Can there be too little unemployment for the health of the economy? The cyclical rate of unemployment can be negative, which implies that the business cycle sometimes produces too little unemployment. How can there be “too little” unemployment for the health of the economy?

Let me answer a simpler question first. Is it possible for there to be too little orange juice in the grocery store? Definitely.

Let's say that the price of OJ is set too low (\$1 per liter) and customers who arrive early in the morning buy all the OJ. Assume that those customers think buying all the OJ is a good deal and they figure they'll enjoy drinking it, but that at regular price (\$4 per liter) they'd buy much less, they wouldn't want any more at those prices, and there would be lots left on the shelves.

People who arrive later in the day want some OJ at \$4 per liter. If they could find them, the early OJ buyers would happily sell them the OJ at that price and pocket the profit (that follows by the demand schedule I sketched out in the second sentence of the last paragraph). That means that there are deals to be done that would improve the allocation of OJ (there are welfare increasing, Pareto-improving, trades to be made). But the early customers and the late customers have trouble finding each other and so the OJ stays in the early shoppers' refrigerators.

Just about everything I just said about OJ holds for worker labor. Surprise! If the price of labor is set below the equilibrium price then early buyers purchase an inefficient quantity. Later buyers can't find the workers they need even though the marginal value of those workers is higher than the price at which the early employers bought them. Because (or perhaps I should say if) it is less efficient to look for a job while you have a job, when unemployment is too low workers ended up employed by firms that do not employ them at their highest marginal product. If only alternative employers could be found output and welfare could be improved. In fact, using a Kaldor-Hicks mechanism it is possible to make the new employer, the old employer, and the employee all better off under such circumstances. Thus it is not efficient under production efficiency or welfare efficiency criteria.

As usual in economics, the question is perplexing when considered from a purely quantitative point of view. However, once we admit qualitative variation, the answer becomes self-evident.

It is possible for there to be too little unemployment when there are too many "bullshit" jobs that do not create value and merely keep people busy for the sake of employment. Arguably, it would be better - and in aggregate cheaper - for those people to be unemployed.

We might venture to call this the "European model".


What is the Walras law vs first welfare theorem As far as I know, both of the first welfare theorem and the Walras law are closely tied to the invisible hand. what is the difference between them?

thank you very much for your help

Walras' law describes market equilibria conditions, which states roughly speaking that if there exists within an exchange economy market equilibria for $n-1$ good markets, then the last good market $n$ is also in equilibrium. Thus, we have a market system with $n$ equations and $n-1$ independent variables, where the last market is linear dependent from the other $n-1$ markets.

Now, the first Welfare Theorem of Arrow states that for every exchange economy with convex preferences, every Walrasian equilibrium is Pareto efficient.

The implication of the first Welfare Theorem is that we need no central planner to achieve a Pareto efficient outcome in an exchange economy. The Pareto efficient outcome is based on decentralized decisions within the exchange economy. If we now introduce transaction costs and incomplete information into the system, then it should be obvious that every decentralized economy is doing better than every centralized one due to the information problem.

Update:

I forget to mention some interesting implications of Walras' law. The law reveals to us that we have only one degree of freedom. This implies that a central instance can only fix one price level, for instance, that of the numeraire good, the others prices of the markets are determined by the market forces. Hence, a central instance has no control on them.

To make this argument more precise, let us apply this law to a central bank policy. We have only one degree of freedom, the central bank can now fix either the interest rate of the money market or a price index, but not both. If it fixes the interest rate, it has to accept the price levels and therefore the inflation rate, and vice versa for the price index. This also implies that a central bank cannot simultaneously targeting the price index and the unemployment rate of an economy.

They are hugely different!! The Walras law is a mathematical result that simplifies the task of characterizing prices and maybe it’s deeper meaning is that price levels are irrelevant in a perfectly competitive economy, rather relative prices is what matters.

In contrast, the first welfare theorem is way more than a mathematical result. It states that any equilibrium of a perfectly competitive market is Pareto efficient. This one is indeed related to the invisible hand argument in favor of capitalism, It’s implication is basically the markets are awesome, since they always lead to socially desirable outcomes.

Of course both theorems depend on assumptions (as they should), and these are debatable, but their implications are hugely distinct.


If production function is concave, then demonstrate that profit function will also be concave Show that concavity of firm's production function implies concavity of its profit function.
(Hint: For a concave function, first order conditions gives the vector that maximizes the function)
Confusing point: How do I relate the concavity of production function to the profit function. And where do I begin this proof mathematically.

The "hint" is wrong and misleading.
It is wrong, because first-order conditions are sufficient for a maximum when the objective function is strictly concave, or at least strictly-quasi-concave, under some conditions. For example, a linear function is also concave (as well as convex), and in such a case, the first-order conditions are not sufficient for a maximum.
It is misleading, because concavity of a multivariate function depends on the signs of its Hessian matrix of second-order derivatives.  So the OP should compute the second derivatives of the profit function, with respect to capital and labor, since I guess the presumption here is that we maximize with respect to input quantities only, treating prices as exogenous constants.
Both of the above are standard material in many microeconomics books or "math for economics" books, so the OP should look them up there.
The proper "hint" would be that costs are linear in capital and labor...
...so the profit function has a non-linear part that relates to production function, and a linear part that relates to costs. And what happens to the second derivative when linearity is present ?


what does historical volatility explain? Let's assume we have close prices of one stock of period one year. As far as I understand historical volatility is standard deviation of log return, however I do not understand what this actually mean.

Let's assume last traded price was $120 and HV is 0.29.

What does this really mean? That we can assume next price will be within the range of 29,58 (which is 29 percent of 120) above or bellow $120?

No. Volatility by itself is a meaningless number.

Volatility becomes relevant when used in a context, such as when comparing between assets, or to identify how much the stability of a financial instrument has changed over time. In these two examples, dividing volatility by the mean rate of return gives a more useful, dimensionless number known as coefficient of variation.

Historical volatility may also serve as input parameter for simulation of an asset price, provided that the analyst already has in mind a probabilistic model. The example you outline is akin to estimating a confidence interval. Your example reflects an assumption that the asset's behavior is modeled with a probability density function which is symmetrical with respect to the latest price.

There are other uses of historical volatility, but the ones above are among the most typical applications of that concept.


How do economists explain why people contribute to Wikipedia? What incentives do contributors have?
I believe they earn no money. And usually, they earn no reputation either, because most of the contributions are anonymous.
I believe this is a public goods game. Have economists studied this "Wikipedia puzzle"? How might they explain it? To what extent would economists consider this a "puzzle"?

By "contributors", I mean those who edit Wikipedia pages, not those who contribute in other ways (e.g. donations).

I wouldn't underestimate the role of learning by answering.
Drafting a significant text typically forces a person to put their thoughts in order, to engage in research, and then to structure the information for the purpose of recording and conveying it. It is not unusual that further insights or questions emerge during this process, the answerer certainly becomes more familiar with the subject, and good communication is itself a skill that requires significant attention and practice to develop.
Moreover, publicising one's thinking (even to a very small audience) typically invites challenge and puts it to the test of what others think of it, which again tends to flush out all kinds of faults and oversights - either faults in the thinking itself, or faults in the way it has been articulated and formulated into words.
Clearly, the assumption embedded in this question is that communication is done purely for the benefit of the listener, and that knowledge transfer is done in a "jug and mug" style, but there is more truth than you might think in that hoary old claim that academics have much to learn from their students.
So part of the answer to why people freely labour to communicate on sites like Wikipedia (not to mention here at StackExchange) is therefore bound up in the question of what stake they have, not just in developing the knowledge they appear to possess, but also in developing and rehearsing all the broadly intellectual skills associated with the development, retention, and communication of knowledge.

How do economists explain unpaid social activities? Sociologically.
In the USA males contribute 85% of editing, and females 15%, even though women have higher education accolades in the USA than men. In the USSR, female contribution is much higher, about 30%.
So, oddly, one of the motivations is masculine psychology.
The reason for that is mostly supposed to be with male ambition, self confidence, and sense of authority on topics, compared to women's trepidation and aversion to conflict.
That reveals interesting dynamics about wikipedia motivations for editing, some reasons for which have been suggested in this list which we can invert, i.e. people edit wiki because:
1/it's simple to edit, easy user interface
2/editors feel confident and want to put their knowledge forwards
3/editors disagree with a particular view of wiki and want to add coutner arguements
4/they think that their addition will be recorded and influential
5/editors like the overall atmosphere of learning and academia
6/it's better to write on wiki than on a social media site like facebook.


Unintended consequences from "fixing" the US financial system Last year, I read the book The Bankers' New Clothes: What's Wrong with Banking and What to Do about It.  The book explained some of the causes of the recent financial crisis of 2007-2009 and gave some steps to prevent a similar crisis from occurring again.  Some of the steps were

  1) eliminating the FDIC,
  2) increasing the capital requirements of banks (up to ~30% instead of the current 2%-3%), and
  3) having liability rest completely on bank owners and decision-makers within the bank (i.e. no government bailouts, depositors receive a certain number of cents on the dollar rather than 0, etc.).

However, economics in plagued by the law of unintended consequences.  If these three points were implemented into the US financial system, what are some unintended consequences that could result?

1) Would lead to the return of general panic led bank runs, and introduce additional instability to the system.

It´s not generally appreciated, that 19th century bank runs were not just a symptom of insolvency or illiquidity, but were also occasionally triggered by competitors (other banks) spreading rumours. Generally this is a bad idea that rests on the fallacy that banks are just another business.

