistribute the tax burden across families.  (Think, for example, about a taxpayer with no kids, or a family that has just immigrated.)

3)  Government debt makes it easier to borrow --- it's better to pay 3% to government bondholders than 18% to your credit card company.  This is possible because the penalty for not paying your taxes is considerably more severe than the penalty for not paying your credit card bill.  (In effect, government debt resurrects the institution of the debtor's prison.)

4)  There are of course issues with misperceptions, where debt can make people feel either richer or poorer than they really are, depending on whether they underestimate or overestimate their future tax burdens, and so can affect consumption paths in either direction.


The problem you are facing has probably both: Moral Hazard and Adverse Selection.

We have hidden action by the doctor (you can't really observe his level of effort during the surgery), therefore we have Moral Hazard.

Additionally, you (probably) can not know beforehand of the doctor is a good or bad doctor, so his type (good or bad) is unknown. So, there is hidden information and therefore possibly Adverse Selection.
One example could be that a good doctor would never work for the amount you pay, so the doctor you hire is of the bad type.

Remark: I did not define good/bad doctor here, as it could be many different things; a bad doctor could just be a lazy doctor or a badly trained doctor.


Transversality Condition in neoclassical growth model

The transversality condition may be more easily understood if we start from a problem with finite horizon.

In the standard version, our objective is to
$$
\max_{\{c_t,k_{t+1}\}_{t=0}^T} \sum_{t=0}^T\beta^t u(c_t)
$$
subject to
$$
\begin{aligned}
f(k_t)-c_t-k_{t+1}&\ge0,\quad t=0,\dots,T &&\text{(resource/budget constraint)}\\
c_t,k_{t+1}&\ge0,\quad t=0,\dots,T &&\text{(non-negativity constraint)}
\end{aligned}
$$
with $k_0$ given. The associated Lagrangian (with multipliers $\lambda_t$, $\mu_t$, and $\omega_t$) is
$$
\max_{\{c_t,k_{t+1},\lambda_t,\mu_t,\omega_t\}_{t=0}^T}
\sum_{t=0}^T \beta^tu(c_t)+\lambda_t(f(k_t)-c_t-k_{t+1})+\mu_tc_t+\omega_tk_{t+1}
$$
The FOCs are
$$
\begin{align}
c_t:&& \beta^tu'(c_t)-\lambda_t+\mu_t&=0,\quad t=0,\dots,T \\
k_{t+1}:&& -\lambda_t+\lambda_{t+1}f'(k_{t+1})+\omega_t&=0,\quad t=0,\dots,T-1 \\
k_{T+1}:&& -\lambda_T+\omega_T&=0,\quad T+1 \tag{1}
\end{align}
$$
with the Kuhn-Tucker complementary slackness conditions: for $t=0,\dots,T$,
$$
\begin{align}
\lambda_t(f(k_t)-c_t-k_{t+1})&=0 & \lambda_t&\ge0 \\
\mu_tc_t&=0 & \mu_t&\ge0\\
\omega_tk_{t+1}&=0&\omega_t&\ge0\tag{2}
\end{align}
$$
Since resource constraint must be binding in all periods, i.e. $\lambda_t>0$ for all $t$, it follows that at the last period $T$, $\omega_T=\lambda_T>0$, which in turn implies $k_{T+1}=0$.

Usually we assume $c_t>0$ for all $t$ (the Inada condition), and this implies $\mu_t=0$ for all $t$. So the consumption FOC becomes
$$
\beta^tu'(c_t)=\lambda_t \tag{3}
$$

Looking at conditions $(1)$ $(2)$ and $(3)$ in the last period $T$, we get
$$\beta^Tu'(c_T)k_{T+1}=0$$
Extending this to the infinite horizon, we get the transversality condition
$$\lim_{T\to\infty}\beta^Tu'(c_T)k_{T+1}=0$$

The intuition of the transversality condition is partly that "there is no savings in the last period". But as there is no "last period" in an infinite horizon environment, we take the limit as time goes to infinity.


How to calculate Real GDP from quarterly change

Assuming 1432195178668.32 was the last value in Q4 2018 you got, just calculate 1432195178668.32 * (1.005) to get the 2019 Q1 Value, save the value. Then take 2019 Q1 * (1.006) to get the next value etc. Easy to do via R or Excel.

