Elasticity of Substitution of CRS Production Function Suppose that $F(\cdot)$ has CRS in $K$ and $L$, the elasticity of Substitution is  $\sigma_{K L} \equiv F_{L} F_{K} / F F_{L K}$.
I once derived this equation but I remember that it takes me quite long time and the process is quite tedious. I wonder is there any easy way to derive this or remember it intuitively?

I am not sure if it is intuitive but this is because because CRS function is homogenous of degree 1.
Full derivation:
First, general formula for any arbitrary elasticity of substitution between $L$ and $K$* is given by (see Sydsæter et al. EMEA pp 430):
$$\sigma_{L,K}  = \frac{-F_K'F_L'(xF_K'+ yF_L')}{xy \left( (F_L')^2F_{KK}^{''} - 2 F_K'F_L'F_{KL}'' + (F_K')^2F_{LL}''\right)}, \text{ for: } F(K,L)=c \tag{1}$$
Where c is arbitrary constant. This is our starting point.
Now by definition property of CRS production function is that they are homogenous of degree 1 (since by definition we have CRS when $F(tK,tL)= tF(K,L)$).
If $F$ is homogenous of degree 1, then the numerator of (1) will be $= −F_K'F_L'F$.
This is because of the Euler's theorem which tells us that if:
$$f(x,y) \text{ is homogenous of degree k} \implies xf_x'(x,y) +  yf_y'(x,y)= kf(x,y)$$
Next Euler theorem also implies that (assuming $f$ is twice continuously differentiable) that:
$$xf_{xx}''(x,y) +  yf_{yx}''(x,y)= (k-1)f_x'(x,y)$$
$$xf_{yx}''(x,y) +  yf_{yy}''(x,y)= (k-1)f_y'(x,y)$$
The above implies that in our case:
$$K F_{KK}'' = - LF_{KL}'' $$ and that $$L F_{LL}'' = - K F_{LK}'' = - K F_{KL}'' $$. Hence the denominator will be given by:
$$ -F{KL}''\left( L^2 (F_L')^2 + 2KLF_K'F_L'+ K^2(F_K')^2\right)= - F_{KL}''(KF_K'+ L F_L')^2 = - F_{KL}''F^2$$
We use Euler theorem above again.
Now finally we are done:
$$\sigma_{LK} = \frac{−F_K'F_L'F}{- F_{KL}''F^2} =\frac{F_K'F_L'}{ F_{KL}''F}  $$
I personally do not think the result above is very intuitive (if it is so its intuition eludes me), but it is a consequence of CRS function being homogenous of degree 1 and this result actually applies for any elasticity of substitution between two variables of arbitrary function that is homogenous of degree 1 and twice continuously differentiable.

 * or $y$ and $x$ for that matter this generalizes to any elasticity of substitution problem


Differing Inflation Rates for Separate Income Groups; Literature? So here's a few ideas that have been floating around my head since undergraduate university. It seems that money owned by the highest net wealth owners is always moving around and making a return, but only in markets that don't particularly affect the lower classes (debt and equity trading for example).

So might there be significantly different rates of inflation or expected rates of inflation for different income groups? As income inequality rises, would money demand also be lower for lower income groups and higher for high income groups, which would create inflation for luxury goods and such? If a central bank cares about population welfare and they know their policy may impact inflation differently for different income groups, couldn't this affect their planning/optimal policy?

I know these are a lot of questions. I am mainly interested in whether there have been studies or theories about any of these sorts of questions before and whether these questions are actually interesting, empirically. Feel free to give me suggestions on how to hone in this post; it's a lot of speculative questions, I know.

Edit: Otherwise, how might you guys approach this problem? How might you guys and gals try to model inflation for different income groups?

Let us first boil this question down to a simple story: Suppose bread prices are very flexible while luxury car prices are very sticky. If the central bank now changes its monetary policy to increase inflation, then bread will become relatively more expensive compared to luxury cars. If the central bank anticipates this, they may prefer a more restrictive monetary policy to avoid redistribution from the bottom to the top.

To analyze this, two literature strands may help you. First, heterogeneous price stickiness has been studied in

Carvalho, Carlos. "Heterogeneity in price stickiness and the real effects of monetary shocks." Frontiers in Macroeconomics 6.3 (2006).

