Did the Marshall Plan cause Western Europe's economic expansion after WWII? It is widely accepted, that the Marshall Plan had a major role in the economic recovery of Western Europe after the end of the Second World War.
The reality is that the total economic support was less than 7% of the 1946 GDP (PPP) of the region. How could that have any statistical significance?

In the period between 1943 and 1945, the GDP (PPP) of Western Europe fell by more than 19%. So, was that caused because there was no Martial Plan then? :)

Before the Keynesians jump on the multiplier effect bandwagon, I would point out, that the US quantitative easing after the 2008 economic crisis was 3.5 trillion USD, which is 20% of the 2013 US nominal GDP.

Barry Eichengreen is one of my favourites for this period. So, I am just going to let him explain it.
From : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.207.1592&rep=rep1&type=pdf

Our central conclusion is that the Marshall Plan did matter. But it
did not matter in the way that the “folk wisdom” of international
relations assumes. Milward (1984) is correct in arguing that Marshall
Plan aid was simply not large enough to significantly stimulate
Western European growth by accelerating the replacement and expansion
of its capital stock. Nor did the Marshall Plan matter by financing
the reconstruction of devastated infrastructure, for as we show below,
reconstruction was largely complete before the program came on
stream.
The Marshall Plan did play a role in alleviating resource
shortages. But this channel was not strong enough to justify the
regard in which the program is held. By 1948 and the beginning of
Marshall Plan aid bottlenecks were scarce, and markets were good at
alleviating their impact. Rather, the Marshall Plan significantly sped
Western European growth by altering the environment in which economic
policy was made. In the immediate aftermath of World War II
politicians who recalled the disasters of the Great Depression were
ill-disposed to “trust the market,” and eager to embrace regulation
and government control. Had European political economy taken a
different turn, post-World War II European
Wartime relief, post-World War II UNRRA aid, and pre-Marshall Plan
“interim aid” may well have significantly speeded up the
reconstruction process. ... recovery might have been hobbled by clumsy
allocative bureaucracies that rationed scarce foreign exchange and
placed ceiling prices on exportables to protect the consumption of
urban working classes. Yet in fact the Marshall Plan era saw a rapid
dismantling of controls over product and factor markets in Western
Europe. It saw the restoration of price and exchange rate stability.
To some degree this came about because underlying political-economic
conditions were favorable (and no one in Europe wanted a repeat of
interwar experience). To some degree it came about because the
governments in power believed that the “mixed economies” they were
building should have a strong pro-market orientation. Marshall Plan
aid gave them room to maneuver in order to carry out their intentions:
without such aid, they would have soon faced a harsh choice between
contraction to balance their international payments and severe
controls on admissible imports.
To some degree it came about because
Marshall Plan administrators it pressured European governments to
decontrol and liberalize even when they wished to do otherwise. In
post-World War II Western Europe the conditions imposed, formally and
informally, for the receipt of U.S. aid encouraged the reductions in
spending needed for financial stability, the relaxation of controls
that prevented markets from allocating resources, and the opening of
economies to trade. Marshall Plan “conditionality” pushed governments
toward versions of the “mixed economy” that had more market
orientation and less directive planning in the mix. While postWorld
War II European welfare states and governments are among the most
extensive in proportion to economic life in history, they are built on
top of, and do not supplant or bypass, the market allocation of goods
5 and factors of production. The Marshall Plan should thus be thought
of as a large and highly successful structural adjustment program.


Mixed strategy Nash equilibrium in 3x3 game What is the MSNE for the following game?

I think you can eliminate strategies $A$ for player 1 and $C$ for player $2$, as these will are weakly dominated by all other strategies. Then, the game becomes a 2x2 game with $B,C$ for $1$ and $A,B$ for $2$.

let $q$ and $1-q$ be the probability $2$ plays $A$ and $B$ resp, and $p$, $1-p$ the probability $1$ plays $B$ and $C$. Then in equilibrium $q=1/4$ and $p=1/3$. Then the equilibrium is

$$(0,1/3,2/3); (1/4,3/4,0).$$

Is this correct?

The general procedure to solve for a MSNE in a 3-by-3 (or larger) game is always a bit tricky and involves some trial and error

Step 1: Conjecture (i.e. guess) a subset of strategies that will be used in equilibrium
Step 2: Calculate their probabilities using the indifference condition
Step 3: Verify that the equilibrium payoff cannot be unilaterally improved upon; that is, no player has a strict incentive to deviate to another strategy

Suppose your conjectured strategies are $\{B,C\}\times\{A,B\}$ (it doesn't really matter what the basis for your conjecture is; you're going to find out one way or another whether that's correct). Next, calculate the probabilities using players' indifference conditions. Let $p=\sigma_1(B)$ and $q=\sigma_2(A)$, we have
\begin{align}
-3p&=-1&&\Rightarrow\quad p=1/3\\
3q+1-q&=1-q&&\Rightarrow\quad q=0.
\end{align}
[This suggests that your calculation for $q$ was incorrect.]

Lastly (this is the most easily forgotten step), check that no one has an incentive to deviate from this equilibrium. In this case, player 1's payoff is $1$, which is already highest given player 2's strategy of choosing $B$ with probability 1. He'd be indifferent between mixing in other proportions over $B$ and $C$, and his payoff is strictly lower if he plays $A$ with positive probability.

Player 2's expected payoff in this equilibrium is $-1$, which is also the highest given player 1's mixed strategy. She's indifferent between mixing over $A$ and $B$ with any other proportions and is strictly worse off if $C$ is played with positive probability.

So, one MSNE is $((0,1/3,2/3),(0,1,0))$. This is only borderline consistent with your initial conjecture because $\sigma_2(A)=0$. But it's nonetheless a MSNE. In fact, there are infinitely many MSNEs of this form: $((0,p,1-p),(0,1,0))$ where $p\ge1/3$. This is a full description of all equilibria (including the pure one) in this game.


please help describe a) what exactly is the Paradox of Profits , b) what is the argument of these papers exactly here are 3 papers that discuss it.
it seems to me that the paradox is that, supposing a closed economy has money M raised through bank loans, then, while that economy can create goods and services and thus can grow in real terms, (ie there are aggregate real profits) it seems that there cannot be any aggregate monetary (nominal) profits since the amount (stock) of money in the economy does not change.

Marx says that under a closed economy under the gold standard , money supply can grow only via finding new gold in gold-mines , and it is ridiculous to think that profits will be equal to the gold found.

It relates to the income/expenditure/output identity of National Income Accounts / NIPA which says that income = expenditure , therefore profits = 0

https://keenomics.s3.amazonaws.com/debtdeflation_media/papers/9780230_203372_10_cha09.pdf

http://www.economics-ejournal.org/economics/journalarticles/2010-31/version_1/at_download/file?fbclid=IwAR0Le51-

http://www.economics-ejournal.org/economics/discussionpapers/2009-52/file

You largely answered this question yourself: you provided this reference to a Gennero Zezza paper: (link to paper)

Zezza states in the second paragraph that most of the thinking about the Paradox of Profits was mistaken, as the authors used models which were not stock-flow consistent (flows disappeared). If people are arguing that there is a paradox, but do the accounting wrong, it is difficult to explain the error - since their arguments are internally inconsistent.

I am not familiar with Marx’s arguments, but based on the question, he is making an argument about a fixed money supply. This adds an extra constraint, that is probably not addressed in the Zezza papper.

For a single time period, there is no difficulty in generating profits. The business sector starts with \$100, pays \$90 in wages, \$10 in dividends, and then the household spends all money received to buy goods - generating \$10 in profits, which is enough to cover the dividend. Profits can be achieved also by the business sector investing in fixed capital or inventories. In any event, this can be achieved with a fixed money supply.

The only challenge is generating a steady state. Can a fixed money supply co-exist with a growing economy in steady state? This is perhaps a challenge, but the reality is that even non-financial entities can issue instruments that are used as money if the money supply is constrained. (For example, the pre-Confederation Canadian colonies had a perpetual shortage of coinage, and a wide variety of entities issued tokens that circulated as money). Since it is hard for a society to survive without government, government-issued money is normally issued in a way to grow in line with the economy.

Marx was writing in an era before fiat currencies had shown much ability to survive. My understanding is that his thinking did not take into account the flexibility of fiat systems.

In summary, since the argument that profits are paradoxical is based on faulty logic, it’s difficult to explain where the problems lie. One would need to delve into the details of each argument, and determine where they made the error - and it’s not necessarily always the same error.


Using web scraped data for consumer price indices Is there information and literature regarding comparative consumer price index methods? Specifically, the web scraping method of index construction?

Take a look at Billion Prices Project:

  The Billion Prices Project is an academic initiative that uses prices
  collected from hundreds of online retailers around the world on a
  daily basis to conduct economic research.

Also take a look at PriceStats

  PriceStats collects online prices to provide daily inflation updates
  for 22 economies.

Overview of the PiceStats approach

More broadly, price index construction is a huge literature full of pitfalls so it is difficult to point you to a generic but also advanced presentation of the issues. But you might start with Consumer Prices, the Consumer Price Index, and the Cost of Living (Boskin, Dulberger, Gordon, Griliches and Jorgenson (1998)), a Journal of Economic Perspectives piece on the subject.


How do I represent this indifference curve graphically? I am not able to visualize this indifference curve.

I consume only two goods: sugar and milk.

I will prefer a bundle X of sugar and milk over a bundle Y only if $x_{sugar} > y_{sugar}$, and $x_{milk} > y_{milk}$.

If $Y_{sugar} > x_{sugar}$ and $y_{milk} > x_{milk}$, then I prefer Y bundle over X.

If neither case is true, I am indifferent between the two bundles.

How do I plot this on a graph? I need to solve a question, and I believe being able to draw a graph will be helpful!

This is how I visualize it. Is this representation correct?

The problem is that there are no indifference "curves" but indifference "areas". Consider the following graph:

For a reference bundle $A$ (equivalent to $\{2,3\}$), the gray regions indicate the areas of indifference, based on your definition of preferences (the black lines are part of the indifference areas).

Thus, by selecting any bundle, you can find the indifference "areas" by plotting the vertical and horizontal lines across that point. Areas to the North-West and South-East will always be the indifference "areas".

