Potential output is the level of output achieved when all resources are employed and put to their most productive uses, and which can be sustained over the long term.

Expansion beyond the current level of potential output usually occurs through technological progress. This is a catch-all phrase that includes the invention of new machines, better education, improvement of workers' skills, etc.

It can also occur through an expansion of the labor force and capital stock (i.e. more workers, more "machines").

Another way it can occur is through overheating. A concrete (but not common) example of overheating would be if we forced everyone to work say 20 hours a day — this might achieve a temporary boost in output, but this is probably not sustainable over the long term. Similarly, we can overwork our machinery, livestock, and other capital goods, but again this would probably not be sustainable.

A more common example of overheating is during a speculative boom -- say a property boom, when due to overoptimism and other factors, we might have a period of a few years when new properties are built at a frenetic pace, so that potential output is exceeded. This, again, is not sustainable.


Why does a rise in the savings rate result in an increase in the capital stock intuitively?

The story in the other answer is not fundamentally wrong but incomplete and bit inaccurate.
Saving does actually affect capital stock through investment in Solow model (assuming based on the Solow tag that is the model you want intuition for), but there is more complexity to it.
What is saving
Investment is actually equal not just to private saving but both private and public saving since saving is actually defined as (following Blanchard et al Macroeconomics: a European Perspective pp 51):
$$S \equiv Y - T-C$$
Combining this definition with output identity for closed economy $Y\equiv C+I+G$ gives us:
$$S = I +T -G$$
However, it is often convenient in Solow model to just ignore government by assuming $G=T$, in which case $S+I$.
Why does saving rate increase capital stock:
Next the way how savings rate affects capital accumulation is depicted in the picture I took from Romer Advanced Macroeconomics 4th ed pp 19.

As you can see the intuition really works this way. Here $s$ is the savings rate and $f(k)=Y$. Higher $s$ means that savings increases, for example if $Y=100$ with $s=0.5$, $S=50$ and with $s=0.7$, $S=70$. Then if we assume away government indeed $S=I$ so $I=70$.
This is why the evolution of capital accumulation (per unit of effective worker) is given by:
$$\dot{k}(t) = sf (k(t)) − (n + g +\delta)k(t)$$
where actually $sf(k(t)) = sY = S =I$, so it is through increased investment. The $n$ and $g$ would be population and technological growth respectively and $\delta$ the rate of depreciation (although these are not important for intuition about raising level of capital).
Does this push capital beyond steady state?
Now this is surprisingly common misconception. Increase in savings rate can increase the level of capital stock - it just cannot increase the growth rate at which new capital per effective worker accumulates.
According to Romer Advanced Macroeconomics [emphasis mine]:

, a change in the saving rate has a level effect but not a growth
effect: it changes the economy’s balanced growth path, and thus the level of
output per worker at any point in time, but it does not affect the growth
rate of output per worker on the balanced growth path.

However, this is quite common misconception because of the confusing terminology. Increase in level in macroeconomic. Consider for example the visualization from Romer Advanced Macroeconomics pp 20:

The upper graph shows you the growth rate of capital per effective worker. Indeed here savings rate has only one-of impact that quickly dies out (in fact this is just level increase in disguise as growth).
However, on the bottom panel you can clearly see that the level of capital per effective worker is now higher thanks to higher savings rate.


The constraint $g(x)\geq 0$ is binding if in optimum $g(x) = 0$ rather than the constraint being slack $g(x)>0$.


Do leverage pools force net negative outcomes? How are leveraged futures profits payed?

Warning
I am currently editing this answer, as I feel like I might have come to incorrect conclusions. (Maybe I didn't, but I am putting this warning in place in case I did). I hope to update this answer with more information soon.

Answer

It appears that a futures market is a zero-sum game.

Futures markets
the sum of all the long positions must be equal to the sum of all the short positions. In other words, risk is transferred from one party to another is a type of a zero sum game

Zero-sum game
a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero

See also another interesting question related to this topic: Where does the profit come from in short selling futures?
Conclusion
When it comes to futures markets, whenever you gain, someone else is losing. This differs from spot markets where, if the general price trajectory is upwards, you can gain without someone else losing. Of course a market cannot have infinite growth so eventually it will stagnate or come down, but as long as it doesn't drop to zero, there is a net-profit outcome. But a futures market always has a net-zero outcome.
With futures markets it is more important than ever to ask yourself why you think you'll be the one gaining and not the one losing. with spot markets, it is possible for more people to gain than to lose, and may be considered less risky if this is the case (long-term investments often match this critera).
In futures markets, funding fees appear to be an example of how gains and losses are redistributed to ensure a zero-sum outcome.

Interesting follow up question: Can futures markets exist that are not zero-sum?


Doing a PhD Economics without background in formal theorems?

I did my undergraduate double majoring in discrete mathematics and economics. I went through the grad micro sequence, the math for economists grad course, and the game theory field course, though. So I have a good idea of what the courses are like on both ends. (Doing the grad school route now, but that's additional commentary with which I won't bore everyone).

Traditionally, coursework like abstract Linear Algebra and Number Theory have been used by math departments to teach proof writing. In the last 15-20 years, an Intro to Proofs class has been added. Number theory doesn't come up appreciably in economics. So I'd punt that. But a solid course in linear algebra is so important. And if you have a strong data science background, then you should be very comfortable with the material, though perhaps not the formalization.

Real analysis is the maturity sequence in the math departments. Rudin is the standard textbook. If you take it, expect to be putting in a solid 20 hours per week, but you will be razor sharp by the end of it. Real analysis is usually a senior or introductory grad sequence. There is often times an introductory analysis class that uses a text like Abbott. This introductory class is still something you shouldn't take lightly, but it should be much easier and sufficient for a lot of what you'll do in economics. If you are working in stochastic processes, martingales, etc., then measure is likely to come up, and so you should take the Rudin sequence at some point and follow it up with measure theory (which is a very tough grad course).

The math for economists course compresses much of these courses (usually not measure) into a semester. When I took it, we trucked through the abstract linear algebra semester-long course in three weeks. It was also an ugly presentation, but that's what happens when you push for speed rather than elegance. And this is one more reason why you should take these courses in the math department.

Combinatorics and graph theory is also becoming increasingly important in economics, with regards to networks. So a course in graph theory wouldn't hurt either. Graph theory proofs are picky in the sense that you have to be very precise in saying "because it looks like it." This is different than analysis and algebra proofs. Graph theory is my particular area, so I can definitely speak to it.

A course in analysis of algorithms or theory of computation wouldn't be a bad thing to have either, with complexity becoming increasingly important in economics (algorithmic mechanism design, algorithmic game theory, strategic network formation, showing computing equilibria is computationally difficult for certain classes of games, etc.).

To sum it up, I'd strongly recommend:
Abstract Linear Algebra
Intro to Real Analysis

I'd recommend you consider:
Real Analysis (Rudin)
Measure Theory

Nice to Have courses:
Graph Theory
Combinatorics
Theory of Computation
Analysis of Algorithms

Let me know if you want book recommendations for any of these courses.


I am copying and pasting from an answer I wrote at From an economics perspective, what are the ramifications of a currency with fixed money supply?

  A moderate degree of currency inflation serves a number of useful functions in the economy. The most obvious are:

  It induces people to spend their money before it loses its value. In
  a deflationary environment there is an incentive to put money under
  your mattress and spend it in a year when it has greater purchasing
  power. If everbody does this then the lack of demand will lead to a
  decrease in overall economic activity (i.e. a recession).
  It provides a weapon against downward nominal rigidities. For example, workers are generally reluctant to accept a nominal pay cut, even if market conditions are such that the current wage is above the equilibrium level. Inflation means that their employer can simply increase wages at less than the inflation rate so that the real wage is decreasing.
  It erodes the real value of nominally denominated debt. Now, this is obviously only a pseudo-advantage because (whilst it benefits debtors) it harms creditors. However, this kind of erosion of debt may be desirable if national economic stability is threatened by high debt levels. Also, since debtors are usually poorer on average than creditors, it can reduce inequality, which may be a normative objective for the government.

  Without inflation you miss out on these benefits. The first benefit might not seem like a big deal if you think you can simply set the rate of inflation at zero percent. But it is very hard to hold inflation constant at some target level so attempting to hit zero inflation will almost certainly result in occasional lapses into deflation, with the attendant negative economic consequences.


This is actually an interesting question that I've never really thought of. What you are essentially describing is a monopoly on the side of the consumers to artificially drive down quantity demanded in order to lower prices.

You didn't state many details in your question but I'm assuming that the good in question is inelastic, is subject to competitive pricing, and has it's current price in competitive equilibrium.

The outcome of consumers collectively refusing to buy a product above a certain price would have the same effect of monopolistic pricing of a firm but in reverse, there would be a shift of some producer surplus into consumer surplus as well as the creation of dead weight loss as some producers are priced out of the market creating shortages.

This could also be empirically the same as the creation of a price ceiling for the good. If collectively consumers refused to buy a product above a certain price then that product would have a price ceiling and producers would produce at that price in accordance with their own supply curve.

As for your question about whether it would be a "good idea" that depends on what your definition of a positive outcome is. This type of action would have the effect of transferring some of the producer surplus to the consumers which would benefit the consumers but it would simultaneously lead to less production on the part of the producers due to the lower price creating dead weight loss and shortages. Empirically this would be bad for the aggregate economy as a whole due to the loss of surplus to dead weight loss, however, depending on the producer supply curve this may or may not lead to an aggregate gain in consumer surplus. An inelastic supply curve would lead to a gain in aggregate consumer surplus while a elastic supply curve would lead to a loss.


Equivalence of Definitions of Continuity of Preferences

We want to show that for $\succcurlyeq$ on $X$, Def 1 $\iff$ Def 2

$\boxed \Longrightarrow$

Assume that $\succcurlyeq$ is continuous by Def 1.

Let us say $x \succ y$. Denote our open-balls as $B(x, r)$, an open ball around $x$ of radius $r$. Suppose $\forall n, \ \exists \ x^n \in B(x, \frac{1}{n}), \ y^n \in B(y, \frac{1}{n})$ such that $y^n \succcurlyeq x^n$. But then we have constructed $\{x^n\} \rightarrow x$ and $\{y^n\} \rightarrow y$, and by Def 1, $y \succcurlyeq x$, which is a contradiction.