This paper essentially breaks with the standard assumption of identical price stickiness across sectors. Thus, at some point one sector (bread) may experience higher inflation than another sector (luxury cars), since luxury car prices are more sticky and there is an expansionary monetary policy. The framework for welfare analysis in sticky price models is given in:

Woodford, Michael. Optimal monetary policy inertia. No. w7261. National Bureau of Economic Research, 1999.

However, you not only have heterogeneity in price stickiness, but also heterogeneity in consumers. This is the second strand in the literature you should consider, the estimation of demand systems and welfare effects therein. The main reference (and recent Nobel memorial prizewinner) is:

Deaton, Angus, and John Muellbauer. "An almost ideal demand system." The American economic review (1980): 312-326.

If you combine these two analyses, you will have an answer to your question. However, this would require you more or less to write a paper about this (which may very well be worth it).


Regulatory differences between stocks and bonds If you buy stocks of a company you are buying a share in that business.
If you buy bonds from the same company you are essentially loaning them money for future payment.

I am guessing (correct me if I am wrong!) that if you buy a bond the terms of repayment have to be very concrete, i.e. you get 2 dollars next year and 10 after that. Otherwise they could tag the repayment to the stock price and what you would have is a bond that behaves like a stock with automated dividends.

My question:
What body of law governs what you can and cannot promise in a bond contract and what agency is overseeing this? (Corporate law and the SEC?) I am most interested in the US setting, but info about other countries is also welcome.

A secondary question is what big practical differences between stocks and bonds the regulation causes. (The common economics/finance wisdom is that stocks have higher yields but bigger 'risk'. I am more interested in practical differences that lie in the mechanisms, such as bond owners having precedence in case of bankruptcy.)

Bonds and stocks, and in general all securities related to a firm, are regulated by the SEC in the US. Some other financial instruments are regulated by the CFTC (mainly commodities and derivatives, though some of the latter are regulated by the SEC)
Stocks
Stocks are a share in the firm. Meaning they are actually ownership securities. Hoilding a stock entitle their holder to earn a part of the earnings of the firm - the dividends, and to have a say in the strategy of the firm, through a vote at the Annual General Meeting.
Different kinds of stocks can be found: The difference usually lies in the number of votes that each share carries, or in their seniority in case of bankruptcy (preferred shares get paid before common shares)
A good example is Alphabet's (Google's) shares:

A shares, which have one vote each (NASDAQ:GOOGL)
B shares, which have 1 vote each (not publicly traded)
C shares, which are capital-only (no votes attached) (NASDAQ:GOOG)

This allows the founders to maintain ownership of the company while raising additional funds. As you can guess, Sergei Brin, Larry Page and then Eric Schmidt own a minority of the total stock, but secure more than 70% of the voting right through their holding of B shares.
Bonds
Bonds are debt securities: they do not represent ownership but they represent a claim. In opposite to stocks, there are plenty of different types of bonds. There is a huge diversity, and the main characteristics that can change are the following:

Maturity (When do you get paid back the nominal amount): it can go to a few months to 30 years or more (the UK still has outstanding debt with no maturity)
Interest rate (How much do you get, and at which frequency?): It can go from zero to any other amount. It can be fixed, or variable, for example indexed on inflation.
The seniority (who gets paid first in case of bankruptcy)
The collateral (Are you entitled to receive a particular asset in case of default?)
Other options, such as convertibility (some bonds can be converted to shares, for example if the firm defaults on these bonds, or if the bondholders asks for the conversion.)

To put everything together, what happens in case of a bankruptcy is that direct creditors are paid first: the government (taxes), the employees, the suppliers, etc. Then, the other creditors are paid, if there is anything less, in order of seniority: either because some debt are embedded with particular seniority level, such as First Lien Debt, or in order of maturity (short term debt first). Some debt have a collateral, which the holders of the debt have a claim on in case of default. For example, ABS and MBS are 'guaranteed' by assets which the lender will get if they aren't paid. The governments can also extend guarantees on private firms lending.
This explains why the two types of security have different risk profile.
For a firm, the rules/regulations on each type of security have a very deep impact. Namely, it is less costly to raise debt: first, debt costs less (interest rates are typically lower than equity yield), and also because the interest rates are tax-deductible. This can cause problems as it incite firms to take on more debt than they otherwise would, as underlined by this article from The Economist.