2) They are typically rather more than 2-3%, 10-12% was the average at the crash, and Basel 3 is moving this up to above 15%. It´s generally a good idea, but it depends on the type of capital - more loss provisions are good, but simple holding extra share capital not so much. There are also side effects with respect to economic growth while the increase is occurring.

3) This seems a little confused. Depositors are not decision makers in banks - they are the customers. Owners, managers and shareholders of the banks are not necessarily the same people, but making in particular the managers and owners stand behind the banks with their entire assets might be interesting. As in ´may you live in interesting times´ interesting. Scottish banking in the 18th-19th century was regarded as more stable by the English since the entire property of the bank´s owners would be seized if the bank failed. In today´s world though, expect that to cause issues, if Banks are the only type of company that this kind of punitive ownership encumbers, then one might imagine that relatively few people will want to own one, or creative ways will be found around the requirement.

Banks are also usually regarded as a fairly safe investment (between major credit crises at least), and a good investment for pension funds and retirees, as their dividends provide a steady stream of income. Blowing those institutions up, might not be entirely desirable.

All of this not withstanding, the main issue with banks, and the answer to why they are not just another company - is that they provide the money supply. The problem posed by any banking crisis, and any proposed reform, is how does this avoid or solve monetary and credit supply contraction in the event of loan default failure. 1 & 3) in particular would be likely to cause significant monetary contraction, and return the financial system to the instabilities of the 19th century, where not to put to fine a point on it, it was bouncing up and down like a yo-yo. Wikipedia has quite a nice list:

List of Banking Crises

This is only a partial answer, but I wanted to note and describe the theoretical literature which will come to mind for many research economists when observing (1), "eliminating the FDIC." The simple framework which is often first used to theoretically discuss this kind of question is the so-called  Diamond–Dybvig model, which tries to set up a very simple theoretical world in which maturity transformation occurs in a straightforward way. (Maturity transformation is defined nicely in this interview, which I shamelessly lifted from the first reference on the current version of the [wikipedia page] :) Other quick references are a bit dry unfortunately.) There's something of an instability in maturity transformation which can lead to to-called bank runs; Diamond–Dybvig ("DD") try to capture this dynamic in a succinct model.

I'll be careful to note that this model itself is very abstract -- the true financial system is very complicated. Regardless, it has been used as a framework for exploring theoretical ideas related to banking stability for a while.

I'll start with the intuition for the model first. In the model, banks function by converting short-term accounts (savings accounts, perhaps money market accounts) into long-term loans. Banks take depositor money, retain a certain amount, and lend out a certain amount as long-term house loans, car loans, or small business loans. This means everyone gets something at the end of the day -- depositors get a safe place to keep their money with some modest return on savings; homeowners and business owners can smooth out the large costs of housing and capital over many years, and everyone gets a little bit of the slice of "added production" which occurs because the loans could be made. There's some investment projects which will fail (houses defaulted, businesses going bankrupt), but that can be planned for appropriately by the bank.

Not all depositors need their money at the same time -- after all, that's why you put it in a safe spot to begin with. The bank knows (or guesses) how many people on average will need to access their funds, and holds on to that much (plus extra for a "safety buffer"). Everything else is lent out to achieve the above-mentioned benefits.

This system works fine unless, for some reason, enough people start to believe that enough other people will want to withdraw their funds more frequently than usual -- perhaps all at once. Everyone generally understands the structure of the game: stage 1, if there are too many people who want to withdraw money, the bank will fail. Stage 2, if everyone realizes this, they will want to get their money first. Stage 3, I personally need to get my money out before anyone else does, and I know everyone else knows this, so now it's a race.

Now this only happens if everyone believes that everyone else believes the bank will not have enough money for everyone. For a bank "standing alone" this is always a danger. However it also demonstrates a way to nip everything in the bud: institute an insurance scheme for individual depositors. You need to be able to credibly tell the borrowers that, "don't worry, even if the bank collapses, your deposits are insured and you'll get at least X back." This promise itself (and it must be a "good" promise; a promise no one trusts will be useless) will prevent many possible instances of bank runs which might occur when there is nothing intrinsically wrong with the bank.

The theoretical illustration of the above points is the well-known Diamond–Dybvig model [wiki page here, which is actually quite good]. The model is really quite beautiful in laying out the constraints faced by everyone in the world -- depositors, banks, loan-takers. It does so in a very clean and clear way, which is one reason it is so popular. If you're ever deeply interested in these things, I'd definitely recommend working through the model at some point, ideally with someone you can "ping" for input (perhaps here, later). It's a great example of a framework one can use to tackle bigger questions (or alternatively, a great example of how to frame an observed phenomena in the simplest way possible, which is always how you want to start).

This is one of those nice theoretical results which is so intuitive and easy to understand that it can be understood by anyone. In fact, it is literally the main plot device for the classic "It's a Wonderful Life," where [SPOILER!] the first bank run in the movie is quelled with the "insuring" of depositors' accounts with the couple's honeymoon fund.  (The real-world equivalent of the honeymoon fund, of course, being the FDIC in the US.)

NOW, all that said, I have no idea what the context of point (1), "eliminate the FDIC," in The Bankers' New Clothes. I suspect the authors are aware of everything outlined above, and they may perhaps have an alternative suggestion for how to handle the "bank runs" problem (aka the "Wonderful Life" problem) which emerges naturally without some deposit insurance system. If they are advocating a "clean sweep" of depositor insurance, that would be very extreme -- but I don't know if that is what they are actually advocating.

There is an enormous empirical literature on bank runs -- see @Lumi's response, particularly the list of bank runs. I'm certain that if you were to choose a bank run from that list at random and search for it in Google Scholar, you would find plenty of empirical papers. (I'm not an expert on this literature so unfortunately cannot answer this more specifically.)


inflation rate vs interest rate on calculating present value of future money i use the formula 100/(1+r)^T to calculate the present value of my future money while r is interest rate and T is year.
However , for my country , interest rate (year) = %8.25 and inflation rate (year) = %12.60
Is it logical if i use inflation rate instead of interest rate at my calculation?

The question has some ambiguity. If you want to calculate something, you need to define what you are interested in. If you want to think in terms of purchasing power, you can use the inflation rate.
However, using inflation would be the wrong answer in the context of finance or project analysis. In the financial context, you are comparing money now versus money in the future. The basis of comparison is an instrument that bridges money from the present to the future, which are debt instruments.
For example, if you are borrowing to finance a project, your profitability depends on the return of the project in nominal terms versus the cost of financing. What the value of the currency does versus a basket of goods during that time does not matter.
The idea of inflation trading off future returns is a beloved concept of conventional economists, but its usefulness is greatly overrated. Since you cannot purchase the CPI basket and store it indefinitely, there is no obvious necessary relationship between inflation rates and the return on investable assets. (People might invoke model relationships, but that puts a lot of faith in the models.)


What are the arguments against a zero corporate tax? I've read a title in the news proposing a zero corporate tax. Thinking about it I couldn't figure a good reason against.

Why couldn't a country just set the corporate tax rate for firms to zero and then tax any gain obtained via negotiating shares or receiving dividends? Tracking the latters seems way easier (via a digital national registry of ownership and trades and mandating disclosure of dividends ) than burdening firms with complicated tax codes and the state with the burden of chasing them.

I am sure I am missing some theoretical and real world complications, so please, enlighten me.

It is possible to structure business entities in most if not all countries as pass through structures (e.g., limited liability corporations, sole proprietorships, or general partnerships).  Such entities are not taxed at the corporate level.  Tax liability instead flows through to the principals who own not shares but partnership interests.

Your question should therefore be restated: what advantage is there to reducing the corporate tax rate to allow shareholders to pay less tax than if profits flowed through to their personal income tax returns?

The answer to that question is data-dependent.  In some economic environments, it is useful to encourage corporate investment through corporate tax cuts.  We are not in such an environment today, however.  There is now a very wide and deep literature on how corporations have been saving more than they have been investing since the 2007-09 financial crisis.  Corporations have been hoarding cash or distributing capital to stockholders in the form of dividends and share buybacks more than they have been investing in future productivity and profitability growth.  Corporate tax cuts would therefore likely increase wealth inequality because they would flow through to already wealthy shareholders.

The only argument for reducing the corporate tax rate today has to do with international competitiveness.  The top tax rate for U.S. corporations is 35%.  In Ireland it is 18%.  If you ran a giant multinational, you might want to "invert" and re-domicile to Ireland or any other lower-taxing country.  The U.S. tax code has so many loopholes that through clever use of intercompany debt, net operating loss carryforwards, and operations overseas, it is possible bring the effective tax rate for a U.S. domiciled multinational closer to 10-15% over longer time horizons.  We should obviously attempt to set corporate tax policy to limit inversions, but many companies already pay less than they would if they were headquartered overseas.

The argument will fall apart when you inspect it with common sense and simple terms.  Tax is anything but "COST" to company. The argument is all about removing such "COST" and convert to "PROFIT GENERATING INVESTMENT". Sound great, but it is anything but playing with sentences.

Let me explain why.  Most people think investment is all about "putting money on create new stuff to generate profit", but there is a hidden investment in modern society :  infrastructure investment: education, utilities, road system, regulation, security, law enforcement , etc.

Zero corporation tax advocate selectively skip cost on infrastructure investment, they keep pretend infrastructure are pop up from nowhere and cost nothing. On the contrast, such infrastructure and bureaucratic are not free, even is not efficient, it is still cheaper than ANY corporation "invest" in such infrastructure.