$\boxed \Longleftarrow$

Assume that $\succcurlyeq$ is continuous by Def 2.

Let us take sequences ${x^n} \subset X$ and ${y^n} \subset X$ where $\forall n, \quad x^n \succcurlyeq y^n$ and $\lim_{n \rightarrow \infty} x^n = x, \quad \lim_{n \rightarrow \infty} y^n = y \quad (\text{where $x, y \in X)$}$ for $n \in \mathbb{N}$,

BUT $x \succcurlyeq y$ is false instead of true. We want to show this leads to a contradiction.

If $x \succcurlyeq y$ is false, (so $y \succ x$) then $\exists B_x, B_y$ such that $\forall y' \in B_y, x' \in B_x$, we have $y' \succ x'$. Because $\{x^n\} \rightarrow x, \{y^n\} \rightarrow y$, there exists $N$ large enough such that $\forall n>N$, we have $y^n \in B_y, x^n \in B_x$.

Thus $\forall n > N$, we have $y^n \succ x^n$, which contradicts $\forall n, \ x^n \succcurlyeq y^n$.


Two possible explanations I have:

The stock market capitalization to GDP in India, although high, is at around 70–80 percent, compared to 100+ percent for countries with more developed capital market. This means that any gains or losses in the stock market would have an average 70% impact on the economy.
Being one of the fastest growing markets in the world (due to its population size, urbanization, and the rise of middle income families), the market has huge potential in the years to come, and the stock market takes that into account.


Interpreting 10-YR TREAS 21/32 yield 2.913%

I have not seen the page, but it is likely to either be the price change or part of the price of a $10$ year benchmark US Treasury bond (probably with a par value of $\$100$ and possibly with an nominal yield of $2.75\%$)

So either the price of this benchmark bond changed by $\$21/32= \$0.65625$ or the price was $\$98\; 21/32=\$98.65625$

Why US markets use eighths or sixteenths or thirty-seconds of a dollar when they have perfectly usable tenths and twentieths and hundredths (i.e. dimes, nickels and cents) to price bonds is another question.


How could the Euro zone be broken up in an ordered way?

No Time To Argue

Most importantly, there cannot be an "18 months period of notice". Tt has to be decided suddenly and there cannot be any period in which individuals could respond to the new plan by withdrawing their money and moving cash from one of the member countries to any of the others.

New Currencies

Each country has to have its own currency. These currencies should be free floating against each other, which on the other hand means that some will value up and some down. That is, Germany's new currency will probably value up against whatever Greece will have.

Capital Controls

Therefore, it will be of higher value to have your Euro exchanged for German money than for Greek money. Any bank account will have to immediately be translated into local currency. Also, no one will be allowed to move cash Euro between the member countries.

One way to immediately establish the new currency would be to simply stamp the old money with country specific stamps.

Citation

Note that Greek's new finance minister implied that their train of thoughts follows exactly these lines of thinking [my own translation]:

  Greece is not going to leave the currency union, as it cannot go back
  to the path of development on which it was on, hadn't it joined the
  union. An exit would lead to chaos in any case: For the moment, there
  is no new Greek currency as a new Drachm. Preparations for the
  introduction of such a currency would take months and would have the
  same effect as announcing a depreciation several months in advance.
  But you can only have a depreciation over night and unexpectedly,
  otherwise there are massive movements of capital flight/export.

From this german article:

  Die Währungsunion verlassen soll Griechenland nach den Worten von
  Varoufakis aber in keinem Fall. Denn damit könne das Land nicht auf
  den Entwicklungspfad zurückkehren, den es ohne Eintritt in den
  Euroraum genommen hätte. Ein Austritt habe auf jeden Fall Chaos zur
  Folge. Denn gegenwärtig gebe es keine griechische Währung wie eine
  neue Drachme. Vorbereitungen für die Einführung einer solchen Währung
  würden Monate dauern und hätten die gleiche Wirkung wie die
  Ankündigung einer Abwertung mehrere Monate im Voraus. Doch eine
  Abwertung könne es immer nur über Nacht und unerwartet geben, sonst
  gebe es riesige Bewegungen zum Kapitalexport, warnt er.


I'm skeptical that this will work. I'm concerned that for the sort of shock that is large enough to be interesting and large enough to study that stock prices will move before they open. You could potentially measure this by looking at the changes in stock price from close to open, but I'm not sure what you'd be measuring. Are changes in Tokyo stock prices in any meaningful sense causing the changes in NYSE price? Or is it simply that all stock prices are moving at once, but you can't easily see the NYSE stock prices until the exchange opens?

In support of this concern, consider that there are (thin but functioning) after hours trading markets in many securities. In addition, through the use of American Depositary Receipts, it is also possible to trade US stocks on foreign stock exchanges. As such, for many or even most securities, markets are almost always open for those willing to pay higher transaction costs.

That said, there is some evidence that when stock exchanges are closed that markets are meaningfully affected. See, for example, Stock returns and the weekend effect (French 1980).  Stock Market Structure and Volatility  (Stoll and Whaley (1990)) contribute to the litterature showing the expected returns and return volatility are different when stock exchanges are closed, including at night. While both important papers, they provide dated evidence. More recent evidence from Overnight stock returns and realized volatility (Ahoniemia and Lanneb (2013)) shows that shares, while stock markets are closed, continue to show different return volatility from when stock markets are open through 2007.


Why does local non satiation imply the constraint is binding?

The OP is correct in pointing out that "Local Non Satiation (LNS) only says there's a (utility) increasing direction but doesn't say which direction it is increasing". Namely, we entertain the possibility on dealing with "bads" also, not only with "goods". MWG Microeconomic Theory book page 43 Figure 3.B.1 depicts exactly such a situation.

But it is the case that, when the bundle set is $\mathbb R_+$, under LNS not all items can be bads. Because then, the zero vector will be a point of satiation (and so it would violate the LNS assumption).

So using non-negative quantities of items and imposing LNS forces us to consider only the cases where at least one item in the bundle is a good and not a bad, in which case "more is better" for this item.

Then, we can prove that local non-satiation implies exhaustion of the available budget.

Ad absurdum, assume that $px^* < m$. Under LNS for every $\epsilon >0$, there exists a $y(\epsilon)$ that is more preferred to $x^*$. If some $y(\epsilon)$ is feasible, $py(\epsilon) \leq m$, then $x^*$ cannot be the optimal choice in the first place.

So the question is : Is it possible that all $y(\epsilon)$ that are preferred to $x^*$ under LNS, are infeasible, $py(\epsilon)>m,\;\; \forall \epsilon>0$?

I guess the OP can take it from here.


I would guess that this Is due to the variance that exists in the tool used to make predictions about unemployment in the economy known as  Okun's Law. As stated on wikipedia as:

  The gap version of Okun's law may be written (Abel & Bernanke 2005) as:

  ${{\displaystyle (Y-{\overline {Y}})\over{\overline {Y}}}=c(u-{\overline {u}})}$

  where

  ${\displaystyle Y}$ is actual output

  ${\overline {Y}}$ is potential GDP
  ${\displaystyle u} $ is actual unemployment rate
  ${\displaystyle {\overline {u}}}$ is the natural rate of unemployment
  ${\displaystyle c}$ is the factor relating changes in unemployment to changes in output (Econ John: This is also known as the "Okun Coefficient")

From the Usefulness section on wikipedia

  Through comparisons between actual data and theoretical forecasting, Okun's law proves to be an invaluable tool in predicting trends between unemployment and real GDP. However, the accuracy of the data theoretically proved through Okun's law compared to real world numbers proves to be generally inaccurate. This is due to the variances in Okun's coefficient. Many conclude that information proved by Okun's law to be acceptable to a certain degree. Also, some findings have concluded that Okun's law tends to have higher rates of accuracy for short-run predictions, rather than long-run predictions. Forecasters have concluded this to be true due to unforeseen market conditions that may affect Okun's coefficient.

  As such, Okun's law is generally acceptable by forecasters as a tool for short-run trend analysis between unemployment and real GDP, rather than being used for long run analysis as well as accurate numerical calculations.

Hope this helps.


Verifying rationalizability of pure strategy

Yes. Generally, the set of best replies is always a mixture over the set of pure best replies.  In particular, there is never a strict incentive to play a mixed strategy, a player playing a mixed best response is indifferent between all pure strategies in the support of the mixed strategy. All this follows from the linearity of expected utility.


What is consumer debt and how could it make businesses vulnerable?

In the long run, consumers cannot spend more than they earn. In the short run they can spend more, increasing consumer debt, or they can spend less, decreasing consumer debt.

There is a limit to how much consumers are allowed to borrow. The limit is determined by consumer income and the interest rate.

If consumer debt increases faster than consumer income then eventually consumer debt will peak; bank and credit companies will stop lending more money causing a halt to the spending spree.

Note that consumer credit tends to increase market fluctuations. When times are good more people have jobs and consumers with jobs are allowed increased credit. When times are bad you see the opposite.


Which area of Economics involves heavy mathematics and also appears to be directly helping the people?

Some ideas based on the course list:

Environmental economics is doing work to try to understand and mitigate the effects of climate change. Key concepts in this debate, such as common action problems and externalities will feature in EC325 Public Economics.
Game theory is used as a basis for auction theory, which plays a major role in the design of important auctions. Auctions are used, for example, to sell licenses to companies wishing to use the radio spectrum. You can read more about spectrum auctions here.
The market design/matching markets idea is a good one with some real practical applications. For a basic intro, take a look at section 20.5 of this free book. In particular, there is a neat video by Alvin Roth, who won the Nobel prize for work in this area.
Development economics studies the process by which countries do (or don't) escape from poverty and can help us to understand what sorts of policy interventions are likely to be helpful.
Industrial economics (also known as industrial organisation) helps us to understand how competition in markets works (and when it doesn't work). The insights from this field underpin the work of organisations such as the Competition and Markets Authority (the UK's competition regulator) in ensuring that markets deliver good outcomes for consumers. You can read more about competition policy here.


Linearity in Pricing and Duality, UMP EMP

Denote a bundle of goods $\mathbf{x}=(x_1,...,x_n)$ and a price vector $\mathbf{p}=(p_1,...,p_n)$. The cost of any bundle is the scalar product $\mathbf{p}\cdot\mathbf{x}$.