Utility functions and positive monotone transformations We let $g(z)$ be a strictly monotonous function so:
$$\frac{dg(z)}{dz}>0$$
Consumer 1 has preferences given by the utility function $u(x_1,x_2)=ln(x_1)+2ln(x_2)$, while consumer 2 has preferences given by n $v(x_1,x_2)=g(x_1x_2^2)$.
Then I have to show that consumer 2 got same preferences as consumer 1.
I think I have to use MSR on $x_1x_2^2$ and on $v(x_1,x_2)$. For MSR on $x_1x_2^2$  I get:
$$MRS=-\frac{\frac{\partial }{\partial x_1}}{\frac{\partial }{\partial x_2}}=-\frac{x_2^2}{2x_1x_2}$$
But How can I find MSR on $v(x_1,x_2)$ (I think I got the same MRS if I use the chain rule, but I'm not sure?), and how can I use this to conclude that the ranking of the two indifference curves is the same when $g(z)$ is monotonous?
I hope that someone can help me?

Note that
$$ln(x_1)+2*ln(x_2) = ln(x_1)+ln(x_2^2) = ln (x_1 * x_2^2),$$
and note that
$$MRS_v = \frac{g'(x_1 * x_2^2) x_1 * 2 x_2}{g'(x_1 * x_2^2)   x_2^2}$$
such that the derivative of $g$ cancels out.
For more intuition, see here.


Economic consequences of a lingua franca Although I'm specifically interested in the likely economic consequences of implementation of an official world auxiliary language, since this is only theoretical, I'd like to know what have been some economic consequences, whether positive or negative, for those nations that endorsed a lingua franca and thereby opened themselves up to segments of the rest of the world (or conversely, I'd be interested in the long-term economic consequences for a country which, perhaps for anti-colonial reasons, rejected a more internationally spoken language in favor of a local one).

For this question, I'm less interested in lingua francas whose effect was primarily domestic. For example, with Modern Hebrew being chosen in Israel, or perhaps Mandarin Chinese in China to a lesser extent, the ability to speak a new official and universally taught common language did not open up the country precipitously to opportunities for communication with other countries.

Note that I'm not asking here about the economic costs of implementing such a language change.

No doubt, and as with free trade, all things being equal, a lingua franca would increase economic opportunities, whether in collaboration possibilities, education opportunities, etc., but, also as with free trade, a lingua franca might precipitously expose a country to competition in certain (intellectual) fields and thereby create resentment within certain industries which in turn led to protectionism. What experiences have been documented on this topic?

(Note: I can't create a "language" tag for this post, due to my being new here, so "free-trade" was the closest tag I could think of.)

(And just for interest's sake, I've asked re: political consequences at https://politics.stackexchange.com/questions/7732/external-political-consequences-of-a-lingua-franca )

These two papers seem relevant. The large Indian wage premium for English language fluency suggests that there would be significant returns at the margin to providing services through trade instead of locally, but they are limited by the supply of foreigners with the right language skills.  However, these premiums are largest among the skilled workers, suggesting that the benefits of a universal language would also accrue disproportionately (in absolute wage premia) to the most skilled.

  Recent studies have shown that trade liberalization increases skilled
  wage premiums in developing countries. This result suggests
  globalization may benefit elite skilled workers relatively more than
  poor unskilled workers, increasing inequality. This effect may be
  mitigated, however, if human capital investment responds to new global
  opportunities. A key question is whether a country with a more
  elastic human capital supply is better positioned to benefit from
  globalization. I study how the impact of globalization varies across
  Indian districts with different costs of skill acquisition. I focus on
  the cost of learning English, a relevant qualification for high-skilled
  export jobs. Linguistic diversity in India compels individuals to
  learn either English or Hindi as a lingua franca. Some districts have
  lower relative costs of learning English due to linguistic
  predispositions and psychic costs associated with past nationalistic
  pressure to adopt Hindi. I demonstrate that districts with a more
  elastic supply of English skills benefited more from globalization:
  they experienced greater growth in both information technology jobs
  and school enrollment. Consistent with this human capital response,
  they experienced smaller increases in skilled wage premiums.