For reference, this is the R code to generate the graph:

remove(list = ls())

a=2
b=3

plot(c(0,5), c(0,5), type = "n", xlab = "Sugar", ylab = "Milk", xaxs="i", yaxs="i")
rect(0, b, a, 5, border = NA, col = "grey60")
rect(a, 0, 5, b, border = NA, col = "grey60")
abline(h = b, col = 1, lwd = 2)
abline(v=a, col = 1, lwd = 2)
points(a, b, type="p", pch=19, col="black", bg=NA, cex=2)
text(1, 4, "Indifferent",cex = 1.3)
text(3.5, 1.5, "Indifferent",cex = 1.3)
text(1, 1.5, "Worse off",cex = 1.3)
text(3.5, 4, "Better off",cex = 1.3)
text(2.2, 3.3, "A",cex = 1.3)


Does inflation equal change in M1 or M2? According to monetarism, inflation can be predicted precisely by the change in money supply and GDP growth.
Does "money supply" here refer to M1 or M2, i.e. does it include debts created by private banks?

The money supply is in theory interpreted broadly so from that perspective $M2$ or even $M3$ would be more appropriate. Also empirical studies in this strand usually use $M2$ see for example Sargent and Surico (2011).
However, you should note that nor the quantity theory of money nor monetarism claims inflation can be predicted solely by change in money supply and GDP growth.
Simple quantity theory of model is given by:
$$P=MV/Y$$
Where $P$ is price level, $M$ money supply, $V$ velocity of money and $Y$ real output. In more complex models expectations of these quantities matter as well. Hence it does not make sense to equate inflation to changes in $M$.
Furthermore, even though the above relationship is useful for structural modeling and creating analytical models it is practically useless for near term forecasting. If that’s your ultimate aim you would have more luck with augmented New Keynesian Philips curve.


Why, in general, do product or service prices rise in time? My question is simple:
Why is it, in general, that the prices of products or services (regardless of demand and supply) are always on the rise in western society? For example, the rent we pay increases every year. The ticket prices for public transport are getting higher every year. The costs of living: higher every year. On the other hand, money income from labor also rises. Why can't they stay stable? Is this inherent in the western economical model?
Or is it because of the constant battle between employees and employers? Which leads to a spiral of ever-increasing prices. Employers ask higher prices, employees higher wages, after which the employers increase the prices, etc.
Government policies can intervene, of which communism is the ultimate example, but that's based on a non-capitalistic economic model, though in the former USSR the number of products increased just as well, although they were state possessed. The visible material world in the former USSR, for example, how the cities and infrastructure looked like didn't differ, that much from how our cities look like. Economic growth and activity took place there too. Hospitals improved, technology in general (the space program among it) made progress, there was a separation between people who lived in bigger state-possessed houses (these were the people who had the power in the state: the employers) and cars different from the Lada, obliged to buy for the employees in the state. It was more uniform though and those who diverted from the norm were put away (as is the case in western societies, calling themselves somewhat arrogant, part of the first world, and communist countries the second one; in current times the borderline between the two has blurred or has vanished altogether). The system, although totally state-controlled, did provide for everyone (as long as you conformed, but that's the case in western societies too, where in fact it provides for everyone too, and also with huge differences between the employees or the employers). And it's a fact that the gap between the people who have a huge amount of private possession and those with a small amount is ever-increasing. Which was also the case in the former USSR but not on such a big scale as in the western world in which we now live. And who cares if you live in a privately owned house or a state possessed house? Only the rich people here, I guess. The more they possess, in general, the more they long to possess, like an addiction. Let it be clear though that communism, as well as capitalism (just look at the national debt of the U.S.A.: 14 000 000 000 000$!), is not my cup of tea!
All of this as an aside though.

Prices increase over time generally because of inflation. Money does not have constant value over time $\\\$1$ in 2010 is not equal to $\\\$1$ in 2020. As you mentioned in your question you can observe that not only prices of products and services increase but also wages. This is precisely because money is becoming less valuable so the same value embedded in work as well as in products and services require more money.
There are various reasons why value of money might decrease over time. Following Blanchard et al. Macroeconomics an European Perspective (a standard undergraduate macro textbook) the money market equilibrium (where the value of money is determined) can be expressed with the equation of exchange as:
$$MV=PY$$
where $M$ is the money supply, $V$ velocity of money, $P$  the overal level of prices  in the economy and $Y$ real output. This model is a bit of an oversimplification in more complex versions expectations of these variables are important as well but for this question it will do. We can solve the model for prices to get:
$$P= MV/Y$$
Hence prices can change either if:

$Y$ drops. This is because if the number of goods and services in the economy decreases but the amount of money and velocity remains fixed the same amount of money will chase lower amount of goods and services which will bid up all prices across an economy. However, it is worth noting that this is not the cause of inflation that we see over long period of time as most economies are on net basis growing (i.e. $Y$ is increasing) with an occasional recession which interrupts the growth.
$M$ increases. The mechanism is similar as with drop in $Y$ but now the amount of money increases in the economy and the number of goods and velocity remains constant. In modern economies $M$ is controlled by government institutions most often by central banks which can contract or expand $M$ directly or indirectly in various ways. Over long periods of time most economists believe that inflation is caused by increase in the money supply so this is the major reason why you will see the inflation going up over long periods of time.
If $V$ increases. Velocity of money is the average number of times a bill is used to purchase goods and services. It tells us how fast are money circulating in the economy. Generally the more faster the money circulate in the economy the higher will be the inflation rate. $V$ changes over business cycle, generally dropping in recessions and increasing in expansion but over long periods of time it remains more or less constant.
Some combination of all of the above.

Why can't they stay stable?

They can be stable. This is ultimately a policy choice, there were historical periods of near zero inflation and in principle central banks/governments, which control $M$ around the world could achieve long term price stability if they wanted (even though they might not be able to do it precisely every single year due to random economic shocks they can do that on average over business cycle).
However, as pointed in the link Brian provided in his +1 comment most economists believe having certain level of inflation is desirable. This was already answered excellently by FooBar so I wont be repeating it here.

Is this inherent in the western economical model?

First of all what is 'western economical model'? Currently almost all countries around the world have a mixed economy - a system that combines free market with central planning. For example USA, South Korea, Japan, UK, Denmark, South African Republic, Russia or China are all mixed economies. Countries differ in the quality of their institutions in policies they follow and in many aspects but looking at the big picture most countries around the world follow the same economic system. Few exceptions would include countries such as North Korea.
Second, inflation is actually  much lower in 'the west' (i.e. Europe and North America and other countries that are colloquially known as 'western' such as Australia or New Zeland) then elsewhere as the data from IMF for year 2019 below show. Feel free to look at any recent year in the IMF dataset and 'western' countries will be always among those with lowest inflation rate.
This is however not due to following some fundamentally different economic system but rather due to different institutions. Most western central banks are independent from government with a mandate that either completely or partially requires them to maintain low inflation. Also just to be clear I am guessing that by 'west' you are not meaning just a western hemisphere which includes many African or South American Countries, but rather you mean nations with roots in the Western Europe (i.e. USA, UK, France, Canada, Australia etc.).
    Region                       Average Inflation Rate in % 2019
    South America                      no data
    Western Europe                      1.3
    Australia and New Zealand           1.6
    Europe                              2
    North America                       2
    Central America                     2.2
    East Asia                           2.3
    Southeast Asia                      2.3
    Caribbean                           2.8
    Pacific Islands                     3.2
    Asia and Pacific                    3.3
    Western Hemisphere (Region)         3.4
    Eastern Europe                      3.9
    South Asia                          4.8
    Middle East (Region)                7.9
    North Africa                        8.2
    Africa (Region)                     9.2
    Sub-Saharan Africa (Region)         9.7
    Central Asia and the Caucasus      11.9


Are Cobb-Douglas preferences monotone according to the marginal utility condition? I understand that Cobb-Douglas preferences represented by $U(x,y)=x^ay^b$ are strictly monotonic, because increasing at least one of the goods in the bundle increases utility.
However, another definition of strict monotonicity says that marginal utility of each good should be strictly positive. This is not the case with the above function at $(0,0)$. Is there a way to resolve this?

They do not satisfy either condition. An increase in the quantity of one good need not increase utility; $U(0,1)=0^a1^b=0=0^a2^b=U(0,2)$.
The condition that all marginal utilities must be positive is inherently problematic because it does depend not just on the underlying preferences. For one, not every utility representation needs to be differentiable. But even that is not enough. Suppose there is a single good and more is better than less. You can represent these preferences by the utility function given by $U(x)=x$. Now $U'(x)=1$ for all $x$, so these preferences are supposedly strictly monotone. But now consider the utility function given by $V(x)=(x-1)^3$. If $x'>x$, then $V(x')>V(x)$, more is better and $V$ represents the same preferences as $U$. But $V'(1)=0$, so the preferences are not strictly monotone according to the definition in terms of marginal utilities.
The problem just mentioned is actually even worse. Let $U$ be a differentiable utility function on $\mathbb{R}_+^2$ with strictly positive partial derivatives everywhere. Let $(x^*,y^*)\gg0$be any commodity bundle. Define $V$ by $$V(x,y)=\big(U(x,y)-U(x^*,y^*)\big)^3.$$ $V$ represents the same preferences as $U$ but the partial derivatives at $(x^*,y^*)$ are zero.
Long story short: Every partial derivative being strictly positive is a sufficient but not necessary condition for a differentiable function to be increasing in every coordinate.
Yet another issue is that it is not entirely clear how one defines the derivative at the boundary of the commodity space. There are different notions of differentiability which need not be equivalent.


Does Inflation Make Money Eventually Worthless? I used this calculator: http://www.buyupside.com/calculators/inflationjan08.htm
to estimate the future worth of 100 dollars in 100 years at 2% inflation. Does this really mean that a decent meal at a restaurant will cost about a $100 in the future or am I misunderstanding something? So basically what I'm asking is if at some point in the future will McDonald's Dollar menu become the Hundred Dollar menu?

"Worth less" than before - yes, that's exactly what inflation does.