Consider first the UMP, which consists in finding the bundle $\mathbf{x}$ that maximizes utility $u(\mathbf{x})$ subject to the budget constraint that the bundle of good costs less than an income $R$:
$$\underset{\mathbf{x}}{\max}u(\mathbf{x}) \text{   s.t.   } \mathbf{p}\cdot\mathbf{x}\leq R.$$

Consider now the EMP, which consists in finding the bundle $\mathbf{x}$ that minimizes expenditures $\mathbf{p}\cdot\mathbf{x}$ subject to achieving a minimal level of utility $\underline{u}$:
$$\underset{\mathbf{x}}{\min}\mathbf{p}\cdot\mathbf{x} \text{   s.t.   } u(\mathbf{x})\geq \underline{u}.$$

These problems are dual in the sense that you can relate the solution of the first one to the solution of the second one. The solution of the UMP gives you the Marshallian demands, $\mathbf{x}^M(\mathbf{p},R)$, as the function of the prices and the income. The solution of the EMP gives you the Hicksian demands, $\mathbf{x}^H(\mathbf{p},\underline{u})$, as the function of the prices and the minimal level of utility.
The link between these two functions is heavily studied in microeconomics, it is rich in many economic intuitions and useful mathematical relationships.

Duality enables you to find one solution once you know the other. For instance suppose we know the function $\mathbf{x}^M(\mathbf{p},R)$ but we do not know the function $\mathbf{x}^H(\mathbf{p},\underline{u})$, how can we find $\mathbf{x}^H(\mathbf{p},\underline{u})$?
First, denote the indirect utility of the first problem by $v(\mathbf{p},R)=u(\mathbf{x}^M(\mathbf{p},R))$. Second define the income $\underline{R}$ as the solution of $v(\mathbf{p},\underline{R})=\underline{u}$ (the existence of $\underline{R}$ comes from the linearity property that is emphasized in the last sention of the citation). $\underline{R}$ is the minimum amount that is required to achieve utility $\underline{u}$. I will not show, but you can understand intuitively that we have:
$$\mathbf{x}^H(\mathbf{p},\underline{u})=\mathbf{x}^M(\mathbf{p},\underline{R})$$

Lastly, note that we should write $\underline{R}$ as a function of $\mathbf{p}$ and $\underline{u}$ to be rigorous.


How do I calculate the amount of money I get from an investor and the percentage I give him in return?

Well basically it pretty easy to calculate:

A + B + C = X

A:  0.25X : 25% of the company for investors

B:  0.5X : 50% you want to be left with

C:  1M : The price for selling to third party

X:  The value of the company that we would like to find

So in your case it's:

0.25X + 0.5X + 1M = X ->
0.25X = 1M ->
X = 4


Log linearization and Conditional Expectation

You need to remember two properties of derivatives and expectations. Everything else stays the same.

$E(f(x))$ is not equal to $f(E(x))$ unless f is linear.
$\partial E(f(x)) / \partial x$  is equal to $E(\partial f(x) / \partial x)$.

Also remember that as a result, linearizing models with uncertainty reduces them to their certainty equivalent version. This may or may not matter for what you are doing.


Substitutive or supportive factors of production

Let's find the Marginal Product of Labor, $MP_L$:
$$
\begin{align}
MP_L \equiv \frac{\partial Y(K,L)}{\partial L} &=\frac{\partial }{\partial L}\left( aK + b L^{0.5} \right) \\
&= 0.5\cdot b \cdot L^{-0.5}
\end{align}
$$
Now finding $\frac{dMP_L}{dK}$ is trivial:
$$
\begin{align}
\frac{dMP_L}{dK} &= \frac{d}{dK} \left( 0.5\cdot b \cdot L^{-0.5}\right) = 0
\end{align}
$$
We see that it does not depend on the capital. So a change in $MP_L$


Why do we consider purchase of house by households as investment?

Definitions:

Investment is the purchase of any (new) capital goods.
A capital good is any good that is used to produce other goods and services.

A house produces a stream of housing services. Hence, a house may be regarded as a capital good. And thus, the purchase of a house may be regarded as investment.

Note though that definitions and lines in economics can often be fuzzy and there can be grey areas. You are quite right to question whether we should count the purchase of a house as investment. One could argue that we shouldn't. However, by convention in national income accounting, we do, with the above as our rationale.
As noted in the UN System of National Accounts (2008, p. 8):

No matter how simple and precise concepts and classifications may appear in principle, there are inevitably difficult borderline cases which cannot easily be fitted into predetermined categories. ...
The general nature and purpose of the distinction between gross fixed capital formation and consumption, whether intermediate or final, is clear. The distinction is fundamental for economic analysis and policymaking. Nevertheless, the borderline between consumption and gross fixed capital formation is not always easy to determine in practice. Certain activities contain some elements that appear to be consumption and at the same time others that appear to be capital formation. In order to try to ensure that the SNA is implemented in a uniform way, decisions have to be taken about the ways in which certain difficult, even controversial, items are to be classified.

In response to an incorrect comment that claims that "The purchase of a new house is not counted as investment":
BEA glossary:

Consists of purchases of private residential structures and residential equipment that is owned by landlords and rented to tenants.

Blanchard, Macroeconomics (2017, p. A-3):

Residential investment (...) is the purchase of new houses or apartments by persons.

Mankiw, Macroeconomics (2015, p. 27):

Residential investment is the purchase of new housing by households and landlords.

Hubbard & O'Brien, Macroeconomics (2017, p. 255):

Residential investment is spending by households and firms on new single-family and multi-unit houses.


The definition of Eurodollar is (see Investopedia):

The term eurodollar refers to U.S. dollar-denominated deposits at foreign banks or at the overseas branches of American banks.

They are distinct from regular dollars because they are not held within the US, and as a consequence eurodollars are generally not subject to regulations by the Fed (e.g. reserve requirements) and other US banking regulations (like the federal deposit insurance). Since historically in the past most of the dollar denominated deposits were held in Europe (this was to considerable  extent due to the Marshall plan which led to relatively high circulation of dollars in the Europe) they became known as "eurodollars."
If you want to learn more about history of eurodollars and the mechanisms behind them then you can have look at Schenk(1998): The origins of the Eurodollar market in London, or Einzig & Quinn (1964): The Euro-dollar system: practice and theory of international interest rates.


An allocation is defined as being a part of the "core" of an economy if there's no coalition of people that blocks the allocation. A coalition will block an allocation if all of its members could be made better off by another allocation (or, more weakly, if at least one of its members could be made better off without others being made worse off).

And so, by definition, for an allocation to be in the core of the economy, there must not be another allocation which any coalition prefers to the given allocation. And since one coalition that could be formed is the "grand coalition" (i.e. everyone in the economy), any allocation in the core must be Pareto optimal, or else the grand coalition would block it.

This probably isn't much more involved or mathematical than the PPT you pulled it from, but that's because it's basically true by definition.


It's not true that "no-one uses matching these days". It's a bit too definitive. For example, see Bilicka (2019) who recently published in the American Economic Review. I am sure it's possible to find other recent examples.
It's true however that the matching estimator is much less popular than the DiD or IV. This is because the results are not always consistent and robust across estimators. They sometimes differ depending on the estimator used (propensity score matching, PSM, or nearest neighbor matching, NNM) and the way in which the treatment and control groups are matched. It is also sometimes difficult to obtain matched samples that are as comparable as those in Bilicka's paper (see her Table 1).
As an example, there is a well know controversy in the Journal of Econometrics, involving Rajeev Dehejia, Jeffrey Smith and Petra Todd.

Smith, Jeffrey and Petra Todd. 2005. "Does Matching Overcome LaLonde's Critique of Nonexperimental Estimators?" Journal of Econometrics 125(1-2):305-353.
Dehejia response (2005)
Smith, Jeffrey and Petra Todd. 2005. "Rejoinder." Journal of Econometrics 125(1-2):365-375.
Dehejia Final Thoughts

My recommendations would be

to be very specific about how you match your treatment and control groups.
to provide lots of robustness checks to show that your results are not sensitive to a particular estimator, for example, PSM or NNM with Euclidean or Mahalanobis distances.

Good luck with your resubmission!


Below please find a portion of a lecture slide a professor of mine used last year. Please note that $\gamma_{\tilde{y}}$ denotes per-capita output growth, $\gamma_{\tilde{k}}$ denotes per-capita capital growth and $\alpha(t)$ denotes the income share of capital. $R(t)$ - the Solow residual - can then be easily computed.

The production function you have stated was the one we used for this example. So it can be applied here directly.

Source: "Growth and Business Cycles" lecture by Professor Gerhard Sorger, University of Vienna


Perfectly competitive firms. Economies of scale

Put simply, a competitive market is one with a larger number of smaller firms — but economies of scale are best exploited by a smaller number of larger firms.

This doesn’t mean that a competitive market can’t take advantage of economies of scale, just that such a market is only guaranteed to reach productive efficiency if the size of the firm isn’t a factor.


Combining Compliment and Substitue Goods

I will leave the clarity of the question aside.

1) If what is meant by perfect substitutes/complements do not imply that these products are necessarily relevant for the preferences of an agent, then the answer is positive, with the utility function $U(x,y,z)$ being defined as
$$
U(x,y,z)=0 \text{ for all } x,y, \text{ and }z.
$$
2) If it is implicitly understood that increasing $x$ and $z$ together would yield a higher utility and one for one transfer between $x$ and $y$ consumption yields the same utility for the agent, then the answer is negative. The reasoning can be seen as follows.
$$
\begin{eqnarray}
\mathbf{U(1,2,0)}&=&U(0,2,0) \text{ by perfect complementarity}\\
&<&U(1,2,1) \text{ since $x$ and $z$ consumption together is good}\\
&=&U(0,3,1) \text{ since $x$ and $y$ are perfect substitutes}\\
&=&U(0,3,0) \text{ due to perfect complementarity between $x$ and $z$}\\
&=&\mathbf{U(1,2,0)} \text{ since $x$ and $y$ are perfect substitutes}\\
\end{eqnarray}
$$
leading to a contradiction. A general proof can be written when the assumptions are relaxed, but I believe this is sufficiently clarifying.


This means items of daily use did not experience price increases as much as items that are not of daily use.