Basically if you had an increase x just multiply by (1+x) where x is in decimals, so a change of -0.75 % becomes * (1 - 0.0075)

Then, simply take the average of the four quarters if you want the annual value:
$$ \frac{(Q1.2019 + Q2.2019 + Q3.2019 + Q4.2019)} {4} $$


Currencies and currency pairs are sometimes classified as Major, Minor, or Exotic, depending on how heavily traded they are (Major most heavily traded, Exotic least).


Economic interpretation of Returns to Scale

Since the OP has labeled their question "Economic Interpretation of Returns to Scale":
The economist mostly responsible for spreading the use of mathematical rigor in economics, Paul Samuelson, who also never lost sight of the essence of economics, writes as follows in "Foundations of Economic Analysis" (1947, Enlarged Edition 1983), p. 84 (emphasis mine):

The problem of homogeneity of the production function is one about
which much controversy has raged. It has long been held on
philosophical grounds that product must be a homogeneous function of
the first order of all the variables, and if this is not so, it must
be either because of "indivisibility" or because not all "factors"
have been taken into account.
With regard to the first point, it is clear that labeling the absence
of homogeneity as due to indivisibility changes nothing and merely
affirms by the implication that "indivisibility" does exist, the
absence of homogeneity.
With respect to the second point, we may reverse the Aristotelian
dictum and affirm that anything that must be true self-evidently
("philosophically"), intuitively -i.e. by conventional definition of the terms involved- that such a principle can have no empirical
content. It is a scientifically meaningless assertion that doubling
all factors must double product. This is not because we do not have
the power to perform such an experiment; such an objection is of
course irrelevant. Rather the statement is meaningless because it
could never be refuted, in the sense that no hypothetically
conceivable experiment could ever controvert the principle enunciated.
This is so because if product did not double, one could always
conclude that some factor was "scarce".

"Principles that have no empirical content" can be seen, and used, as methodological / modeling choices.
For example declaring that a production function $Q = F(K,L)$ has constant returns to scale (homogeneous of first order/degree, or "linearly homogeneous"), is equivalent to declare that we understand the symbols $K$ and $L$ as capturing all forces affecting the level of output.
Samuelson goes on to write

...the expression "factor of production"... has been used in at least
two senses... First it has been used to denote broad composite
quantities such as "labor, land and capital". On the other hand, it
has been used to denote any aspect of the environment which has any
influence on production. I suggest that only "inputs" be explicitly
included in the production function, and that this term be confined to
denote measurable quantitative economic goods or services... So
defined the production function need not be homogeneous of the first
order.

The profession has implemented his suggestion exactly, and this is why we see models with decreasing or increasing returns to scale. But in light of the above wise comments, we must keep in mind that, say, a production function with increasing returns to scale does not reflect some real-world impressive technology that can more than double output if we only double inputs. It is just a methodological / modelling choice we have made, following Samuelson's suggestion.
A way to justify Samuelson's suggestion as regards what to include in the "production function" construct, is that he essentially suggests to include those output-affecting factors related to which the firm has a strong degree of control and decision making over their quantities employed.

Responding to comments by the OP

Thanks for the answer! Summarizing Samuelson's points I understand the
following: if we are able to capture all forces affecting production,
than the production function is homogenous of first order. However,
since we are not able to measure all inputs/factors, then it is
reasonable to assume that the production function is not linearly
homogenous. If so, then I assume that the production function is never
linearly homogenous, because K and L are measurable, but A (TFP) is
never measurable.
Aside from that, from your answer I assume that there is no strong
ground to find any economic interpretation of the returns to scale,
since it is merely methodological/modeling choices, right?

Don't confuse data availability on a factor with symbolic representation of a factor. So one could in principle say that $A(TFP)$ are "all other factors" and so we have constant returns to scale, but then $A(TFP)$ would become a catch-all concept devoid of any economic meaning.
Returns to scale are indeed a methodological/modeling choice so they do not have "intrinsic" economic interpretation. But they affect the results of the model. As such, they are effective, because they indirectly reflect the existence (or not) of factors that will not enter a specific model quantitatively.
So choosing diminishing/constant/increasing returns to scale will reflect the knowledge/belief of the researcher as to whether there is some important factor that affects output and stays out of the model. So in a sense the represent an aspect of the model that has this indirect economic meaning.


Lexicographic Preference Relation on the QxR

Note first that for each nontrivial (more than one point) compact interval $I$, there exists a strictly increasing function from $\mathbb{R}$ to $I$.

