How has decreasing quality (or the need to pay more for the same quality) tracked with inflation? I'm trying to identity a missing variable that could affect poor and middle class consumers more than more wealthy/resourceful individuals.

Assuming that there are decisions regarding cost reductions that also affects product quality, how does "the need to pay more to obtain the same quality/benefit" align with inflation? ... cost of living?

Simple example, in the 1950's all farms sold (implicitly non-GMO) chickens at a given price. Cost minimization introduced decades later affected quality. No matter what drove the new consumer market for non-GMO/grass fed/humane treatment, these additional "features" now come at a premium.

There is probably a well known marketing/business school of thought about this pattern of getting consumers to pay more for what they are already paying for.

How can I track cost of living with quality of living. Is there any metric that would help identify what I'm referring to "shadow inflation" that affects product quality?
Since it's difficult to get a fiscal correlation over time for this, perhaps the quantity of students enrolled in curriculum X which promotes said business methodology?

...Or the revenue of companies that offer consulting services to enact this change?

I will respond to a few points.

The first thing is that although I am old enough to be able to complain about declining quality in many products, it is very unclear how widespread it is. Official methodology takes into account quality changes already. However, it appears unlikely that the change of agricultural production is captured, as that is not really observable at the supermarket.

Over a multi-decade span, things like the CPI have inherent flaws with measuring changes. This is known as “the index number problem.” I am not too familiar with this, so I will let the reader ask another question, or do a web search for more information.

At the same time, the belief is that the CPI overstates changes in the cost of living. In the US, this was the subject of the Boskin Commission.

  There is probably a well known marketing/business school of thought about this pattern of getting consumers to pay more for what they are already paying for.

If we are talking about agriculture, this is off-base. All the changes made were the result of research in agriculture. One can debate the wisdom of the philosophy (like organic farming proponents do), but changes made were considered “best practice.” (Note that even organic farmers look at agricultural research to raise crop yields.)

  How can I track cost of living with quality of living. Is there any metric that would help identify what I'm referring to "shadow inflation" that affects product quality?

If you go to the Bureau of Labor Statistics website (link), I think you will find a statement to the effect that “the CPI is not a cost of living index.” You might get an explanation about that distinction (or ask another question here about the distinction).

At present, the CPI methodology distinguishes between organic/non-organic food. So the inflation rates now are not affected. If you want to compare versus the 1950s, building a new index is going to be nearly impossible, since it seems unlikely that you could find the equivalent of organic prices in the 1970s. All you could do is try to make an adjusted cost-of-living comparison from an earlier period to the present. However, given the large changes in the consumption basket, it is unclear how meaningful that is.


Why we introduce the intermediate good producers into RBC model? I am learning the RBC model and find some papers that use the intermediate good producers under the monopolistic competitive market. Could you tell me the benefit of this method? Thanks.

In the classic RBC model you don't need intermediate good producers. They are introduced, for instance, in the New Keynesian model so that firms have some amount of monopoly power and don't always have to price their goods at the marginal cost of production.


Is it reasonable to consider government bonds as money Some measures of the money supply include governments bonds... but I wonder to what degree governments bonds can be considered money.

IMHO the degree to which X can be thought of as money equals the degree to which you can easily buy things with X. What can you buy with bonds? If your answer is that "you can sell your bonds for money and then buy things" - that simply underlines that the bonds themselves were not money.

Perhaps some mega purchases like buying companies could involve the transfer of bonds directly?? I have no idea how common this is.

Are there any other reasons that bonds can be considered money?

Short answer: Yes, there's another important reason that government bonds are often considered money, which is the role they play as a store of value.

There are three dimensions of money that form the long-standing textbook definition of money (see Mankiw, “Principles of Economics, 8th Edition.” p. 605):

Use as a medium of exchange (i.e., its value for settlement of claims).
Use as a store of value (the degree to which it is a "safe asset”).
Use as a unit of account (the degree to which it is used to denominate claims).

In the modern framework different assets are considered to fulfill these dimensions to differing degrees, which is why different measures of money include or exclude different assets.

Thus, the state of the art is not to think of assets as being either "money" or "not money," but to think of different assets as being more or less "money-like," or having differing degrees of "moneyness."

Dimension three, for example, is generally fulfilled only by physical cash and claims on banks. Claims aren't settled for "20 units" of Treasury bonds, they're settled for a certain par value of those bonds, denominated in dollars. So clearly Treasury bonds are not at all money-like along this dimension.

Dimension one, the one you raise in your question, is fulfilled by Treasury bonds to a greater degree than one might expect, though still only to a very limited amount. While Treasuries are not used for settlement in the real economy, they are used for settlement somewhat frequently in the financial system, which is responsible for a disproportionate amount of financial transactions (though even in finance they are used far less often than settlement for cash). For example, Treasuries are commonly used in securities lending transactions to obtain other securities, and they're often used to meet default and liquidity fund obligations to central counterparties.

Where Treasury bonds shine, though, is on dimension two, their use as a "store of value,” or as a “safe asset.” Per Gorton:

  Safe assets play a critical role in an(y) economy. A “safe asset” is an asset that is (almost always) valued at face value without expensive and prolonged analysis. That is, by design there is no benefit to producing (private) information about its value. And this is common knowledge. Consequently, agents need not fear adverse selection when buying or selling safe assets. Safe assets can easily be used to exchange for goods or services or to exchange for another asset. These short-term safe assets are money or money-like.

The “short-term” part of this refers to the fact that their usefulness as a store of value rises as their residual maturity (and thus their duration, or sensitivity to changes in interest rates) falls. Once their residual maturity falls below three months, they're treated for accounting purposes as being equivalent to cash, because their value isn't likely to change significantly in response to changes in the interest rate environment (this is true under both US GAAP and IFRS):

  Cash and cash equivalents comprise cash on hand and demand deposits, together with short-term, highly liquid investments that are readily convertible to a known amount of cash, and that are subject to an insignificant risk of changes in value. Guidance notes indicate that an investment normally meets the definition of a cash equivalent when it has a maturity of three months or less from the date of acquisition.

Importantly, Treasury bonds solve a very real problem for many firms that have large cash balances, which is that for large-value claims, they are actually more money-like than bank deposits. This is because there's a limit on deposit insurance (currently in the U.S., \$250k per bank, per account type, of which there are two, so \$500k per bank). As a result, for firms that hold large amounts of cash, bank deposits become a relatively poor form of money, because they're not eligible for the government guarantee. As a result, if the bank fails, they're exposed to both credit and liquidity risk (they may not get all their money back, and even if they do, it may not be available for quite a long time).

This is actually why firms frequently either hold balances in institutional money funds that do repos against government securities, or lend them in repo themselves— it allows them to upgrade what would otherwise unsecured claims on banks to claims that are secured by Treasury bonds, highlighting the "safe asset" role that these bonds play.

A very good summary of this concept, the "hierarchy of money," can be found in Pozsar's "Shadow Banking: The Money View." As he discusses in the paper, for many financial market participants, safety (dimension two) is more important than settlement value (dimension one) (emphasis mine):

  [T]here is a strong case for the introduction of a new set
  of monetary aggregates that track the supply of money and money-like claims held not for real
  economy but for financial economy transactions. The Federal Reserve’s M2 aggregate measures the
  money demand of households and has been used to analyze growth dynamics and threats to price
  stability. Because the bulk of money claims included in M2 are insured, it was built following a
  hierarchy based on transactional liquidity. But for institutional cash pools, money begins where M2
  ends, and as the crisis has shown, intra-system holdings of uninsured money market instruments can
  pose threats to financial stability. Institutional cash pools hold money claims mostly for portfolio
  management reasons and because they are too large to be eligible for deposit insurance, their focus is
  on money claims’ safety – that is, proximity to the government – first, and transactional liquidity
  second.

This is, of course, why the Fed had to create the Reverse Repurchase Program. Without it, cash lenders in repo were occasionally so eager to exchange their "cash" in the form of claims on banks for claims on Treasuries that they were willing to accept negative real (and, in certain circumstances, negative nominal) yields on general collateral repos against Treasuries— they were literally willing to pay to hold Treasuries rather than bank deposits. As a result, the Fed set up the RRP to allow their counterparties to do unlimited amounts of repo at a fixed rate, setting a floor under short rates in money markets.

Finally, there is a good working paper out of the Federal Reserve, authored in part by former Fed governor Jeremy Stein, that goes into further detail on the use of Treasuries as money-like claims.


Game Theory: T-Fold Repetition Game Lets say two players, $i=2$ compete in a standard prisoners dilemma game where the action space of each player $a_i \in A_i=\{C,D\}$

Let say the game is repeated $T$ times and all information of past histories is common knowledge.

the strategy function for any player $i$ at time period $t$ is $$s_i^{t}:H_t \rightarrow A_i$$

where the history set at time $t$ is $H_t=A^t=(\{C,D\} \times \{C,D\})^t$

Hence the strategy set $S_i$ of player $i$ for the entire T-repetition game is the cartesian product

$$S_i={\sf X}^{t-1}_{t=1} A_i^{A^t}  $$

My question is this:

Did I define the strategy set (above equation) of the player for the $T$ repetition game correctly? The reason why I ask if because lots of books define the strategy set differently, as the union of all histories mapped into the action space of the player, as such:

$$S_i={\sf \cup}^{t-1}_{t=1} H_t\rightarrow A_i  $$

You mostly got it, there are some minor mistakes.

You cannot have the moving index $t$ of the Cartesian product in the superscript of said product
$$S_i={\sf X}^{t-1}_{t=1} A_i^{A^t}.$$
At the start there have been no moves, so in round 1 you should map the empty history $H_0 = A^0$ to $A_i$, not $H_1 = A^1$ as you seem to have done.

Considering these I think the strategy set of $i$ is
$$
S_i={\sf X}^{T-1}_{t=0} A_i^{A^t}.
$$


Can geography explain differences in economic development between present day economies? Just wondered if anyone considered this. Do simple geographic factors explain differences in economic development?