Let's say half expenditures are on items of daily use. Then an increase of 2.2 percentage points will make these contribute 1.1 percentage points in total inflation. To make numbers match, the remaining 3.4 percentage points of total inflation must then have been contributed by a 6.8 percentage point price increase in items not of daily use.


For question 1), take the expectation of both sides, assume that the expectation of Y is the same in both periods (the definition of stationarity) and see what conditions the coefficients on X must satisfy.

For question 2), try rearranging the equation to be in terms of X and see what determines its variation.

P.S. I am still getting the hang of the mathematical notation on here, but I figure too much working out would be giving it away anyway


Trying to understanding Mark Blyth’s statement about Keynes

Without context, it is unclear what Blyth meant. However, the usual argument runs as follows. The worker starts out with a certain nominal wage, and nominal debts. If wages and prices fall by some percentage, for current spending, the two changes cancel out - goods will cost the same percentage of weekly wages as before. However, the drop in prices does not reduce debt payments, and so those are larger relative to wages.


A doubt on the Regression of Mankiw, Romer, Weil 1992 paper

I had a look at the data, and it is like @denesp says in his comment: e.g. a $2.60\%=0.0261$ population growth rate is written as $2.60$, a $24\%=0.24$ investment-to-output ratio is written like $24.0$, etc.
So they must be divided by $100$.


You have that price elasticity is defined by:

$$\varepsilon_{d} = -\frac{\partial Q}{\partial P}\frac{P}{Q} \approx -\frac{P}{Q}\frac{\Delta Q}{\Delta P}$$

Initially we have $P = P_{1}$ and $Q=Q_{1}$ and after the perturbation we have $\Delta P = (P_{2} - P_{1})$ and $\Delta Q = (Q_{2} - Q_{1})$, therefore:

$$-\frac{P_{1}}{Q_{1}}\frac{Q_{2}-Q_{1}}{P_{2}-P_{1}}=-8 \implies Q_{2}-Q_{1}=\frac{8Q_{1}(P_{2}-P_{1})}{P_{1}}$$

And therefore:

$$ Q_{2}=Q_{1}+\frac{8Q_{1}(P_{2}-P_{1})}{P_{1}}=\frac{8800000}{3} $$

This is so large, partly because the price elasticity is so large, but also probably because of the error in the finite difference approximation method over such large changes in $P$.


What does perfectly inelastic demand imply about gains from trade and domestic consumers?

@VicAche this is incorrect. While the consumer may be willing to pay a large amount, consumer surplus is defined as the willingness to pay minus the price she pays. So if the willingness to pay is infinite as you correctly asserted, then the consumer surplus is also infinite. See my answer to this question.


Do house prices increases affect inflation?

Here's what the Bureau of Labor Statistics' FAQ has to say on CPI and housing costs:

Q: The CPI used to include the value of a house in calculating inflation and now they use an estimate of what each house would rent for -- doesn't this switch simply lower the official inflation rate?
A: No. Until 1983, the CPI measure of homeowner cost was based largely on house prices. The long-recognized flaw of that approach was that owner-occupied housing combines both consumption and investment elements, and the CPI is designed to exclude investment items. The approach now used in the CPI, called rental equivalence, measures the value of shelter to owner-occupants as the amount they forgo by not renting out their homes.
The rental equivalence approach is grounded in economic theory, receives broad support from academic economists and each of the prominent panels, and agencies that have reviewed the CPI, and is the most commonly used method by countries in the Organization for Economic Cooperation and Development (OECD). Critics often assume that the BLS adopted rental equivalence in order to lower the measured rate of inflation. It is certainly true that an index based on home prices would be more volatile, and might move differently from other CPI indexes over any given time period. However, when it was first introduced, rental equivalence actually increased the rate of change of the CPI shelter index, and in the long run there is no evidence that the CPI method yields lower inflation rates than some other alternatives. For example, according to the National Association of Realtors, between 1983 and 2007 the monthly principal and interest payment required to purchase a median-priced existing home in the United States rose by 79 percent, much less than the rental equivalence increase of 140 percent over that same period.

Ordinarily, because people can substitute between renting or owning a house, the price of a house should broadly reflect its rental value (e.g. if it were much cheaper to rent than to buy then people would stop buying and start renting until prices 'equalised'). However, if a bubble is being driven by speculation on future house price increases then it is likely that house prices will become decoupled from the long-run rental value of a house. You can see what this looked like during the last housing bubble in the below figure. It can clearly be seen that house prices (the blue line) were not well-reflected by the owner-equivalent rent included in CPI.


Where to find the latest statistics of brain drain in the world?

Well this is not easy to answer because there is no single measure of brain drain.

For example, many times brain drain is just measured as net immigration from a country (since it is reasonable to assume, and also supported by evidence, that its the smarter and more entrepreneurial people who leave). If you want to measure it by just immigration you could use the UN migration stock data.

Of course, the above approach is very crude. There are other approaches that look migration by education levels. These usually use census data that you can find for every particular country at their statistical office web page. There is also interesting dataset on this commissioned by European Commission, see here, but it only covers OECD countries and its recorded only in 5-year intervals.

There are also some 'fancy' ways how brain circulation can be measured such as by tracking author affiliations, like in this report, but I am not aware of any dataset on this that would be consistently kept up to date. However, nowadays many journals require authors to make their dataset public so you can just search in google scholar the recent articles on this and make data request to journal.


Does Household final consumption Expenditure include Consumption expenditure of Imported Goods

Yes.

Household final consumption expenditure consists of the expenditure, including expenditure whose value must be estimated indirectly, incurred by resident households on individual consumption goods and services, including those sold at prices that are not economically significant and including consumption goods and services acquired abroad.
(From System of National Accounts, 2008, p. 623, PDF).

To elaborate, in the familiar identity $$Y = C + I + G + (X - M),$$ the reason we subtract $M$ (imports) is that the terms $C$, $I$, and $G$ also include imported goods and services.
In particular and to your secondary question, let:

$C_d =$ Consumption of domestically-produced goods and services.
$C_m =$ Consumption of foreign-produced goods and services.

Then: $$C=C_d+C_m.$$
And what I believe you want is $\frac{C_d}{C}$ or equivalently $1-\frac{Cm}{C}$.


difference between screening game and moral hazard game

Moral hazard models feature agents' hidden actions (or these actions are not contractible). For example, a manager's contract cannot determine a wage contingent on the manager's effort, only contingent on other observable outcomes such as "success" / "no success" of a project.

The next two classes of models assume that actions are observable/contractible, but entail different costs to different unobservable types.

In screening models, a principal offers a contract to a privately informed agent. It is not an action, but an inherent type which is not known. For example, a seller does not know a buyer's willingness to pay. Taking the manager example, the principal would offer different contracts for different "manager types" (e.g., "motivated+productive" / "not motivated+unproductive") in which the "effort level" is already set (and by assumption is observable and contractible such as "hours worked"). Then manager types could self-select into the different contracts as working hours are less troublesome for the 'motivated type'.

Another interesting class of models are signaling models. Here the informed party moves first and offers the contract. Taking the same example, motivated managers would offer to work longer for a higher wage which they deserve as they are more productive. The unmotivated manager would love to pocket the higher wage, but the longer hours are too costly for him - so he would not offer such a contract.


What is the difference between constant elasticity of substitution and elasticity of substitution?

Well, you didn't get the math all right, otherwise you might have seen it yourself!

By Elasticity of substitution, you should refer to

$$ \sigma(x,y) = \frac{\mathrm{d}\log \left(\frac{x}{y}\right)}{\mathrm{d}\log \left(\frac{U_y}{U_x}\right)} $$

Then, constant elasticity of substitution is a property of a function $U$ such that for some constant $\bar \sigma$,

$$ \sigma(x,y) = \bar\sigma \, \forall y, x$$

That is, the elasticity doesn't depend on $x,y$. What you showed as $U$ is a function that has exactly that feature. If you compute $\sigma(x,y)$ (do it!), you will see that

$$ \sigma(x,y) = \bar\sigma = \frac{1}{1+\rho}$$

That is, the elasticity of your $U$ function is constant for any allocation. Hence, we refer to that class of function (for different $\rho$) to Constant-Elasticity-of-Substitution-Functions (with share parameters $\alpha$). Cobb-Douglas preferences would be a special (limiting) case of that, with $\sigma(x,y) = 1$

Example

Say, we produce happiness ($U$) with apples ($x$) and oranges ($y$). Lets look at the allocation $\{5,1\}$. We only have one orange, but we would really want more. Hence, we are willing to give up 2 apples to get one orange, and we would be indifferent:

$$ U(5,1) = U(3,2)$$

It is very easy to substitute apples with oranges, we have a high elasticity of substitution.

Now look at the allocation $\{1,6\}$. Do you think that you would again be willing to lose $40\%$ of $x$ to get an increase of $50\%$ in $y$? Is it true that

$$ U(1,6) = U(0.6, 12)$$

If yes, that means that the elasticity of substitution of $U$ (or my rather handwaving approximation to it) is the same at the two allocations $\{1,6\}$ and $\{5,1\}$. If that was true for all possible allocations, $U$ was CES.

There are some reasons why you would think some preferences are perhaps not CES: For example, if $x$ and $y$ are good complements. Then, when you have little of $x$, you're willing to give up a lot for the other, but that elasticity might decrease the closer you are to equality between the two inputs.


Does SARP imply WARP? and GARP imply SARP?

Yes, SARP implies WARP. Since all choices are singletons under SARP, we abuse notation and write $C$ as a function that takes alternatives as values.
We prove the contrapositive, every violation of WARP in a setting where choices are unique give rise to a violation of SARP. So assume there are sets $B$, $B'$ containing $x$ and $y$ such that $c(B)=x$ and $C(B')=y$. Letting $B_1=B$ and $B_2=B'$, you get a direct violation of SARP (I take it you require $x_i\neq x_{i+1}$ in the definition of SARP).

In the context of budget sets, SARP implies GARP. Let $B_i=\{x\mid p_ix\leq p_ix_i\}$. Then SARP says that if $p_i x_{i+1}\leq p_i x_i$ but $x_i$ is the unique choice from $B_i$ for $i\in\{1,\ldots,N_1\}$, then $p_N x_i>p_N x_N$. So the case $p_N x_i\leq p_N x_N$ can never occur; GARP cannot be violated.

Now GARP as usually formulated is a condition on data sets consisting of price-choice combinations. It is not required that the same price system leads to the same choice, so GARP does not imply SARP.