Let $\langle q_1,q_2, q_3,\ldots\rangle$ be an enumeration of $\mathbb{Q}$. We will define $u:\mathbb{Q}\times\mathbb{R}\to\mathbb{R}$ inductively, one $q_n$ after another.

Let $I_1$ be a nontrivial compact interval and $u_1:\mathbb{R}\to I_1$ be strictly increasing.

Now assume there are disjoint nontrivial compact intervals $I_1,\ldots,I_n$ that ordered on the line like $q_1,\ldots,q_n$, and strictly increasing functions $u_m:\mathbb{R}\to I_m$ for $m\leq n$. Since these intervals are closed and disjoint, there is space between any two consecutive intervals. So one can put a nontrivial compact interval $I_{n+1}$ in a place corresponding to $q_{n+1}$ among $q_1,\ldots, q_n$. Choose also some strictly increasing function $u_{n+1}:\mathbb{R}\to I_{n+1}$.

This will give you a disjoint sequence $\langle I_1, I_2, \ldots\rangle$ of nontrivial intervals and a sequence of functions $\langle u_1, u_2, \ldots\rangle$ with $u_n:\mathbb{R}\to I$ be strictly increasing. Now define $u:\mathbb{Q}\times\mathbb{R}\to \mathbb{R}$ by $u(q_n,r)=u_n(r)$.

You can verify that $u$ represents the lexicographic ordering on $\mathbb{Q}\times\mathbb{R}$.

Warning: The existence of a countably infinite number of disjoint nontrivial intervals might appear very strange, but is perfectly fine.


General Results on First or Second Mover Advantage?

One nice reference that seeks to answer your question is the following paper,

https://link.springer.com/content/pdf/10.1007/BF01076104.pdf

The paper's main results are contained in the following theorem (Theorem I):

a. If both players have a dominant strategy in the basic game, the game is the same. (where the basic game is just the 2x2 bimatrix game)

b. If only one player has a dominant strategy in the basic game, then
the extended game has a unique equilibrium in un-dominated strategies.
It's different from the  basic game outcome iff that outcome is Pareto dominated by another pure strategy outcome. The extended game equilibrium achieves
these Pareto dominating payoffs by having the player with the dominant
strategy play first and the other second.

Think of this as a way to achieve a Pareto superior vector of payoffs.

(C) If the unique simultaneous play equilibrium of the basic game is
in mixed strategies, then like in part (B) there won't be a change unless there's a Pareto superior P.S. vector. If Pareto dominance does
not exist, both players will wait until the second period and play
simultaneously. If Pareto dominance does exist, the unique extended
game equilibrium attains the Pareto dominating payoffs by selecting one
of the sequential move games.


Decision over "max" production function:

Hint

For profit maximization, either $x_1$ or $x_2$ (but not both) must be zero. If not, say $x_1^*>x_2^*>0$ at the optimum, then one could increase profit by lowering cost by reducing $x_2^*$ without affecting output and thus revenue.

Let $z=\max\{x_1,8x_2\}$. The profit function can be written as
\begin{equation}
p[3(x_3)^{1/3}(z)^{1/3}]-w_3x_3-c_zz,\tag1
\end{equation}
where
\begin{equation}
c_z=
\begin{cases}
w_1&\text{if }x_1>8x_2\\
w_2/8&\text{if }x_1<8x_2\\
\min\{w_1,w_2/8\}&\text{if }x_1=8x_2
\end{cases}
\end{equation}

Solve $(1)$ for the condition determining the optimal level of $z$, and compare the costs of achieving this level using either $x_1$ or $x_2$. Use the one that entails the lower cost.


How come the average studio rent in Vietnam is bigger than the average salary?

The rent figure in the question relates to the centre of Ho Chi Minh City and it is a fallacy to infer that it is typical of the whole of Vietnam.  There is a body of theory going back to von Thunen suggesting that land rents will generally fall with distance from a city centre, forming a rent gradient. Given a free market in land and property, residents and entrepreneurs will choose where to live or site their businesses with regard both to price and to costs of travel and transport, and this tends to result in such a gradient in land rents.  Property rents will depend on the size and type of property as well as land rents per unit of area, but otherwise similar properties will tend to be cheaper with greater distance from a city centre.

In the case of Ho Chi Minh City, this World Bank Report indicates (p 153 Section 3.4.1. Prices) that the market for land is subject to considerable government intervention, but that land prices are nevertheless much lower in peripheral districts than in the city centre.