Dani Rodrik, Arvind Subramanian, Francesco Trebbi have a paper on "Institutions Rule: The Primacy of Institutions over Geography and Integration in Economic Development", Journal of Economic Growth, June 2004, 9(2): pp.131-165.

They estimate the respective contributions of institutions, geography, and trade in determining income levels around the world, using recently developed instruments for institutions and trade. They results indicate that the quality of institutions trumps' everything else. They add that once institutions are controlled for, measures of geography have at best weak direct effects on incomes, although they have a strong indirect effect by influencing the quality of institutions.


Increasing returns to scale Let $f=f(K,L)$ - production function.
Let $f(1,2) \le4 $ and a production function is defined to have increasing returns to scale.
What maximum product can the firm produce using K=3 and L=6?

So we know that $f(3,6) = f(3*1, 3*2) > 3*f(1,2)$ and $f(1,2)\le4$

But what should I do next?

What I believe you mean is that a production function has Constant Returns to Scale.

i.e. $$f(\lambda K, \lambda L)= \lambda f(K, L) $$

Where $\lambda \ge 0$

Thus in your case where $K=3$ and $L=6$

$$f(3,6)=3 \times f(1,2)$$

and since ${f_{max}(1,2)=4}$  (i.e. $f(1,2) \le4$) the maximum product a firm can produce using $K=3$ and $L=6$ would be

$$3 \times f(1,2)= 3 \times 4 =12$$

Hope this helps!


How does one deflate weekly price data? It seems the highest-frequency consumer price index (CPI) data available is monthly. How does one convert weekly or daily price data into real prices?

You don’t. CPI is a proxy for the fantastical concept of a real price. Any measure will have theoretical implications (Australia’s CPI makes some very funny housing assumptions, for example).

As the measure is a proxy for a theorised but unreachable category, and as the measure is only available at its noted frequencies you can’t create a line. Part of the measure is its frequency.

This is impossible for two reasons:

proxies are just that
a measure which is grounded in theoretical assumptions and produced with a frequency can’t be resolved smaller than that frequency

You might look into producing a new measure acting as a proxy with a desired frequency, but only state agents and historians tend to go about these windmill fights.


Relationship between elasticity and interpretation of approximate percentage change Let's define elasticity, in a regression setting, as $\frac{\partial \log E(y|u)}{\partial \log x_j }$. How do we relate this definition to the percentage change interpretation, i.e., seeing this elasticity as the approximate change in $E(y|x)$, when $x_j$ increases by 1 percent? I'm reading Wooldridge.

Any help would be appreciated.

The derivative of $log(x)$ is $1/x$, which implies that $dlog(x)=(dx)/x$. Therefore, $e=dlog(y)/dlog(x)$ is the same as $e=(dy)/y/(dx)/x$. This ratio $e$ is known as the elasticity of $y$ with respect to $x$. We usually express derivatives $f′(x)$ as the change in $f$ when $x$ moves one unit, but $f(x)+1∗f′(x)$ is just an approximation (a Taylor approximation) of $f(x+1)$. Therefore, saying that a 1% change in $x$ will lead to an $e$ change in $y$ is just an approximation. It's a rate of change that is exact only at the $x$ point, but not exact as you move away from it to $x+0.01∗x$.


What is the impact on the money supply of a reduction in the required reserve ratio? In April 2011, the money supply was estimated to be 52 million hurls.
At the same time, bank reserves were 6.24 million hurls and the
reserve requirement was 12 percent. The banking industry, being
“loaned up,” lobbied the Congress to cut the reserve ratio. The
Congress yielded and cut required reserves to 10 percent. What is
the impact on the money supply?

From my calculation, a decrease in the required reserve ratio would mean that the reserves of 6.24 million will support 62.4 million hurl. Does this means that the money supply increases by 10.4 million?

Theoretically, reducing the required reserve ratio will increase the money supply by allowing banks to produce more loans and keep less in reserve.  Theoretically your simple (ie basic homework) calculation would show that the money supply could increase by that amount.  In practice there are of course many other factors, such as the interest rate, velocity and reliablility of the people taking out the loans.


Book Recommendation for Microeconometrics of Discrete Data I am looking for a few good books pitched at different levels to help analyse discrete data.

Specifically: Specification, Estimation and the application of econometric methods to model discrete choices by individuals, households or firms.

Personally, for choice analysis, I like

Discrete Choice Methods with Simulation by Ken Train (pdf)
Applied Choice Analysis: A Primer by Hensher and Greene (2nd edition, book)
Modeling Ordered Choices by Hensher and Greene (pdf)
Regression Models for Categorical Dependent Variables Using Stata by Long and Freese (3rd edition, book)

(1) is a fairly short, readable classic. (2) is much more introductory, with lots of intuition, though it devotes a lot of space to the nlogit software. (3) has the same features as (2), but for a more focused set of topics. (4) is also pretty introductory and focuses on using Stata. It is perhaps the least "economisty" of the four, but still quite good.

For count data, I like Cameron and Trivedi's count data book, followed by Winkelmann's.

The books you have listed are good, particularly Wooldridge, but they cover much more ground than just discrete data at the expense of depth.


Do contemporary Marxist economists still deny the utility/value theory which underpins classical economics? Do contemporary Marxist economists still apply the labor theory of value when analysing economic phenomena? Or do they e.g. acknowledge that value (and utility) is subjective as is common knowledge in modern economics?

I am not familiar with contemporary Marxist economists, but the labour theory of value as formulated in Das Kapital does not deny that the usefulness (use value, in Marx' terms) of an item is subjective. Moreover, the fact that an item is useful to someone (however this usefulness is determined by each individual subject) is a precondition for it to be exchanged on the market.

For items that are exchanged on the market (commodities) the exchange value is the ratio between the quantity of one good that is exchanged for a unit of another good. Money is a special commodity
chosen by a society to measure the exchange values of all other commodities (price).
Items that are not exchanged (e.g. air, or something that is produced for personal use but not sold) have no exchange value / price, however useful they may be.

The prices of commodities that are sold only occasionally (e.g. a painting) may vary considerably and are rather unpredictable.
On the other hand, commodities that are produced, exchanged and consumed on a regular basis (and this is the topic of Marx' analysis) tend to have more stable prices.

According to the labour theory of value (LTV), this equilibrium price is related to the
average amount of labour necessary in a given society to produce each unit of the commodity (value).
The reason for this is that, if producers sell a commodity at a low price that does not reflect all the labour that went into making it, they will make no profit or even go bankrupt; on the other hand, if they try to sell at a very high price that is totally unrelated to the necessary labour, there will probably be competitors selling the same commodity at a lower price (unless there is a monopoly).
This situation is different from the case of a painting, because the buyer of a painting cannot find another seller selling the exact same painting at a lower price: LTV considers equilibrium prices of reproducible commodities under a given average productivity.

Once you have a certain number of people who decide to buy a certain product (whatever personal / subjective reasons they may have) and an average productivity for that product, you can use LTV to explain certain aspects of prices.
E.g. LTV would explain why a toothbrush costs less than a Boeing 747 even though the demand for toothbrushes is much higher than that for Boeing 747s by saying that the production of a toothbrush requires (much) less labour.

So, as far as I understand, even in Marx' original formulation there is no contradiction between the LTV and a subjective theory of value (use value) in that the LTV does not deny that the judgment about the usefulness of a given product is subjective.


What does this phrase mean? I'm reading a paper and at some point the author writes :

"We do this by decomposing monthly real crude oil prices and analyzing the
effect of the smooth part on the degree of the stock market instability."

What does he mean by "smooth part"? Is it the same meaning we have when dealing with integers?(factoring to prime numbers) Or is it something else? I don't understand what "the smooth part" means and how it is of any importance.

Sorry in advance if the question is too beginner.

I'm guessing the author has split the series between a trend component and noise component, for example with the HP-filter, and studies the smooth trend component.


Effect of prediction of later catastrophe Say a catastrophic worldwide event is predicted likely for exactly 100 years from now, but it will not affect anyone til then. Say a large meteor hit.

Would markets budge much?

My only relevant observation is governments tend to invest in the future, but begrudgingly. (Climate change). So there will be some money in disaster aversion etc.

This is a very open ended question, that could be researched. I can start to give some direction. For a realistic answer, one of the most important assumptions to your questions is how strongly everyone believes a meteor will hit 100 years from now, and second, how strongly everyone believes it is preventable/management.

Consider Two Scenarios:

A. The meteor will hit in 100 years. In the first 2 years, we developed a solution to it all, and everyone is convinced it will work. Will markets budge much? Probably not much afterward. Depending on the cost of the solution (\$1 million vs. \$10 trillion) markets may have moved.

B. The meteor will hit in 100 years. Everyone has fully accepted there is nothing we can do about it, and we all will be annihilated. Market will budge significantly, especially as the date gets closer. People's investment for future will change, how we think about raising kids, etc. How markets will change would be pretty hard to describe, but there may be outside literature that postulates ideas.

Overall, the biggest factor is humanities belief in their future. You can start by modeling the distribution of humanity that believes we will exist for $t$ more years. This now gets into probability theory.


Print money to buy and nationalise companies If there's a water company worth £4 billion making £500 million a year profit, the government "prints" £4 billion and buys the company, then every year "burns" half the profit and reinvests the other half.  Would this work or create damaging inflation in the economy?

This is a transaction where productive assets change hands, it is not a transaction that reflects production.

Moreover assume that the company oparates exactly as before, producing the same output in quantity and quality and with the same prices and with the same costs.

Then nothing has changed in the economy as regards production (and so income).

The only difference is that the previous owners of the company now have in their hand 4 billion pounds. What will they do with it?

Assume they just keep it in the bank. Then under fractional reserve banking, the bank will be able to offer more loans at a total principal value a multiple of the 4 billion. Will the bank attempt to offer more loans? If it does, will it have to offer lower interest rates to attract willing (and solvent) borrowers? The questions have no ending.