Why is it assumed that covariance equal to $0$ or independence between $y$'s in the simple linear regression model?

The first assumption $E(y|x)=\beta_1+\beta_2 x$ identifies $\beta_2$. The roles of the rest are limited (if not nil) in terms of the identification of $\beta_2$ (identification = answer to the question 'what is $\beta_2$?').

Assumptions other than the first are all "if"s. They are useful for finding properties of OLS estimators, e.g., Gauss-Markov theorem, variance, efficiency, etc.

The third assumption should be written as $cov(y_i,y_j | x_1, \ldots, x_n)=0$ for $i\ne j$. Unconditionally, $cov(y_i,y_j)$ does not have to be zero. (If $x_i$ and $x_j$ are correlated, then $y_i$ and $y_j$ can be correlated.) But under the fourth assumption (nonrandomness), $cov(y_i,y_j)=0$ is equivalent to $cov(y_i,y_j | x_1, \ldots, x_n)=0$.

The fourth assumption is usually not well understood by beginners. It sometimes helps to state that $x_1$ is nonrandom, $x_2$ is nonrandom, and so on (instead of $x$ being nonrandom) in the context of repeated samples.

To the no autocorrelation assumption, it is usually regarded as sensible and acceptable to assume that individuals are independent each other. But it does not mean that it is true. Then what happens if it is violated? In fact, that's the question you want to ask, not why.

If you are doubt about the assumptions, the question goes this way: What happens to OLS and what should we do if the normality assumption is violated; what happens to OLS and what should we do if the heteroskedasticity assumption is violated; what happens to OLS and what should we do if the no autocorrelation assumption is violated; what happens to OLS and what should we do if $x_1, \ldots, x_n$ are random; what happens to OLS and what should we do if $E(u|x)\ne 0$?

So my answer to "why no autocorrelation" is: because it is a leading case and it is believed to be empirically relevant. And its violation does not necessarily mean the model is wrong. It only means that the unobserved determinants are correlated among individuals. The $\beta_2$ is  still the causal effect of $x$ on $y$. The identification of $\beta_2$ is the very starting point. Don't let the tail wag the dog. (That said, someone might want to identify $\beta_2$ by the no autocorrelation condition. This is rather unusual. $\beta_2$ is usually identified by $E(y|x)=\beta_1+\beta_2 x$.)

Related is, I don't think it is possible in general to completely account for autocorrelation by adding more $x$ variables. (For example, family members sharing the same experience but can this factor be sufficiently well observed?) More importantly, adding more variables to the right-hand side changes your model, by which you change the definition of your $\beta_2$. Sometimes you can do it (e.g., randomized experiments) but in most cases your definition of $\beta_2$ changes by changing your model.

My answer pertains to econometrics that tries to find causal effects. There can be other areas of statistics that have different approaches.


How to utilize the projection matrix in econometrics?

This kind of projections in econometrics are usually employed for partialling out some covariates from a linear regression.

Observe that in general $P_X\neq I$. Consider $X=\begin{bmatrix}1&5\\1&0\\1&1\end{bmatrix}$. Then $X'X=\begin{bmatrix}3&6\\6&26\end{bmatrix}$ and $(X'X)^{-1}=\begin{bmatrix}26/42&-6/42\\-6/42&3/42\end{bmatrix}$ then $X(X'X)^{-1}X^T=\frac{1}{42}\begin{bmatrix}41&-4&5\\-4&26&20\\5&20&17\end{bmatrix}\neq I$.

First problem: $X^TP_X=X^TX(X'X)^{-1}X^T=(X^TX)(X'X)^{-1}X^T=I_{(\tilde k\times\tilde k)}X^T=X^T$

Similarly: $X^TM_X=X^T[I_{(\tilde k\times\tilde k)}-P_X]=X^TI_{(\tilde k\times\tilde k)}-X^TP_X=X^T-X^T=0$

The second problem is a direct consequence of $X^TM_X=0$, simply now you can post-multiply for $X_{(i)}$ since you are considering just one single column. The approach of $X_{(i)}=XA$ where $A$ is a vector $\tilde k\times 1$ of 0 apart from the $i$-th element which is 1. Then it should be straightforward to see: $0=(XA)^TM_X=M_XX_{(i)}$


Profit maximization and returns to scale relation

Are you assuming a perfectly competitive market? If so, then a profit-maximizing firm with constant returns to scale (CRS) production can only feasibly earn zero economic profits as $P = MC$ in the long-run. If not, then either $P > MC$ and the firm continues to produce indefinitely until it hits capacity constraints or $P < MC$ and the firm ceases to operate since producing any units would be unprofitable (in which case doubling inputs would be even more unprofitable).

To see this, it's easiest to consider the firm's cost function $C(w, r, y)$. Since the firm's production is CRS, the firm's average cost of producing $y$ is constant and thus $C(w, r, y) = C(w, r, 1)y$. The firm's unconstrained profit maximization problem is thus

\begin{align*}
\max_{y} \prod = Py - C(w,r,1)y.
\end{align*}

Assuming an interior solution, the first-order condition is

\begin{gather*}
\frac{\partial \Pi}{\partial y} = P - C(w,r,1) = 0 \\
\implies P = C(w,r,1).
\end{gather*}

So at $P = C(w, r, 1)$, profits are zero and output $y$ is indeterminate. If instead $P > C(w,r,1)$, for instance, then we are no longer at an interior solution and it is clear that the firm will continue to produce and use more inputs up until capacity constraints bind.


Intuition behind the positive slope of LM curve : 'Income must increase'?

The intertemporal consumption equation is :

$$Y_{1}+\frac{Y_{2}}{(1+r)} = W$$

where $W$ is total wealth and $Y$ is revenue.

When interest rate rise investiment drops and savings rise, so lets say someone choses to save all his revenu from period 1 (this is just to calculate his total wealth), then in period 2 his total wealth will be :

$$Y_{1}(1+r)+Y_{2} = W(1+r)$$

So as you can see his total wealth in 2nd period grows when interest rate grows

Also we can isolate $Y_{1}$ :

$$Y_{1}= W-\frac{Y_{2}}{(1+r)}$$

And you see that when interest rate rises your revenu in period one rises.

I am not sure if this is a valid answer but it seems correct


Expected utility theory (Lottery notation)

$$
\left(\frac{2}{100} \cdot 1000 \oplus \frac{98}{100}\cdot 0\right)
$$
is the lottery where you get $1000$ with probability $2/100$ and $0$ with probability $98/100$.
The expression
$$
20 \sim \left(\frac{2}{100} \cdot 1000 \oplus \frac{98}{100}\cdot 0\right)
$$
usually says that the decision maker is indifferent (in terms of preferences) between taking the lottery and having $20$ for sure.


Question on Central bank loss function interpretation

The loss function reflects the central bank’s policy objective (i.e. their preferences for stabilizing inflation and some real variable around target levels, in this case output), and it says that the central bank is concerned about inflation fluctuating from their target level ($\pi^{T}$) and their perception of the equilibrium output (here reflected in the output gap).

Now, because the objective of the central bank includes two factors (output and inflation), we can know from the loss function how concerned the central bank is about stabilizing the output gap from the size of coefficient $\alpha$. Indeed, at varying levels of $\alpha$ it is easy to see that the reaction of the central bank to the same output gap will differ. Since $\alpha$ > 0 we know that they are concerned about the welfare loss associated with the output gap (if = 0 they would simply not be concerned about this, and if < 0 this would reflect that bigger output gaps are best since the function is to be minimized).

I can imagine that when looking at the geometry of the loss function in the Phillips curve diagram this may become clearer to you as someone from maths.

And just to note that once you derive the policy rule - the slope of the MR curve - (as in your other question), you will see that this policy rule not only depends on the central bank’s preferences $\alpha$ but also on the behavior of the private sector, the price flexibility as given by the parameter $\theta$.


Is $y$ always output per person in DSGE/RBC models?

As far as Gali is concerned he defines (on page 16 of his book) $N$ as "hours of work or employment", noting that "$N_t$ can be interpreted as the number of household members employed, assuming a large household and ignoring integer constraints".

Then on chapter 3 he talks about a continuum of firms $Y_t(i), \ \ i \in [0,1]$ producing the aggregate output:
$$
Y_t \equiv \left( \int_0^1 Y_t(i)^{1 - \frac{1}{\epsilon}}\mathrm{d}i\right)^\frac{\epsilon}{\epsilon -1}$$

But small-case $y_t$ refers to the output of the log-linearized equations. Somebody can use $y_t$ as the logarithm of the Gross National Product, so as I perceive it that, this is not output per person.


What does the adjective "structural" mean in "structural reforms" or "structural effects"?

A structural reform is a reform that literally tries to change the fabric or structure of an economy. A structural reform has to significantly change the regulatory or institutional framework in which economy operates.

For example if a country has inflexible labor market laws and they change them to flexible labor laws that actually changes the structure of economy, the optimal way of how people are hired and fired, the optimal way of how goods and services are produced, workers trained and so on. Often structural reform is used as synonym for supply side reform - which is not entirely correct but not without merit as a supply side reforms are inherently structural in nature as they focus on improving regulations in way that allow for higher production (although some demand side policies can be considered structural as well).

Opposite of structural reform is not non-structural reform but just an reform that will not make much difference to the fabric of the economy. For example, if you have inflexible labor market laws and you just reform your laws to keep them inflexible but maybe modernize them in some way or do some changes that fundamentally do not change how economy operates. Also an reform that would be only temporary, for example for some crisis situation, would not be structural.

A structural effect would again be some effect that has impact on the fabric of the economy. For example R&D can cause structural change in economy. Thanks to the internet now we have all the ride/house sharing services that fundamentally change how taxi or hotel markets operate.


Is there a comprehensive list of all market failures ever discovered?

Market failures often arise due to deviations from the classical assumptions of economics (e.g. Perfect Competition, Perfect Rationality, Perfect Information, Unbounded Computational Capacity, ...etc). There are lists of well-documented and studied market failures and the factors driving them (monopoly is sometimes considered a case of market failure); however, there cannot be an exhaustive list as that would be equivalent to placing a bound on the number of ways people can behave unexpectedly


Why are labor, capital, and land traditionally denoted by the letters L, K, and T?