If all corporation exploit on the collective "infrastructure investment" to generate profits, but nobody pay "cost" (AKA TAX) , then who is going to pay for the such "investment"?

In entrepreneurship, we call the cost that pay to use some other facilities as "rent",  which is categorised "cost". OTH, Tax is anything but actually a "rent". Ironically, corporate tax are somewhat "generous" in a way that base on "profit".

Argument may continue and say the "tax"(AKA rent) not justifiable and proportion to the facilities consume. I will say , we are not living in a perfect world.


What is the purpose of interest? What is the purpose of interest? Why do most economies permit the charging of interest? Could an economy function without interest at all, or is interest necessary for an economy to function?

Interest is a key mechanism to ensure that resources are properly allocated within an economy. There are lots of uses to which money can be put: consuming goods, building highways, constructing a new factory, investing to develop a new drug, etc. Just like goods, the allocation of money is governed by the price system—where the interest rate is the price (because the interest rate is how much you have to pay to get access to money). If the price is too low (i.e. if there is no interest) then few people will be willing to lend money and valuable investments (in, for example, infrastructure or new business ventures) will not take place because the funds aren't available to pay for them. A positive interest rate ensures that people with money they don't need right now have an incentive to lend it to people with valuable projects to fund.

We know that it is possible for economies to function without interest, though, because the charging/payment of interest is prohibited by Sharia law, giving rise to so-called Islamic banking.

I disagree with these answers.
Interest must exist in the enconomy as long as there is inflation, because inflation creates a relationship between value and time.
For example, assume there is inflation. Joe asks you for $20 to return to you in a year. You can buy a lunch with that or lend him the money. but you'll not be able to buy the same lunch with $20 next year because of inflation so you'd ask him for an interest.

Now why cannot we kill inflation?
We can! These crazy economists claim that we need some inflation to allow the economy to be more dynamic to facilitate trades. (canada aims at 2.5% inflation)

I speculate that governments, politicians and millionars put that in as a source of income. How do you think they pay for campaign adds?
Now the other answer says that they use it to build highways, drugs...No way! Those come from our taxes.

Some things are best not to know.


What would monetarists do when interest rates approach zero and become ineffective? So monetarist economists such as Milton Friedman focus on managing the money supply and lower interest rates as a solution to economic downturn. But what would they do in a recession as the interest rate approaches zero and recognises that monetary policy becomes ineffective? Would they turn to fiscal policy even though they highly oppose government intervention?

An excellent overview of not just monetarist view on this issue but all other mainstream views on monetary policy at zero lower bound  (ZLB) can be found in Ullersma (2002) The Zero Lower Bound  on Nominal Interest Rates and Monetary Policy Effectiveness: a Survey - which is an excellent literature review on this subject (albeit slightly dated).
In short, under the monetarists view 'true' liquidity trap should not exist. Even though there is zero lower bound monetarists would argue that central banks can still stimulate economy through other transmission channels. For example,  Meltzer (1963, 1995, 1999) and Brunner and Meltzer (1968), would argue that central bank can still stimulate the economy through asset purchases with implicit assumption that even when the short-run nominal interest rates are at the zero lower bound, yields on non-monetary assets are not necessarily at their lower bounds.
Bernanke and Gertler (1995) would argue that central banks can stimulate economy also through the credit channel that is not affected by ZLB. Basically this amounts to central bank making sure banks are willing to extend credit as much as possible by providing incentives for them to do so. For example, this is actually being tested in the Europe by ECB through long-term repo operations (LTROS). LTROS is a way how central bank should can borrow money to commercial banks and in theory encourage them to lend more. Furthermore, there is no ZLB when it comes to LTROS as long as central bank is just willing to soak up the losses it makes on such lending (at it can always do that by creating more money).  See this article in the Economist that talks about LTROS in greater detail.
Lastly, Milton Friedman  himself would probably just suggest that central bank engages in 'helicopter money', that is directly giving money to households/firms in some form (see Friedman (1969) The Optimum Quantity of Money: And Other Essays). Such a direct transfer should in principle 'circumvent' the liquidity trap. However, for many central bankers this would be quite radical as such practice could lead to politicization of central banks (since once people learn they can get 'free money' from central banks there might be political pressures for such transfers even when they are not needed).
However, it is worth while noting that the monetarist view above, while still technically being part of mainstream, is not the predominant view in the macroeconomic profession. The current predominant view on ZLB would be more close to the New Keynesian (NK) view on liquidity trap which in the paper cited above is denoted as the 'Krugman's View'). Under the NK view the above mentioned prescriptions would still be helpful, but insufficient and government spending would still be necessary.

Given that several central banks have negative interest rates today, the idea of ZLB seems clearly flawed, but brings up a useful point: Interest rates also reflect risk as well as value of money. Losing a little bit of money through negative rates can be seen as preferable to losing a lot of money through risky investment, or tying up funds so they can't be used later, at a more productive rate. A negative interest rate is a bit like paying a value contingent fee on a deposit at the bank--paying for the security and convenience of storage. Seems theoretically sound for a central bank to just keep lowering rates (and increasing the fee).
The default assumption has always been that when rates went negative, it's possible to keep things in cash or gold. But both have their own costs associated with storage/security, and with fluctuation in value over time.


The Oil hike of the 2000's: Did it go unnoticed, and why? I'm reading a macro text book, the authors stated that in the 2000's we witnessed the greatest increase in oil prices ever, even when compared to the 70's oil shocks. To most of us, this fact went a bit unnoticed, at least when compared to the 70's. Usually in this shocks, we have a trade and supply shock. If the CB only considers the trade shock component, then the economy will face the usual stagflation. Some of the reasons the authors give for the lack of stagflation are increased lending from financial institutions, which prevented a marked decrease in consumption and eventually in output, and that workers were 'less inclined or able to get compensation through their wages' making the Equilibrium rate of Unemployment(ERU) curves to shift less than expected.

I would like to assess the truth of such claim. I've been trying to get some data, but I'm really bad at it. So, my question is: Are the authors right? From, the two pictures below (the last is US GDP growth rate if I'm not mistaken), I would say that it might have gone unnoticed, but I wasn't able to check if real wages decreased, and by how much...

Any help would be appreciated.

P.S.: In your answers, could you please name your data sources, and give some indication as to how we could replicate the graphs? I'm interested in learning how to do it. Many thanks.

I consider the very rapid growth of infrastructure in the BRIC countries to be a strong driver of the high oil prices (as well as other building commodities) in the mid-2000s.  It takes a lot of energy to build roads, mine copper and iron, make cement, etc...

I would disagree with two of the implications in the statement: "in the 2000's we witnessed the greatest increase in oil prices ever, even when compared to the 70's oil shocks. To most of us, this fact went a bit unnoticed..."  I disagree with the comparison of the early '73 OPEC oil embargo and the oil spike in 2008, and I disagree that it went unnoticed.  This is not an apples to apples comparison.  In 1973 there were times that you could not buy gasoline.  In 2008, gasoline was always available, it was just more expensive.  And I, and all of my acquaintances, noticed it, and we complained about it, but we always had it available.  That's a very big difference to not being able to buy something crucial to your livelihood.

That being said, I would agree that increased lending in the mid 2000s and a very strong world economy may be a reason that the spike of oil prices in 2008 wasn't considered a crisis.

I would also agree that oil prices did not cause the late 2000s recession.  The recession was caused by an abrupt evaporation of interbank lending and a hasty tightening of credit.

Since you are a student of Economics (and I assume of markets), let me say something that wasn't clear to me until I spent 30 years working in investment management: the economy and markets are very different.  The economy is 7 billion people a day waking up and having to be productive to survive.  It is real, and it is very hard for any government to derail it, as hard as they might try.  I have huge faith in the economy. The securities markets, rather, are places built on fear and greed, two very intense emotions that are self-reinforcing, meaning that the more the emotion is fed, the stronger it becomes, thus feeding that emotion even more.  That is why we get bull market bubbles and bear market cliff dives that do not correlate in their magnitude with the underlying economy.

The stock market is a leading indicator of economic direction, but not of magnitude.  Keep this in mind.

Alright, sorry for the preachiness.  Good luck.

It destabilized the third world via food prices and killed economic growth. Yes it was noticed.

Energy prices increase before every major recession. The financial and demand-based theories of recessions, although widely believed, are completely baseless and unfalsifiable.


Exogenous Money Supply In the first 10 seconds of the following video: https://youtu.be/anZ58gZcxqk,
A claim is made that in the Exogenous Money Supply Model, Money Supply is not determined by interest rates. The person further adds that the money supply is independently determined by the central bank.
My question is that isn't the central bank only responsible for determining the interest rates? I know there are other tools such as open market operations that can be used to control the money supply in an Economy. But, If the central bank is determining the money supply, shouldn't it then be a function of interest rates.

My question is that isn't the central bank only responsible for determining the interest rates?