"Worthless" - not quite. No percentage-based reduction in value can make something worth 0, but there are extreme examples from history of times inflation has spiralled so far out of control ("hyperinflation"), money became worth less than the paper it was printed on, and life savings became almost worthless.

1920s Germany is the most famous example, but there are more recent examples, such as Zimbabwe.

This is a real Zimbabwean banknote from 2009 - you don't need the terrifying inflation rates to see that savings of thousands of Zimbabwean dollars made in the early 2000s had become effectively worthless:

But those are extreme examples.

As for the idea of a McDonald's $100 Menu - it wouldn't be unbelievable looking at history.

According to measuringworth.com, $1 one hundred years ago would buy the equivalent of $24 of common retail goods and the equivalent of $99 of the time of an unskilled labourer. A time-traveller from 1914 would expect a "$1 menu" to be high quality dining, worth days' wages for the average Joe. Not so different to how the idea of a $100 menu seems to us today,

This seems like a big change - but even this is a small change by international standards.

The US dollar has historically been one of the world's most stable currencies, partly related to its use in international trading and its status as a reserve currency. In other countries, even countries with relatively stable economies, such changes do happen in a person's lifetime. Here in the UK, it's a cliche for elderly people to complain that "in our day", meals could be bought for sums of money that today would considered small change.

But even though it'd be perfectly believable, it might not happen. Beware of extrapolations that assume trends won't change (cartoon from XKCD):

Anything could change. The US dollar might not keep its current world status. Governments influence inflation, and may sometimes simply change currency values if they feel it's getting out of hand. For example, in 2005 Romania knocked 4 zeros off its currency. 10,000RON became 1RON overnight.


Is there a game that cannot be represented by a game tree? Is there a finite game that cannot be represented by an extensive form or a game tree?

I know that many games are too long and complex to be represented by a tree of a reasonable size, but that's not what I'm looking for because it is in part a computational limitation.

Instead I wonder if there is something simple out there that just doesn't fit into an extensive form? All the books that I've read say something like

  Various games can be represented by trees

But I haven't seen "all games" claim anywhere. Are there any known exceptions?

Well, for this you need to define what a "finite game" is. The usual way to do so, is to define it as an extensive form game, which makes the whole issue circular. But there are different ways to model extensive form games at different levels of generality. For example, the first definition due to John von Neumann and Oskar Morgenstern made a number of strong restrictions on timing that look somewhat archaic from today's perspective. The subsequent definition by Harold Kuhn significantly generalized the class of possible extensive form games. An implicit restriction in the way Kuhn defined extensive form games was that no player is allowed to move through the same information set twice, an assumption weakened in the Ph.D. thesis of John Isbell. So there are various notions of extensive form games at various levels of generality, including versions that allow for infinite games.


Interpreting 10-YR TREAS 21/32 yield 2.913% As I see the WSJ front page, I saw 10-YR TREAS 21/32 yield 2.913%.
I know what the yield means but I don't know what the 21/32 means and how it relates to the yield. Could you please tell me?

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.


What actually went wrong in the economy as described by "The Big Short"? Part of my personality is Engineering, so I look for root causes. I suppose that the cause of any bubble is "speculation", which just means pretending that ghosts are real, or that the word "LION" is an actual Lion. (So ironic when it eats you.) But because this has happened before, would someone please explain the chain of causality from people buying houses to the world economy nearly failing, through the sideroads of drinking and strip clubs? Was it just that people were selling the "actual value" of a long term asset like a house or land, and using it to buy immediate disposable things with no value, like drinks and entertainment?

What is the basic human failing that allows people to seem to do this repeatedly and not learn from it? I don't want to hear "greed". Greed is one person acting one time. I mean: how can people believe in ghosts? How can many many people pile on thinking that something holds up the entire scheme, and that it will not eventually come crashing down and crush them inside? How can people make this particular mistake? "Stupidity"?

The problem at the bottom of the 2008 crash is that the values of multiple instruments were dramatically over estimated because the risk of default in the various underlyings was dramatically underestimated since it was assumed that they were fully backed by the US government.

Although many commentaries focus on the securitization of debt that was not where the real problem lay, in fact the securitization of sub-prime mortgages into CDOs (collateralized debt obligations) covered by CDSs (credit default swaps - a type of default insurance) was as a result of firms wanting to divest themselves of risks surrounding unknown quantities.

In the (first?) Clinton and Bush administrations there was a political will (rightly or wrongly; it isn't important) to help people buy their own homes. This applied particularly to low income families who previously had not been able to buy, in many cases for generations. To do this bills were passed to offer subprime loans with the implicit backing of the US government. Since these people had never been mortgage borrowers before their ability to repay was not well understood or modelled and came with an assumption that they would continue to have jobs and that their homes would be worth at least what they paid for them. These extra buyers put upward pressure on the housing market (i.e. buyers exceeded sellers so prices rose) meaning that it looked like that latter assumption would prove true at least.

The mortgage companies then had a large tranches of debt on their books that, although apparently backed by Sam, were riskier than their previously core business. To mitigate this risk they rolled them up into CDOs which, given that the probability of any one loan defaulting was taken to be independent of any and all others defaulting, supposedly held lower risk than the individual loans. To further reduce default risk these were further rolled up with high credit rating corporate, municipal, and national bonds. In case there was a default in these wrappered securities insurance companies, such as AIG, wrote CDSs that would pay out a sum to cover losses in return for premia (as is usual with insurance).

Then the economy slowed down a little, house prices started to stall, and unemployment rose. As people who were the borrowers in these subprime mortgages had wages cut and lost jobs they began to default on loans and the value of the collateral (the house) fell, sometimes to less than the original value at purchase, as the bubble burst. The assumption that defaults were uncorrelated turned out to be unfounded and, as you can probably guess, that triggered CDS payouts and huge losses for many of the companies holding the CDOs and writing the CDSs. Drinking and strip clubs were basically what the borrowers preferred to spend their money on instead of their mortgages. Slightly less glibly the value of their house counted as an asset to them against which they could take out further debts (credit cards, personal loans etc.) so that they could afford to live outside their means under the assumption that they would pay it back using future months' salaries. When they lost their jobs they could no longer do so. Remember from earlier that these were people who had never been offered credit before and even professionals make mistakes in their finances when it comes to credit and loans so they were doubly cursed by a lack of understanding of credit and a lack of experience.

A major issue in all of this was hubris and people's belief that current trends would never end; the economy had been growing for the longest time in recorded history therefore it would continue to and everyone would always be employed and able to pay their bills. Add to this that the managers of the funds etc. that held these debt based derivatives believed that their models of the risks of holding them, underpinned by the fallacious assumption of the lack correlation of defaults, were accurate and would model potential profits and losses, and that, in any case, they had insurance if anything bad happened and you have the problem.

These were massively leveraged positions in little understood instruments that wrapped around very risky debts for which there were no good models of repayment and default rates, and those models that did exist did so under the fatefully incorrect assumption that defaults would be totally independent.


Is Keynesian economic theory still considered capitalism? When we compare neoclassical economic theory with Keynesian economic theory as they pertain to capitalism, do they both fall within the spectrum of capitalism? or is Keynes's idea of state intervention considered socialism rather than capitalism?

What I'm struggling to understand is does capitalism exist in a singular form which is the one proposed by neoclassical economists or could it take different forms that involve some state intervention and still be considered Capitalism?

I don't have an economics background and am currently reading 'Contending Economic Theories' by Richard Wolff and Stephen Resnick and this is a point that I'm trying to clarify so please excuse me if I have misunderstood some concepts.

Capitalism is not well-defined in economics. In most economic textbooks the word capitalism is not even printed.

However, according to dictionary (Merriam-Webster) definition:

  an economic system characterized by private or corporate ownership of capital goods, by investments that are determined by private decision, and by prices, production, and the distribution of goods that are determined mainly by competition in a free market [emphasis added]

The above definition does not seem to exclude the kind of macroeconomic management intervention prescribed by Keynes theory and its newer interpretations. Moreover, I know that political science happens to distinguish between different capitalism such as state capitalism or market capitalism but this is not done in economic theory where the word is scantly used.

Socialism is bit better defined in economics (but it is still term that is not commonly used and avoided as its too value laden and scientists try to avoid value laden terms as much as possible), and it is defined as an economy where means of production are predominantly owned/controlled collectively by the state (see this article on investopedia). Nothing in either original or New Keynesian theory calls for state/collective ownership at all, let alone making that the predominant mode of production, so I dont see any way how the sort of policy prescriptions made by Keynes could be considered 'socialistic' per se in economic meaning of the word.

Furthermore, neither neoclassical or Keynesian theory pertain to any particular economic system in principle. Both schools focus mainly on describing mixed predominantly market economies because those happen to be the kind of economies that are most common in the real world. However, some parts of both neoclassical theory and Keynesian theory would be applicable to centrally  planed 'socialistic'  economies as well.  For example, as @BrianRomanchuk correctly points in his comment the Keynesian aggregate demand management policies are avaiable to any government no matter what economic form of organization/ideology it follows.


How to borrow at risk free rate When learning about derivatives, we learnt about risk-free hedges and portfolios. However, one of the concepts was about borrowing and lending at the risk free rate. Now, for lending it's as simple as buying government bonds. However, how does one borrow at the risk free rate? I doubt it's about selling your own bonds. I'm just trying to work out how to apply these economic theories in real life, so any help will be greatly appreciated.

A private person will almost never have an access to borrowing at risk free rate. However, governments such as Germany or Switzerland can borrow at essentially for all practical purposes at risk free rate by issuing government bonds.

As a private person you might get access to risk free loan if you are rich enough to be able to negotiate the rate with bank and if your project is extremely safe (think of Jeff Bezos asking for small loan to build a private parking lot).


Data for the distribution of US household annual income by year and state I am looking for data regarding the annual household income distribution filtered by year and state (and finer geographical feature like cities). In other words, I am looking for data with the following features (label being the number of earners):

year
state
income range (e.g. 10K-20K, finer better)

Does anyone know if there is a publicly available dataset containing these?

Have you checked the US census bureau? Income related website here.

Furthermore there is a kaggle training competition about the census data. Have a look here for the available data tables. Data straight from the census bureau.