I'm only guessing (sorry) that $T$ for terre comes from the Physiocrats' work. K for capital is easiest than $c$ (for consumption).

Btw, labor is not always $L$ but sometimes $N$ depending of if you mean labor force vs working population (or hours). And I've no ideas why $N$!


Connection between low demand for US Treasuries and expectation of inflation

There’s a few points to cover in this question.

The description of market events in newspapers is not necessarily reliable. The job of a newspaper editor is to sell newspapers. Readers of the business press like to hear that government borrowing raises interest rates, and so the editors give them that story - a lot. Financial market analysts are paid to give good forecasts, and their explanations are often quite different. (That assertion is based on my experience of writing and reading interest rate commentary.) In this case, the newspaper account may be an accurate reading, but you must keep in mind the prior knowledge that they blame practically every tick up in yields on fiscal policy.
Treasury bond auctions are announced in advance, with the amounts fixed. (They move around money market auctions to deal with fluctuations in cash.) the sizes are based on a lot of consultations with the Primary Dealers and investors, and internal analysis. However, since they fixed the quantity, the price (yield) has to swing. If investors think the yield is too low, it will affect the bids at auction. Going into the auction, there is “when issued” trading, which is based on where dealers think the auction will clear. If they are wrong about demand, actual yields will not end up where the “when issued” pricing was, and the whole curve moves. (Dealers will end up receiving more bonds than they expected, and so will have to trade out of their larger-than-desired duration position.) This dynamic is behind the legitimate stories about tepid auction demand.
The best approximation of inflation expectations is to look at the spread between conventional bonds and TIPS (inflation-linked Treasury securities). The spread roughly equals the future rate of inflation that gives the two securities equal returns. E.g., if the 10-year nominal yield is 4%, and the 10-year TIPS yield is 2%, an inflation rate of 2% results in the two securities having the same return. (One can argue that there are risk premia that drives this breakeven inflation rate away from the true expectation.) There is no guarantee that inflation expectations (by this measure) and nominal interest rates move in the same direction, so one should not use the concepts interchangeably.
The usual explanation for the linkage between higher future deficits and higher nominal interest rates is that “all else equal”, a relaxation of fiscal policy would result in higher nominal GDP (with higher inflation). The presumption is that the Federal Reserve would raise interest rates to keep inflation near its implicit target (offsetting fiscal policy). The expected change in the policy rate affects nominal bond pricing. The exact mix of what happens depends on the specifics of the change to fiscal policy, and your beliefs how fiscal policy works. In any event, all the bond market participants care about is what the Fed does. Otherwise, stories that increasing fiscal deficits raise interest rates run into the counter-example of modern Japan. The debate about that effect is highly political. See also this question: link to question on interest rates and deficits


Is market failure constant? What properly defines it?

I have to intervene to say that market failure and externality are not the same thing. So I do not think it is at all correct to define market failure as

  when "the production or consumption of a good or service causes additional positive or negative externalities on a third party not involved in the economic activity".

Externalities are but one example of market failure. Market failure is more properly defined as any situation in which a market, left to operate without any intervention, fails to produce the efficient (welfare-maximising) allocation.

Sources of market failure include

Externalities: if there is a negative externality then there will tend to be too much of an activity from a social perspective—resulting in inefficiency.
Market power: if the market is not perfectly competitive then firms will tend to increase price above marginal cost to increase their profit. This results in consumers not buying the good even though they are willing to pay more than its cost of production—which is inefficient.
Information asymmetries: If one party in a transaction has an informational advantage over the other then s/he will try to exploit it to the counterparty's detriment. This, in turn will lead to transactions taking place where it would be efficient for them not to (or to mistrust and the failure to realise efficient transactions).
Missing markets: sometimes efficient trades don't occur because the market simply doesn't exist. For example, there is no market to insure against the risk that an unborn child will be born disabled and requiring a lifetime of care even though many parents and their children would like such insurance (an argument often used to for the existence of state-provided social security schemes).

To address your actual questions:

"Don't all activities produce externalities"? Yes, but many of these externalities are priced. For example, if I buy an apple then you can no longer consume that apple, which is an externality. However, this does not result in a market failure because the price mechanism in a competitive market ensures that I get an apple and you don't only if I am willing to pay more for that apple than you are. So the apples go to the people who value them the most, which is the efficient thing to do. Since we are doing the efficient thing, there is no market failure.

So, when should we worry about externalities? We should check whether the net effects can cancel each other out. For example, suppose that the private benefit of some action was lower than the social benefit, but that the private cost was also lower than the social cost by exactly the same amount. Then the net effect would be that MPB=MPC at exactly the same quantity where MSB=MSC. The private individual would then take the socially optimal action and there would be no market failure. A market failure only occurs if the externality is such that MPB=MPC at a quantity different to that where MSB=MSC. Only then will the behaviour of the private individual (whose optimal action is to equalise private marginal benefit and private marginal cost) differ from that which is socially optimal.

A note on marginal benefit and cost:

When performing this kind of analysis, We typically assume that the objective is to maximise to total social welfare (green line), which is defined as the difference between the total accumulated benefit of the activity (blue line) and the total accumulated cost (red line):

The marginal social benefit is the benefit society gains if we increase consumption by one unit. In other words, the MSB is given by the slope of the TSB curve. Similarly, the MSC (defined as the extra cost bourne by society if consumption increases by one unit) is equal to the slope of the TSC curve.

Now, we observe something interesting: the total welfare curve obtains its maximum at exactly the point where the slopes of the TSB and TSC curves are equal:

In other words, welfare is maximised when MSB=MSC. This is not a coincidence for this particular graph, but rather is a far more general property.

This is actually quite intuitive. Suppose that MSB > MSC. If we increased consumption by one unit then society would get MSB units of extra benefit and MSC units of extra cost. Since MSB > MSC, this results in an increase in total social welfare. Similarly, if MSB < MSC then we could reduce consumption by one unit and society would save more in costs than it would loose in benefits. So neither $MSB>MSC$ nor $MSB<MSC$ can be consistent with maximised social welfare. Only when MSB=MSC do we find that there is no way to increase welfare by increasing or reducing consumption.


Is investment a type of saving or expenditure

In simplistic national accounts terms $$Y=C+I+X-M$$ is an  expenditure identity while $$Y=C+S$$ is a use of income identity.

Implicitly this gives $$S-I=X-M$$ suggesting an excess of saving over investment in an open economy corresponds to a trade surplus in the current account, which in turn corresponds to an outflow in the financial account: the excess of savings over investment leads to an increase in overseas assets.

In a closed economy with no exports, imports or international financial flows, this forces $S=I$ and so no excess of saving over investment. Any production not used for consumption or normal investment has the effects either of increasing stocks (another form of investment) or of being valueless (so not counting towards income or saving).


Let me pick up the discussion in the comments.
Consider any diagonal through the origin. Suppose it intersects some IC more than once. Pick two of these points and call them A and B. Because they are on a straight increasing line, one of the bundles, say B, has more of both good 1 and good 2. By monotonicity, bundle B should be preferred over A, which contradicts the statement that they are on the same IC.

If that is what you mean, your intuition is correct. However, there seems to be a jump in your argument: By saying
"if one indifference curve intersects the diagonal line n times (say), then (n-1) points belong to different indifference curves" you seem to be already assuming that the statement to be shown is correct and the n intersections could not exist in the first place.


Each of the aspects mentioned by Kyle points to a useful definition of "liquidity."
Tightness of the market refers to the bid-ask spread, the price difference between the highest bid price across all venues and the lowest offer price across all venues. Theory by Black (1971) suggests that the size at the inside bid and offer will, however, be small. So this measure of liquidity is useful for a small order or a a baseline for larger orders.
Depth of the market refers to the rate at which size cumulates if you add orders sizes moving away from the bid-ask spread. We often model this by thinking first about the slope of those cumulated sizes. If a market has a lot of depth, we can trade large orders and will not need to pay much beyond the bid-ask spread.
Resiliency of prices refers to the rate at which the order book refills. If you were to exhaust the inside bid or ask (or even a few price levels beyond that), resilience measures how quickly those levels will refill with new orders.
For more on these ideas, I would suggest reading up on market microstructure. Hasbrouck's Empirical Market Microstructure is very good as is Foucault, Pagano, and Röell's Market Liquidity: Theory, Evidence, and Policy.


Where is the money that was in the economy pre-lockdown?

A very insightful question. The thing I'll add here is the famous identity, MV=PQ. Essentially you're asking why Q dropped (real goods & services), while M (money supply) likely is the same. There are (at least) two answers:

V (Velocity) could have dropped - which has the same effect as shrinking M. $100 making 10 round trips is very different from $100 making only 1 round trip.
More nuancedly (sp?) - You could be seeing a collapse in the "composition" of the Money Supply. I.e. Maybe M2 collapsed back into M1, etc. If lots of people called in their loans (M2+) & converted to cash (M0), the same amount of money might be there...but it would have been "sucked" from the system, in a sense.


Suppose you are Japanese and you sold your Japanese-made car for say $\$15,000$

You now own $\$15,000$ of a foreign financial asset you did not have before, whether a debt from a US company or individual or US cash or a bank deposit. This is what you are describing as a capital outflow from Japan, though I would call it a financial outflow

You then sell this asset for say $\yen 1,650,000$ which you can use in Japan

You may have acquired these yen from some other Japanese person or company.  They now hold the foreign financial asset, so this does not have a further effect of the international financial position
You may have acquired these yen from some US person or company, or from an entity from a third country.  They now hold fewer financial Japanese assets, so your subsequent negative financial outflow (wiping out your original positive outflow) is balanced by the negative financial inflow (from a Japanese perspective) of the US or other foreign entity reducing its Japanese assets. This negative financial inflow is equivalent to a positive financial outflow


Monopsonistic & competitive labour market, which one is better for the labour buyers?

Having monopsony power means that all suppliers of labour have to come to you to sell their labour. This gives the monopolist the possibility to extract more surplus from the market than in the case of was a competitive labour market.

More rigourously, in a competitive market, labour supply for the individual firm is perfectly wage elastic. The height of this wage (w*, the fixed wage you refer to) is determined at the labour market, where aggregated labour supply meets labour demand, and will equal the value of its marginal product (vmpl, represented by the demand curve).
When the firm has monopsony power in the labour market, it can pay wages lower than the vmpl. That's the benefit of the monopsonist. To the monopsonist, having monopsony power is never disadvantageous.