No, central banks do not even have directly responsibility to adjust interest rate. Depending on which country we talk about they will have responsibility to keep prices stable, high employment and bank regulation and often combination of the above. In order to follow their mandates they will often fiddle with interest rates but typical central bank has many instruments at its disposal. For example, they can also increase money supply or even adjust reserve requirements that also affect money supply (Fed recently set them to zero in their effort to increase inflation).
As mentioned above  most of the time contemporary central banks adjust interest rates on their reserves that influences interest rate in the economy and let the new money supply be determined by what the interest rate is but I don't know of any central bank that would not be allowed to directly increase $M$ if they would want to in some way. Also, note even if central bank sets itself some goal achieving some interest rate without stating any goals in terms of money supply, since interest rates depend on what $M$ is, they in principle could fully control interest rate just by varying $M$. They might want to use more tools because relying only on $M$ would be more difficult but it is possible.
In fact the open market operations that you mentioned are one way how central bank can directly increase money supply in the economy and the open market operations are not that scarce. These are becoming increasingly common, for example you can see from the graph below what an effect QE (which is not fundamentally much different from OMO expect in its scale and that it is part of holistic strategy that includes other tools) had on increase in monetary base in the US (first round of QE started in 2009 you can easily spot it by the shar increase in monetary base), so that is non-trivial  change in $M$ (technically $M0$ but $M$ consist of base money as well) that wasn't created with interest rates.

The original question has a link to a video where the presenter states, "Exogenous means determined outside the model by something else." Then endogenous means determined inside the model.
The model variables in question are the size of the money supply and the monetary policy interest rate.
In general if the central bank can control the monetary policy interest rate, which is usually the case, then this parameter would be exogenous or determined outside a model for the operations of a market economy.
If there is a deterministic relation between exogenous monetary policy rate and the size of the money supply then both interest rate and money supply would be exogenous variables.
The so-called "money multiplier" is a ratio of the money supply (measured as specified liabilities on the books of the aggregate bank sector) to the monetary base (measured as central bank liabilities). This ratio varies without any deterministic math model to account for such variation. Any model that specifies a deterministic relation is an ideal or toy model not an empirical measure.
If there is no deterministic relation between the exogenous monetary policy interest rate and the size of the money supply then one should conclude that the money supply is endogenous. In other words banks and financial market dealers expand or contract the money supply using the monetary policy interest rate as a non-deterministic factor in their credit deals.
How would a central bank prevent inflation if it only sets the monetary policy rate of interest and otherwise has no deterministic control over the size of the money supply? In the United States inflation was broken in the 1980s by aggressive actions of the Federal Reserve which led to a rash of bank failures and bankruptcies during an ensuing recession. So the rational person should think of the central bank as being able to induce bankruptcy among the weakest units in the economy including perhaps banks and other financial intermediaries as well as employers in the real sectors. This bankruptcy would disrupt rising credit and price spiral. So I would argue that the central bank has disruptive yet non-deterministic exogenous power partly related to how it sets the monetary policy interest rate.
The working paper below argues that money is not neutral in a modern economy and the quote below from nominal page 15 describes the disruptive power of the central bank:
https://files.stlouisfed.org/files/htdocs/wp/2012/2012-020.pdf

Oxygen is not responsible for fire, but the fire cannot exist without it. Ironically, this was the view of Federal Reserve Chairman, Arthur Burns, who many (if not most) economists believe bears responsibility for the Great Inflation. At the March 18-19, 1974, FOMC meeting, Burns noted that while he was not a monetarist, he found “a basic and inescapable truth in the monetarist position that inflation could not have persisted over a long period of time without a highly accommodative monetary policy.”21 Burns (1979) reiterated this point in his Per Jacobsson Lecture (which ironically was delivered just six days prior to Volcker’s FOMC’s dramatic change in monetary policy) saying, “the Federal Reserve System had the power to abort the inflation at its incipient stage fifteen years ago or at any later point, and it has the power to end it today...at any time within that period, it could have restricted the money supply and created sufficient strains in the financial and industrial markets to terminate inflation with little delay.”  Burn’s belief that central banks could control inflation was dramatically demonstrated by Volcker’s actions, which brought an end to the Great Inflation.

The central bank induces "strains in the financial and industrial markets" that either reduce expected future profits or induce an actual loss for some units of the economy. If the central bank is captive to political influence it may not use the power to disrupt money and credit markets necessary to end rampant inflation.
When the central bank is fighting deflation and high unemployment it uses tools other than the monetary policy interest rate such as large scale asset purchases and other credit policy tools which would also be exogenous to a market model of the economy.


Why can Iceland setup and maintain a single-payer system but Vermont can't? Vermont apparently tried to setup a single-payer healthcare system, only to have various healthcare and pharmaceutical companies threaten to ruin them if they did so, at which point Vermont, a state not large enough to take them on, backed down.

Despite this, countries like Iceland have single-payer systems, and don't have to deal with things like nonsense pharmaceutical price gouging despite having only around half the population of Vermont, and six billion dollars less in GDP.

Why is it that Iceland can setup a single-payer system, but Vermont couldn't? What does Iceland have that Vermont doesn't? And how can these differences be generalized such to explain what the requirements are for a state, or country, or healthcare providing NGO to be able to run a single-payer system?

From what Wikipedia tells me on the Vermont case, the Vermont government feared increases in costs and taxes from such a reform. In the end, it boils down to what people/voters/decision-makers are willing to pay for a health care system they believe to be good for the people. Scandinavian countries provide lots of top-class public services (health care, child care, education) but also collect the highest tax rates in the world. Apparently, political will and public opinion in Iceland were willing to accept the price attached, which was not the case in Vermont. Beyond, it is possible that the move from the previous system was less drastic in Iceland, requiring fewer things to change.

Single payer systems are primarily an interest group policy. Giving and taking money from the same person is never rational. All major social security systems are PAYGO.

So vermont is simply too small to have the necessary political infrastructure for a funded system to be viable.


convexity of the profit function for profit maximization the profit function is convex in prices and wages (output and input prices respectively). How does this interact with profit maximization since convexity implies tangents always lie below the curve I would have thought convexity would be necessary for minimization rather than maximization.

It is true that we are usually interested in minimizing convex functions or maximizing concave functions, typically over convex sets. But I think you have two confusions:

The profit function is the result of a profit maximization problem. Not the objective function in the maximization problem. A profit function $\pi^*(p, w, r)$ identifies maximum profit given the price levels (p, w, r).
In the profit maximization problem, the objective function $\pi = pf(k, l) - wl - kr$ is concave in $k$ and $l$, the choice variables of the maximization problem.

Profit functions are convex in output price that is :
π (tp + (1- t)p′) ≤ tπ(p) + (1- t)π(p′)
Intuitively this implies that if price of output increases by one unite the profit will rise by exactly or more than one unite.


Adam Smith and wage gap? Recently I was reading up on Adam Smith's economic philosophy of competition (i.e self interest) and division of labor.

While I understand (and agree) with Smith's commentary that free markets and division of labor spur innovation, production, and general well-being of the average individual, it appears that there isn't commentary on wage gaps.

I would assume that through specialization (and self interest) some labor is more valuable than others (e.g CEO salary vs factory worker salary). Couple this with competition and I would expect wage gaps to quickly form.

Does Adam Smith ever address the issue of self-interest, competition, and division of labor and any potential wage gaps that post risk to a healthy economy?

Yes, Smith addresses these issues in Book 1 Chapter 10 of The Wealth of Nations. Firstly, he notes that where two jobs are in almost every respect equivalent, we should expect them to pay the same wage:

  "THE whole of the advantages and disadvantages of the different employments of labour and stock must, in the same neighbourhood, be either perfectly equal or continually tending to equality. If in the same neighbourhood, there was any employment evidently either more or less advantageous than the rest, so many people would crowd into it in the one case, and so many would desert it in the other, that its advantages would soon return to the level of other employments. This at least would be the case in a society where things were left to follow their natural course, where there was perfect liberty, and where every man was perfectly free both to choose what occupation he thought proper, and to change it as often as he thought proper. Every man's interest would prompt him to seek the advantageous, and to shun the disadvantageous employment."

This is related to the observation made by MH.Q: if A and B are two equivalent jobs, but A pays more then everyone would rather work in A than B. This results in a shortage of labour in B and/or an excess of labour in A so that the wages converge by natural market forces and the wage gap disappears.

Most of the rest of the chapter is spent discussing reasons why we might diverge from this ideal of uniform wages. The need to compensate skilled workers for the cost of their education and for the chance that they will not be successful in their chosen profession, for example, are offered as key reasons why wages might differ. I recommend you take a look at the chapter to get a handle on Smith's thinking.

This reasoning still forms part of our understanding of the modern labour market: if the wage premium for a job is not sufficient to compensate a worker for the (opportunity) cost of training to do that job then workers will not become trained and there will be a shortage of labour in the industry. This will drive up prices by natural market forces.

More generally, we now understand that wage differentials are an important means by which the market informs participants about how they should act. An extremely talented person who could, in principle, tranin to perform any of a large range of difficult jobs has no way to know where society needs his/her talents most. But the market provides this information by providing a mechanism for prices (i.e. wages) to increase in areas where skilled workers are short relative to prices in areas where workers are plentiful. The true beauty of this market mechanism is that is simultaneously provides information about the needs for workers, and provides the incentives for workers to enter the appropriate industries.

Whatever problems the wage gap might cause in the economy, they must be weighed against the large efficiency gains that come from allocated talent where it is needed most.

I have thought about this issue as well. But through self-interest, don't you think that most people want the best for themselves and therefore, nobody would be willing to be a factory worker in this case?

If everybody strives for the best for themselves (i.e. all are trying to be CEO), the free market then puts upward pressure on "lower-end" jobs' wages pulling the wage gap closer.

To say that there would be no wage gaps in an economy is a lie in my opinion. You cannot expect a skilled worker, who at some point in their life, has sacrificed something in order to be skilled, to receive the same amount of wages as an unskilled worker. Wage gaps will always exist, the question is how wide of a gap can the society accept?