Assume instead that the owners try to spend the 4 billion by purchasing goods from domestic businesses. Is a 4 billion-increased-demand large enough to push prices up (is supply capacity at its limits and stock low) or suppliers will be happy to accommodate, no problem? The questions have no ending.

Assume instead that the owners attempt to import goods from another country...

My point is that such questions can in principle be answered only after assumptions as to the state of the economy have been clearly spelled out (i.e. only in the context of a model). Moreover, for a specific case study, the relative size of the transaction compared to the economic system matters. How is a 4-billion increase in government debt perceived by economic agents?

...and I haven't even touched and the "burning the profits" strategy proposed in the question (and it wouldn't burn it in any case, it would repay its debt to the central bank, which, granted, is the economic equivalent of destroying money).


Market Value of a publicly traded company I want to know the market value (market capitalization) of a company on a particular day in the recent past (within the past 5 years). How can I do this, may be with the help of Google Finance or Yahoo Finance or some other tool?

One possibility would be to use Wolfram Alpha.

If I type the search phrase market capitalization msft 3rd December 2010 then the search engine returns the following:

If you use Wolfram Mathematica on your PC then you can import the data directly for processing using the FinancialData command (see here).


Is there inverse relationship betweet prices of interest-bearing assets and the interest rate? I was wondering about why investors converting out of interest-bearing assets into money in the money market cause the interest rate to increase. Then I remembered that there is inverse relationship between prices of bonds and the interest rate. In case of bonds investors converting out of them would increase their supply, consequently lowering their prices. But lower prices of bonds mean higher de-facto interest rate for your investment into bonds because the quantity of money that you needed to make investment has decreased. Then it happened to me that the same logic can apply to interest-bearing assets in the general, not just to the bonds. And if it's correct it can serve as an explanation for exact mechanism of for increasing interest rate in the money market.
Am I correct about the relationship? Is there inverse relationship between interest-bearing assets and the interest rate? And if not, why?

The shortest possible answer to the question in the title (as stated now): “Yes.”
However, based on the comments, there are questions about definitions. I will attempt to answer them.
A fixed income instrument is anything that pays the owner cashflows on a fixed legal schedule, and the owner is not obligated to make any payments (other than the initial payment). This covers bonds, loans, and other forms of debt.
If there is no optionality in the structure (not prepayable, etc.), the internal rate of return of the security is unique and has an inverse relationship with the initial price. (Excluding corner cases such as zero cost, etc.)
This internal rate of return is typically referred to as the rate of interest or yield of the instrument. (Bond and money markets have specific calculation conventions, which end up being a more complex version of the internal rate of return.)
When trading fixed income securities, they can be traded in terms of yield or price interchangeably (although markets follow conventions for which to use in a quote). As such, prices and “interest rates” are mechanically always moving inversely.
The question seems to be focussed more on the policy rate, which is often “the” interest rate in simplistic economic models. Modern central banks force a short-term nominal instrument rate (often overnight, but can be two weeks or even three months) to some target level, that is changed over time as a policy tool.
Despite what simplistic models say, there is no relationship between the “money supply” and this rate. (People discussing this relationship are typically using Economics 101 textbooks that are decades out of date.)
The yields on other instruments move around on a daily basis. Many factors can influence prices, but there are bedrock valuation principles.

Instruments that have no perceived default risk (e.g. most non-Euro area developed country sovereigns) have a fair value that matches the expected path of short-term rates. The set out of outstanding bonds defines a risk-free yield curve.
Other instruments will incorporate a default risk premium and/or a liquidity premium that is added to the risk-free yield curve.


Are services included in the calculation of a trade deficit? Are services included in the calculation of a trade deficit?

Presumably measuring service exports is more difficult/less accurate(?) than for goods?

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


If a best-response dynamic converges, does it converge to a Nash equilibrium? Consider a game with a finite number of players and finite action space. Suppose we consider a sequential iterative game-playing process in which, in
each period, players myopically select actions that are a best-response to the actions last
chosen by all other players.
Question: suppose that after a certain number of iterations no player wants to change action.
Hence, the best-response dynamic has converged to some action profile. Is this action profile necessarily a pure strategy Nash equilibrium?

Given that the system does converge, i.e. $a_i^t=a_i^{t+1}=a_i^*$ for all $i$ after some $T<\infty$, and that $a_i^{t+1}\in BR_i(a_{-i}^{t})$, it follows that $a_i^*\in BR_i(a_{-i}^*)$ for all $i$. Hence $a^*$ is a Nash equilibrium of the underlying game.


How is money created? This might seem like a really simple question, but I am really troubled by it on a macro scale. The money has to come from somewhere. Someone might start up a business that creates things or takes things from the Earth. You could say this is "creating" money, but I argue it isn't, or I am missing something.

Here is how I see it. In order for that company to work, they have to make a profit which means they have to take more money than they are giving. This is the way all companies work. In the end logically, this money becomes concentrated in a few people. If this is the case, on the broadest level, how is it that standards of living increase? Isn't it inevitable that the rich get richer and the poor get poorer, with money being concentrated in fewer and fewer people over time? And if that is the case, won't capitalism eventually fall apart, with fewer and fewer people being able to purchase goods? If not, how is this corrected? Is there a way the rich can get richer with the poor also getting richer (which means money is magically coming out of thin air)? (The buying power of the poor becomes less as the amount of money they possess lessens; the opposite being true of the rich) (Poor = possessing small monetary volume; rich = large monetary volume)

I also have a similar question with trade deficits. How is it the United States can still grow, despite sending more money out than it takes in? Perhaps the answer to this question will solve the one above.

Re: "You could say this is 'creating' money" - no you couldn't. This would be conflating money and wealth. Wealth can be created without new money being created - indeed wealth was created before money even existed. Conversely money can be created without creating wealth. So they are entirely separate things. A crude analogy: wealth is to money as apples are to numbers. You can count apples using numbers, but growing new apples does not create new numbers.

With regard "In the end logically, this money becomes concentrated in a few people." - not true. People don't earn money in order to collect big piles of it and spend all day counting it. Instead they use it to buy stuff which means that the money circulates through the rest of the economy.

With regard "How is it the United States can still grow, despite sending more money out than it takes in?"... it doesn't send out more money than in takes in (at least not to any great extent). Foreigners do not accumulate great piles of dollars that they earned from selling American's stuff - instead they use their dollars to buy American assets, like US government bonds.

With regard how money is created, please be aware that this is a controversial area and there is a huge amount of misinformation on this subject. The best document to read that I know of on the subject of money creation is this one published in the Bank of England Quarterly bulletin in 2014.


Can consumer surplus be negative if a consumer is forced to make a purchase? Assume there is a good that a producer sells for $100$. A consumer's willingness to pay for that good is $50$. However a government program forces consumers to purchase the good irrespective of their willingness to pay (assume budget constraints are not an issue right now). Would this imply their consumer surplus would be $-50$?

Or do we reflect the negative consumer surplus as producer surplus (this doesn't make sense to me)?

Consumer surplus is their willingness to pay minus the price they pay,  and producer surplus is the price they receive minus their willingness to receive. So if you are assuming that consumers are forced to buy at a price of 100, yes the consumer surplus is negative. and according to your example, the producer surplus will be zero. You are right it does not make sense whatsoever to reflect it as producer surplus.


Why do rich countries remain rich? I can think of two possible explanations:

People there inherited the wealth of their ancestors (and of the companies of their generation).

Advances in technology allows you to earn money more easily.

Despite other factors at play: Approximately how big percent of the rich countries' wealth is caused by the first one and how big by the second one?

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

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

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

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


Is it better for economic growth to invest in stocks or to purchase products? I've recently been interested in economics and I admit that my understanding concerning it is limited. However my question is if investing in stocks is good for the economy. From my understanding, it is just the redistribution of ownership and wealth from individuals. The businesses are not gaining money, and so profit can be gained there.  It seems that it would be substantially better for the economy to purchase products directly from the company, so that the businesses may gain money from consumer spending.

The means by which purchasing stock effects economic growth is not as clear as purchasing companies' goods.  Nonetheless, there is tremendous benefit for firms (and hence the economy at large) when one decides to purchase their stock, to help understand this I recommend Why Do Companies Care About Their Stock Prices?

First in their IPO, the capital gained they can invest in R&D - as you will learn, some models posit technological shocks are the only effects on long-term economic growth
Second they continue to benefit from a high stock price in the secondary market with stronger financing and M&A's, and can continue to issue more stock at a higher price will yield more value which they will hopefully use to fund further R&D!


Imports/Exports in the equation of exchange From the equation of exchange: $MV=PY$, where $M$ is the money aggregate, $Y$ is the real output, $P$ is the price level and $V$ is the velocity of money, we derive $\% \Delta M + \% \Delta V = inflation + growth\ rate$. How will these equations be affected by inclusion of imports/exports, and international financial transactions?

Mine is not an expert opinion, but just adding my thought since the question went unanswered.
MV=PQ has got nothing to do with trade deficit. Nor the equation will be impacted by varying import/export.
This is because PY is the nominal GDP. Which means, PY is inclusive of real gdp(C+I+G+(X-M)), where as (X-M) is the export-import.
Putting it plainly will be like, it doest matter if the exports or import varies or if it is impacted. This variation will be adjusted in the RHS of the equation. So when we calculate Velocity it should not matter theoretically.


statistical discrimination VS taste based discrimination Given the progress in the literature on economics of discrimination. What is the reason for still believing in the dichotomy taste-based VS statistical discrimination. I think the first theory is just a specific case of statistical discrimination, where information on discriminated workers' productivity is weighted by the discrimination coefficient (which basically is just a scaling factor). Any attempt to disentangle the two types of discrimination is pointless. Or?

You will find below two good and recent surveys on the literature on economics of discrimination and they all point out a clear difference between taste-based and statistical discrimination. We can imagine a situation where the employer's information about workers' productivity is perfect, such that there is no statistical discrimination, and still observe a racial wage discrimination for example because the employer has a taste for discrimination. Knowing the source of discrimination seems crucial to fight against discrimination and its consequences.