A graph or some algebra will certainly prove this point.
http://econpage.com/301/handouts/labormkts/monopsony.GIF


Static wage posting model and indifference to wage levels

The profit function is an optimal relation. So it must satisfy the first-order conditions for a maximum:

$$ \text{f.o.c} : w^*: PL' - L - w^*L' =0 \implies L\left[ (P-w^*) \frac {L'}{L}-1\right] = 0$$

In order for this condition to be satisfied no matter what the wage is, it must be the case that, for all wage-levels we have

$$(P-w) \frac {L'}{L}-1 = 0 \;\;\forall w \implies L' = \frac{1}{P-w}L \;\;\forall w$$

Of course this looks exactly like the first-order condition - the critical difference is that it now must hold for all $w$, and so it is not any more a condition that can hold for a specific $w$, but a differential equation in $w$, that falls in the general category $y'_x = f(x)\cdot y$. It can be solved (it is "separable").

I guess you can finish this.


Market structure and price setting: Imperfect competition in the final good sector

One solution to this problem is to use monopolistic competition (sometimes called the differentiated goods monopoly) in the final good sector.  For example, households might consume a continuum of final goods, each different, and aggregated with a constant elasticity of substitution utility function. This is the setting in the hugely influential Dixit and Stiglitz  (1977) paper. The approach of Dixit and Stiglitz is heavily used directly or as motivation in new Keynesian modeling because monopoly pricing power allows for sticky prices.


Was there any use of scoring rules in economics or finance before Hanson published about LMSR?

Hanson wasn't the first one.

"Scoring rules and the evaluation of probability assessors" by Winkler was published in the Journal of the American Statistical Association in 1969 wasn't published in an economics journal but already mentioned economic applications.

Other examples (probably also not the first publications in economics journals, but still earlier than Hanson) are:

Selten (1991), "Properties of a Measure of Predictive Success?" in Mathematical Social Sciences.

Selten (1998), "Axiomatic characterization of the quadratic scoring rule" in Experimental Economics.


Does any international organization (such as IMF) provide data on capital control / financial openness?

Indeed the IMF reports on this. A recent review-overview paper is

Quinn, D., Schindler, M., & Toyoda, A. M. (2011). Assessing measures of financial openness and integration. IMF Economic Review, 59(3), 488-522.

In the introduction, the authors write

  "The aim of this article is to help researchers better understand the range of choices they have in measuring financial integration and
  globalization, the pros and cons associated with each, and some of the
  reasons behind the divergence in findings in the literature. In
  particular, it describes de jure, de facto, and “hybrid” indicators,
  and comparatively analyzes their data properties and how these
  measures relate to one another"

The main "De jure" (as the authors characterize it) resource (on which many scholars have built various indexes using wildly different methodologies) is the IMF's report Annual Report on Exchange
Arrangements and Exchange Restrictions (AREAER)

As the authors write, after presenting the various "De jure" indices,

  "De jure indices of financial globalization do not reflect the extent to which actual capital flows evolve in response to legal
  restrictions, either because of a lack of enforcement, or because
  controls in one area may induce a response in other asset flows. Also,
  even the more disaggregated indices may not capture subtle, but
  possibly important differences between countries’ capital control
  regimes. De jure measures, therefore, do not necessarily reflect a
  country’s actual degree of financial integration, highlighted by the
  fact that even countries with relatively closed capital accounts
  became substantially more financially integrated over the past
  decades... Thus, "de facto", or in some cases “blended,” measures
  present an alternative way to measure a country’s integration into
  global finance markets. These can be divided into three categories:
  quantity-based, price-based, and hybrid measures."

They then move on to a detailed study of many of all the above indices, and they conclude (they have also conveniently summarized qualitative assessments of each index in tables):

  "A key result is that most of the measures provide information that is linked in a meaningful way to economic outcomes. The exception is
  IF-Heritage, an indicator that we found not to be correlated with
  other indices, to have no measurable impact on economic growth, and to
  be linked in the factor analysis to unique dynamics that are not
  easily interpretable. Correlation and factor analyses suggest that
  investigators using de facto indicators of financial globalization
  will find differing identifying variances from those found in the de
  jure measures. In part, this is because de facto measures likely
  reflect the influences of many political and economic factors, of
  which legal restrictions of the capital accounts, as indicated by the
  de jure measures, are but one."

and

  "The bottom line of this paper is that researchers in this field have an unusually large choice of indicators, most of which are valid, with
  unique advantages and disadvantages."


Why are most of open market orders so far from the mid price?

Three suggestions:

Spoofing: some people place buy and sell orders that they do not want executed (so away from the mid-price) to create a false impression of demand or supply , so that the market moves in their desired direction
Catching the flashcrash: occasionally the market has a blip with a temporary gross excess of supply or demand causing a volatile price shift which then returns to close to the original price when other players outside the market notice the unjustified price swing; leaving a bid some way away from the midprice can profit from such events providing that the price returns
Volatility survival: rather like opposing WWI trenches which got further apart over time as proximity became unsurvivable, short-term small-scale volatility will tend to pick off many of the bids close to the midprice, while leaving those further away untouched for longer periods of time

Market regulators tend to regard the first of these as bad (illegal in the US), the second as good, and the third as a natural though undesirable indicator of lack of liquidity


Are white collar workers the blue collar workers of the future?

the long-awaited, long-delayed increase in the efficiency of
  office-work has finally arrived

Actually, so far opposite has turn out to be true. The article was written in nineties, in time of boom of productivity. Contrary to expectations, technological advances did not bring higher efficiency of work. As a matter of fact, the productivity has stagnated, as shown in the data below (note that the chart presents all nonfarm labour, including services, office support, admin., etc.).

Source: U.S. Bureau of Labor Statistics, United States Nonfarm Labour Productivity, 1988-2018

Not only software did not boost the office productivity, it is also one of the major factors of the stagnation - after all there are more distractions than ever in today’s workplace (social media, online games, etc.).

It seems that software designed to monitor employee productivity is not widely used. There are lots of time management apps (like TimeDoctor or WorkIQ, to name the few), budgeting apps, workflow apps, but it cannot be said that they expose
'white-collar workers to the work-place dislocations, mass firings or at least diminishing employment prospects'.

With that being said, there are plenty of white-collar occupations that can be completely automated (for example bank tellers, bookkeepers, basically all the white collar jobs that include collecting and processing data), but that’s another issue. This is one of the main factors why employment in services in US, understood as % of total employment, never went back to the levels prior to the crisis of 2008.

Source: World Bank, Employment in services (% of total employment) in US, 1991-2017

Precariat is something different, but related to the loss of job and overall lack of security in life. It was highly used in public debate amids of the crisis in eurozone (you can read one viewpoint from Guy Standing, who popularized the term).

** As a side note, I used U.S. data, since USA is deemed to be pioneer in technological advances in services, but Japan would be another interesting example.


Theoretical market capitalisation of a crypto currency?

As there is no practical limit on the number of cryptocurrencies that can be created, and as no one crpytocurrency has a unique advantage over any other, and as no cryptocurrencies are legal tender anywhere, the theoretical market cap of any one cryptocurrency has zero underlying value.

What its actual market cap is, will depend on how many suckers can be lured into purchasing it, and what their combined purchasing power is.

Furthermore, even if all your incorrect assumptions were correct, your conclusion would not be: the total capitalisation of all existing sovereign currencies is finite. If they were all to be replaced by a cryptocurrency, then its capitalisation would be much less than the existing total capitalisation of all sovereign currencies, because economic activity would have taken a huge downturn. That's because the world is not an Optimal Currency Area.

This is not to say that cryptocurrencies will never have any value. But at time of writing, there is no visible legitimate application that gives them value.


Why is matching function increasing in arguments?

Think about it this way. The function is measuring the number of new matches being created. If we increase either the vacancies or the amount of unemployed, the function will generate more matches. Therefore, the partial derivatives are expected to be positive.

For example consider the matching function with something other than employment. If we consider a marriage game where we have a pool of single men and women, increasing either the amount of single men or the amount of single women, the amount of new matches created should increase. Note, that while increasing one of the two arguments might not actually increase the amount of matches, at worst it has no impact (such as in the edge case where we have only men and add another man). Since our function only considers new matches created in time T, increasing either argument should have a partial derivative of greater than or equal to zero. i.e. creating more matches.

Imagine now that instead of single men we have active job seekers (analogue to unemployment), increasing unemployment causes an increase in new matches.


People pathologically hoard so much cash that they impoverish the entire nation

But when people pathologically hoard so much cash that they impoverish
  the entire nation

This sentence seems to imply that we should fault the rich not because they are rich, but because they do not spend their riches.

Ok, let's scrutinize this assertion, and not go into philosophical and sociopolitical arguments about inequality, justice, etc, which is a totally different discussion and off-topic on this site (although I suspect that your aunt may in the end has something like this in mind...)

Who said rich people don't spend their riches?

1) Last time I heard, we are all too ready to criticize them for "lavish life-styles". But lavish life-styles cost a lot of money, so it appears they do spend a lot...so part of their riches becomes income for the rest.

But they are still rich!

2) Yes, because most of their wealth is invested in productive economic activities (directly or indirectly through mutual funds etc).

It follows that wealth is NOT "hoarded" - because hoarding means "stash away wealth, don't spend it, don't invest it, just stash it away from any interaction with other humans and economic activities". A "Scrooge McDuck" kind of situation.

This is not what is happening in today's world, and so the specific sentence from this excerpt is simply factually wrong.

Now, the fact that even without hoarding, rich people may stay rich or become richer, the fact that there are people dying of hunger while others live lavish life-styles, in other words the issue of wealth and income inequality could be certainly an on-topic subject here if, indicatively,

a) It was examined as regards its effects on economic efficiency (there is growing evidence that efficiency and distribution are linked and that inequality affects negatively efficiency and economic growth, see for example this recent IMF report)

or

b) It was placed and studied in the context of normative economics (and "normative" is not a synonym for "value judgements" or "opinions"). I would suggest to check this meta-thread on the matter.