I feel like what we are seeing today is the amount of information the internet has provided has managed to help the educated/skilled to gain more knowledge/skills quicker than those who are unskilled and are unwilling to improve which is leading to a wider wage gap. In the free market context, we assume that every man is hardworking and looks to seek the best of himself/herself which is not true realistically. But I would agree to a larger extent that the free market model is the best approach for any person to have a fair chance in getting ahead in life and Milton Friedman's Negative Income Tax can address the issue of people who are just unmotivated naturally.


Is the global Automobile Industry changing from an oligopoly to monopolistic competition? The current situation is the automobile industry is an oligopoly as there are few big firms and massive barriers to entry due to cost.

However, The industry seems like it is changing to a monopolist competition structure as new firms join the industry (Apple, Google). This is as a result of bigger differentiation’s in cars product (due to software)

The automotive industry is being disrupted by new trends such as electric vehicles and self-driving cars. These, still, represent a minor part of the market.

So the answer would be no, for the moment besides media attention, there weren't gigantic shifts in the industry as to have monopolies. Looking at the last years data it seems to remain an oligopoly with 4 very large manufacturers.

If you need further info this is usually not free - look for the automotive industry in business databases such as IBIS world, or get a report from a consulting firm such as this one.

There are still a number of car makers, so at this point it is NOT a monopolistic sector. Barriers to entry are also reduced globally (Asia) due to a decrease in the cost to make a car. I do understand your point on new software, however, the cost of vehicles with the newest and best software is still high to the extent that there is a semi competitive market for individuals who can't afford the newest software. At this point, we an oligopoly. Even if you consider new electric vehicles, multiple players (BMW, AUDI, GM, obviously TESLA, and some Asian companies) are even getting into that market, and the costs are sky high. As costs fall, you will see a scenario in which the marginal cost to entering the market will begin to come closer to the marginal benefit, which will lead more players into the market, which is what happened post model T. It is a similar scenario, just with 21st century technology. The economics are the same. Instead of the model t, we have teslas model s coming, but just like with the model t, we could predict that the market will become more saturated, resembling more of an oligopoly. Google, Microsoft, and Apple are not comparable in that regard. I can only do so many things with a MAC until I HAVE TO GET a Microsoft (as a programmer). However, a car is a car. Slightly different software won't give you a monopoly, because of how individuals use software, compared to how individuals use a vehicle. There are relative substitutes to a model S. There is no substitute to C# with Microsoft if I have to use C#. There is no substitute to SWIFT on IOS if I HAVE TO USE Swift.


Time Value of Money Question For the following Question

The Answer is

First:
Scenario 1 : I wonder how the customer pay as whole 12000 dollar after 12 years for a 8525 dollar product if the interest rate = 0%

I think that , there is about 3% interest

Second:
What is the criteria upon which the company decide in first scenario to pay 1000$ /year and for the second scenario to pay the full amount?

This is a very poorly written question.

The gist of the question is this: should a company take a lump-sum payment from a customer of \$8,525 or a \$12k payment that is spread uniformly over 12 years. The thing the question wants you to consider between 1a and 1b is that in 1a the company cannot earn interest (which the answer just assumes is compounding) and in 1b the company can earn 7% interest.

For the given answer, part 1a is saying that, since the company cannot earn interest on investments, it is better to just take the \$12k. However, one ought to know something about how this company discounts to actually answer this question. That is, one should make this comparison by comparing \$8,525 to the discounted present value of the \$12k, taking into account that the \$12k is received in payments spread uniformly over 12 years. The real answer to this question as written is, ' IT DEPENDS'.

Part 1b is saying that $8,525(1+.07)^{12} \equiv 19,199.93 > 12,000$ and so the company should take the lump-sum payment and invest it. HOWEVER, this is again the wrong way to answer this question. Instead, one should compare
$8,525(1+.07)^{12}$ with the money the firm will have if it chooses the \$12k and subsequently invests each annual payment. This value is \$19,140.64 (link to calculate). The answer here is correct but for the wrong reason.

Really, this is a very bad question and a very bad answer.

The question asks you to compare the value of an immediate payment and a series of payments in the future.  In finance, every set of future payments has an immediate payment equivalent, which we get by dividing each future payment by a discount rate.  When this question says "interest rate," it means "discount rate."  The two terms are used interchangeably where there is little ambiguity about what is meant.

To answer your first question, it doesn't matter what the true risk-free or risky interest rates are now...that's not part of the question.  It's a hypothetical world in which there is an interest rate of zero.  In that case, future dollars are worth the same as present dollars, so we are comparing the value of \$8,525 with \$12,000.  Clearly the latter is better.

For the second question, how do we find the present value (immediate lump sum equivalent) of these payments?

$$
PV = \frac{1000}{0.07}\left(1-\frac{1}{1.07^{12}}\right) = $7,942.69
$$

Using the formula for the present value of an annuity.  We could also do it using the direct approach

$$
PV = \sum_{i=1}^{12}\frac{1000}{1.07^{i}}
$$

to get the same result.  We see that \$8,525 > \$7,942.69 so it's better to take the immediate payment.

The answers seem like they were hastily and erroneously written--better to ignore them and rely on my solution than to try and figure them out. The question here is a typical and straightforward introductory undergraduate finance question, though, and well worth understanding.


Why Constant Returns to Scale Suggests Certain Relation I'm self studying intermediate macroeconomics by reading a textbook and I came across a relationship that I'm not quite sure how it is derived.

Let $F(K,L)$ be a production function where $K$ is capital stock and $L$ is the labor force. Assuming constant returns to scale, I'm not sure how to derive $$F(K,L) = F_K(K,L)K + F_L(K,L)L,$$ where $F_x$ denotes the partial derivative of $F$ with respect to $x$.

The result follows from Euler's Theorem on homogenous equations. This theorem states that if a function $f(x,y)$ is homogeneous of degree $\lambda$ then the following holds:

$\lambda f(x,y)= x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y}$

A (production) function with constant returns to scale is homogeneous of degree 1 by definition. The definition of constant returns to scale is basically the same as the definition of homogeneity of degree 1. That means $\lambda=1$, which proves the result you need.

Constant returns to scale simply means that if K and L are increases by 10%, Y will also be increases by 10%. Y will never be increases by more than F(K, L), so profit for additional labor is not possible in that simplified model. I’m assuming this textbook could be Macroeconomics by Mankiw because this concept looks familiar? So Fk and FL would increase by the same % and your output (Y) increases by the same percentage in a constant returns to scale model.


Partial vs. general equilibrium Microeconomic models are usually classified as partial and general equilibrium models. As a layman, I understand that partial equilibrium focuses attention on a few economic variables to find the equilibrium, while general eq. models capture a larger interaction.

Besides this, what are the key differences between the two kinds of modelling? Are there advantages and downsides to each of them?

Let's put the succinct answer by @TheAlmightyBob into an abstract model:

We want to model the labor market.

Markets' structure assumptions: goods market and labor markets are perfectly competitive. All participants are "too small" economically, and they cannot affect equilibrium price through their quantities demanded/supplied - they are "price takers". Markets "clear" - i.e. prices adjust so that quantity actually supplied equals quantity actually bought.

Agents assumption: There are $n$ identical workers, and $m$ identical firms, that participate in the market. Both populations are fixed.

Other assumptions: a) deterministic environment, b) one perishable good produced, c) model in "real terms" (real wage etc, scaled by the price of the good produced).

The typical firm produces according to the technology
$$Y_j = F_j(K_j,L_j;\mathbf q)  \tag{1}$$

where $\mathbf q$ is a vector of parameters. Perfect competition in the goods market, and a perishable good imply that all output produced is sold.The goal of the firm is maximization of capital returns over the choice of labor.

$$\max_{L_j} \pi_j = F_j(K_j,L_j;\mathbf q) - wL_j$$

We are modelling the labor market, so we are interested in the first-order condition

$$\frac {\partial \pi_j}{\partial L_j} = 0 \tag{2}$$
and the corresponding input demand schedule

$$L_j^* = L_j^*\left(K_j, \mathbf q, w\right) \tag{3}$$

Total Labor demand is $L_d = m\cdot L_j^*$.
The labor market equilibrium assumption implies

$$ L_d = L_s \Rightarrow m\cdot L_j^*\left(K_j, \mathbf q, w\right) = L_s \tag{4}$$

which implicitly expresses the equilibrium wage as a function of technology constants, of per-firm capital, and of labor supplied. In order to fully characterize the labor market, we need to derive also the optimal labor supply.

Each identical worker derives utility from consumption and leisure, subject to a biological limit of available time, $T$, and the budget constraint that consumption equals wage income:

$$\max_{L_i} U(C_i, T-L_i;\mathbf \gamma),\;\; \text{s.t.} \;C_i= wL_i$$

where $\gamma$ is a vector of preference parameters, indicating the relative weight between utility from consumption, and from leisure.
This will give us individual labor supply as

$$L_i^* = L_i^*(T,w, \mathbf \gamma)  \tag{5}$$

and total labor supply is $L_s = n\cdot L_i^*$. Plugging this into $(4)$  we obtain

$$mL_j^*\left(K_j, \mathbf q, w\right) =n L_i^*(T,w, \mathbf \gamma) \tag{6}$$

If we stop here, we have a partial equilibrium model that examines the labor market. We have fully described the market, and the goals and the constraints of the participants in it (firms and workers), related to the specific market. We can perform comparative statics in order to see how the various components of $(6)$ affect the equilibrium wage. Among them, there is the capital-per-firm term, whose effects on wage we can also consider based on $(6)$, by treating it as varying arbitrarily.