Charles, K. K., and J. Guryan (2011): “Studying Discrimination: Fundamental
Challenges and Recent Progress,” Annual Review of Economics,
3(1), 479–511.

Lang, K., and J.-Y. K. Lehmann (2012): “Racial Discrimination in the
Labor Market: Theory and Empirics,” Journal of Economic Literature,
50(4), 959–1006.


What happens to an MBS if all the underlying mortgages are fully paid back by the borrowers much before the maturity date? What would happen to an MBS (mortgage-backed security) if hypothetically speaking all the underlying mortgages were fully paid back by the mortgagees (borrowers), much before the maturity date?
I request the repliers of this question to follow this pattern:

If the answer is w.r.t. a global context, please start it with "In a
global context..." .
If the answer is w.r.t. only a country(XYZ)'s
context, please start it with "In XYZ , ....".

Thank you in advance!!!

Depends on the structure.

In the US, most residential MBS are pass-through, so the MBS is prepaid.
In Canada, MBS are (or at least were) mostly packaged into non-passthrough structures, so MBS cash flows follow fixed coupon schedule. There are prepayment penalties which are used to absorb the cash flows.
My understanding is that European pfandebriefe markets use a collateral pool, which absorbs prepayments.


Difference between the International Dollar and PPP This may be a very rudimentary question but I am trying to discern the difference between purchasing power parity and the international dollar.

I am starting to work on a project where we are trying to look at infant mortality rates and their relation to GDP along with some other indicators from different countries. I have started to look for different data through GapMinder.

Reading some of the variable descriptions they claim to have the GDP in PPP and then some other reference GDP PPP in international dollars.

So I then took to the internet looking for the difference. The Wikipedia artilce on the Geary–Khamis dollar is leading me to believe they are the same thing if i am using USD as my base dollar unit?

So my question ultimately would be: What is the difference between the international dollar and PPP?

They are different stages of the same process. You convert a country's GDP into international dollars USING PPP.

PPP are rates. They are a relation between prices in different countries. International dollars is a unit of measurement.

The World Bank says "GDP per capita based on purchasing power parity (PPP). PPP GDP is gross domestic product converted to international dollars using purchasing power parity rates. An international dollar has the same purchasing power over GDP as the U.S. dollar has in the United States"


CRRA utility function with a scale parameter I am wondering if it is possible to write down a following CRRA utility function ;

$$u\left(c(t)\right)=a\frac{c\left(t\right)^{1-\sigma}}{1-\sigma}$$ where $a>0$ is a constant scale parameter. I need this $a$ to have some numerical results but I am not sure if $a$ can be justified.
In a growh model, I am trying to show the existence of Hopf bifurcation and limit cycles. Then, with a scale parameter like that, I can show that it exists.

Normally, it does not change the usual assumptions on a CRRA utility function, (an increasing concave function)

Is there any way to justify it (are there some examples of this kind ?) or are there any types of utility function with constant scale parameters ?

As it is well-known, preferences (even under risk) are invariant to affine transformations of the utility function. Therefore, adding a 'scale' parameter adds nothing in terms of fundamental preferences (i.e. in terms of comparing streams of consumption). I cannot even imagine what kind of 'numerical results' would be sensitive to it.


Getting a Paper Published I have a nice and (I think) significant result. I would like to publish it, but I have no idea how. It's a proof of an optimal institutional structure. Who do I contact?

If your paper is rigorous enough, you might want to submit it to a peer-reviewed specialized journal. Journals pertaining to Economics are the Quarterly Journal of Economics, Journal of Macroeconomics, The Economic Journal, and many others. Many of these journals have a link for writers to submit their paper and a "guide for authors". Likewise, search on Google for Call For Papers.

The question by @MichaelGreinecker (whether you know anyone in the field) makes me wonder whether being accepted for publication also depends on having connections with the editorial, rather than being exclusively a matter of rigor of the research.


What are the benefits of a first price sealed bid auction? All parties make a single bid. But do not disclose the bid to peers. The organizer chooses the maximum (or minimum) bid as the winner. What are benefits of such a system as opposed to normal auction where bidders openly declare the bids and keep updating based on the current maximum ( or minimum )?

A good article to read about this is by Susan Athey, Jonathan Levin and Enrique Seira. It has the title: "Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions," was published in the Quarterly Journal of Economics, vol. 126(1), 2011, 207-257, and is available online at:

http://faculty-gsb.stanford.edu/athey/documents/comparingformats.pdf.

The abstract includes this: "We study entry and bidding patterns in sealed bid and open auctions. Using data from U.S. Forest Service timber auctions, we document a set of systematic effects: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. A private value auction model with endogenous participation can account for these
qualitative effects of auction format."


Will inflation rate be the same if we use different base year? I saw this chart where CPI for 2003 is 1.84, for 2004, is 1.889. I dont know the base year because its not in the chart. But base year has to have CPI of 1.

If we instead use 2003 as base year, is the inflation rate during 2003-2004 period, going to be different?

Not at all.
Assuming You wanted to calculate the inflation rate from between 2003 to 2004, you only need to know the CPI for the starting and ending dates.  So the CPI index in 2003 is 1.84 and the CPI index is 1.889 in 2004.

The formula is: (end -start)/start

so we have (1.889-1.84)/1.84 = giving us 0.02663 or a percentage change of 2.663% -This is the inflation rate-.

If we moved the base year to 2003 and assigned the CPI of 1, we can use this calculate the CPI in 2004.

(X-1)/1 = 0.02663
X-1 = 0.02663
X = 1.02663 * 100 is a CPI for 2004 of 102.663.

Made this table for you to get an idea of how it is calculated based on your example.


Real Exchange Rates calculation I am struggling with something as simple as real exchange rate calculation!

I get the theory: RER = NOM * (P*/P) i.e. nominal exchange rate times price level ratios. Apparently, using CPI (consumer price index) is common practice for P.

I have the nominal exchange rate and I have both CPI for country A and country B as index 100=2005.

What I don't understand is that in 2005, the nominal rate = real exchange rate. But that makes sense only because of the 2005 index - not in the real world. What am I doing wrong?

you cannot compute real exchange rates based on the data you have. What you can do, and what is often done (not sure what it is good for though) is to use relative PPP to calculate changes in RER using some base year.
The OECD publishes some statistics on P*/P, you could also use that, although I am not sure what methodology they use.
In practice, you would need the actual prices of a basket of goods to calculate the RER, once you somehow normalize prices within a country you can no longer calculate the RER.
hence the appeal of stuff like the Big Mac Index.


What does Smith mean by "price of work" in this context? I've read these excerpts from The Wealth of Nations multiple times:

In reality high profits tend much more to raise the price of work than high wages
In raising the price of commodities the rise of wages operates in the same manner as simple interest does in the accumulation of debt. The rise of profit operates like compound interest.

But I struggle to grok what he means.
What is "price of work" and how is it different to "wage", and why does profit have an exponential relative growth, not a linear one?

Smith was talking of "the price of work" as meaning the price of economic products bought from the employers and merchants, not the price of labour bought from the workers.
"Work" had this dual meaning historically, referring to both the activity of work and the result of work, whereas nowadays the latter meaning tends to be qualified (like a "work of art", or a "piece of work", etc.).
The distinction Smith makes is that if you put the wages of every worker involved up by 5%, the overall market price rises by 5%, because the 5% increase is by reference to their old wages.
Whereas if you increase the profits of a chain of merchants by 5%, the output price rises by much more than 5%, because each merchant in the chain takes 5% on top of all what the previous merchant took. The increase is by reference to the difference between input and output prices, not by reference to the merchant's old income.
Hence, in Smith's view, increases in wages result in "simple" percentage increases in output cost, whereas increases in profits result in "compound" increases in output cost.


When the ECB does QE, does it print new money? I knew that when the Fed in the US buys bonds through Quantitative Easing, it does so using money it has from previous profits and that it doesn't print new money.

However, I was reading this article about QE, which states that the European Central Bank prints new money when doing QE.

So the ECB, unlike the Fed, does print new money when doing QE?

First of all, I'm not sure you are reading that article correctly, as I cannot find any mention of the claim you make. In any case, you can find here a superb comparative analysis of QE for the Fed, the Bank of Japan, the ECB and the Bank of England.

Regarding money creation, the key difference between conventional monetary policy and QE is the type of asset being transacted (short-term government debt versus long-term government/private debt, respectively; again it depends on the central bank, see referred document). There is, to my understanding, no difference on how the monetary operations are carried out in each policy.

In fact, these operations are quite standard. The central bank buys assets by crediting the seller's bank account, in exchange for the ownership of the assets, which are then added to the central bank assets and eliminated from the sellers assets. This is akin to you receiving a deposit in your current account. You have been credited with some amount. There is no physical money creation or physical money transfered in the process itself. There is indirect money creation (all electronic) if such transactions enable the banks to expand their credit to other institutions or companies (provided demand for such credit exist and banks are willing to do so, e.g. in an economic boom), whilst still complying with the regulation.

To learn more about money creating and modern banking, I suggest this page, this page or this post.


How is using a reserve fund different from printing money? It is a common knowledge and has been explained here on SE that the source of value is production and consumption rather than money, and that accumulating money is thus pointless. Yet, "rainy day funds" do just that. What is their purpose?
For a layman like me, it seems extracting money from circulation to a reserve decreases inflation, while using that money later would just increase inflation. Then, I must be misunderstanding some basics.
Indeed, a sovereign does not normally save in its own currency, but rather in foreign currencies or other valuable assets, over the value of which it has no direct control, but only an indirect influence as any other actor. However, for a governmental-scale fund, the influence (presumably deflationary for increasing the fund and inflationary for spending it) would be so strong that it may print new money as well. Where is my understanding flawed?