How are elasticity of demand, marginal revenue, and total revenue connected? I am completely new to economics, and am looking at some old exam papers. The question is as following:

"In a normal marked, where there is a negative correlation between quantity and price, which of the following are true for elasticity of demand, marginal revenue, and total revenue?"

The correct alternative was:

d) When the absolute value of elasticity is 1, the marginal revenue is 0, and total revenue is maximized

I was wondering:

Why is the total revenue maximized when marginal revenue is 0? I know that, usually, total revenue is maximized when marginal revenue = marginal cost. In this case, however, no information is given about the marginal cost, so it does not make sense to me that it should be 0.

Also, is the marginal revenue always 0, when elasticity is exactly equal to 1? How does that make sense?

Marginal cost is irrelevant to total revenue. It's relevant to profit, but not total revenue.

Total revenue is just price x quantity.

Marginal revenue is a monotonic decreasing function. That is, as quantity increases, marginal revenue decreases. So, let's take the quantity Q to be the point at which marginal revenue is zero.

For quantities below Q, marginal revenue is positive, so total revenue increases with quantity.

For quantities above Q, marginal revenue is negative, so total revenue decreases with quantity.

Hence Q is the turning point of the curve: it is the point of maximum total revenue.

Elasticity of 1 means that a tiny % change, $\Delta$ in price in one direction (equivalent to multiplying price by $1+\Delta$),  will be met by a reciprocal proportional change in quantity in the other direction, equivalent to multipying it by $\frac{1}{1+\Delta}$: that's straight from the definition of elasticity.

So total revenue, the product of price and quantity, remains the same:

$$(1+\Delta) P \times \frac{1}{(1+\Delta)} Q = P \times Q$$

Hence marginal revenue always 0, when elasticity is exactly equal to 1.


Dimensional analysis of GDP The GDP is sometimes given by
$$
GDP=P\cdot h\cdot e \cdot F
$$

Where $P$ is the Productivity, $h$ is the number of hours worked, $e$ is the employment rate and $F$ is the size of the labor force.

If we do a dimensional analysis, we see that the left hand side of that equation i $\left[ GDP \right]= \text{value / time}$

On the right hand side we have:

$$
[P]=\text{value/time}\\
[h]=\text{time}\\
[e]=\text{dimensionless}\\
[F]=\text{dimensionless}.
$$

This analysis yields that the dimension of the RHS is value.

Hence, the dimension of the left hand side and the right hand side is not equal, which would constitute a contradiction.

Does anyone know why that is?

If GDP is measured (as it usually is) for a period such as a year, then number of hours worked ($h$) should be measured for the same period.  Thus $h$ is dimensionless and the dimension of the right hand side is also value / time.


Finding a stable equilibrium I'm trying to determine which strategy is stochastically stable.

In my lecture notes, we assign probabilities $a$, $b$ $1-a-b$ to player 2 strategies $T,M,B$ resp.
Hence we have the payoffs
$$u(t)=2a+1-a-b$$ $$u(m)=b+2-2a$$ $$u(b)=4-2b-3a$$
And it is inferred from this that $b,b$ is stochastically stable. I tried using the utilities to derive a system of three equations, and showing that $B$ yields the highest payoff for the largest range of $a$ and $b$, but this did not seem to succeed.

As a caveat, disclaimer, I am not too familiar with Evolutionary Game Theory and it is quite outside my research area/main areas of expertise. However, I can show here that range of $(a,b)$ for which $B$ is a best response is strictly greater than for either of the other two strategies. To that end,

You can characterize the range of $(a,b)$ for which $B$ is a (strict) best response by solving the system

$$\begin{split}
4−2b−3a &\> b+2-2a\\
4−2b−3a &> 1+a-b\\
\end{split}$$

Or,

$$\begin{split}
2 &> 3b + a\\
3 &> 4a + b\\
\end{split}$$

Or,

$$\begin{split}
a &> 7/11, b<3-4a\\
a &\leq 7/11, b<\frac{2-a}{3}\\
\end{split}$$

We can solve for the area of this quadrilateral:

$$\begin{split}
B &= \int_{0}^{7/11}\frac{2-a}{3}da + \int_{7/11}^{3/4}(3-4a)da\\
&= \frac{259}{726} + \frac{25}{968} = \frac{101}{264} \approx .382\bar{57}
\end{split}$$

Through similar analysis for $M$, we obtain

$$\begin{split}
a &> 7/11, b>\frac{3a-1}{2}\\
a &\leq 7/11, b>\frac{2-a}{3}\\
\end{split}$$

Hence,

$$\begin{split}
M &= 1 - \int_{0}^{7/11}\frac{2-a}{3}da - \int_{7/11}^{1}\frac{3a-1}{2}da\\
&= 1 - \frac{259}{726} - \frac{32}{121} = \frac{25}{66} \approx .3\bar{78}
\end{split}$$

Finally,

$$T=1-\frac{25}{66}-\frac{101}{264} = \frac{21}{88} \approx .238\bar{63}$$

Since $$\begin{split}
\frac{101}{264} &> \frac{25}{66}\\ \frac{101}{264} &> \frac{21}{88}
\end{split}$$
the result is shown.


How do excessive foreign reserves cause inflation? I have studied that accumulation of foreign reserve has the potential to raise inflation levels in economy as the money base increases (= domestic currency + foreign reserve increases) and if it overshoots the money demand in the economy then it will raise price levels.
My question here is that how the foreign reserves which are under the custody of the central bank go into the system and cause inflation. Say, China has huge reserves of USD but it rests with the central bank mostly. So, how does it get into the economy and raise prices ?

Because you are taking other currencies off the market and/or selling your own currency, and increasing the supply of your own currency relative to others.


What are the 'best' variables out there to forecast accurately GDP and inflation according to macro literature? What are the best variables out there to forecast accurately GDP and inflation according to macro literature?

I'd like to forecast the next quarter, not the long-run.

Some time-series ideas I gathered:

industry production
employment
important export-import partners production
business confidence indexes (e.g. INSEE)

You likely want to do this in real time which means you want to do a nowcasting. This is tricky because many economic series are revised, which means you also need real time data (what were the figures when released rather than what is known with hindsight).

The Atlanta Federal Reserve Bank uses this approach in their GDP Now product. You should check out their methodology and inputs to get started on your attempt.

  The growth rate of real gross domestic product (GDP) measured by the
  U.S. Bureau of Economic Analysis (BEA) is a key metric of the pace of
  economic activity. It is one of the four variables included in the
  economic projections of Federal Reserve Board members and Bank
  presidents for every other Federal Open Market Committee (FOMC)
  meeting. As with many economic statistics, GDP estimates are released
  with a lag whose timing can be important for policymakers. For
  example, of the four scheduled 2014 release dates of an “advance” (or
  first) estimate of GDP growth, two are on the second day of a
  scheduled FOMC meeting with the other two on the day after the
  meeting. In preparation for FOMC meetings, policymakers have the Fed
  Board staff projection of this “advance” estimate at their disposal.
  These projections—available through 2008 at the Philadelphia Fed’s
  Real Time Data Center—have generally been more accurate than forecasts
  from simple statistical models. As stated by economists Jon Faust and
  Jonathan H. Wright in a 2009 paper, “by mirroring key elements of the
  data construction machinery of the Bureau of Economic Analysis, the
  Fed staff forms a relatively precise estimate of what BEA will
  announce for the previous quarter’s GDP even before it is announced.”

  The Atlanta Fed GDPNow model also mimics the methods used by the BEA
  to estimate real GDP growth. The GDPNow forecast is constructed by
  aggregating statistical model forecasts of 13 subcomponents that
  comprise GDP. Other private forecasters use similar approaches to
  “nowcast” GDP growth. However, these forecasts are not updated more
  than once a month or quarter, are not publicly available, or do not
  have forecasts of the subcomponents of GDP that add “color” to the
  top-line number. The Atlanta Fed GDPNow model fills these three voids.

  The BEA’s advance estimates of the subcomponents of GDP use publicly
  released data from the U.S. Census Bureau, U.S. Bureau of Labor
  Statistics, and other sources. Much of this data is displayed in the
  BEA’s Key Source Data and Assumptions table that accompanies the
  “advance” GDP estimate. GDPNow relates these source data to their
  corresponding GDP subcomponents using a “bridge equation” approach
  similar to the one described in a Minneapolis Fed study by Preston J.
  Miller and Daniel M. Chin. Whenever the monthly source data is not
  available, the missing values are forecasted using econometric
  techniques similar to those described in papers by James H. Stock and
  Mark W. Watson and Domenico Giannone, Lucrezia Reichlin, and David
  Small. A detailed description of the data sources and methods used in
  the GDPNow model is provided in an accompanying Atlanta Fed working
  paper.

  As more monthly source data becomes available, the GDPNow forecast for
  a particular quarter evolves and generally becomes more accurate. That
  said, the forecasting error can still be substantial just prior to the
  “advance” GDP estimate release. It is important to emphasize that the
  Atlanta Fed GDPNow forecast is a model projection not subject to
  judgmental adjustments. It is not an official forecast of the Federal
  Reserve Bank of Atlanta, its president, the Federal Reserve System, or
  the FOMC.


The Frisch-Waugh-Lovell Theorem: an exercise I have an equation of the form(all vectors): $y=X_1\beta_1+X_2\beta_2+u$.

I'm interested in knowing if the beta OLS estimators and respective residual for this equation are the same as for when we apply OLS to the following equations:

$P_{X_1}y=P_{X_1}X_2\beta_2+v$
$P_Xy=X_1\beta_1+X_2\beta_2+v$,

where the $P_Z$ are the usual definition of projection matrices, using $Z$.

So, I've tried using the FWL theorem, and I've got respectively:

$\hat\beta_2 = (X_2' P_{X_1}X_2)^{-1}X_2'P_{X_1}y$, and $\hat v = (I- P_{X_1}X_2(X_2'P_{X_1}X_2)^{-1}X_2'P_{X_1})P_{X_1}y$. I was wondering if I miscalculated $\hat u$ since looking at equation 1, since both $y$ and $X_2\beta_2$ are projected in to the space spanned by columns of $X_1$, the residuals would be zero.
$\hat\beta_2 = (X_2' M_{X_1}X_2)^{-1}X_2'M_{X_1}P_X y$, and $\hat v = (I- M_{X_1}X_2(X_2'M_{X_1}X_2)^{-1}X_2'M_{X_1})P_{X}y$.  However, I do not see how the estimate for $\beta_2$ is equal in both cases, since if you notice that applying OLS to equation 2, we get $\hat \beta=(X'X)^{-1}X'P_X y=(X'X)^{-1}X'y$.