Human Capital Response to Globalization: Education and Information Technology in India

  India's colonial legacy and linguistic diversity give English an
  important role in its economy, and this role has expanded due to
  globalization in recent decades. It is widely believed that there are
  sizable economic returns to English-language skills in India, but the
  extent of these returns is unknown due to lack of a microdata set
  containing measures of both earnings and English ability. In this
  paper, we use a newly available data set - the India Human Development
  Survey, 2005 to quantify the effects of English-speaking ability on
  wages. We find that being fluent in English (compared to not
  speaking any English) increases hourly wages of men by 34%, which is
  as much as the return to completing secondary school and half as much
  as the return to completing a Bachelor's degree. Being able to speak a
  little English significantly increases male hourly wages 13%. There is
  considerable heterogeneity in returns to English. More experienced and
  more educated workers receive higher returns to English. The
  complementarity between English skills and education appears to have
  strengthened over time. Only the more educated among young workers
  earn a premium for English skill, whereas older workers across all
  education groups do.

The Returns to English-Language Skills in India

Here is a natural experiment that provides an example of the negative effect of the opening of labor markets on the existing population the new workers will compete with (in this case, the arrival of Russian mathematicians on Western mathematicians' wages and job prospects).

  The fall of the Iron Curtain in late 1991 ended nearly 70 years of
  isolation of Soviet mathematicians from the world mathematical
  community. Suddenly free to travel and emigrate, approximately 1000
  Soviet mathematicians, mostly highly productive researchers, relocated
  to other countries. Three-hundred-thirty-six scientists came to the
  United States.

  During the decades of scant contact with foreign colleagues, Russian
  mathematicians, for political reasons that Borjas and Doran explain,
  concentrated on certain fields that tended to get much less attention
  in the West. American mathematicians, meanwhile, had moved ahead in
  areas that Russians largely ignored. When the émigrés arrived in
  America, therefore, they had a great impact on certain mathematical
  fields but much less on others.

  These differential impacts allow Borjas and Doran to compare what
  happened in fields heavily and lightly affected by the influx and to
  analyze what a large infusion of new talent and ideas does to a field
  of research. Combining information from several large databases, they
  track the productivity and affiliations of the Russian and American
  mathematicians. Their inquiry concentrates on two major effects; the
  “knowledge shock” from all of the new approaches and insights suddenly
  available to American mathematics, and the “labor market shock” from
  all the new people suddenly on the American mathematics job market.

  What they found does not support what Borjas calls the conventional
  “rubbing-off” theory, which holds that if “we get all these highly
  skilled immigrants, … somehow there’s a rubbing-off effect that makes
  you and me more innovative.”

  Since the fields with heavy Russian influence had “incredibly bright
  new mathematicians coming in, with all these new theorems, all these
  new techniques flooding the market, you would expect that people
  working in those areas are going to learn quite a lot from them,”
  Borjas says. “At the same time, the number of academic jobs where
  mathematical research is actually done is really not increasing all
  that much. So something has to give.”

  That something, the study found, was the career prospects and
  productivity of many of the mathematicians already here. “When you
  increase the number of very smart people in a field by a substantial
  amount,” Borjas says, “… not everybody benefits. The typical
  pre-existing American mathematician actually lost out.”

  That’s because “a generation of American mathematicians at the very
  peak of their mathematical efficiency by luck just happened to
  graduate at the same time these Russians [were] coming in,” Borjas
  explains. The people of that young generation lost the most. Faculty
  members protected by tenure kept their jobs, but mathematicians who
  had not yet attained it found themselves facing sharply heightened
  competition, which produced an “unprecedented 12 percent unemployment
  rate for new American mathematics PhDs” and “a dramatic decrease in
  the probability of obtaining a position in research universities,” the
  article says. The overall unemployment rate for college graduates,
  meanwhile, was dropping rapidly, from 3.2% to 2.2% between 1992 and
  1996. Many of the young mathematicians in heavily affected fields ended up moving to lower-ranking institutions or leaving academic
  mathematics altogether.

  The situation “drove a lot of American mathematicians into Wall
  Street,” Borjas says. There, in their new role as “quants”
  (quantitative analysts), they turned their talents to inventing
  intricate financial instruments. Ironically, one of Borjas’s
  colleagues has joked, the migration from the formerly communist
  country probably helped to fuel the 2008 economic crisis that nearly
  > brought down American capitalism.
  Taken for Granted: Foreign Invasion


Can marketing efforts be considered to be a factor of production? This is a sightly unconventional question, but I want to know whether marketing efforts can be considered as a factor of production. After all, if no one knows about your product, you can't make a profit. Also, marketing efforts may, in some or most cases, show diminishing returns. It is a kind of labor.