No, accumulating money is not pointless. Money not being the source of value does not lead to it being of no value.
Money, including the type we use right now -called "fiat money"-, has 3 properties.

It is an accepted tool for carrying out transactions.
It is a way to measure a product's value.
It is a store of value.

The 3rd point is the one you're looking for. As long as the value of money (its purchasing power) does not drop then it is a proper way of storing value; you can keep your money and use it in the future (a "rainy day fund" perhaps)- this wouldn't happen if you were exchanging fish for cows for example.
It is apparent that money is not the best store of value, since it doesn't give its holder any interest just for holding it, unlike deposits in a bank, bonds and stocks.
A state can have multiple sources of property, money being one type of it. For reasons of diversification to risk it is preferred that assets are not of the same type.
On the topic of inflation and efficiency;
Neoclassical theory suggests that storing a reserve fund is not the same with money being destroyed and then printed anew. Everyone knows this money exists and is being stored, and will be used in case of need. So people, having rational expectations, already understand this amount of money as part of monetary policy and the implications of such policy (including inflation); which means that the current price level is already adjusted for this inflation.


Interest rates in Quantitative Easing of 2008 When the US govt printed money in 2008 and lend it to the banks, how much the banks had to pay in interest?

Quantitative Easing is the purchase of bonds by the central bank. The purchases leave private banks with balances at the central bank (reserves). The private banks are “lending” the Fed money (not that it needs it). The rate if interest paid is set by the Federal Reserve.
The rate paid is shown at: Link to FRED seeies.
(Note that some balance sheet expansion was repurchase agreements - repos - which are a matched pair of transactions where the Fed buys a Treasurybond, then sells it back at a pre-determined price. This can be interpreted as a loan, with an implied interest rate - the repo rate.  These are “open market transactions,” and the exact details are not publicly disclosed. However, the repo market is a large market, and repo trades near the Fed Funds rate, as both represent lending backed by the Federal government.)


Interacting covariates with the instrument in the first stage If I want to run a 2 stage least squares (2SLS) regression with:
Relationship of interest: $Y = \alpha + \beta X + \varepsilon $, where $X$ is the endogenous explanatory variable of interest.
If I have an instrument $Z$ where I can safely assume that it is both relevant and fulfils the exclusion restriction, can I interact it with other variables in the first stage, that do not fulfil the exclusion restriction, as long as I control for these other variables in the second stage?
So I am thinking
Estimating the first stage: $X = \gamma + \delta_1 Z + \delta_2 W_1 + \delta_3 W_2 + \delta_4 Z*W_1 + \delta_5 Z* W_2 + \epsilon$, where the exclusion restriction only holds for $Z$ but not for the $W$s, to get $\hat X$
Second stage: $Y = \omega + \eta_1 \hat X + \eta_2 W_1 + \eta_3 W_2 + e $
So does this procedure allow me to kind of side-step the exclusion restriction? If so, is there any paper / book / article that talks about that?

Short answer: No.
Your model is $Y=\alpha + \beta X + \varepsilon$. Even when $X$ is exogenous, if you regress $Y$ on $X$, $W_1$ and $W_2$, then the OLS estimator is inconsistent (for $\beta$) unless $W_1$ and $W_2$ do not affect $Y$ on average (after controlling for $X$) or $X$ is uncorrelated with $W_1$ and $W_2$. When $X$ is endogenous, there is no reason why your strategy should work.
Now suppose that your model is $Y=\alpha + \delta X + \gamma_1 W_1 + \gamma_2 W_2 + \varepsilon$, instead. (This is not your model; $\delta \ne \beta$.) You are saying $X$, $W_1$ and $W_2$ are endogenous, while $Z$ is exogenous. You need instruments for $X$, $W_1$ and $W_2$, but you don't. The parameters are not identified.


How to perform unbalanced panel data regression in R? I am attempting to perform an unbalanced panel data regression in R.  My code is as follows:

pdata <- plm.data(b2, index = c("ticker", "year"))
try1 <- plm(formula = logDipLoanTotal ~ PrimeFiling  +
logLiabBefore + logSalesBefore + EmplBefore + DebttoAssetRatio +
squareDebttoAssetRatio + FSCashShortTermInvestments + Percent +
NUM_OF_EMPLOYEES, data = pdata, model = "within", effect = "time")
summary(try1)

I run into the following error:

duplicate couples (id-time) in resulting pdata.frame
to find out which, use e.g. table(index(your_pdataframe), useNA = "ifany")
duplicate couples (id-time)

This is obvious - I am having issues because my panel data is unbalanced, where the ticker/year combination can be associated with multiple lines of data. This is because multiple "deals" were done in the year associated with the company ticker in the year, or sometimes no deals were run in the ticker/year combination. How do I run this kind of model in RStudio with unbalanced data? Let me know if this doesn't make sense and I can edit the question.

Here the solution would depend on what you want to accomplish. Note the problem is not just that the series is unbalanced, for an ordinary unbalanced panel data-set where firms have different number of $T$ observation the command would still work. Here no adjustments are necessary, you can easily try it yourself:

 install.packages("plm")
library("plm")
data("EmplUK", package="plm")
result<-plm(formula = wage ~ emp, data = EmplUK, model = "within")
summary(result)

Which gives you this output:

  Unbalanced Panel: n = 140, T = 7-9, N = 1031

  Residuals:
       Min.   1st Qu.    Median   3rd Qu.      Max.
  -12.13926  -1.21442  -0.20655   1.02437  17.11197

  Coefficients:
       Estimate Std. Error t-value  Pr(>|t|)     emp -0.119813   0.031103 -3.8521 0.0001255 ***

So you can use unbalanced data without any additional adjustment to the plm code itself. I think authors there refer to adjustments that have to be made when programming the function to account for this (as this creates some problems with matrices - at least that is my understanding from the document you linked).

However, if I understand you correctly the problem you have is not just about panel being unbalanced but because there are duplicate observations like this:

Firm ID | Year  | event          | x  | Y |
  1      | 1999   |  1jan2000     |  2 | 4 |
  1      | 1999   |  20jan2000    |  24| 54 |

This is more serious problem than just unbalanced panel. Here the problem is not the 'unbalanceness' but the fact that you will have 'duplicate' observations if you will run any panel model with Firm ID and Year as panel identifiers because you cant have one panel identifier assigned to two different different observations as that means your observations are not unique.

This could be solved in one of few ways:

Run the model on dates instead of years if the events do not occur at exactly the same time. So now your panel identifiers would be: Firm ID Event instead of Firm ID Year.
Create new firm ID for each event. So you could create new firm ID like this:

Firm ID | Year   | event         | x  | Y |
  1_1    | 1999   |  1jan2000     |  2 | 4 |
  1_2    | 1999   |  20jan2000    |  24| 54 |

however, downside with within estimator would be that if these
    multiple events on same day occur only once these would drop, and also my intuition tells me this would led to some methodological issues if you would try to lets say cluster errors on firm level as one firm would be treated differently based on no of events.

You could also aggregate values of X and Y across events on a single day and just include extra dummy for firms with multiple events in a given year.
Consider different estimator. For example, instead of within estimator you could use pooled OLS where you treat each observation as individual event with firm fixed effects. I cant think of any reason why that could not be applied here.

Also here I would recommend for searching for panels with duplicates, I know this is not a genuine duplicate, but mostly when this issue is being discussed many people call these observations duplicates so it will probably give you better results than searching just for unbalanced panel data which is usually applied to panel data where you just have different $T$ for each panel ID.


Question About Basic Supply/Demand Concepts I am learning the basics of Supply/Demand, and I came across this question (it's not a part of my homework; I just want to know the answer/explanation because I'm doing some extra practice problems for a test).

Question: "Starch from the stalks of potato plants is used to make packing peanuts, a complement in production. A decrease in potato demand that lowers potato prices will cause which of the following in the packing-peanut market?"

My thoughts:

So, we know potato prices decrease, and potatoes are a complement in production. From what I've learned, a decrease in the price of a complement in production leads to a decrease in supply of the original good (ie decrease in potato prices leads to decrease in supply of packing peanuts).

Now, what I don't understand is how demand plays a factor.  I know that when the price of a complementary good is decreased, demand for the original good increases.  But what's different in this case is that potatoes are a complement in production, NOT consumption.  From the examples given in the text, everytime they mention how changes in complement goods affect demand, they are referring to a complement in CONSUMPTION.

What I'm confused about is potatoes' relationship to packing peanuts.  Potatoes are a complement in production, so I'm thinking it shouldn't have any affect on demand for packing peanuts, since consumers are not concerned with processes of production, right? (So my answer would be that a decrease in potato prices leads to a DECREASE in supply of packing peanuts and NO CHANGE in demand of packing peanuts).

You are right that most discussions talk about complementarity in consumption, which is why this question is all the more interesting.

Demand falls for potatoes, which causes the price of potatoes to fall, which causes the supply of potatoes to fall. This means there is less starch available. This in turn means that we can make less packing-peanuts, hence supply of packing peanuts falls.

You are right that demand for packing peanuts does not change. The supply will nevertheless change however. This is because the supply of starch falls and the input factor of packaging peanuts is more expensive, so less is optimally produced. I.e. the supply curve of packaging peanuts changes, in this case shifts to the left so there is less equilibrium supply even though demand for packaging peanuts has not changed.


Does a monotonic transformation of a homothetic utility function imply the preference relation on the set of consumption bundles is still homothetic? Does a monotonic transformation of a homothetic utility function imply the preference relation on the set of consumption bundles is still homothetic?

Obviously, if a utility function on a set of  consumption bundles is homothetic, then the preference relation is homothetic.

Yes.
We know that a monotonic transformation of a utility function still represents the same preferences and as the old utility function represented homothetic preferences the new one does, too.

As an easy example you could look at Cobb-Douglas utility functions of the form $u(x,y) = a\left(x y\right)^\alpha$. For $\alpha = \frac12$ the utility function is homogeneous of degree 1, but for every $\alpha,a>0,$ the preference relation is homogeneous of degree 1.