In order to turn this model into a general equilibrium model:
a) We need to specify things about capital: who owns it/controls it/makes decisions on it. What is the objective functions of these decision makers. This will lead us to an optimal $K_j^*$ as a function of the structure we will impose here. Then, comparative statics with respect to $K_j$ will turn into comparative statics with respect to the factors that affect the determination of $K_j^*$, which may very well prove to involve also $\mathbf q, w$ and even the other parameters in $(6)$, changing in this way the comparative statics results obtained in a partial equilibrium setting.

b) We also need to take into account any macroeconomic identities that characterize this economy, something along the lines of $mY_j \equiv ...$ where the right hand side will be determined by the assumptions we make related to capital, but also, for example, by whether we will assume that the economy is closed or open, or partially open to the outside economic system.

So, apart from being more complicated as a model, it may also lead us to different conclusions than partial equilibrium analysis.

The partial equilibrium analysis studies the relationship between only selected few variables, keeping others unchanged. Whereas the general equilibrium analysis enables us to study the behaviour of economic variables taking full account of the interaction between those variables and the rest of the economy.
In partial equilibrium analysis, the determination of the price of a good is simplified by just looking at the price of one good, and assuming that the prices of all other goods remain constant. Thus the economy is in general equilibrium when commodity prices make each demand equal to its supply and factor prices make the demand for each factor equal to its supply so that all product markets and factor markets are simultaneously in equilibrium.


Should I deflate a nominal variable when forecasting it? Say I have a structural equation that is forecasting Y. Y is a nominal financial variable that grows with time due to inflation. I have an economic determinant that is a rate and therefore does not increase with time. Is it wise or necessary to deflate Y so that the variables behave the same way? I do not particularly want Y deflated as this regression will be forecasted and this just introduces another hard to forecast variable.

In macro, the standard approach to forecast variables which are intrinsically nominal like GDP seems to be to separate the forecast. This is, you want to have a model for real GDP and for inflation. The final forecast for nominal GDP is the "combination" of both. This is for instance the standard practice of the Fed (of Atlanta) and the Bank of England (pages 39 to 41).

In your case of a financial variable, you could model the real (deflated) variable, and then, as inflation is given by the economy, just take the official inflation forecast of your country from the central bank. They are the real experts on this so is a safe thing to do in my opinion. Also, the market expectations of inflation, crucial in finance, are very much informed by central bank estimates. This approach gives you a cleaner estimation of your model too. As you say, your determinant is a rate, and thus inflation is just molesting in the left hand side.


Strictly increasing function transformation I have utility function given by:

$U(x_1, x_2) =
  \begin{cases}
                                   x_1+x_2 & \text{if $x_1+x_2<6$} \\
                                   6 & \text{if $6\leq x_1+x_2\leq10$} \\
                                   x_1 + x_2 & \text{if $x_1+x_2>10$}
  \end{cases}$

If I transform this to this:

$F(U(x_1, x_2)) =
  \begin{cases}
                                   U(x_1, x_2)+4 & \text{if $U(x_1, x_2)<6$} \\
                                   10 & \text{if $U(x_1, x_2)=6$} \\
                                   U(x_1, x_2) & \text{if $U(x_1, x_2)>10$}
  \end{cases}$

Is it strictly increasing function transformation?

Thanks guys

This is a strictly increasing monotonic transformation simply because the preferences in the previous function are the same in the transformed function as well.


Is the international economic system too chaotic to "work towards" carbon emission reduction I often get frustrated when I read calls to action on climate change.   It goes something like this: "Solutions are within reach - but we must act now!"

If one assumes that the international economic system is chaotic and reactive,  and that no one is in charge, where is the theory to back up what seems to be a wild claim that "we can act".  Who are "we", and are markets even able to deal with information about the common good or the future.

Suggestions for further reading on relevant theory would be appreciated.

There are already precedents that show the international capacity is there, technically, and economically to deliver the carbon reduction necessary, in time. And there are indications that the political will to do so is growing to sufficient levels, too.

Firstly, with the number of participating nations being 195 (the UNFCCC nation parties), that's about the right size to create a management group that prevents the destruction of the commons, despite the short-run market incentives being ones that would otherwise lead to such destruction: see the Nobel-winning work by Elinor Ostrom for lots of information on this - I highly recommend it, it's a very good read. This addresses the aspect of your question about whether the market can accommodate information about the common good and the future.

Secondly, there are already examples of individual nations putting primary legislation in place, and acting on it: the UK's Climate Change Act was the first such law in a major industrialised nation; other countries have done similar.

Thirdly, there are already examples of nations collaborating on global environmental problems successfully: the international action to reduce emissions of ozone-destroying chemicals, the Montreal Protocol, is working.

And fourthly, the COP21 Paris Agreement showed unanimity among the 195 nations plus the institution of the EU in the need to address this problem. Pause for a moment to consider the enormity of that. The Paris Agreement wasn't just approved by majority consensus, but unanimously by all 195 countries.

All of these things happened within the context of the international economic system. So it's certainly not a barrier.

And we know that the economic incentives to prevent catastrophic climate change far outweigh the costs of doing so, at any sane discount rate. However, there is a principal-agent problem, and decades of lag between cause and full outcome; therefore market mechanisms alone cannot be sufficient. But there are no pure market economies - it's all a blend of private and public agents - so that's only a hindrance, but not a barrier.

The chaos of the international economic system is certainly no obstacle to carbon emission control. In its crudest form, environmentalism can achieve its goals simply by destroying capital or hindering capital accumulation, which is basically the point of most environmental regulation.


How does an elastic Money Demand affects the effectiveness of fiscal policy? From my notes:

'The elasticity of Money Demand reduces the impact on the interest rate of the increase in government spending...'

My question is: if the Money Supply is inelastic, the elasticity of Md wouldn't matter, because the Md would just shift up/down by the same amount regardless of its slope, and it is the shift that determines the change in interest rate, which doesn't fit with my notes.

Maybe another way to put it is: does the elasticity of Money Demand affects how much it changes in response to a change in government spending? If so, how?

a small rise in interest elasticity shifts the equilibrium position of IS-LM CURVES to the right


Fair and efficient allocation of "family goods" Consider an exchange economy with two goods, e.g. home furniture (x) and electrical equipment (y). The interesting thing about these goods is that, when a family owns a bundle, all members of the family enjoy the same bundle (it is like a "club good" but only for the family).

There are two families. In each family, there are different members with different preferences over bundles. Assume that all preferences are monotonically-increasing and strictly convex.

An allocation is a pair of bundles, $(x_1,y_1)$ for family 1 and $(x_2,y_2)$ for family 2.

An allocation is called envy-free if:

All members of family 1 believe that $(x_1,y_1)$ is at least as good as $(x_2,y_2)$;
All members of family 2 believe that $(x_2,y_2)$ is at least as good as $(x_1,y_1)$.

An allocation is called Pareto-efficient if there is no other allocation of bundles to families such that all members of all families weakly prefer and at least one member of one family strictly prefers.

Under what conditions does a Pareto-efficient envy-free allocation exist?

If each family has a single member, then a Pareto-efficient envy-free allocation exists; this is a famous theorem of Varian. Has this theorem been generalized from individuals to families?

Right now I'm not sure about the equivalence of the relabeling, and therefore the usefulness of this anwer -- see comments below.

This is the beginning of an answer and an attempt to demonstrate how strong the necessary assumptions would have to be to guarantee existence.

Let's transform the problem into one that's equivalent but a bit easier to work with. Instead of indexing over families, let's instead index over the agents (members of families). The key to this relabeling is understanding that families can be written as constraints: If agents $i$ and $j$ belong to the same family, then $x_i=x_j$ and $y_i = y_j$.

Now we're back in the standard environment with individual agents (not families) but with these familial constraints. Recall the proof of Varian's theorem, which you link in the question. It uses the existence of a competitive equilibrium from equal incomes. In this context, we would need the existence of a competitive equilibrium from equal incomes in which the familial constraints were also met. This is going to be very difficult to do. For instance, consider $i$ and $j$ are in a family, and
$$
u_i=x_i + \varepsilon y_i \:\: \text{ and } \:\: u_j = \varepsilon x_j + y_j
$$
where $\varepsilon>0$ is tiny. These preferences are monotonic and convex. Basically, one family member cares about $x$ and the other cares about $y$. If each of the two agents is purchasing $x$ and $y$ to maximize his or her utility, you would not expect $x_i^* = x_j^*$ or $y_i^* = y_j^*$ in the competitive equilibrium (see addendum at end).

This is why you certainly need some assumption on preference similarities within families (at least to use a version of Varian's proof). My sense is that if you give me any arbitrarily small difference in preferences between family members, I can construct an example around it where there exists no CEEI in which they choose the same allocation. And then, at the very least, you can't use Varian's proof.

Two questions:

Do you agree that my reformulation of the problem is formally equivalent to yous?
Can you think of any assumption weaker than assuming preference homogeneity within the family that I can try to invalidate with a counter-example?

Addendum: Remember that in a competitive equilibrium, each agent's marginal rate of substitution (MRS) equals the price ratio. Here, my agents have constant and different MRS's, so there can exist no competitive equilibrium with a price ratio that equals both of their MRS's. If each agent has an MRS that varies, then perhaps they could happen to be equal at the equilibrium price ratio. So maybe you could get away with some notion of local homogeneity of familial preferences. But you need to have them be locally homogenous at the competitive equilibrium, which is exactly what you're trying to prove exists, so it would be a bit circular.