Marketing is obviously relevant. We can observe that firms spend money on marketing. If it had no effect, they wouldn't do it. Whether it is a "factor of production" depends on your definition.

In my book, a factor of production is any input that directly contributes to the production (creation) of the good or service. That is, it enters some production function $f$ that maps "factors of production" into "output", a quantity of the produced good. In that sense, marketing is not a factor of production, because it has no direct effect on how many goods are produced. In my eyes, marketing is supposed to influence the demanded quantity, not the produced quantity. Of course the two are related, but not directly.

Belleflamme and Peitz have a nice subsection on adverstising (6.1), where they discuss three distinct aspects of how advertising (which I use synonomously with marketing) affects demand: it can be persuasive, informative or complimentary. Such a distinction matters, because the welfare effects differ. For instance, informative ads may increase welfare as consumers can make better-informed choices, whereas persuasive ads may decrease welfare as it distorts consumers' real preferences.


Estimation of point-identified Dynamic Discrete Choice models with moment inequalities I'm trying to understand and implement in code the method in Bajari, Benkard, Levin (2007). The first stage is clear to me, as well as how to forward-simulate to obtain an estimate of the value function. What I don't get is:

What are the moment conditions? In the paper, the moments are expressed as the difference of the simulated value employing the policy obtained from the first stage, and some other policy:

For example, I tried choosing N randomly selected states and obtaining the simulated value for simulated paths of length T, by using the first-stage policy and some perturbed version of that policy. Is this one way of generating moment inequalities?

Then, the paper refers to the true parameters as those that minimize the following target function:

I understand that the expected difference in simulated values is strictly positive according to Revealed Preferences, but I don't understand why the true parameters are the ones that minimize the function above. For example, if the value function becomes zero at any state and choice for a given set of parameters, the simulated values will be zero as well under any policy, even if the true parameters are not such.

Any help or reference of a concrete example will be greatly appreciated.

Function $Q$ has to be minimized wrt $(\theta,\alpha)$.
The parameters $(\theta,\alpha)$ compatible with Nash equilibrium and rationalizing (or generating) the data have to satisfy $$g(x;\theta,\alpha)\leq0.$$
In the case where, for given $x$, $$g(x;\theta,\alpha)>0,$$ the parameter values have to be changed in order to possibly reverse the strict inequality and minimize $Q$.
If $$g(x;\theta,\alpha)\leq0$$ for some $(\theta,\alpha)$, then this should not contribute to increase $Q$, because it is fully compatible with the data and model. Hence the term $\min\{g(x;\theta,\alpha),0\}$ in the expression of $Q$.


Constant marginal cost for a firm and perfect competition What happens if the demand curve is flat because the firm is a price-taker in the market, but the firm has a constant marginal cost. If the equations are the same I assume the price would be set with a theoretically infinite quantity, but what happens if they are different?

This is somewhat unrealistic, but so be it...
If $p=MC$, then for each additional unit you get as much as you pay, therefore your profit is constant in quantity, either 0 or negative (because of fixed costs). In the latter case you would exit the market in the long run, but in the short run your profit maximization problem is indeterminate (every quantity is optimal). In the former case your profit maximization problem is indeterminate in the short and in the long run.
If $p<MC$, then you would shut down to minimize your loss.
If $p>MC$, then your profit maximization problem has no solution in the real numbers. (You want to produce an "infinite quantity".)


Real world example of using difference quotient vs. derivative When would you use the difference quotient in an economic model rather than the derivative to assess the change in some endogenous variable?  Real world examples seem to be lacking in textbooks on basic mathematical economics.

You can see the applications in microeconomics. A tiny example could be on elasticity of demand.

Let's say

$$ D = \frac{tC}{P+t} $$

where $P, t, C$ are respectively price, tax and constant. If you like to see the effect of tax change on demand you can use the difference quotient ;

$$\Delta D = \frac{(t + \Delta t C)}{P + t + \Delta t} - \frac{tC}{P + t}$$

I skip the intermediary calculations. This one yields ;

$$\frac{\Delta P}{\Delta t} = \frac{P.C}{(P+t)^{2}+\Delta t.(P+t)}$$

Hope that it helps.