We never used homothetic as a property of the utility function to answer your question (as it works for every utility function).
A homothetic utility function is, to the best of my knowledge, not very clearly defined, I have see two different versions:

Homothetic as different name for homogeneous of degree 1
A homothetic utility function is a utility function that represents
a homothetic preference relation.

Which means, with definition 2 Cobb-Douglas utility functions with equal weights are always homothetic, with definition 2 only some of them are:
$$u(tx,ty) = (tx)^\frac12 (ty)^\frac12 = t xy = t u(x,y)$$
and some are not
$$u(tx,ty) = (tx) (ty) = t^2 xy \neq t u(x,y)$$


Best terminology for "inverse" preferences This might be related to : Symmetric and asymmetric preferences.

In your experience, what is the best terminology to denote a pair of preference relations $(R,R')$ over some set of alternatives $A$ such that, for all $a,b \in A$, $a~R~b$ implies $b~R'~a$?

@Oliv's comment lead me to the following wikipedia article https://en.wikipedia.org/wiki/Inverse_relation
which indicates that the term "inverse" is used to define the kind of relation between $R$ and $R'$ that I described in the question.

The wikipedia article recommends to use $R^{-1}$ to denote the inverse relation of $R$.


Sunk costs - Book value and Market value i try to understand the concept of sunk cost and how we compute sunk costs when there is a difference between book and market value.
For example, if the book value of assets is $300 000 and the market value of the assets is $150 000.
Sunk costs = ($300 000 - $150 000 (depreciation)) = $150 000 ?
Or the sunk costs = 300 000 because the assets have been already paid ?
Many thanks,

Sunk cost "is a cost that has already been incurred and cannot be recovered." For example, paying people to dig a hole in the ground. If you can sell the asset then the money you get can't be part of the sunk cost because that portion of the cost was recoverable.


Why doesn't QE cause the federal funds rate to continue decreasing? Quantitative easing (QE) is essentially a large-scale form of open market operations, in which the Fed buys large amounts of treasury bills of all maturities (ranging from 1-month to 30-year) and mortgage-backed securities from commercial banks. By doing so, they are crediting these depository institutions with large amounts of electronic money. Thus, wouldn't there be a large expansion of the supply of federal funds in the federal funds market as a result of QE? And hence, wouldn't the federal funds rate keep on decreasing, even below zero, as the Fed's massive "QE infinity" programme continues?

At the time of writing this answer, the Federal Reserve pays 0.1% on reserves: link to Fed webpage.

Banks have no incentive to lend Fed Funds at rates below 0.1%, as they can keep the excess reserves and earn a higher rate of interest.

Interest rates are largely set by price signals made by central banks, not quantities.


Buying stocks in company merging/acquisitions Does an acquiring company have to buy all the stocks of a target company to acquire/merge with it?
If so, why? I thought stocks give voting rights and dividends, but not direct control of company management.
If not, why do they usually do it?

Stocks/shares are equity (a share is 'a part of' something) and are thus essential to ownership of a company. Owning shares means that you own part nof a company. The ownership, as a side effect, gives voting rights on the C-suite and dividends.

Acquiring a company requires you to buy all of the shares of that company (so that you own it).


Are there examples of strategies where a combination of third degree pricing and two-part tariffs are used together? Of course, I am only interested in instances where the combination of the two strategies ultimately lead to higher profits than if the monopolistic firm had used only one.

Here's an easy example: movie theaters.

If you view theater pricing models as a two-part tariff (ticket + snacks) then any time there's a "seniors discount" or something like it, this would fit your strategy.  It's a simple exercise to determine the conditions for profitability of such a campaign, but the fact that they've been around forever suggests that on net, they are.


What does this phrase about economics mean [Lionel Robbins]? Lionel Robbins once said, "Economics is the study of scarce resources which have alternative uses."

Would someone mind explaining what he meant by this?
I, as a naive 14 yr. old, think about this economics quote as meaning 'a person studying how to use scarce resources in any context and those resources have many uses'. e.g. It is cold outside and I don't have enough money to buy gloves, but I do have an extra pair of socks, thus I use socks as gloves.

If you cannot understand this, please let me know and I will clear it up!
 Thanks for your time -

To me, the quote seems to be about what economics is, and, more subtly, what it isn't. Robbins claims economics is about scarce resources that people can use for multiple things. The implication, and you will find this in undergraduate economics textbooks, is that economics is concerned with efficiency. Economists are simply looking for ways to make the most out of scarce resources. An outflow of this focus on efficiency is the paradigm of utility or profit optimization under constraints.

Perhaps more interesting is the subtle claim of what economics is not about: the distribution of resources. This does not seem particularly radical now, but it was much more so at the time. Keynes and Marx still dominated the political discourse in the early 20th century, and both were very much concerned with the distribution of resources. By focusing on efficiency rather than distribution, Robbins puts himself firmly in the neoliberal paradigm.


How to deal with misspecification of models in Macroeconomics? I'm wondering what methods are used in economics, specially in macro, to deal with model misspecification.

I've already searched the web, but I may be missing some methods. Therefore, I ask you for some help.

Thomas Sargent and Lars Peter Hansen have a series of work on "robustness", a theory (and technique) that deals directly with potential model misspecifications in the context of macro. [The term "robustness" derives from robust control theory].
Sargent's website has a page dedicated to this topic. The two also published a book, Robustness, that contains the main results of their work to date. Below is the publisher's description:

The standard theory of decision making under uncertainty advises the decision maker to form a statistical model linking outcomes to decisions and then to choose the optimal distribution of outcomes. This assumes that the decision maker trusts the model completely. But what should a decision maker do if the model cannot be trusted?
Lars Hansen and Thomas Sargent, two leading macroeconomists, push the field forward as they set about answering this question. They adapt robust control techniques and apply them to economics. By using this theory to let decision makers acknowledge misspecification in economic modeling, the authors develop applications to a variety of problems in dynamic macroeconomics.
Technical, rigorous, and self-contained, this book will be useful for macroeconomists who seek to improve the robustness of decision-making processes.


What are the known refutations of Mises' Axiom of Human Action? From Mises' Human Action

  Human action is purposeful behavior. Or we may say: Action is will put into operation and transformed into an agency, is aiming at ends and goals, is the ego's meaningful response to stimuli and to the conditions of its environment, is a person's conscious adjustment to the state of the universe that determines his life.

Are there any criticisms of this axiom as not being a complete description? By complete, I mean not that it describes all aspects of human behavior or fully explores it, rather I am asking whether or not it fully expounds some first cause of human action from which we can deduce answers to other questions about human economic behavior?

This question is not about whether or not the corollaries deduced from this axiom are true, simply: Is this description sufficient to allow us to, from it, describe corollaries of human behavior?

I am asking whether or not it fully expounds some first cause of human
  action from which we can deduce answers to other questions about human
  economic behavior?

What it is getting at:

Praxeology [the science of human action] says that all economic propositions which claim to be true must be shown to be deducible by means of formal logic from the incontestably true material knowledge regarding the meaning of action. Specifically, all economic reasoning consists of the following:

an understanding of the categories of action and the meaning of a change occurring in such things as values, preferences, knowledge, means, costs, etc;
a description of a world in which the categories of action assume concrete meaning, where definite people are identified as actors with definite objects specified as their means of action, with some definite goals identified as values and definite things specified as costs. Such description could be one of a Robinson Crusoe world, or a world with more than one actor in which interpersonal relationships are possible; of a world of barter exchange or of money and exchanges that make use of money as a common medium of exchange; of a world of only land, labor, and time as factors of production, or a world with capital products; of a world with perfectly divisible or indivisible, specific or unspecific factors of production; or of a world with diverse social institutions, treating diverse actions as aggression and threatening them with physical punishment, etc; and
a logical deduction of the consequences which result from the performance of some specified action within this world, or of the consequences which result for a specific actor if this situation is changed in a specified way.

Provided there is no flaw in the process of deduction, the conclusions that such reasoning yield must be valid a priori because their validity would ultimately go back to nothing but the indisputable axiom of action. If the situation and the changes introduced into it are fictional or assumptional (a Robinson Crusoe world, or a world with only indivisible or only completely specific factors of production), then the conclusions are, of course, a priori true only of such a “possible world.” If, on the other hand, the situation and changes can be identified as real, perceived and conceptualized as such by real actors, then the conclusions are a priori true propositions about the world as it really is. [19]

Such is the idea of economics as praxeology. And such then is the ultimate disagreement that Austrians have with their colleagues: Their pronouncements cannot be deduced from the axiom of action or even stand in clear-cut contradiction to propositions that can be deduced from the axiom of action.
— Hans-Hermann Hoppe, Economic Science and the Austrian Method, pg 25.

  What are the known refutations of Mises' Axiom of Human Action?

There aren't any that have been successful...

"All of these categories which we know to be the very heart of economics—values, ends, means, choice, preference, cost, profit and loss—are implied in the axiom of action. Like the axiom itself, they are not derived from observation. Rather, that one is able to interpret observations in terms of such categories requires that one already knows what it means to act.

No one who is not an actor could ever understand them, as they are not “given,” ready to be observed, but observational experience is cast in these terms as it is construed by an actor. And while they and their interrelations were not obviously implied in the action axiom, once it has been made explicit that they are implied, and how, one no longer has any difficulty recognizing them as being a priori true in the same sense as the axiom itself is.

For any attempt to disprove the validity of what Mises has reconstructed as implied in the very concept of action would have to be aimed at a _goal_, requiring _means_, excluding other courses of action, incurring _costs_, subjecting the actor to the possibility of achieving or not achieving the desired goal and so leading to a _profit_ or a _loss_.