Any help would be appreciated.

Edit1: well, I found out how to do the 2nd point. We have to notice that $M_{X_1}P_X=(I-P_{X_1})P_X=P_X-P_{X_1}=P_X'-P_{X_1}'=(M_{X_1}P_X)'=P_X'M_{X_1}'=P_X M_{X_1}$ and that $ X_2'P_X=(P_X X_2)=X_2'$.
As to the 1st point I have no idea...

What we know from FWL theorem, is that the regression

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

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

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

where

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

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

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

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

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

which is

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

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

Well,

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

while

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

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

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


Perfect risk sharing in Arrow-Debreu w/ the same subjective beliefs over states So I'm looking at a 2-agent Arrow-Debreu economy with one good. Consumption and endowments are zero in t=0, and 2 states are possible in t=1 with aggregate endowment in both states equal to 1.

We assume utility is strictly increasing and strictly quasiconcave. My question is this:

My professor says by strict monotonicity

$\dfrac{v^{'}_{1}\left(x^1_1\right)}{v^{'}_{1}\left(x^2_1\right)} = \dfrac{v^{'}_{2}\left(1 - x^1_1\right)}{v^{'}_{2}\left(1 - x^2_1\right)} \Rightarrow x^1_1 = x^2_1$

I can see this is obviously true if $v(\cdot)$ is concave, but we only have strict quasi-concavity. For example $f(x) = x^2$ is strictly convex yet strictly quasiconcave. Since agent 1 and agent 2 are not required to have the same utility function, it is possible for agent 1 to have a convex utility and agent 2 to have a concave one. In short, we cannot say the second derivatives are the same sign without the concavity assumption.

Moreover, wouldn't a counter example be aif $v_i(x) = x$ for $i = 1,2$. Then $x_1^1 \neq x_1^2$ would still imply the ratio holds. Is it then something about an interior solution?

In two details you seem to be mistaken:

You need strict concavity of $v(\cdot)$, not concavity.
According to the definition of quasiconcavity, the function $x^2$ is not quasiconcave, it is quasiconvex.

Your main point is correct. If both functions are linear, then $x_i^1 = x_i^2$ no longer needs to hold, as the goods $x_i^1$ and $x_i^2$
are perfect substitutes for consumer $i$. Hence all consumption decisions are correct as long as $i$ trades at a price ratio of 1. This is indeed the equilibrium price ratio. The same can be said for the other consumer.


What is the difference between aggregate supply and GDP? Usually when I read online, I see the following repeated frequently: aggregate demand is equal to GDP. I understand that aggregate expenditures is the aggregate demand at a particular price level, and that sometimes AE will exceed GDP (causing growth in GDP) and vice versa, according to the Keynesian cross model.

Obviously at equilibrium, AS = AD = GDP. But I've never seen anywhere that aggregate supply in general is equal to GDP. Yet this definition makes more sense to me.

One definition that I've seen for aggregate supply is "the total supply of goods and services produced within an economy at a given overall price level in a given time period" (source). Another that I've seen is "the total supply of goods and services that firms in a national economy plan on selling during a specific time period" (Wikipedia).

Which of these definitions is correct? If it's the latter, I can see some obvious differences (it doesn't include inventories, for example). But if it's the former, that seems to be the same as GDP: "the monetary value of all goods and services produced within a nation's geographic borders over a specified period of time." To rephrase, how is the concept of aggregate output distinguished from aggregate supply? I guess the first two questions should naturally answer this last one, since aggregate output is GDP.

Aggregate supply is a relationship of price level and output. It is a function, or a curve, or a table. It is not a single value. If we know a particular price level, then we can determine the level of output that would correspond with that. The GDP for 2006 is determined by plugging in the price level of 2006 to the AS curve for 2006, and seeing what output is produced at that price level.


Calculating the impact of a per-unit Subsidy given to Consumers? I am somewhat confused about the concept of calculating the prices payed by consumers and producers after a subsidy has been applied.

For example, say a good is being traded at 100 dollar at the market equilibrium. If the government were to give a 50 dollar subsidy to the consumer, would the price the consumer actually pays now (post-subsidy) be greater than 50$ due to differing elasticities? Would some of that subsidy be translated over to the price the producer receives? Or, would the price the consumer pays always be the (Equilibrium Price - Subsidy)?

Is the price reduction for the consumer (as a result of the subsidy) a function of the elasticity of demand or would the subsidy always fully fall on the consumer?

This is a great question which economists have a pretty good answer to. Let's first suppose the market is in an equilibrium with no intervention at price $P^*$.

If there is a tax of value $t$ we have a new equilibrium with a consumer price $P^*_c$ and producer price $P^*_s$. These prices surely do not equal each other any more, and the difference of the two is not necessarily equal to the value of the tax.

You can think of a subsidy as a negative tax.

The change in consumer price due to a marginal tax or subsidy is called the pass through rate, $\rho$. For a sufficiently small tax, the relationship is $P^*_c=P^*+\rho\cdot t$.

Clearly, if the pass-through rate is one the consumer completely pays for the tax. If it is zero, the consumer does not at all pay for the tax. It is not impossible for $\rho$ to be negative or greater than one.

In perfectly competitive markets the pass through rate depends on the elasticity of demand, $\varepsilon_D$, and the elasticity of supply, $\varepsilon_S$. $$\rho=\frac{1}{1+\frac{\varepsilon_D}{\varepsilon_S}}$$

From this we can see that the pass through rate is larger when demand is more inelastic, and smaller when supply is more inelastic. This is where we get the adage "the more inelastic side of the market bares the burden of a tax."

For pass through to be equal to one, we either need (a) perfectly inelastic demand or (b) perfectly elastic supply. A lot of the time (b) can be satisfied by assuming constant marginal cost of production.

For imperfectly competitive situations, the pass through rate depends on firm conduct as well as the curvature of demand. I suggest Weyl and Fabinger "Pass through as an economic tool" 2013, Journal of Political Economy, publication for the details.


Why does the real wage = W/P? Im reading about labour markets, and the notes mention that the real wage 'w' = W/P, where W = the nominal wage, and P = the price level. Could someone please use some 'W' and 'P' as an example to show me how real wages emerge from the ratio W/P?

Thanks!

Whenever we go from nominal to real terms, we need a base year.  As an example, let's use 2016 as the base year.  In the base year, the nominal wage $W$ is always equal to the real wage $w$ (this is true for any price or cost, not just wage).  Also, we always set the price level $P$ equal to 1 in the base year.  That's what makes it the base year.

Anyway, let's say that, in 2016, $w_{2016}=W_{2016}=15$.  Suppose that, between 2016 and 2017, there's 2% inflation - that is, the price level $P$ increases by 2% from $P_{2016}=1$ to $P_{2017}=1.02$.  Then, it follows that the real wage in 2017 will be $w_{2017}=\frac{W_{2016}}{P_{2017}}=\frac{15}{1.02}=14.706$.  I hope this example helped.

In case it didn't, you can think about it like this:  Dividing the nominal wage by the price level is just how you adjust for inflation, thus giving you the real wage.


What is autocorrelation of prices? In my econometrics and economics classes, the term autocorrelation has come up this quarter. I have read the Wikipedia pages about it and tried to understand them, but they are a bit beyond me. They use too much math from signal analysis that I don't have time to study at the moment. But I would still like to understand the general idea.

Can someone provide a brief explanation of what autocorrelation is and how this concept is used to understand price and analyze price trends?

Autocorrelated is the opposite of independent, which is a term easier to understand (and explain). If you throw one die, the probability of getting the number any number is 1/6. If you throw it again, the probability of guessing the result number is 1/6. If you do it again and again and again the probability of getting it right is always 1/6 (provided that the die is «fair»). This means that the next outcome is independent to the previous one. Whether you get a 3 or a 5, the outcome of the next «experiment» is not affected.

The opposite would be, for instance, if you have a set of 20 cards, and then you draw one, the probability that the card drawn is the one you predicted is 1/20th. But this time, things have changed: you are left with only 19 cards on your hand. So the next time, you have a probability of 1/19th of guessing the card. If you do it again and again the probability of guessing the next card is greater. Since the outcome of the previous event helps to predict the next one, we say that this process is autocorrelated.

One doesn't need to be an expert on statistics to see that these two examples are different. This is why it is important.

Now, when it comes to prices, it simply means that the price of a good today helps predicting its price for tomorrow. Take currencies: If 1€ = USD \$1.1193 today, it would be very unlikely (but never impossible) that 1€ = USD \$10 tomorrow. It is more likely that the price will be around USD \$1.1193.


Central Bank liabilities and assets - Money and Bonds I'm reading a book on macroeconomics, and on a chapter on the money market, when explaining how the central banks(CB) determine the interest rate, there is a balance sheet for the CB. In it, under the assets we have bonds, and under liabilities we have currency and bank reserves. My question is which bonds are these? Do these bonds belong to the same country that the CB belongs to? Isn't in this case the bond of the CB a liability/debt that will have to be repaid in the future? Because if so, it seems that we're just exchanging one liability (bond) for another (money).

Or are these bonds from any entities other than the CB itself?

Any help would be appreciated.

My question is which bonds are these? Do these bonds belong to the same country that the CB belongs to?

This will vary a lot from central bank to central bank. Most of the assets of the US Federal Reserve are indeed government securities, but the European Central Bank is prohibited from buying such securities (because of the crisis, it now buys limited amounts of them, but the legal grounds are shaky).

Since 2009, central bank balance sheets have changed quite a bit. In 2008 the Federal Reserve did not hold any mortgage backed securities. Now, they comprise about 40% of the Fed's total assets.

Take a look at the Fed's balance sheet in Table 1 of the August 2015 report.