Economics Behind the Insulin Shortage? A lot of my family is concerned about a future insulin shortage and it's reported that this shortage is growing.  When I read articles from Harvard about it, they imply it's pure greed:

  There are no generic insulins. Over the past twenty years, prices for the most commonly prescribed “analog” insulins have risen from about $20 per vial to well over \$250 per 10 mL vial, an over 700% increase after accounting for inflation. In contrast, insulin today costs roughly five dollars per vial to produce. With deductibles far outpacing wages, insulin has become unaffordable even for well-off Americans.

If it costs us 5 dollars to produce, why don't we all start insulin companies and sell it for $15, attracting all the business (as well as popularity since we have better prices).  Is greed really the issue, or is there another economic explanation, like the resources involved in insulin-making are in a shortage?  Or the regulation of producers?  Or the possible lawsuits producers face if they make a mistake?

It sounds like anyone could compete against these greedy companies and put them out of business.  What am I missing?

You are missing patents.

I recommend reading the paper "Why Is There No Generic Insulin? Historical Origins
of a Modern Problem" by doctors Greene and Riggs.

  ...high costs of
  pharmaceutical research and development are
  often invoked to justify the high price tags of new
  medications. Although the price point of effective new drugs — from hepatitis cures to new
  agents for heart failure — may initially be out of
  reach for many patients, market laws predict
  that drugs with strong demand should become
  more accessible after market exclusivity ends
  and generic competition begins. Since 1984,
  when the Drug Price Competition and Patent
  Term Restoration Act was passed, pharmaceutical innovation and access have been balanced on
  that premise: innovative drugs are rewarded
  with high prices during their window of patent
  protection, and generic competition reduces
  prices thereafter.

  [...] incremental innovation has repeatedly precluded the formation of a generic insulin industry in North America when earlier
  patents expired. The history of insulin hasn’t followed the standard chronology of pharmaceutical innovation, in which patent monopolies predictably give way to generic competition.

  Viewed in historical perspective, insulin is not
  a single entity but a family of related products
  that has evolved through incremental improvements. Subsequent iterations of insulin represented actual innovations, each one being safer,
  more effective, or more convenient than its predecessor. And yet after generations of incremental
  innovation, insulin may be no more affordable
  than it was when the original patent holders
  sold their stake for $1 to ensure access to this
  essential medicine.
  Pharmaceutical-industry analysts have described a repatenting tactic called evergreening,
  in which a series of related patents — often on
  metabolites or optical isomers — extend the life
  of a product after initial patent expiration.


Does non-binding price ceiling effect the market? If the Price of a commodity is 1 dollar and this price is the equilibrium price. At this price, the quantity demanded & supplied is 100(KGs). If government sets the price ceiling of 10 dollars, What would be the effects on the market?

My curve for this question is:

No there is no impact at all. A price ceiling of $10 means that the price cannot go above $10. Since the equilibrium price is already below $10 the creation of a price ceiling will not effect anything at all.

It is called an ineffective ceiling because it is precisely that, ineffective.


Can biotechnology be a bad thing? My textbook (Economic Issues and Policy by Jacqueline Murray Brux) says:

  In addition to health and environmental concerns about biotechnology,
  the most likely economic effects will be large increases in world food production, causing lower prices of agricultural products and
  preventing poor farmers from succeeding in agriculture. And it is the
  latter outcome that may serve to increase, rather than decrease, world
  hunger.

This statement seems utterly nonsensical to me. Are we actually to believe that large increases in world food production may serve to increase world hunger? Poor farmers using outdated technology may be forced to upgrade or find other jobs, but the lower prices will surely help non-farmers. Thus they (non-farmers) will have more money and this will create new demand and thereby new jobs for farmers who have lost their jobs.

Am I right? This isn't the first error I've encountered in this textbook.

You are right to be sceptical of this statement.  Let's take it step by step.

Will developments in biotechnology increase world food production?  Almost certainly yes, provided other things are equal.  But the reality is that other things are not equal.  Climate change is likely, other things being equal to reduce agricultural productivity in some parts of the world. Whether the positive effect of biotechnology will more than offset the negative effect of climate change is unclear.

If world food production increases, will prices of agricultural products fall? Not necessarily.  Demand for food is rising due to rising population and to rising incomes in much of the world. Again, the net effect (of rising supply and rising demand) is unclear.