Thus, it is manifestly impossible to ever dispute or falsify the validity of Mises’s insights. In fact, a situation in which the categories of action would cease to have a real existence could itself never be observed or spoken of, since to make an observation and to speak are themselves actions.
— Hans-Hermann Hoppe, ESAM


A question about Lagrange multiplier(when $\lambda=0$) I need help in a maximization problem(finding the optimal investment portfolio).

where $R_s$ and $\Phi$ are $n$ by $1$, with other variables being scalars.
$C^s$ is consumption (or wealth) of an investor, $R_s$ (or $R$) is the return rates of risky assets while $R_f$ is the return rate of a risk-free asset(say government bond), $\Phi$ is the quantities of risky assets, $\phi_f$ is the quantity of the risk-free asset, $\omega$ is the quantity of all the assets(so $\phi_f+\Phi' \cdot 1=\omega$), and $u(\cdot)$ is the investor's utility function.
The solution to this problem gives the following first order condition(FOC) i.e. taking derivative w.r.t. $\Phi$ (assuming integration and differentiation can be exchanged):

But there's actually a constraint: $\phi_f+\Phi' \cdot 1=\omega$, so I tried Lagrange but couldn't get the same result:
$$L(\Phi, \lambda)=E[u(c)]+\lambda(\omega-\phi_f-\Phi' \cdot 1 )$$ with FOCs:
$$\partial L/\partial \Phi =E[u'(c)(R-1\cdot R_f)]-\lambda \cdot 1=0$$
$$\partial L/\partial \lambda =\omega-\phi_f-\Phi' \cdot 1 =0$$
I couldn't get the same result from above. To have the result in the solution I must have $\lambda=0$ but I'm not sure in what cases it can hold. Please let me know which parts I did wrong.

A $\lambda = 0$ means that the objetive function's derivative with respect to the restriction is zero. In more intuitive terms, one cannot change the expected utility of consumption by relaxing or tightening the budget restriction. This is a weird case, for sure, I think you're missing something here. Maybe telling us what the variables mean can help?


Why is the derivative of this SWF non-positive? This question is related to the development of The Joint Giving Theorem (by S. Kolm).

There are two types of agents: benevolent and beneficiaries.

Benevolents' preferences are represented by utilities: $u^i=u^i(x_i,x,c_i,g_i,c_{-i},g_{-i})$

Where $x_i=X_i-g_i-t_i$ is final wealth, $X_i$ initial wealth, $g_i$ some private gift made to the poor, $t_i$ is the transfer to the public sector (who then gives it to the poor). $x$ is the final wealth of the beneficiaries. $c_i=g_i+t_i$ is total contribution of agent $i$. Subscripts $~_{-i}$ denote variables of other benevolents.

Beneficiary's preferences are represented by an increasing ordinal utility function $u=u(x)$.

The assumptions are (subscripts mean derivatives): $u^i_{x_i}>0,u^i_{x}\geq 0, u^i_{c_i}\geq 0, u^i_{g_i}\geq u^i_{c_j} \leq 0$

The theorem then says (I quote):

  Pareto efficiency for this society of potential givers and receivers implies that there
  exist coefficients $\lambda_i >0$ such that $U=\sum \lambda_j u^j +u$ is maximal (without loss of generality). Public policy chooses taxes $t_i$. When it implements a Pareto efficient social state, this choice maximizes such a function $U$. This implies, for tax $t_i$ :

  $\lambda_i \cdot (-u^i_{x_i}+u^i_{x}+u^i_{c_i})+\sum_{j\neq i} \lambda_j \cdot (u^j_{x}+u^j_{c_i})+u'\leq 0$

  with $=0$ if $t_i>0$ and $\leq 0$ if $t_i=0$.

My question is: Why is the derivative of $U$ with respect to taxes $t$ non positive? More precisely, why is it non-positive if taxes are zero?

This looks like a simple first order condition from constrained optimization. If the maximum is interior, i.e. if $t_i>0$, then the first derivative must be zero. If the maximum is on the boundary, i.e. if $t_i=0$, then the first derivative must be $\leq 0$. If it were $>0$, then we can't have an optimum, because then the value of $U$ could be raised by increasing $t_i$. It can be negative, though, assuming that $t_i$ cannot be negative.


Why isn't "long-run aggregate demand (or LRAD)" a thing? To give you a sense of where I am in my understanding of economics, I've just learned about long-run aggregate supply in the neoclassical/monetarist view as a vertical curve. It occurred to me why doesn't the same thing that happens to SRAS happen to aggregate demand over the long run - I'm envisioning that prices adjust in the long-run such that prices have no effect on anything; whether supply, demand, or anything else to do with purchasing habits. By the same reasoning as for aggregate supply, it seems like aggregate demand in the long run is also a graphically a vertical line. In the long run, where wages can adjust to match prices, people will continue buying the same quantity demanded as before just with a higher price level, right?

But I'm assuming, from what I've seen, that we don't differentiate between aggregate demand in the long and short run. What knowledge am I missing?

I'm in SL IB economics and we've just reached macro. I also have a shallow understanding of the Keynesian AS curve.

The main reason why long run aggregate supply is vertical is that in the end the production capacity of every country is limited. In the end there is always some maximum number of number of stuff we can produce (of course, there can be economic growth which expands our production possibilities but the LRAS is basically given by the production possibility frontier that will at every point in time be finite).

However, there is no such restriction on people’s demand. One of the basic assumptions of economics is non-satiation. More is always better than less. However, another basic principle in economics is that marginal utility of consumption is increasing but at a decreasing rate. That is more is always better but the more you have of something the less valuable the thing to you becomes. This is what makes demand decreasing function of price. The thing is that this holds both in short and long term. It’s not like people are only non-satiated in short run, and also it’s not like the marginal utility of consumption increases at decreasing rate only in short run.

Vertical demand curve would basically imply that consumers would never want to buy more of the aggregate product which is certainly not true.

So to sum up, LRAS is vertical because of physical limitation on our production. At some point no matter what’s the price it is not possible to produce more. For example, a writer can only write so much hours in a day so even if someone would offered the writer million euros per hour he or she can never work more than 24h per day (and considering that would kill the person probably I should say not more than max 18h) so the supply will be at some point completely vertical given by the production possibility of the economy. However, no such restriction exists on people’s demand. People’s needs are endless and people will always prefer more to less if the price drops sufficiently (since utility is not increasing at constant but at decreasing rate).


Are market structures on a spectrum? So I understand that each market structure has their own characteristics, and that for instance Perfect Competition involves high competition, and I believe Monopolistic competition slightly less so, oligopoly even less, and monopoly virtually none.

However, is a market structure pretty much set in stone? Or does the structure change within a spectrum depending on competition for instance?

i.e. Would it be right to say that if competition in a market which was an oligopoly has increased and dominative firms have lost some of their market power, then the market is beginning to resemble that of monopolistic competition and less like an oligopoly?

If there were such a spectrum, it would not be one dimensional. For instance, we could compare the competitiveness of markets with homogeneous products in terms of the number of firms in that market, and have the following spectrum:

monopoly: one firm, no competition
(Cournot) oligopoly: $n$ firms ($n<\infty$), imperfect competition
perfect competition: infinitely many firms, perfect competition.

However, this spectrum only works homogeneous products. When you talk about monopolistic competition, i.e. firms competing with differentiated products, then a new dimension opens up: non-price differences in products. An example would be cell phones with different operating systems (e.g. iOS and Android). A small increase in the number Android-powered phone brands is not necessarily going to reduce the market power of iPhones.

So the spectrum of market competitiveness is not as straightforward as you envisioned. While the two extreme cases, perfect competition and monopoly, are pretty clear, things in between are much less so. For example, a 2-firm Cournot market could be more competitive than a 2-firm monopolistically competitive market, if you carefully choose the demand functions for the latter. So at least in the comparison between oligopoly and monopolistic competition things are not as deterministic as you thought.


Why don't central banks just donate money to their poor citizens, rather than QE? Why don't they prioritize paying their citizens directly (Americans in this case) over providing liquidity, repo, buying bonds, and lowering interest rates? I have a BA in Economics, so hope this isn't bad economics! I ask for central banks in general, not just the US Federal Reserve.

  Comment:

    SO we can afford this but not Medicare for All? Okay. Yeah, thanks.

  Pretty basic distinction here, this action was undertaken by the Federal Reserve, which is not the same thing as the federal government. The Federal Reserve does not need to raise money from taxpayers, they have the authority to create new money for these operations.

  Also, the Federal Reserve does not handle healthcare policy.

On Mar 16 2020, Federal Reserve cuts rates to zero and launches massive \$700 billion quantitative easing program. On Mar 17 2020, Fed announces move to help businesses get short-term funding in commercial paper market, and Mnuchin says Trump administration is looking to get cash to Americans 'immediately'. Why doesn't the Fed just donate that \$700B to poor private individuals?

  On Friday Mar. 20 2020 morning, the Fed announced that it would be increasing the frequency of its 7-day maturity operations with the world’s major central banks: the Bank of Canada, the Bank of England, the Bank of Japan, the European Central Bank, and the Swiss National Bank. The swap lines will now be offered daily instead of weekly.

  The announcement comes one day after the Fed announced \$60 billion of swap lines each with the central banks of Australia, Brazil, South Korea, Mexico, Singapore, and Sweden. It also unveiled lines of \$30 billion each with the central banks of Denmark, Norway, and New Zealand.

On May 4 2020, the US Treasury Department announced Monday it is borrowing about $3 trillion this quarter. The money is being used in large part to subsidize economic rescue efforts in the wake of the coronavirus pandemic.

Most federal banks don't have the legal authority to do this, but the notion is definitely sometimes discussed, often under the informal name "helicoptering money". Former Fed Chairman Ben Bernanke discusses his thinking on the subject here, and some economists have called for this response to the current economic crisis. Rep. Maxine Waters has proposed a bill that would authorize the Fed to do roughly this idea.


Application of Poisson process in economic modelling To understand the emergence of constitution, Myerson (2008) models a scernario that a political leader gathers supports from captains in order to defeat challengers whose arrival is modelled by a Poisson process.