While the factors listed by emeryville may also play a part, a large part of the answer to the question "How do Vietnamese people pay their rent?" is probably therefore that most poorer people do not live in the parts of large cities where the rents are highest.


Why do the gross return of wealth and wealth move in opposite direction?

Per our comments above, I believe the expression you have is incorrect.  Your confusion is worsened by some poor terminology use.

Gross return can be written as $R = 1 + \frac{a}{w}$ where $w$ is initial wealth (or more accurately, the initial investment) and $a$ is new cash flow generated by the investment.  So for example, with $w = 100$ and $a = 5$, the gross return is $R = 1 + \frac{5}{100}$ = 1.05, representing a 5% return on $100.

What you call the "gross return of wealth" is, I think, just the derivative of $R$ with respect to $w$: $\frac{dR}{dw} = -\frac{a}{w^2}$.  The question is, why is this negative?  Because what this quantity tells you is how your gross return changes when your initial investment grows, holding the new cash flow constant.

It really just follows from the arithmetic of proportions. Return is a proportion while wealth is a number.  As wealth $w$ increases, the return from a new cash flow $a$ is reduced, because it is a smaller proportion of a larger whole.  So in the example above, if we double our investment to $w = 200$ but we keep $a = 5$, then the return is $R = 1 + \frac{5}{200} = 1.025$.  Because we had to invest more to get the same amount of new dollars, our return is smaller.


What does economics say about "price gouging" during an emergency?

Actually economics does not even officially use term price gouging. Your analysis is right, actually economists dislike anti-price gauging legislation for this reason.

For example, when the IGM panel of top policy economists were asked about one piece of price gouging legislation in the US, vast majority disagreed with it:

However, an important caveat to keep in mind is that due to menu costs some firm would not be able to change prices quickly enough even in absence of anti-gouging regulation - meaning such regulation is not the sole source of shortages, there would be some even without them although less severe (and of course it goes without saying this is not any justification for them).

However, beside that yes, you are actually missing the main factor that justifies the anti-price-gouging legislation. Which is moral philosophy. There is argument to be made that such practices as gouging are immoral (you can see some ethical arguments against gouging in this paper for example). While I personally dont identify with such moral views, its not our role as economists to pass moral judgements. If people pass anti-gouging legislature well aware of all the negative economic consequences but they still do it despite them then there is no objection an economist can make against them as we are scientists not moral philosophers and such questions are beyond our discipline.


My suggestions:

the best ever written advanced book on game theory is 'Game Theory' by Fudenberg and Tirole: it deals with a lot of material used in research and many applications. When you work on a game theory paper and, for instance, u'r unsure about what kind of equilibrium applies to your case, the book will save your life. It's a bible
but if you want to get inside the game theory world, learn about what kind of problems game theory is able to deal wth, or even getting some interesting ideas to work on your own, after learning the necessary tools..in these cases I strongly suggests to use 'Game theory evolving' by Herbert Gintis. He was my professor at the PhD, and I appreciated his ability as educator (other than a researcher)

I hope you'll find it useful.
Enjoy!


Why the treasury is buying back its treasury securities during the coronavirus economic crisis?

The following link was provided: Link to Moroccan news article, in French

My French is somewhat rusty, and I am completely unfamiliar with the structure of the Moroccan financial system. But I think I understood the basic idea.

As a result of the worries around COVID-19, there was added demand for liquidity in the banking system. The Treasury sits on a buffer of cash (presumably sitting at the central bank). What it is doing is using that buffer to purchase back some short maturity bonds. This injects money into the banking system, which can then be used for liquidity management, or to buy newly-issued long-term Treasury bonds.

The central bank could have done this, but since the Treasury presumably had cash reserves, it did the operation.

From a theoretical point of view, it would not matter whether these bond purchases were done by the central bank or the Treasury - in either case, the private sector is exchanging bonds for cash. However, the central bankers might not agree with that assessment, and there may be institutional rules (that I am unaware of) in Morocco that pushed the Treasury to do this.

Generally speaking, in the developed countries, the central bank would handle such an operation, and the Treasury would not get involved. The closest operation I can think of is in Canada, where the Ministry of Finance lends to the private banks out of its balance at the Bank of Canada.


Higher order beliefs and coherency in game theory

The way hierarchies of beliefs are specified, beliefs on the same events are encoded in different places.