Important note: As mentioned previously, I'm assuming that the only way to prove existence is how Varian did it, via CEEI. There may be other proof techniques that skirt these issues, but I suspect not.

Beyond CEEI: As the OP points out in the comments, proving existence of PEEFs through CEEI as Varian does is somewhat restrictive. I do not have a lot to say about proving existence of PEEFs directly, but the following is readily apparent: For any allocation satisfying your Pareto efficiency condition (ignore envy-freeness for the moment), for any $i,j$ such that $x_i, x_j, y_i, y_j > 0$,
$$MRS_i = MRS_j$$
If this weren't true, there would be a Pareto improvement. Competitive equilibrium essentially equates the MRS's through the price ratio, but you still need to equate these MRS's just to find a Pareto efficient allocation. I think the familial constraints will make this very difficult -- it's not hard to come up with an environment and familial constraints such that there exists no Pareto efficient equilibrium satisfying those constraints. In any case, this could be another partial step towards an answer: Forget about envy-freeness. First try to come up with an assumption on preferences (and maybe on familial constraints) that guarantees the existence of a Pareto efficient allocation that satisfies familial constraints. Then worry about envy.

The problem statement seems to imply that X and Y cannot be substitutes (an electrical device cannot be used as home furniture).

A Pareto-efficient envy-free allocation exists when:

For at least one agent, at least some goods have negative utility or are complements, and agents can chose to not consume.

Example:

Agents A and B are in family F1.
The utility function of agent A is:

Ua = -X1-X2-Y1-Y2

The utility function of agent B is:

Ub = X1-X2+Y1-Y2

Agents C and D are in family 2.
Agent C has a utility function:

Uc = -X1-X2-Y1-Y2

Agent D has utility function:

Ud = -X1+X2-Y1+Y2

Solution:

F1 prefers (X1, Y1) and agent A will chose to not consume any good.

F2 prefers (X2, Y2) and agent C chosen to not consume any good.

These are really semantic arguments and there is no meaningful equilibrium without assuming shared preferences.


Who exploits comparative advantage in international trade? Suppose that under autarky, Colombia makes coffee and cars at \$1 and \$2 each, and Japan makes coffee and cars at \$20 and \$10 each. Since Japan has a comparative advantage in car manufacture, the standard theory says that Colombia will import cars and export coffee.

However, I'm having a hard time imagining how this actually happens in practice. If I run a Colombian car business, why would I import cars from Japan, when they cost five times as much? Why not just buy cars at home?

In general, I see no reason why any business dealing in a single market should care about price ratios; they only see the absolute prices of a single good. For the trade to actually happen in this case, you'd either need a company that trades both cars and coffee (do those actually exist?) or government-controlled trade. Neither of these feel realistic.

If we can look at Ricardo's original example, the same problem appears. Ricardo is assuming that production across an entire country is synchronized in some way; his theory would work if a single business in each country controlled all production of all goods there. But I don't see how the logic holds if there are separate companies producing cloth and wine.

In real life, how are comparative advantages actually exploited?

It's fine to make a supposition that it costs Colombia twice as much to make cars as coffee, and Japan twice as much to make coffee as cars.  It's also fine to express these ratios in terms of the respective local currencies.

The apparent problem you describe only arises because you go beyond the above and express the costs in terms of a common currency (\$).  But in a situation of autarky, there is no way in which the exchange rates needed to convert prices in other currencies to \$ could be determined. Thus your supposition is incoherent.

The way in which comparative advantage would be exploited, given the ratios you describe and given free trade, is that the rate of exchange of Colombian to Japanese currency would adjust to a level at which, in both countries, Colombian coffee is cheaper than Japanese, and Japanese cars are cheaper than Colombian. The Colombian car business will then be able to benefit from comparative advantage while not needing to look beyond the relative prices of locally produced and imported cars.

Addendum:  If, in the past, two countries both used gold as a currency, this would not, given autarky, be equivalent to a common currency. Even if the gold were physically the same, it might just happen (eg for geological reasons) to be scarcer and therefore more valuable in one country than the other.  In the absence of international trade and of payment in gold for traded goods, there would be no mechanism to equalize the value of gold in the two countries.  It would therefore be feasible that the cost, in terms of their respective gold currencies, of producing every good would be higher in one country than the other.  Given free trade, however, the value of gold in the two countries would be equalized at a level at which some goods would be cheaper in one country and some in the other.  The mechanism for equalization would be that people and businesses in the more expensive (and therefore more gold-abundant) country,  taking their own rational decisions and without any need for central control, would import goods from the cheaper country, paying in gold and therefore causing an outflow of gold to the cheaper country.

This model has a number of limitations (as you yourself cited some). The main idea here is that most countries have different opportunity costs between producing different goods, because there are resources that can be used in producing both (like labor). Focusing on what you have comparative advantage and trading allows you to consume outside your production possibility frontier.
In practice, industries that are labor intensive tend to go to countries with a lot of labor (like China and India), because opportunity cost tends to be lower than countries where it isn't so abundant, which in its turn tend to focus on capital intensive industries, since capital tends to be more costly in labor abundant countries.


Marshallian demand help Consider a consumer with a Cobb-Douglas utility function over three goods of the form $u=(x_1+z_1)^\alpha \cdot (x_2+z_2)^\beta \cdot (x_3+z_3)^\gamma$ with $\alpha, \ \beta, \ \gamma, \ z_1, \ z_2, \ z_3>0$, and $\alpha+\beta+\gamma=1$. The consumer has income $m$, and pays prices $p_1, p_2, p_3$ for the three goods.

Find the Marshallian demands for goods 1, 2 and 3 for this consumer, using the
Lagrangian method.

Hint: I won't give a full answer since this is a very specific question, but I can give you a long outline here. A Lagrangian is set-up with an objective function (in this case utility) plus or minus (depending on Kuhn Tucker constraints, which we won't worry about) a constraint function (in this case, income) which is set to zero and then multiplied by the Lagrange multiplier, which we will denote $\lambda$.

So we set up the Lagrangian function. (Plug in the utility function yourself.)

$$\mathcal{L} = u(x_1, x_2, x_3) - \lambda (p_1x_1 + p_2x_2 + p_3x_3 - m)$$

Solve for the partial derivatives $\frac{\partial \mathcal{L}}{\partial x_1}$, $\frac{\partial \mathcal{L}}{\partial x_2}$, and $\frac{\partial \mathcal{L}}{\partial x_3}$ and set them equal to zero (You can also solve for the partial of $\lambda$, but it just gives you back the budget constraint, which I skip to). For example, you get for your first derivative:

$$\frac{\partial \mathcal{L}}{\partial x_1} = \alpha (x_1 + z_1)^{\alpha - 1} - \lambda p_1 = 0$$

Once you solve the three partials, the easiest thing for you to do is solve for $\lambda$ with respect to the other variables for all three partials, and then figure out how to substitute them into the budget constraint. You should solve for each $x$ in terms of the prices, maybe some $z$'s, the greek letters $(\alpha, \beta, \gamma)$ and income $m$. (I tried working some of it out; enjoy your algebra.)

The Marshallian demand functions are basically partial derivatives of the Cobb-Douglas utility function. You should consider that you want to maximize spending first, then derive the functions to get the optimal prices, demand and a equilibrium with both - not sure if I used the correct words.

Nevertheless, here's an example with 2 products, here, from SE.


Why would the rich care about the poor's overinvestment in riskier investments? Glasbeek, Harry. BA, LLB (Melbourne), JD (Chicago).
 Class Privilege: How Law Shelters Shareholders and Coddles Capitalism (2017). p. 196 Bottom.

    Also, from an investor's point of view, limited liability frees investment
  shareholders from the burden of involving themselves in the daily operation
  of the corporation. The contributed capital is transferred to the corporation
  where a board of directors and executives are to take charge of it. The corporation is duty-bound to chase profits, that is, the very efforts the
  would have made on their own account will still be made. But the contribu-tors of capital do not have to expend any effort of their own. In other words,
  limited liability is good because shareholders do not have to do anything.
    Two further arguments are made in favour of limited liability. The first
  arises directly from the fact we are supposed to like the idea of a thriving

p. 197

  market in which shares can be sold and bought. Limited liability helps that
  cause by eliminating some of the volatility that might otherwise prevail. In the
  absence of limited liability, less-well-off investors might invest in higher-risk
  investments than would wealthier ones, because they have less non-invested
  assets to lose. Wealthier investors would then have a different appraisal of
  what makes a share's price affordable than their less wealthy comrades would.
  This could lead to unpredictability in the valuation of shares and, therefore,
  to less attractive stock markets.2 Here the assumption is that robust stock
  markets are a plus for the economy—a highly contestable assumption.

I know that  the rich are more likely to be able to afford investment advisors who can help them appraise share prices differently (e.g. more accurately), and who don't cater to the poor.

But can someone please expound the emboldened sentence? How does the poor's larger investment in riskier investments, affect wealthier investors' appraisal of what makes a share's price affordable?

How does the poor's larger investment in riskier investments, affect
  wealthier investors' appraisal of what makes a share's price
  affordable?

It does not. The author purportedly (and mistakenly) thinks that tolerance to risk is governed solely by the investor's wealth.

Your question mistakenly conveys that a wealthy investor's method of valuation of share's price consists of merely reading (or as your question portrays, is "affect[ed]" by) the non-wealthy investor's assessment. But that reading significantly differs from what the author wrote.