I found using Poisson process seems to be simple and reasonable, but it is the only model I know that utilizes Poisson process.Are there any other well-known models utilizing Poisson process in a similar way? If not, what's drawback of Poisson process?

Most of the literature on "Strategic experimentation" (or Bandits) uses Poisson processes. Here players can use either a risky or safe arm and one of them generates a fixed stream of payoffs (usually the safe arm) the other one generates lump-sum payments whose arrival times are described by a Poisson process.

Some examples are:

Klein, Nicolas, and Sven Rady. "Negatively correlated bandits." The Review of Economic Studies (2011).

Keller, Godfrey, and Sven Rady. "Strategic experimentation with Poisson bandits." Theoretical Economics 5.2 (2010): 275-311.

Keller, Godfrey, Sven Rady, and Martin Cripps. "Strategic experimentation with exponential bandits." Econometrica 73.1 (2005): 39-68.


What obstacles/economic barriers do stock exchanges face in developing countries? My friend is doing research on cyber security in stock exchanges, and she noticed that the stock exchanges in developing countries aren't as popular or well put together as stock exchanges in developed countries. Not necessarily in terms of cyber security, but just in general.

Why is that? Could the stock exchange's management be to blame for the lesser quality? Or what supply/demand forces are at work that might put exogenous barriers on the management?

Stock Exchanges are made of the investments, and serve as meeting point for company's ownership to be traded fast and legally. It's need and value increases with the the number of investors and companies in the market.

Several developing countries lack legislation and law enforcement that would incentivize the use of a stock exchange. On the other hand, in developing countries the ownership of the largest companies is typically in the hands of a few powerful elites or foreign investors, and neither benefit from using a stock exchange, as they are usually not looking to exchange their investments.


To bet or not to bet Your utility from having $x$ dolars is $u(x)$.

There is a gamble in which the winnings in dollars are a random variable, $Y$. It is known that $E[u(Y)]>E[u(1)]$, so you prefer to bet than to get one dollar for sure.

But now you are offered the following options. You select a large number $T$ (which may depend on the distribution of $Y$), and then you can choose between two options:

A. Receive $T+1$ dollars.

B. Bet $T$ times, where all bets are statistically independent and distributed like $Y$.

For what utility functions $u$ would you prefer option B (for a sufficiently large $T$)?

The expected utility of option B is:

$$E\left[u\left(\sum_{t=1}^T Y_t\right)\right]$$

where $Y_t$ are i.i.d. variables distributed like $Y$. So the question is actually: for what functions is it true that, for a sufficiently large $T$:

$$E\left[u\left(\sum_{t=1}^T Y_t\right)\right] > u(1 + T)\; ?$$

One obvious answer is when $u(x)=x$, since in that case:

$$E\left[u\left(\sum_{t=1}^T Y_t\right)\right] = \sum_{t=1}^T E[Y_t] = T E[Y_t]$$

since $E[Y_t]>E[u(1)]=1$, it is clear that for a sufficiently large $T$:

$$T \cdot E[Y_t] > T + 1$$

What other utility functions have this property?

I think the answer depends on the space $Y$ is coming from. Consider if $Y \in \{ 1, \frac{T+1}{T}+\epsilon \}$, where $\epsilon > 0$ and the probability $p$ of the better result is

$$p > \frac{T^2}{\epsilon T + 1}$$

(Which just comes from solving:)

$$1\cdot (1-p) + \left(\frac{T+1}{T} + \epsilon \right)\cdot p > T+1$$

Then no matter what utility function you have, risk averse or risk loving, you will always take the gamble (option B).

Did you mean to have some sort of restriction on $Y$ for this question? Otherwise we'd have to consider both $Y$ and $u$ to determine whether the player will take option B.


Can anyone recommend a resource for monthly trade data for Mexico from before 2010? Can anyone point me to a resource where I can find monthly series data (specifically for 2003-2013) on Mexico's imports and exports in nominal (current) Mexican Pesos (MEP) including broken down by major industry?

I've found UN data and OECD, but am having trouble navigating the INEGI site (since my grasp of Spanish is limited to the colloquial).

I had a look for a few places. Looks like the WTO have something relevant. I haven't looked at the dataset but hopefully it is useful. This only has annual trade. The World Bank also has some data also covers annual data.

http://imts.wto.org/CDS/gp/tsselection.aspx

I think this one has your answer. It has monthly data. Only 1000 records at a time but up to 5000 if you sign up. You will probably have to be a bit clever with your queries and then merge a few spreadsheets as well. Clunky interface but the data looks vast.

http://comtrade.un.org/monthly/Main/Data.aspx


Why does loan waiving lead to a decrease of Non performing assets? Context: Loan waving  to small and marginal farmers in India.

  In wake of fulfilling poll promises and increasing farmer protests and
  suicides in India, many state (federal) governments have decided to
  waive loans to small and medium scale farmers.

However, I found on going through various newspaper sources that loan waiving is not a good idea from the economic point of view. Why does then loan waiving lead to a decrease of the NPAs (Non performing assets)?

"Loan waiving" means "loan write-off": the debt is eliminated. Therefore it is subtracted from the assets of the lender, and if it was already a non-performing loan (asset for the lender), the total of non-performing assets is now reduced.

The value of the debt that has been wrtten-off appears as  a once-off "loss" in the Profit & Loss statement of the lender.

Whether debt write-off is or is not "a good idea" has no single/simple answer, and it depends on a lot of factors that may change in time and country.

The main abstarct arguments against is that
a) writing-off debt signals to other borrowers that they can too leave their debts unserviced on purpose, even though they are financially able to service them, in expectation of a future new write-off: in other words, it creates what is called "moral hazard",

b) seeing debts being written off, lenders will be less willing to lend funds in the future, even to prospective borrowers in good financial standing.

c) finally a pure economics agument, says that businesses that cannot repay their loans are inefficient businesses and so it is not in the economy's best interest to "provide a lease of life" through debt write-off to such inefficient entities.

Again, the above are the abstarct arguments. The OP has a specific situation in mind, and a specific study should be carried out to evaluate and quantify the socio-economic pros and cons of debt write-off for the specific case.


In most New Keynesian models, can monetary shock affect technology shock also? One simple New Keynesian model would be http://crei.cat/people/gali/pdf_files/monograph/slides-ch3.pdf but I do not restrict my question to this model only.

Let us for now ignore the problem of linearizing around zero-growth-rate, and assume that there is no problem in modelling constant natural growth rate.

Let us suppose that monetary shock occurred, due to stochastic or forecast errors or intentional deviation. Can this shock result in technology shock also? (ex. change in $A_t$ in production function?)

I am sure that there exists a model that does this, but in most models, and especially Gali's model as linked above, is this true?

No it usually does not.

There is an intuitive reason why: We interpret the technology shock as a residual, the unexplainable part in TFP changes. If we knew that there was a specific causal relationship between monetary policy and future TFP, that part of future TFP would now was explained.

It's true that the MP shock is excluded in standard Solow Regressions, but if you believe there is a causal effect, you need to regress it out of it. Since after all, we understand $A_t$ to be independent.

Note that still, implicitly, through its effects on capital accumulation (which does not exist in standard NK models), monetary policy should impact future TFP. Then, you could make $A_t$ dependent and argue it being a shortcut in the absence of capital.


How does one derive the elasticity of substitution? For two goods $x$ and $y$, the elasticity of substitution is defined as $$\sigma \equiv \frac{d\log\left(\frac{y}{x}\right)}{ d\log\left(\frac{U_x}{U_y}\right) }= \frac{\frac{d\left(\frac{y}{x}\right)}{\frac{y}{x}}}{ \frac{d\left(\frac{U_x}{U_y}\right)}{\frac{U_x}{U_y}}} $$

I am confused by two things:

Why do we just write $d\log\left(\frac{y}{x}\right)$? What are we differentiating with respect to?
How do I use that that to show the above relation?

Can someone explain?

How to derive elasticity of substitution
The first step is to recall the definition of a differential. If you have a function $f: \Bbb R^n \to \Bbb R$, say, $f(x_1,\cdots,x_n)$, then: $${\rm d}f = \frac{\partial f}{\partial x_1}{\rm d}x_1 + \cdots + \frac{\partial f}{\partial x_n}\,{\rm d}x_n. $$
For example,  $$d\log v = \frac{1}{v}dv$$
Now suppose $v = \tfrac{y}{x}$, then we have $$ d\log(y/x)=\frac{d(y/x)}{(y/x)}$$
and for $v = \tfrac{U_x}{U_y}$
$$ d\log(U_x/U_y)=\frac{d(U_x/U_y)}{(U_x/U_y)}$$
In other words, if you reduce the problem to (1) understanding the definition of a differential and (2) use a simple change of variable, the problem becomes very straightforward.
You then get
$$\sigma \equiv \frac{d\log\left(\frac{y}{x}\right)}{ d\log\left(\frac{U_x}{U_y}\right) }= \frac{ \frac{d(y/x)}{(y/x)} }{ \frac{d(U_x/U_y)}{(U_x/U_y)} } $$
ASIDE:
Note, it is important to recognize that $ d(y/x)$ is a meaningful concept. You simply apply quotient rule and you find
$$ d(y/x)= \frac{xdy-ydx}{x^2}$$
This makes sense because
$$ d\log(y/x) = d\log(y) - d\log(x) = \frac{dy}{y}-\frac{dx}{x}$$
And if you compute
$$ d\log(y/x)=\frac{d(y/x)}{(y/x)}=\frac{ \frac{xdy-ydx}{x^2}}{y/x} =  \frac{xdy-ydx}{xy} = \frac{dy}{y}-\frac{dx}{x}$$
Same logic applies to $d(U_x/U_y)$.
Thus, all of $\sigma$ is well-defined in the sense we are using the calculus tools correctly / legally.

What is elasticity of substitution?
Elasticity is by how much % one thing changes relative to a % change in another. Therefore, in this case, it is % change in ratio of two goods  relative to a single % change in the $MRS$ for those two goods.