Multicollinearity in Transformed model: GLS

For every $k \times 1$ vector $\mathbf c\neq \mathbf 0$, we have that $\mathbf X \mathbf c \neq \mathbf 0$.
Choose $\mathbf e_i$ to be a standard basis $k \times 1$ vector having $1$ in the $i$-th position, and $0$ everywhere else. $\mathbf X\mathbf e_i \neq \mathbf 0$ is a $n \times 1$ vector, and equal to the $i$-th column of $\mathbf X$.
So in block matrix notation we have that

$$\mathbf X = \left[ \begin{matrix} \mathbf X\mathbf e_1\;\; ...\;\;\mathbf X\mathbf e_k\end{matrix}\right] $$

Note that the set of vectors $\mathbf X\mathbf e_i$ also form a basis.
Now,

$$\mathbf C \mathbf X =\left[ \begin{matrix} \mathbf C\mathbf X\mathbf e_1\;\; ...\;\;\mathbf C\mathbf X\mathbf e_k\end{matrix}\right]$$

Since $\mathbf C$ is non-singular (and so of full column rank), and $n \times n$,it follows that the $n \times 1$ vectors $\mathbf C(\mathbf X \mathbf e_i) \neq \mathbf 0$. Moreover they are linearly independent by virtue of the full set of basis vectors used. So $\mathbf CX$ is of full column rank.


How do I distinguish price-taking in perfect competition from monopsony?

You may notice that the price would almost surely vary with the quantity the firm wants to sell if it were operating on a monopsonic market. (Exotic cases when this is not true may be ignored as then competitive and monopsonic markets are indistinguishable). As you are given price and not price schedule, it is a sure indication that market can be considered competitive for any practical purpose.


how to raise utility of an individual having min utility function

Given a utility function of the form $U(a,b)=min\{a,b\}$. Suppose that currently $a<b$. To increase utility, you should allocate more of $a$ to this person until $a=b$ and then increase $a,b$ proportionally.


Multiplant Monopoly With Third Degree Price Discrimination

Hint.
The following are the necessary conditions for profit maximization:
Monopoly with 1 plant and 1 market: $MR = MC$
Monopoly with 1 plant and 2 markets: $MR_1=MR_2=MC$
Monopoly with 2 plants and 1 market: $MR = MC_1=MC_2$
I'll let you figure out the rest.


Is it possible for a Central Bank to escape from a deflation trap by 'hiding' information?

It is certainly possible for a central bank to move the economy away from liquidity trap or deflation trap by proper signals. Signals and targets are undoubtedly effective, as this NBER paper discusses http://www.nber.org/papers/w13932. I read an article, which I cannot find now, saying that signalling and targeting by central banks are sometimes more effective than actual policy changes. The problem is that the economy and financial markets have a huge amount of different players with different interests and goals so it is hard to predict with certainty the effect of the CB revealing certain information.

One thing I have to disagree with is that signalling higher expectations would reduce real interest rates and move the economy away from deflation trap. The equation  it=rt+πt+1 would be more accurate as it+1=rt+1+πt+1. If you write it like that, then you can see that signalling higher inflation expectations would also signal an incoming interest rate hike, given that any central bank has the policy to keep inflation low and stable. When markets expect a rate hike, they reduce their equity and commodity positions (sell stocks, oil, gold etc.) and move into bonds and other cash positions. This sucks the money out of economy and creates more deflation. So if the CB wants to reduce deflation, the ideal strategy would be the opposite: signal sluggish growth and prolonged low interest rates. This is just what Fed has been doing for several years now and, arguably, it has worked.

I can also add, as @ChingG noted in comments, the CB has to maintain credibility and not lie. On top of hurting its reputation, the central bank board members are also liable to the government for saying the truth. For example, if the Fed Chairwoman lied to Congress, she would be breaking the law. It makes more sense for the CB disclose the true data and to interpret the information the way the CB sees fit and give the signals and targets it deems necessary, but not "hide" information.


How are cryptocurrencies reported in GDP?

Mining cryptocurrency can be considered an export of computing processing time, which is paid in a foreign currency (e.g. BitCoin).

The GDP is a measure of production of wealth of a nation. Exports and imports are considered in every method of calculating the GDP. You can read more on how each country calculates their GDP in this Economist article.

It is important to note that the actual GDP for each country is an estimate: it is very hard to calculate accurately the GDP, as you can imagine it is hard to calculate all of the consumption information about a given economy (cash transactions, informal markets, etc.).
However, economists try to include every single expenditure via estimations: the UK includes estimates of drug sales and prostitution as an illustration of the attempts to be accurate. I believe cryptocurrencies could fall in the same category.

Additional reading on the guesstimates of the GDP here.


How to understand share value vs real worth of the company

When a stock price changes, it implies that the present value of future cash flows from the company to investors has changed.

A multitude of different things can change that number, and ascertaining why a stock price changed is often difficult or near impossible.

Simple example: one period cash flow, no uncertainty

Let $r^f$ be the risk free rate. Let $c$ be some cash flow one period ahead.

The present value of the cash flow is:

$$ p = \frac{1}{1+r^f} c$$ And that's what it would trade for in efficient market. Two key observations:

If the discount rate $\frac{1}{1 + r^f}$ were different, then the price would be different.
If the future cash flow $c$ were different, the price would also be different.

Conceptually, the price of a financial asset can be decomposed into some discount rate times the quantity of a future cash flow.

More complicated setup, one period cash flow, uncertainty

With the addition of uncertainty, you get a conceptually similar result: the price of a financial asset should be the inner product of a discount factor with the future cash flow. Let $\mathbf{s}$ be a random variable denoting the stochastic discount factor, and let $\mathbf{c}$ be a random variable denoting the future cash flow. The Law of One Price (LOOP) implies the existence of a stochastic discount factor $\mathbf{s}$ such that:

$$ p = E[\mathbf{s}\cdot\mathbf{c}] $$

Let $\mathcal{F}_t$ be the set of information available at time $t$. As new information becomes available, the conditional expectation will change:

$$ p_t = E\left[\left. \mathbf{s}\cdot \mathbf{c} \, \right| \, \mathcal{F}_t \right] $$

This looks fancy, but it's almost the same idea as the simple, one period cash flow case. The price of an asset today is the product of a discount factor and future cash flows. In an efficient market, changes in asset prices may be due to news about discount rates or news about cash flows!

If the share price triples, that's almost certainly due to positive news about future cash flows. Small changes though, or changes at the level of the overall S&P500 index are trickier.

Practical Implications

In the fall of 2008, the stock market collapsed! Asset prices fell. What did this mean though? The decline may have be due to declining expectations of future cash flows from the corporate sector. But it also may have been due to rising discount rates, that risky future cash flows were being assigned a lower price! In a strict sense, disentangling discount rate news from cash flow news is nearly impossible. In general though, when looking at an individual company, you're almost certainly seeing more variation due to cash flow news than discount rate news, but strictly speaking, there's no way to make a clean decomposition.

Sensitivity of the current price to future cash flow news...

A number of features can make the price very sensitive to news:

Leverage: If a company has a lot of debt and is near bankruptcy, the cash flows to equity may be massively different depending on whether the company survives or not.
Time horizon: How much is something like Uber worth? Will it take over global transportation with robotic, AI vehicles? Or will it sink under a morass of rising labor costs and government regulation? The big payoffs from something like Uber are in the distant future, and forecasts of the distant future may be volatile, sensitive to certain types of news.


Utility function types - request for review

Currently (Dec-1-2015) I see listed Linear, Leontief, Cobb-Douglas, and Maximum.

To incorporate here a comment by @denesp the C.E.S utility function (that nests the Leontief and Cobb-Douglas) should certainly be included

$$u(x,y) = B\big(ax^{-\rho}+(1-a)y^{-\rho}\big)^{-1/\rho}$$,

(which also is a functional form that has non-zero cross partial derivatives),

as should the quasi-linear form

$$u(x,m) = h(x) + m$$

which is very often used, with $m$ standing for residual money income (what's left after purchasing $x$).

I would also include the Translog utility function.

Finally, I think you should increase the scope of the page and also include in a separate section univariate utility functions that are used in environments with uncertainty and in macroeconomics (say, the HARA class of functions). We may keep in our minds these subfields of economics clearly distinct and also from basic consumer theory, but what you build is a wiki page that is likely to be visited by outsiders (e.g. mathematicians or engineers interested in the subject) or just-arrived students, so a broader scope appears useful.


I think that you are more or less than correct in thinking that cash that is never spent (nor expected to be) may as well not exist. Thought experiment: suppose that, unbeknownst to you and everyone else, £1 million suddenly appears under your mattress. If you never discover the money, it is hard to see how it could change anything in a meaningful way.

There are some caveats, however. First, a game theoretic point: even if rich people never spend their money, threats to spend their money might influence outcomes. For example, they could pledge to donate lots of money to the political opposition unless the government does what they say. If this threat works, they will never need to pay out.

Second, a ‘non-economic’ point: money gives you options, and people might enjoy having options in itself (even if they don’t spend the money). One might object to the kind of ‘options inequality’ brought about by an unequal wealth distribution even if rich people never spend their cash.

Third, to bring us back to the real world, we should stress that, usually, rich people do consume more than poorer people. So while it might be interesting to discuss wealth inequality without consumption inequality, this is not a phenomenon which we are actually facing today.


Why does a currency devaluation make a country more attractive for foreign direct investment?

A depreciation in the Yuan will result in an increase of Chinese exports as where countries compete on price for goods like steel and tires the demand is very elastic. A small change in price will lead to a large shift in the quantity demanded. India knows this and after a succession of poor last few months exports will stand to lose out even more now that the Yuan has devalued.

Also now that China has changed its exchange rate, China could be leaning to a more flexible exchange rate (which the article suggests) opening up for an increase in capital mobility which investors look favourably upon. The devaluation of the yuan has also decreased the price of Chinese assets thus making it cheaper to invest.

It is likely that the further reduction of the price of Chinese exports will cause the currency to appreciate once again as demand for Chinese goods increases. Some investors will take on Chinese assets and currency, predicting the currency will appreciate in the future, resulting in a nice profit.

Finally as India's export reliant sectors struggle to compete with supplying major industries around the world,  the drop in market share will be swallowed up by China resulting in more attractive Chinese businesses (which may be open to FDI). India is also struggling to supply its domestic industries as it cannot compete on prices. This uncertainty around India and its lacklustre performance will likely see FDI being pulled out and reinvested into more lucrative opportunities.