The excerpts you reproduce reflect the author's cluelessness about basic concepts in finance. The end of the first excerpt seems to be inaccurately transcribed: The poor grammar in "The first arises directly from the fact are supposed to like the idea of a thriving" do not allow us to grasp the point the author is trying to make. More important, the second excerpt is nonsense.

The author wrote:

  less-well-off investors might invest in higher-risk investments than
  would wealthier ones, because they have less non-invested assets to
  lose.

Causation as purported by the author is wrong. It is true that some non-affluent investors might be more tolerant to risk, but that tolerance is not solely determined by their non-affluence. Their expertise (or lack thereof, as you later point out), and/or their ambitions (meaning a person's legitimate sake of wealth) influence the levels of risk each individual investor is willing to incur.

As a counterexample to refute the author's point, Nathan Rothschild and James de Rothschild continued getting into high-risk investments even after they had made fortunes, and much to the dismay of the next generation in the family.

Next, the author alleges that:

  Wealthier investors would then have a different appraisal of what
  makes a share's price affordable than their less wealthy comrades
  would.

If a share's price is affordable to a non-affluent investor, then it obviously is affordable to the wealthier investor as well. The author might have meant a more appropriate term such as risk-worthiness as a function of expected profit, which brings us back to my previous comment on being more (or less) risk-tolerant than other investors.

An investor buys stock because he has the expectation that the share price will go up. The fact that different investors have different appraisals on the future price of a stock has little or nothing to do with each investor's wealth. Of course, there is a phenomenon known as herd mentality where a multitude of agents are influenced by a contagious and/or blind belief that a share price will continue certain trend. That leads to price bubbles or collapse, accordingly, but that mechanism of affecting each investor's appraisals is unrelated to what the author and your question portray.

Unpredictability and difference of appraisals are precisely what allow the price of some stocks to fulfill some investors' expectations of profit. If everybody were able to predict the future value of an asset, for instance \$90 per share (for simplicity, assume a risk-free interest rate of 0%), nobody would be willing to sell his share for less than \$90, and nobody would be willing to buy a share for more than \$90. Consequently, the share price would stay at \$90, thereby failing every shareholder's expectation of profit.

The author does not substantiate, at least in those excerpts, why the assumption that "robust stock markets are a plus for the economy" is highly contestable.

  I understand how hedge fund managers with PhDs in Finance (who serve
  only the rich) can help the rich to appraise share prices differently
  (e.g. more accurately)

That is unsubstantiated, highly debatable, and very opinion-based. But I don't vote down questions (or answers) merely for a difference of opinions.

Edited on July 5, 2018, to address OP's follow-up comment, and to add last paragraph

(1) Edited, although see "the fact are supposed to like" in the excerpt. I assume the author meant to type something like "the fact that people|investors are supposed to like the idea of a thriving market". But the whole sentence is still unclear: Is it a fact that they like the idea of a thriving market? or are they supposed to like that idea? Saying "the fact that something is supposed" is rather meaningless for his argumentation.

More important, the author's inaccuracies and gaps reflect he does not handle some financial concepts well, and yet he tries to premise on those flawed arguments his proposition about a limited liability schema. I am not knowledgeable enough to support or criticize the author's conclusion(s) about LLCs/LLPs, but he should definitely rework his arguments away from engendering unwarranted confusion & controversy about "classes".

(2) You ask whether the following would change the sense of my answer:

  I know that the rich are more likely to be able to afford investment
  advisors who can help them appraise share prices differently (e.g.
  more accurately), and who don't cater to the poor.

There are two reasons why it wouldn't lead to a different answer. First: Paying an expensive financial advisor does not guarantee that the investor will obtain competent --let alone accurate-- advice. An advisor's certifications or designations certainly, and only, signal that he has demonstrated (typically via exams) standard knowledge of some prerequisite syllabi. However, the advisor remains subject to the aforementioned unpredictability of markets, and to internal policy at his employer agency.

Second: An advisor might recommend the same to wealthy and poor investors, yet the wealthy respond with "I hear you, advisor, but I still want you to do xyz with my funds" based on that investor's risk profile, scrutiny, fiscal planning, expertise, or moral/religious considerations.

I should have added yesterday that, even if the wealthy investor cared about the appraisals made by the poor investor, such reading of appraisals is impossible in today's stock markets because these involve so many buyers and sellers. The author "highly contests" (albeit without substantiating why) that "robust stock markets are a plus for the economy", but it is precisely that inability (in today's markets) to cross-read investments what strikes the author's insinuation that appraisals vary by "class".

Liability applies whether your assets are in cash, stock, real estate or other. For example, if a company goes bankrupt, it may have to liquidate to pay creditors. Limited liability which prevents shareholders from being liable for additional debts that cannot be paid from such a liquidation would tend to benefit those whose liability is limited, i.e., those with assets to invest, but that is a separate question from whether the perceived marginal benefit associated with a risk differs systematically from wealth.


Why isn't there an "ideal value" for a given currency? If a currency can be worth too little (e.g. needing \$10,000,000,000 to buy a loaf of bread) and worth too much (e.g. being able to buy a loaf of bread for $0.00001), why isn't there an "ideal value" (a point, range, or a shifting set of priorities based on market conditions) that a currency could be fixed or drawn toward?

Many everyday transactions are still done in cash, requiring mental calculations from the transacting parties. Too large numbers and too small numbers create transaction costs that, at least for the extremes, cannot be ignored.  So conceivably, some "middle" point could be considered "ideal" as regards the efficiency of money as medium of transactions.

What forces may prevent such an "ideal value" for a currency from being established?

Because money is really just arbitrary numbers, and those numbers only really have any meaning in relation to the other numbers in the set. For example:

Average salary is \$50,000 and a entry-level car costs \$10,000. If the price drops by \$5,000, it's well known that sales will go up, ceteris paribus. But what we increased all prices and all wages by a factor of 100,000? Would that change people's behavior in an otherwise identical system? E.G. now the average salary is \$5,000,000,000 and the average car costs \$1,000,000,000 and the price drops 500,000,000, then what happens?

Well there is a fancy economic name for the theory that covers this (which I forget at the moment), but the answer is No, nothing would change. It's quite obvious that humans are very insensitive to absolute price and very, very sensitive to relative price. (There have been several economy-wide currency revaluations in other countries that serve as examples of this.) Adding or taking away a couple zeros at the end of the numbers doesn't change the really make a difference (provided you apply the change uniformly to all numbers everywhere).

The two major problems that hyperinflation a la Weimar Republic cause are 1.) governments are slow moving beasts and don't react quickly enough to start printing 1 billion dollar notes, etc. so you end up having to use a wheelbarrow full of cash for purchases (which in today's economy isn't as big of a concern since almost all money is just electrons in a computer somewhere,) and 2.) changing prices and adjusting to changing prices and adjusting your forward looking predictions about prices are all not costless actions. It takes time and energy to do any one of those three things. Because of that fact, it imposes a very real dead weight loss on the economy as a whole when prices increase or decrease very rapidly. The faster things move, the more costly it is to adjust and the more often you have to do so, so the DWL becomes exponentially greater than a more slowly-paced situation.

First of all, money has three basic functions: a store of value, a medium of exchange, and a unit of account.  Markets are able to work with any form of "money" as long as it is able to satisfy each of these conditions.  This explains why economies are still able to work with dollars, euros, mackerel, and cigarettes.

You are correct in saying that hyperinflation is bad, but the new numbers produced from the inflation is not necessarily bad.  Hyperinflation is merely a high rate of inflation and causes an overall increase in the prices of goods.  The reason inflation/hyperinflation is bad is because it destabilizes the money as a store of value.  The money is able to perform best in the economy when it can best fulfill it's three-pronged purpose.

Also, remember that the market prices are completely dependent upon the supply and demand of the good.  Let's say that you want to purchase a good but will only buy it if it cost less than a certain amount, say one hour of your per hour wage.  Let us also say that the good is being sold at the price of one hour of your per hour wage.  In this example, regardless of how much the prices have been changed by inflation, you are still going to value the good at the same "price"; the good still costs you the same amount of time and effort (in this example, one hour at your job).
In the strictest sense, the price of the good does not matter.  The value of the good is determined by how much you are willing to pay for it, and you arbitrarily decided that you would not pay more than the per hour value of your job.  Because the value that you assigned the good is not an objective number value, it is impossible for us to find a good's "ideal value" and keep the price "anchored" to that standard.


Are White's Robust standard errors robust to clustered errors? I want to ask about OLS White's 1980 "robust" standard errors.
The key assumption, is that regression errors $u_i$ have distinct variances $σ_i^2$. Then the variance matrix is: $$\Sigma = \operatorname{diag}(\sigma_1^2, \ldots, \sigma_n^2)$$ with its White's estimator: $$\hat\sigma_i^2 = \hat u_i^2$$ This is the HCE (heteroscedasticity-consistent estimator).
 Is the White's robust variance of $\hat{\beta}$ estimated by OLS assuming  independence? For example, assume that there is some $i,j$ such that $$Cov(u_i,u_j)\neq0$$ Because $i,j$ are part of a cluster. In that case $\Sigma$ is not diagonal but has the same diagonal as before. Will the White estimator converge to the diagonal of the true $\Sigma$?

No. White's robust errors are only robust to errors that vary linearly based on X(t).  If you have a type of serial correlation or clustering you will want to use Hansen method to adjust standard errors.

Read Arellano (1987, Oxford Bulletin of Economics and Statistics)