If agricultural prices fall, could this increase hunger for some people? Yes, this is certainly possible.  Those most at risk would be people in poor countries who have relied on farming for their income and, due to limited education and training and/or location, have limited opportunities for alternative employment or other income sources.  The book is right to imply that hunger is as much due to low incomes as to food supply.  But the argument that the overall effect of biotechnology will be to increase world hunger is unconvincing.


What is the difference between a free market and a perfectly competitive market? I am trying to find the distinction between a free market and a perfectly competitive market, and I can't find the right definition on what makes them different. Can someone give me a clearly expressed definition on what makes one different from the other.

Please Note: I am looking for a reference based answer.

Perfectly competitive market: Numerous participants, so that no single participant has any influence.

  A perfectly competitive economic model is meant to describe a situation in which there are many participants, and the influence of each one individually is negligible. The state of the economy is thus insensitive to the actions
  of any single agent; only the aggregate behaviour matters. (Source.)

Free market: Voluntary exchanges; no coercion (in particular, no government coercion).

  "Free market” is a summary term for an array of exchanges that take place in society. Each exchange is undertaken as a voluntary agreement between two people or between groups of people represented by agents. (Source.)

Notes:

The two terms are not mutually exclusive.
Neither exists in the real world, though we can imagine examples of both.


What does negative surprise mean? I have a look at the meaning of "negative surprise" from google but there is no clear explanation so far.
When listening to Bloomberg Market Concept, in the picture, Surv(M) < Actual,
while  Surv(M) is the median of analysts about what the value of economic indicator would be upon release and the Actual is the one from the official announcement. In this case, they say that it is a negative surprise.
I am wondering why they use the word "negative surprise" and whether there is any easy-to-understand explanation for this term in real life?

(This is an English language question, not an economic one. Next time consider asking at English Language & Usage.)
A surprise is negative, if it is a bad surprise (for someone). In this context they probably mean that the revealed value of the indicator (PMI) is lower than they expected, which shows that the economy is in worse shape than they expected.
(For different indicators, such as the unemployment rate, it could be that the negative surprise is a higher than expected value.)


Syndicated Loans Terminology - Borrower & Sponsor I am trying to understand what is the difference between the Borrower and the Sponsor entities in a syndicate loan agreement.

Namely, it looks like quite often, the Borrower entity will be a Company that is getting acquired by the Sponsor entity - what I don't understand is if the Sponsor is acquiring the Company, why isn't the Sponsor borrowing the money?

It sounds like you're talking about a leveraged buyout. In these transactions, a private equity firm (or sponsor as you call them) will acquire an operating company. The debt for the acquisition - raised via the capital markets - will reside on the target company's balance sheet. This debt will be used to pay the previous owners (another PE firm, founders, etc.. whoever owned the company previously). The PE firms will never take debt onto their own balance sheet, and during the course of ownership often raise additional debt on the company to pay themselves dividends.


What are the advantages and disadvantages to a country's people when the national currency is the world's reserve currency? Today, the world's reserve currency is USD. At the start of the 20th century, the reserve currency was the British Pound GBP.

Using U.S as an example to narrow the scope, what are the advantages and disadvantages Americans face with the USD being the reserve currency today?

I cannot believe no one answered this. Someone could have easily given a one phrase answer, its called Triffins Paradox.

The core of Triffin's Paradox is that the issuer of a reserve currency must serve two entirely different sets of users: the domestic economy, and the international economy, but you will not be able to make both sets of users happy.

So our Federal Reserve needs to print USD to meet global demand for US dollars, but this money printing can lead to the devaluation of the currency which hurts the people of the issuing country by losing purchasing power, but does help foreign governments to be able to make their debt payments in USDs and certainly the people of these other nations like to stockpile USD in case their local currency goes kaput, but to meet their needs, you then have Americans who have to pay $4 a gallon for gas and are seeing prices in other commodities go up.


Why does price elasticity of demand formula work? Hi there,

I understand how to use the price elasticity of demand formula (mid-point method), shown in the picture above.

However, I'm not too sure why exactly it works.

Why are dividing the change in quantity and price by the averages of the quantity and price change? Is that a way of calculating the percentage change?

And why is elasticity a fraction and not a ratio? Would it be better to write: as price changes by 5 percent, quantity decreases by 10 percent, and write that as 5:10?

Why are dividing the change in quantity and price by the averages of the quantity and price change? Is that a way of calculating the percentage change?