  Because if so, it seems that we're just exchanging one liability (bond) for another (money). Or are these bonds from any entities other than the CB itself?

Yes, they are from other entities. For example, US Treasury bonds are about half of the Fed's balance sheet. These bonds are issued by the Department of the Treasury and must be pay back to the Fed on maturity, using money collected from taxes or the proceeds from new bond issues.


How exactly does the black market affect a country's economy? Disclaimer: I'm far from an expert on economics. I apologize if the question seems poorly asked or not clear.

Take for example the drug trafficking business and cartels in the past. It seems to me that the production cost of illegal drug substances was quite low. Most of the usual substances back then were either a form of plant or extracted from certain kinds of plants.

In contrast, the demand of those substances was tremendous, mostly because of their unusual properties and effects on the human body.

How this low production cost - enormously high demand combo affected the economy of the countries where drug trafficking was taking place?

I think the question is extremely broad. The effects of drug dealing on the whole economy depend on many things, for example, on how strict is the country at enforcing the ban, how violent the drug dealers are, and what is done with the profits. The experiences in Mexico and Colombia, for example, are substantially different. While many drug lords have developed complete cities from the gains from trafficking, others have simply wasted it all. In most cases, the government is involved in the trafficking (via corruption) so it can have some positive effects in terms of govt budget, but if it becomes violent, the costs are clear.

If there is any generality I would say that the combo of low cost and huge demand makes it really hard to prohibit. There are a few studies trying to measure the economic effect of the violence of drug dealing, but any empirical work is limited due to the lack of reliable data on basically every aspect of illegal markets.


Which one of these intepretations of belonging of a factor of production is correct in context of calculating "income of our citizens abroad"? NFFI can be calculated as income of foreigners here MINUS income of our citizens/corporations abroad. As far as I understand, it's assumed that our citizens earn income by using OUR factors of production (factors of production:enterpreneurship, capital, labor, land) abroad. Here I'm interested NOT in NFFI itself, but in it's component, namely "income of our citizens/corporations abroad".

I wonder, "What to count as OUR factor of production?". There are two intepretations:

1.It's decided by location of the factor of production. So a factory that works on territory of our country is OUR factory, no matter who owns it. (With exception for enterpreneurship and labor, these are decided by citizenship of entrepreneurs and workers, thus our enterpreneurs and workers can be employed abroad.)

2.It's decided by ownership of given factor of production. So if our citizen/corporation owns a factory located in a foreign country, then it's OUR factor of production.

The right (and shorter) name for " income of our citizens/corporations abroad" is "the national FFI", where FFI stands for Foreign Factor Income. I will use this name.

The second interpretation is correct, it will lead to correct calculation of the national FFI. If our corporation/citizen gets income from a factory that they own, but said factory is located abroad, then said income will contribute to size of the national FFI. Also, if instead of the national FFI we will calculate FFI of foreigners, then we will calculate their FFI taking in account what factors they own in our country. For an example, if Ivan from Russia will get income from a factory that they own in the UK (We assume that the UK is our country), then said income will increase FFI of foreigners.

The second interpretation also applies to the land. Just replace a factory with a mine.

P.S.

Comment by @1muflon1 that made this answer possible

  @user161005 okay
  but that’s then completely different question then your original. Here
  the answer would be that for GDP you use 1. i.e. the location. For GNP
  2. i.e the ownership. For NFFI both 1 and 2 at the same time. For FFI of home citizens you would use 2. For FFI of foreigners you would use
  also 2 but from their perspective. btw if this is what you ask pls
  edit your question and I will update your answer accordingly. In you
  question you only ask about NFFI which has to use both 1 and 2 at the
  same time since NFFI basically gives you difference between measuring
  with these definitions


How to obtain standard surveys / measures to use at end of experiment to "control for altruism" etc? When running an economics experiment, how and where are experimental graduate students supposed to obtain the surveys (such as standard measures of altruism, risk aversion, social dominance...) that often come at the end of experiments (so that researchers can "control for altruism" etc)? Do researchers purchase such measures / inventories, or are they part of the public domain and can be freely copied from previous research papers that use them? I am interested in using those from my own field as well as using one that is not from my own field (the Bem Sex Role Inventory) that appears to not be readily available online -- at least not for free.

In experimental economics, the classic ways to measure/control for participants' social preferences are variants of the following games:

The ultimatum game measures a participant's preference for fairness or justice.
The dictator game measures a participant's other-regarding preference.
The trust game measures the level of trust and trustworthiness among a group of participants.

Risk preferences (and time preferences/impatience) can be elicited using either of the following:

Multiple price lists (see Holt & Laury (2001))
BRET (Bomb Risk Elicitation Task)
Convex Time Budget (CTB) method (for time preference, see Andreoni & Sprenger (2012))

The games other than CTB are simple enough to be ran in the "survey" form, e.g. with pencil/paper. There are also free computer programs (e.g. zTree) that implement those games.

NB. If your main audience is economists, you'd also want to run these games in an incentivzed way, namely participants get paid and their earnings are directly related to their choices in those games. Responses to survey questions, especially the hypothetical type, do not get much credit from economists.


Certainty Equivalent The certainty equivalent is a guaranteed return that someone would accept now, rather than taking a chance on a higher, but uncertain, return in the future. Otherwise, some definitions say that the certainty equivalentis the mean income of a gamble. If we see the vast literature of microeconomic and game theory papers, then we shall see that they assume CARA Gaussian normal preferences (or negative expnential utility, i.e. $\mathbb{U}(\widetilde{W})=-e^{\rho\widetilde{W}}$). Specifically the certainty equivalent in such case is $$CE(\widetilde{W})=\mathbb{E}(\widetilde{W})-\frac{\rho}{2}\mathbb{V}ar(\widetilde{W})$$
How can someone claim that this return is guaranteed, since we need to use $\mathbb{V}ar(\widetilde{W})$ to measure the utility gain of an individual?

How can someone claim that this return is guaranteed, since we need to use $\mathbb{V}ar(\widetilde{W})$ to measure the utility gain of an individual?

Maybe I misunderstand your point, but though $\widetilde{W}$ is a random variable, $\mathbb{E}(\widetilde{W})-\frac{\rho}{2}\mathbb{V}ar(\widetilde{W})$ and hence $CE(\widetilde{W})$ is a real number. So $CE(\widetilde{W})$ is a measure of a certain income which to the consumer has the same utility as $\widetilde{W}$.


Puzzle: Fairness of consumer price indices I have learned a bit how the consumer price index (= inflation rate) in Germany is calculated.

It's a complex process, which takes into account a lot of measured values (mainly specific prices for specific goods along specific distribution channels) and complex weightings (taking into account the volume of distribution channels). At some point in the process, when consumer price indices of Germany's federated states have been calculated, a weighted average consumer price index is calculated for Germany as a whole.

As I have learned, the weight by which a federated state enters the Germany-wide average index used to be proportional to its population (until approx. 2002-2005, Gerhard Schröder's reign?, I did not verify), but since then it's the "market volume", i.e. the total amount of money spent by households in the state. (I don't know the correct technical term.)

This may make sense from an macroeconomical or monetary/fiscal perspective, but it feels somehow "unjust". In the long run it might be to the benefit of all (even the poorer states with lesser market volume), but how do I know, and at first sight it seems "unfair" in the sense of "one man, one vote".

So I wonder, if there are good arguments that this way of calculating the Germany-wide consumer price index is "fair" and to the same benefit for all, or if – in the long run – it privileges the richer (or maybe the poorer) states?

  For a layman like me, this question is not easy to answer. It strongly
  depends on how the officially calculated and reported consumer price
  index (= inflation rate) affects (by very different measures) the
  overall but also the regionally distributed wealth of a state or
  nation.

What I don't know (and didn't try to find out) is how the harmonized index of consumer prices for the whole EU takes the single EU-members into account: by population or by market volume? My same questions would hold on this higher level, too.

The economic purpose of the CPI is to convert nominal units of consumption (goods and services) into real units of consumption. I understand that the CPI is used for other many purposes, but that's the economic purpose. For example, say that there  is one consumption good, corn, and corn is priced in denarii. We know that in 2010 50 billion denarii of corn was consumed while in 2018 100 billion denarii of corn was consumed. Was more corn consumed in 2010 or 2018? To answer this, you need to know the price of a kilogram of corn in denarii in 2010 and 2018. Say that $P_{2010}=25\:denarii/kilogram$ and $P_{2018}=100\:denarii / kilogram$ In this case consumption was 2 billion kilograms in 2010 and 1 billion kilograms in 2018.

When we get to multiple goods there is a complication because you can't add up or otherwise compare quantities of different goods. Therefore, it is convenient to pick a common numeraire. In the example, if we pick 2010 dollars as the numeraire then we see that consumption was 50 billion 2010 denarii in 2010 and 25 billion 2018 denarii in 2018. Both versions tell the same story, that real consumption was halved in 2018 relative to 2010.

This same logic holds when there are multiple goods. Let $t=0$ be the base (numeraire) year and $t=\tau$ be the year of comparison:
$$Real\: t=\tau\: Output\:in\:t=0\:prices =Expenditure_{good\:1,\tau}\cdot P_{1,0} / P_{1,\tau} + Expenditure_{good\:2,\tau} \cdot P_{2,0} / P_{2,\tau}\ldots + Expenditure_{good\:n,\tau} \cdot P_{n,0} / P_{n,\tau}$$

Recall that expenditures are prices times quantities, so expenditures divided by prices are quantities.
$$Real\: t=\tau\: Output\:in\:t=0\:prices =Q{1,\tau}\cdot P_{1,0}  + Q{2,\tau} \cdot P_{2,0} \ldots + Q{n,\tau} \cdot P_{n,0}$$
While nominal output is:
$$Nominal\: t=\tau\: Output\:in\:t=\tau\:prices = Q{1,\tau}\cdot P_{1,\tau}  + Q{2,\tau} \cdot P_{2,\tau} \ldots + Q{n,\tau} \cdot P_{n,\tau}$$
This lets us define the CPI:
$$\frac{Nominal\: t=\tau\: Output\:in\:t=\tau\:prices}{Real\: t=\tau\: Output\:in\:t=0\:prices} = CPI_{\tau}$$
That is, the relative change in the price level is the relative change in each prices weighted by the size of their expenditures.