The basic idea is actually quite simple. You have two players, Ann and Bob, say. Ann's first order beliefs specify how likely she thinks each strategy choice of Bob. Ann's second order beliefs specify how likely she thinks each combination of a strategy choice of Bob and a belief of Bob on Ann's strategy choices. Second order beliefs are joint probabilities.

Now suppose Ann's first order beliefs specify that she believes that Bob plays the strategies C and D with probability $1/2$ each.

Suppose also that Ann believes with probability $1/4$ that "Bob plays C and believes with probability 1 that Ann plays D for sure" and believes with probability $3/4$ that "Bob plays D and believes Ann plays D for sure".

If you ask someone who knows only Ann's first order beliefs how likely Ann thinks it is that Bob will play C, that person will answer with $1/2$. If you ask someone who knows only Ann's second order beliefs how likely Ann thinks it is that Bob will play C, that person will answer with $1/4$. Indeed, that is what the marginal of her second order belief on the space of strategies says.

This is absurd and makes no sense. Ann's beliefs on how likely it is that Bob plays C should be the same according to her first order beliefs as to her second order beliefs. Now coherency is exactly the condition that guarantees that. If some belief on an event E is specified in more than one level of the hierarchy of beliefs, each hierarchy should specify that the same belief on the event E.

In terms of the formalism: The marginal of a probability measure is again a probability measure, so $marg(b_i^2;\Sigma_j)=b_i^1(E)$ is comparing apples and oranges; on the left is a probability measure, on the right a number. What you want is $marg(b_i^2;\Sigma_j)(E)=b_i^1(E)$, as prescribed by coherency- and indeed by common sense.


Utility function is given as $U = \sqrt{XY}$ find

Rather than write a complete answer, I am going to post a couple of hints that will hopefully get you underway.

For part (i), note that

You have two equations: $\dfrac{MU_x}{MU_y} = \dfrac{P_x}{P_y}$ and $I = P_x \cdot x + P_y \cdot y$.
Since we know $MU_x$, $MU_y$, $P_x$, $P_y$, and $I$, these two equations contain two unknowns.
Usually, so long as we have at least as many equations as there are unknown variables, we can find the value of those variables by simultaneously solving the equations.
the $x$ in $I = P_x \cdot x + P_y \cdot y$ is the quantity of hot dogs that you are asked to compute in part (i), so ultimately you are going to have to solve for the value of this variable.
my suggestion would therefore be that you try substituting into your two equations all of the things whose value you know and then try solving for $x$.

Since a budget line is a straight line, it is characterised by an intercept, $c$, and a slope, $m$.

If you think about drawing this line geometrically then you should recognise that

the intercept is the amount of $y$ you could afford if you didn't buy any $x$ and spent all of your available money on $y$.
the slope is the number of units of $y$ you would have to give up to save enough money to afford one more unit of $x$.

Once you know the slope and the intercept, you can write down the equation for your budget line, $y=mx+c$, and answering part (ii) is then just a matter of algebra.


What is the impact of inflation on Pakistan's exports?

There are some academic papers dealing with this question (but beyond the specific case of Pakistan)

Note first that inflation is inversely correlated with real exchange rates (as long as nominal exchange rates do not adjust instantaneously to prices).

The following numerical example from Gylafson (1999) illustrates the point.

Suppose the real exchange rate index $R$ is initially 100 and the inflation rate $p$ is 10% per year, so that $R$ decreases gradually to 100/1.1= 90.9 at the end of the year.
Suppose, moreover, that the nominal exchange rate adjusts fully to prices with a one-year lag, restoring $R$ to 100 at the beginning of next year. This means that the average value of R over the year is (100 + 90.9)/2=95.45.
Now suppose inflation increases to 20%, so that R falls to 100/1.2=83.3 at year's end. Then the average value of $R$ over the year is (100 + 83.3)/2=91.67.
Therefore, the real exchange rate is inversely related to inflation as long as the adjustment of the nominal exchange rate to prices is not instantaneous.

Then, currency overluation may hurt exports.

Gylafson (1999)'s paper is interesting because it relates exports and inlfation to growth. His main conclusion is that, in the period under review (1985-94), high inflation and an abundance of natural resources tended to be associated with low exports and slow growth.