For welfare purposes, it is important to understand that there are income and substitution effects from price changes. We can buy more of relatively cheaper goods and less of relatively expensive ones. A high price of a good we consume makes us effectively poorer. Both income and substitution can change our consumption bundles, and the Paasche, Laspeyres, and Fisher indices are attempts to deal with these issues. And there are other complications like changes in product availability, change in quality and features, and other measurement issues. But the overall idea is as above.

Therefore, if we are interested in making consumption comparisons across time, there really is only one way to do it, to weight the changes in prices by expenditures, and this means over-weighting the consumption of the risk because the consume more.

What happens if the weighted average change in the prices of the goods consumed by the poor is different than that of the rich? In this case the index is going to look more like the consumption of the rich than the poor. That, in and of itself, is not unfair, it is just an accounting result. This can become unfair when taxes and benefits are tied to indexed values. So, for example, if the goal is to guarantee everyone a minimum real income, and prices go up faster for the bundle consumed by the poor than the rich, the real value of a fixed benefit will go down.

This shows that the CPI is not the ideal index for all purposes. In my eyes, it is valuable to know (or at least well approximate) the real consumption output. If the goal is instead to create an index for the benefits of the poor to preserve their real value then a separate index should be made for that purpose. The sensible goal of tying the index to its purpose leads to a proliferation of indices. In addition to the CPI, the US has the producer price index ( measure of intermediate good pricing), the personal consumption expenditures index (CPI is based on a survey of what households are buying; the PCE is based on surveys of what businesses are selling), and a consumer price index for the elderly. There probably are many others.

To my knowledge, there is no regularly updated government price index for the consumption of the poor. However Garner, Johnson, and Kokoski (1996) do develop such an index, and find it is very similar in trends to that of the more general CPI. Broda, Leibtag,  and Weinstein (2009) and find "By examining scanner data on thousands of household purchases we find that the poor pay less —not more—for the goods they purchase." However, there does seem to be some contrary evidence more recently like Inflation May Hit the Poor Hardest (Casselman (2014)).


Independent identically distributed When we are talking about the least squares assumptions, one of the assumpions is that (X,Y) are i.i.d. What bothers me is that if we take an example population and research distributions of age and salaries and lets imagine that distribution of salaries (Y) in the population looks somewhat like chi squared distribution with df=10 and distribution of age (X) resembles exponential distribution. So how can we have an i.i.d. variable when sampling?

The "identically - independently distributed" assumption (or any restriction thereof) on a sample, refers to the relation between random variables in different observations, not between the variables forming the same observation.

So in a multidimensional sample "of size $n$"

$$\{(y_1, x_{11}, x_{21}),(y_2, x_{12}, x_{22}),...,(y_n, x_{1n}, x_{2n})\}$$

the assumption applies between the variables of observation $i$ and all variables in any other observation. So $y_1$ is assumed independent from, say $y_2$, but it is also assumed indepedent from $x_{12}$. Also $x_{11}$ is assumed independent from $x_{12}$ but also from $x_{22}$, etc.

Certainly, $y_i$ is assumed stochastically dependent with $x_{1i}, x_{2i}$, while also $x_{1i}$ and $x_{2i}$ can be stochastically dependent for the same $i$, i.e. inside each observation.


How to calculate the spending multiplier from a given set of equations? So i have this question:

I go along and get

Then i need to calculate the effect on the optimal output is G increases by 80:

And on the answer sheet it states that the spending multiplier is:

From my knowledge i know that

Now how come that the spending multiplier is 1/0.4? Where are they getting the 0.4, which should be 1-c1-d1 from the original equations?

A friend told me that the 1/0.4 is derived from 1/1-c1(1-t)

then 1/1-0.8(0.75)= 1/0.4. He said that since there is no d1 in the equations ( in the investment equation) we don't use it.

Can somebody explain the meaning behind this 1/0.4) Thanks!

Your friend is right. If you look at the initial investment equation, and comparing it to your definition, you have:
$$I=900+(0)Y-50i$$
So $d_{1}=0$ and $c_{1}=0.8(0.75)$ and thats why you get the spending multiplier as $\frac{1}{0.4}$


Net Preference Relations Let say the electorate consists of three segments of voters: 1, 2, and 3 with corresponding weak preference relations defined over the candidates. Let the preferences be given by --

Segment 1: Biden > Warren > Sanders; Biden > Sanders.

Segment 2: Warren > Sanders > Biden; Warren > Biden.

Segment 3: Sanders > Biden > Waren; Sanders > Warren.

Question: Derive the preference relation of the electorate, decided by majority rule. As a preferences of the electorate as a whole rational? Why or why not.

For this question, I feel like it would not be possible to derive a preference relation of the entire electorate because it seems that no one candidate is strongly/weakly preferred. Therefore, it would seem that the preferences of the entire electorate would not be rational because it does not satisfy the transitive and completeness principles. Would I be correct in thinking this way and that a net preferece relation may not be derived? Any help would be greatly appreciated. Thank you.

Have you tried writing down your intuition? Maybe the preference relationship of the electorate as a whole is transitive, but not complete, or complete but not transitive, etc.

I would start, for example asking the electorate, which one is preferred Biden or Warren? 2 voters would prefer Biden and one would prefer warren, so using the majority rule, we can conclude that for the electorate as a whole: Biden $>_{elect}$ Warren. Keep going with all the pairs and conclude whether the  preferences are complete or transitive.


How do I calculate the cost per usage of a machine? If you buy a machine for 10.000 dollars, which costs as a yearly write-off 2000 dollars, how do I calculate the cost per usage of a machine? Do you just divide the the yearly write-off by the times you use it per year? Or do you divide the yearly write-off by the times you potentially could use it per year?
How do you take into account the wear and tear/loss of value of using it?
Or is there some other way?

The machine is used in diagnostic medicine. I'm trying to calculate how much 1 test costs.

Is it just 2000/(Number of times used per year)?

Correct approach: there is reliable information (from the vendor and/or from past experience), that the machine can perform $T$ number of tests in total before being scrapped or taken out of service. Then the cost of the machine per se allocated to the execution of one test is $10.000 / T$.

In the OP's case, a straight-line depreciation method is applied, writing-off $2.000$ per year. The problem here in the calculation $2.000/T_i$ for year $i$, is that next year, if the number of tests is more/less, one will get a different cost allocation of the value of the machine on a single test -and it will be misleading. So for economic-costing purposes this is not advised. But for purposes of reconciliation with accounting practice year-by-year, then one could accept the artificial variation, if one cannot apply the correct approach.

A mitigating approach, if historical data exist, is to take "average yearly tests performed", and divide $2.000$ with this average.


How does an UHN individual leverage their wealth? How does an UHN individual leverage their wealth? Do they in fact do so, and should for example Bill Gates' 80 billion be understood as 800 - 900 billion dollar if he leverage his wealth 10 x?

Someone else said that this leveraging indeed occurs and magnifies the impact of these fortunes on an economy. But how should this be understood precisely?

Leveraging is done with debt. Most high net worth individuals are debt free and even if they take out loans, it is to reduce taxes.

However, high net worth individuals normally have their wealth in a form of equities or stocks. For example Bill Gates' wealth is mostly in Microsoft stock, Warren Buffet's is in Berkshire Hathaway's, etc. The corporations that these rich people own can take on a lot of debt and therefore become leveraged. Debt to equity ratio of corporations like Microsoft and Berkshire Hathaway is not very high though, in fact it is below 50% for those two. You can say that Microsoft's use of debt, or leverage, amplifies its impact on the economy by 1.4x, which is not a bad thing.

A hedge fund or some investment institution, on the other hand, can easily have several times more debt on their balance sheet than equity. On top of that, hedge funds can buy/sell leveraged derivatives like futures, for examples, which have a 10x leverage of their own. As a result, owners of such investment institutions CAN have a considerably impact on the economy as a result of the use of leverage.


Precautionary Savings Two-Period model with a second period quadratic utility function So preferences are defined as $u(c_0)+Ev(c_1)$

Both utility functions are strictly increasing, concave, and twice differentiable.

I understand in the setting of $u(c_0)+Eu(c_1)$ when $u(c_0)$ is quadratic that it will induce no precautionary savings. (that is the two periods share the same functional form)

However, my problem is that the explicit function of $u(c_0)$ is not given in my case, only that $v(c_1)$ is quadratic.

How do I assess the first period utility function?

The two papers that explored first savings under uncertainty in a two-period setting are

Leland, H. E. (1968). Saving and uncertainty: The precautionary demand for saving. The Quarterly Journal of Economics, 82(3), 465-473.

and

Sandmo, A. (1970). The effect of uncertainty on saving decisions. The Review of Economic Studies, 37(3), 353-360.

They both deal with a general two period utility function $U(c_0,c_1)$ not necessarily additive. But both remark the following related to such a case:
The condition for precautionary savings depends on third cross partial derivatives, as well as on the third own derivative with respect to future consumption only.

If the utility function is additive $U=u(c_0)+Ev(c_1)$, then cross-partials are zero, so the result hinges only on the third own derivative for the second-period consumption.

It follows that with an additive over time utility function, it suffices that the second-period utility is quadratic (so third own derivative is zero), in order to not get precautionary savings, irrespective of the form of the first-period utility.


What are the main drivers of insolvency at a macro level? In July, Euler Hermes published a report that claimed that insolvency will explode due to covid by late 2020, the first half of 2021.
To support their statement, they show the evolution of what they call the "global insolvency index". I want to further understand how they compute this index. Unfortunately, they give very few details on this, probably because this index is a proprietary tool and they want to protect their IP.
I was nevertheless wondering what are the main factors that can explain insolvency at the macro level. I can think about:

global debt
interest rate
corporate profitability

Am I missing some important factors here?
Any references or links to online resources that can help me to better understand the dynamics of insolvency at a macro level will be highly appreciated.