Books for microeconomics and macroeconomics for selected topics

From Varian (7th edition):

Consumer behavior: at least chapters 1–6; preferably also chapters 7, 8, and 12.
Perfect competition and Theory of production: chapters 15, 16, and 18-23.
Monopoly price discrimination: chapter 25 (you might want to look at chapter 24; it seems a bit odd to study price discrimination without first looking at a non-discriminating monopolist).
Bertrand/Cournot duopoly: chapter 27.
Welfare economics is a bit tougher, because this could mean a number of things. I would suggest chapters 31 and 33 (and maybe chapters 32, 34 and 36).


Rosen's uniqueness theorem: Why is the Jacobian Square?

While there are $n$ players, a player's strategy is not single dimensional.  The total dimension of the strategies is $m$.  So the vector of strategies $s$ is $m$ dimensional.  $g(s,z)$ is also $m$ dimensional, which is why the Jacobian is $m \times m$


Mathematical Proof as to why does the total revenue increase when the prices are increased for an inelastic product?

(I do not agree that this is a duplicate of the answer proposed by other members here).

Total Revenue is

$$TR = Q(P)\cdot P$$

The derivative with respect to price is

$$\frac{\partial TR}{\partial P} = Q'(P)\cdot P + Q(P)$$

For this to be positive (and so total revenue to increase with price), we require

$$\frac{\partial TR}{\partial P} > 0 \implies  Q'(P)\cdot P + Q(P) >0 $$

$$\implies \frac{Q'(P)\cdot P}{Q(P)} > -1$$

The left-hand-side is the price elasticity of demand. Now, greater than minus unity means smaller than unity in absolute terms. And it is in that sense that demand at the region is "price inelastic" (the minus sign indicating direction of movement).


Differential form of the quantity theory of money

Well you do not provide any source for the $dM+dV = dP+dY$ so it is hard to say why someone written that. That is certainly not normal total derivative of QTM.
You are right that the correct total derivative of QTM will be given by:
$$VdM+MdV=YdP+PdY $$
Possible explanation why you saw it somewhere written differently:

Note the above can be divided by $MV=PY$ to get:

$$(M dV)/(MV) + (V dM)/(MV) = (P dY)/(PY) + (Y dP)/(PY)$$
which after simplification yields:
$$\frac{dV}{V} + \frac{dM}{M} = \frac{dY}{Y} + \frac{dP}{P}$$
the above expression is quite common in the literature and it is possible someone just decided to substitute $dx = \frac{dX}{X}$ to clean up the expression: $dv + dm = dy +dp$,

Alternatively it is possible that the 'unnamed source' wanted to express the equation in percentage changes via log linearization and just used the same symbol for change as differential symbol. Log linearizing QTM yields:

$$\ln M + \ln V = \ln P + \ln Y$$
which is equivalent to:
$$\Delta \% M + \Delta \% V = \Delta \% P + \Delta \% Y$$
Some people will use $d$ or $\delta$ instead of $\Delta$ and omit $%$ sign.

There are some missing assumptions transformations that would make it right.

Source you got it from made a mistake.


Calculating Real Budget Deficit, given Nominal Deficit and Inflation

Edit: based on the video I get the logic that the person was trying to get across.

Basically the argument is that if in year $t$ deficit was 100mil but the same year the total debt 5billion and inflation was 10% that means that in real terms the value of debt is 500mill less and the teacher of that course treats this as 500mill revenue so under that definition even though you had 100mill deficit you would end up with 400mill surplus because thanks to inflation the net real debt decreased.

However, I must say it’s quite unusual to define real deficits in this way (see Barro’s Macroeconomics).


What makes a factor valid in a factor pricing model of assets?

This is a partial answer (see section 5.1, p. 79 of Cochrane's book, "Asset Pricing"). Suppose you wanted to treat the size of the firm as a factor. Stocks of smaller firms typically have higher average returns. You could then form a "large" holding company comprised of smaller firms. The new, large company would then have returns like a smaller company but would in fact be large and "the managers could enjoy the difference."

  What ruins this promising idea? The "large" holding company will still behave like a portfolio of small stocks---it will have their high betas. Thus, only if asset returns depend on how you behave, not who you are---on betas rather than characteristics---can a market equilibrium survive such simple repackaging schemes.

(How would I formalize this concept?)

EDIT: Also, in Financial Asset Pricing Theory by Munk (chapter 10, p.371) it says

  It is worth emphasizing that the general theoretical results of the consumption-based asset pricing framework are not challenged by factor models. ... Factor models do not invalidate the consumption-based asset pricing framework but are special cases that may be easier to apply and test. Therefore factors should generally help explain typical indiviudals' marginal utilities of consumption.

(Emphasis added) This helps to understand the role of factors in the ICAPM.


What is the general rule for classifying factor that only shift one supply/demand curve or two supply/demand curve?

Treating supply and demand as functions that relate the price and quantity for a good, a variable that appears as a parameter in both functions will shift both curves. In macro and micro theories, the details of the model will determine what these are.

When we consider supply and demand with econometrics, the fact that prices and quantities affect each other through two processes (are jointly determined)  results in endogeneity problems. Wooldridge's Introductory Econometrics has an excellent chapter on simultaneous equations models.


Measuring demand for banking services - (Maximum) Market Size

There is no quantifiable answer as the concept is illusory.  Banks operate by mismatching short term debt with long term assets.  This has no benefit to the economy as a whole and in fact creates inflation, risk and volitionality.  Banks operate maturity mismatching because they can and it serves their own interest.  There is no natural demand for banks which is why they are in need of constant artificial support from central banks (much of which happens on a daily basis).  Without central bank support, banks would be accountable for mismatching short term debt with long term assets and they would quickly and rightly so burn up in a liquidity fire.

Perhaps a better premise to start before mathematically quantifying the demand for banks is to ask conceptually the role banks play in an economy first.  Without conceptual and contextual understanding, math is meaningless number juggling designed to impress and confuse those that don't know better.

Now...it can be said it said there is a demand for money of which banks create.  Imagine if we were to switch to the gold standard all of sudden.  Only gold could be exchanged for services.  Because gold is limited, the price for it (to acquire as a means of exchange) would shoot up astronomically.  This profiting (from gold sellers to gold buyers) represents economic loss for the buyers.  If they could acquire another means of exchange (say gold deposits that were not tied 100% to gold) they would not have to pay as much for the gold.  So in a way banks can create competition for money.  But in doing so they create either their own inflation or profiteering.  Then there is of course the matter of fiat currencies competing which never ends well...

Personally, that is why I'm in favor of a national depository that would negate the need for deposit banking.


How to calculate gdp of a company during promotion and loss?

As noted in a comment, GDP is associated with a country, not a firm.

But if we are talking about the contribution to GDP, the operating assumption is that calculations are based on observed (market) prices. So the value of consumption is \$100 if we are calculating GDP based on expenditures. If we are looking at domestic income, it would be \$100: \$200 wage income, and -\$100 business income.

Statisticians do not attempt to decide what goods are “really worth”, they use data based on actual transactions. Since GDP numbers are estimates based on a variety of sources, it is unlikely that they capture when particular firms have promotional sales.


This isn't really a proper question for this network, but try:

http://data.worldbank.org/indicator/PA.NUS.FCRF
https://www.imf.org/external/np/fin/data/param_rms_mth.aspx


What amount of share buy-backs are legitimate?

If the company has excess cash or excess liquidity that it cannot effectively deploy in capital investments, and it has reason to believe that the expected value of returns from purchasing shares will be higher than alternatives (such as buying equities or financial instruments), this would be legitimate, where "legitimate" can be defined as an increase in the long-term value for anyone holding shares in the company.

As for determining how often this is done "legitimately", as opposed to being done manipulatively in order for inside traders to profit from reducing the supply of shares and thus illegitimately driving up prices, that's a different question.

The question of whether it is "legitimate" in terms of share buybacks giving the executive board control out of proportion to shares held, this should be considered separately from the question of whether excess cash legitimizes the buyback from a long-term profit maximization perspective.

As for the question of whether excess cash that cannot be deployed effectively is a sign of a "healthy economy" or not, this need not be determined by the observation of excess cash of a specific corporation considering share buybacks. For example, one company may have excess cash that it cannot deploy effectively in a situation where it expects to earn higher returns from a share buyback than investing in alternative financial assets or securities, without this necessarily applying on an economy-wide basis (which would contradict a variety of theoretical assumptions about financial markets always efficiently reallocating capital to its most profitable use ... but that could happen.)

Relevant regulatory approaches to "illegitimate" share buybacks could fall under shareholder rights (other shareholders would be poorly represented by executives deciding on share buybacks to temporarily inflate share prices for their personal profit), or possibly in some cases insider trading. The regulatory framework, and its application, varies across jurisdictions.