Regarding the Index

I want to further understand how they compute this index. Unfortunately, they give very few details on this, probably because this index is a proprietary tool and they want to protect their IP

Their index is actually open access, you can access the data here and the index is based on evolution of insolvencies with base year being 2000.
They also provide data on the evolution of insolvencies but I can't see anywhere any methodology of how the evolution of insolvencies was itself created (which is a red flag if you ask me). Based on the way how data look it seems it is the percentage change in in how many insolvencies occurred. So that would imply they have access to data on number of insolvencies which is also corroborated by the their references to number of filled insolvencies within the report.
However, the report includes author will full contact information, so I would hope that if you would reach out they would share their methodology with you.
Regarding Factors affecting Insolvency:
I am not completely sure what you mean by explaining insolvency at a macro level. Any macroeconomic aggregate of insolvencies will be based on individual insolvencies driven primarily by microeconomic factors - but they would still affect any aggregate of insolvency, so I suppose they would affect insolvency on 'macro level', but I assume you wanted only macroeconomic variables.
According to Sang et al. 2013 examining impact of macroeconomic variables affecting insolvencies in construction industry in South Korea the authors show that insolvencies can be affected by:

changes in GDP (especially negative changes; recessions)
interest rates
consumer price index
corporate bond yields
exchange rate (this is most likely due to S. Korea being small open economy)

In addition other studies (e.g. Bonfim, 2009; Bhattacharjee, et al. 2009 and sources cited therein) generally find that what is driving firm insolvency from macroeconomic is general macroeconomic instability (in fact many of the above listed variables can be considered proxies for macroeconomic stability e.g. change in GDP, inflation etc.) and also to non-trivial degree country specific institutional framework (which is not surprising since true economic insolvency is difficult to observe so often firm is considered insolvent when it is declared insolvent by law).  However, the above answer is quite general the drivers can actually differ by industry as studies also show competition is important factor. Furthermore, the insolvencies in financial sector and real economy are not necessary affected by the same factors, but to go further in depth within a single answer on these issues is beyond the scope of SE.


Is a financial bubble harmless if rich people choose to hoard their wealth? The real question is longer than the title suggests.

I was reading about Principles For Navigating Big Debt Crisis by Ray Dalio, and he mentioned that an economic bubble happens when too much money was chasing after too little goods. Effectively, it also implies that incomes should not rise faster than productivity.

However, what if rich people (or those who own overvalued assets) don't spend their "profits" and hoard them? Wouldn't that mean the real money that was circulated in the economy will still remain stagnant, people's income did not actually rise faster than productivity, and that the bubble will just result in an arbitrary growing wealth gap that wouldn't have any real consequences until the rich decides to spend/distribute them?

an economic bubble happens when too much money was chasing after too little goods

This is not correct statement. When too much money chases too little goods you get inflation including asset prices inflation but asset prices inflation or inflation in general does not necessarily leads to bubbles. Bubbles are often thought to be behavioral in origin, see for example Minsky's Stabilizing an Unstable Economy or Shiller’s  Irrational Exuberance. For example Minsky argues that bubbles ultimately start whenever investors get excited about some new paradigm which can be some new technology or it could also be financial in nature such as shift to permanently more loose monetary policy but it is not the increase in money itself that creates bubble but rather the exuberance investors feel. There is no guarantee that just having too much money will do this. The Shiller's work has similar message.

There can also be rational bubbles where the expectation of an asset price deviates progressively from the path dictated by its economic fundamentals  (see Nelson Mark's textbook international Macroeconomics and Finance) which could be caused for any number of reasons unrelated to the amount of money in circulation.

Hence already the whole premise of your question is not generally valid as bubbles are not necessarily linked to the amount of money in economy.

Furthermore, whether there is an bubble or not, just hoarding money can be harmless or detrimental to the economy but it is definitely not a positive. If rich people would just hoard money by not spending them or not reinvesting them then the money would become 'sterile' - it would be an equivalent of removing the money from the economy which would create deflationary pressure for the economy.

Arguably, during boom such deflationary pressure is more or less harmless, although even then it would be better for an economy if the money would be invested into some productive activities instead of just hoarded. If an economy is in recession creating additional deflationary pressure is just doing extra harm to the economy as due to wage stickiness it will lead to increase in real wages precisely at times when they should be cut.  In addition, if there already is bubble on the market then the deflationary pressure would just make it burst not keep going (although arguably it might be better to burst bubble sooner than latter). Deflationary pressure at right times could help prevent asset bubbles but that would be only in cases where it is actually exuberance about inflation that causes the bubble and besides your question implies that the bubble already exists. It would also be unlikely that rich people would just 'hoard' money to create the optimum level of monetary contraction to prevent it so any such task should be preferably done by central bank.

To sum up, hoarding money does not make bubbles harmless and it is not positive for economy. Hoarding money itself might be in some situation harmless to the economy but in most cases it would actually be detrimental in itself. Furthermore, by creating deflationary pressure it would actually make peoples real incomes raise faster than the productivity in presence of 'sticky wages' (at least in the short run until the deflationary pressure would become part of peoples expectations).


Welfare analysis for a military draft How would the welfare analysis of a military draft look? My intuition tells me that it would look similar to a price ceiling below the equilibrium, with the exception that suppliers (civilians) are forced to supply the draft.

So we supply beyond P* x Q* and all the way out to the intersection of the demand curve and P-draft.

If we say that consumer surplus is the area above P-draft and below the demand curve, then how would we interpret the area that isn't our typical DWL? The area above P-draft, below the demand curve, and above the supply curve.

An obligatory draft is a tax collected in kind - productive time. Instead of producing in the private sector, citizens of the economy offer their services to the army.

Now, we should acknowledge that the existence of an army offers some desired public good (or at least that the society implementing the draft thinks so). Is this a utility-enhancing, or a production-enhancing public good?

Thompson, E. A. (1974). Taxation and national defense. Journal of political economy, 82(4), 755-782.

argued that it is safeguarding property rights of the local population against foreign aggressors, and so it is production-enhancing. Moreover it is subject to congestion: the larger the output/capital base of the economy, the larger military spending has to be to provide the same degree of security (one can find a mention of the above as well as a related model in Barro's book on growth but only on the 1st edition, p. 160).

Here, the tax to fund military expenses is collected in kind, so we could model this situation with the following tweaked Cobb-Douglas production function

$$Y = AK^a(N -L_a)^{1-a}\cdot (BL_a/Y)^\gamma \tag{1}$$

where $N$ is population/total available productive time, there is no labor-leisure choice, $L_a$ is the time spent in producing security services through the draft. The last term is the indirect contribution of military spending in output (by safeguarding property rights), and it is divided by output in order to reflect the congestion characteristic. It is treated as an externality from the private sector.

But the government/social planner can maximize output for any choices of the private sector regarding investment in physical capital, by maximizing the above production function, after taking into account the externality, i.e. by maximizing

$$Y = A^{1/(1+\gamma)}K^{a/(1+\gamma)}(N -L_a)^{(1-a)/(1+\gamma)}\cdot (BL_a)^{\gamma/(1+\gamma)} \tag{2}$$

with respect to $L_a$. We obtain

$$L_a^* = \frac {\gamma}{1-a+\gamma}N$$

namely, that the "size of the draft" in terms of productive time should be a constant proportion of the population.

The problem here is that the private sector looks at $(1)$ and "ignores" the last term. So it behaves as though the capital elasticity of output is $a$ while in reality is smaller, $a/(1+\gamma)$ as we see from $(2)$ (this is due to the existence of congestion in the public good).

This means that the private sector will tend to over-invest. In such cases a proportional tax on output is optimal from a welfare point of view because it would internalize the externality...

...and this means that it would be better, aside from possible non-economic issues, if instead of an obligatory draft the government applied a proportional tax on output in order to fund military expenses (i.e. have a professional, paid army). In this way it would both provide this desired public good, and internalize the externality, reducing the rate of capital investment down to the optimal level.

(Note: obviously the above is a very abstract approach. One could point out that armies need much more than just the labor of their soldiers, in terms of equipment, but even in terms of the subsistence expenses of the soldiers themselves. Then one could model the existence of a tax to fund these, and examine whether it can sustain the output maximizing level of Labor drafted and be at the optimal level as regards the target of internalizing the externality).


Is special case of utility function in "Intertemporal Substitution in Macroeconomics" also a special case of a Ramsey growth model utility function? So in RBC and Ramsey-derived utility function, the following is usually the form of utility:

$$u(c,l) = c^{1-\sigma}(1 + \omega(l))$$

where $\omega(l)$ is arbitrary function of $l$, labor, that satisfies $u_c>0$, $u_l <0$, $u_{ll} \leq 0$ and $u_{cc} < 0$. $c$ is consumption.

In Mankiw/Rotemberg/Summers paper Intertemporal Substitution in Macroeconomics (link: http://scholar.harvard.edu/files/mankiw/files/intertemporal_substitution.pdf), utility function of following is used to test RBC model:

$$u(c,l) = \frac{1}{1-\gamma}\left[\frac{c^{1-\alpha} - 1}{1-\alpha} + d\frac{l^{1-\beta} - 1}{1-\beta}\right]^{1-\gamma}$$

As a special case, not considering multiplicative and additive constants, a special case of
$$u(c,l) = \frac{c^{1-\alpha}}{1-\alpha} - \frac{l^{1+\beta}}{1+\beta}$$
can be considered.

Now for the third utility, it seems that third utility must be special case of the first utility functional form, but I cannot see how this is possible.

Let's call your first utility function [1], and the third utility function [3].

If [3] is a special case of [1], then for some [1] we can find parameter values such that the first derivatives of [1] and [3] will be equal for all values of $c$ and $l$.

So the following must hold:

$$c^{1-\sigma} = -(1+\beta)l^{\beta}/\omega_l(l)$$

$$c^{\sigma -\alpha} = (1-\sigma)(1+\omega(l))$$

Solving both for $c$, and the setting the equations equal to one another, you'll find a functional equation which we need to solve for $\omega$ given its restrictions.

$$ (-(1+\beta)l^{\beta}/\omega_l(l))^{1/(1-\sigma)} = ((1-\sigma)(1+\omega(l)))^{1/(\sigma-\alpha)}$$

Now check this equation to see if you can satisfy the sign restrictions on $\omega$'s derivatives, and you fill find that you cannot for any meaningful specification.