Yes, elasticity is a measure of proportional response.  The math you've shown is the "midpoint" method.  It's basically a linear approximation of elasticity, and you'll abandon it once calculus starts showing up in your learning.  I would suggest not spending a huge amount of time trying to understand it, but only for this reason.  As long as you understand that elasticity of demand says something about how consumers respond to price changes at a certain price level, that's the key message.

  And why is elasticity a fraction and not a ratio?

It's really neither - it's a quotient of quotients, which yields a pure (that is, unitless) number. You can check this for yourself if you explicitly write out the units for the things you're looking at.  This is called "dimensional analysis" and can be extremely useful for interpreting complicated expressions.  The way you do it is to replace each quantity with the thing it "counts" in [square brackets]:

$\frac{2(Q_2 - Q_1)}{Q_1 + Q_2} \longrightarrow \frac{[purenumber]([apples]-[apples])}{[apples]+[apples]} \longrightarrow \frac{[purenumber][apples]}{[apples]} \longrightarrow [purenumber]$

  Would it be better to write: as price changes by 5 percent, quantity decreases by 10 percent, and write that as 5:10?

In general I would caution against using ratio notation except when playing with statistics (and even then, I personally find them tricky to work with). Here, you may risk confusing a ratio of absolute changes (not what you want to express) for a ratio of percentage changes (this is what elasticity actually is).


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".


What is the relationship between S&P500 and the US dollar In the recent past, both the S&P 500 and the USD (against other currencies) have appreciated a lot.

From what I understand, if USD goes up against other companies, the major companies of the S&P 500 suffer because many of them earn foreign revenue in foreign currencies.

So, the S&P500 and the USD should have an inverse relationship with each other.
So how come both S&P 500 and the USD have risen so sharply this year?

You're doing the traditional mistake of people not familiar with Econometrics: You mistake correlation and causality.

You look at a change in the USD, assume it to be exogenous, and then predict an impact onto the S&P.

However, changes in the USD are not exogenous. For example, an increase in US productivity (compared to the productivity of firms in other countries) will both increase the S&P and valuate the USD.

For what you're trying to do, you need to separate different effects, which is virtually impossible - or look for random variation in the USD, of which I'm also unfamiliar with.


Economic Data - Frequency I obtained the historical CPI data available in monthly and quarterly format from a data repository. It seems that the Q1, Q2, etc. data are the average of the monthly data.

I thought that if I were to get quarterly data from monthly data, I can just take the March, June, Sept, and December closing figures. If I were to get the quarterly data for stock price or stock index, should I can just take the 4 month closing price or would I have to take the average of 3 months in each quarter?

Given that this is a macroeconomic study, the cost to write a script to average your data is simple and effectively costless. If you obtain your variables based off of monthly formats, then it would be wise to also obtain your other variables also in the same format.

Each time you simplify, you may potentially lose small but significant outliers in your data that are averaged out as part of your calculations. But if you have more granular data at hand, you can revisit your figures and revise your analysis as needed.

In other words, if you can do your analysis month-by-month I would recommend that you do so, it is relatively simple to scale up and analyze it by quarter as needed; it is however difficult to 'scale' down, don't mix and match two variables measured by different time segments.


COVID-19 Policy Analysis Let's assume I have a dataset consisting of fiscal/monetary policy responses and non-pharmaceutical interventions to the COVID-19 crisis in tens of countries.

How would I go about analyzing their effectiveness in terms of, e.g., GDP growth (other variables also possible), in short term? What would be suitable methodologies? Let's say I would have quarterly GDP growth data up until Q2 2021. Any interesting papers that focus on similar methodologies?

I am not sure about a way to look at it from an economics perspective since I am no economist. However, I am someone interested in this question and looking into doing academic research into this. Here is a few way I would look at this:

Economic Perspective: One of the things I would be interested in is looking at the correlations between the severity of the outbreak (cases and deaths) and the economic prospects of a country. I have already seen one article that discusses this in greater detail through examining the analysis of vintage data. Check: [Growth forecasts and the
Covid-19 recession they convey:
End-2020 update][1]: https://cepr.org/content/covid-economics-vetted-and-real-time-papers-0
In terms of GDP, I would look at the GDP (any of the multiple versions of GDP) growth rates and the growth rates of the outbreak. After all, I would expect their to be a correlation between the two since greater outbreak usually corresponds to a lower supply of labor (due deaths and absenteeism). Also a greater outbreak should be signaling a greater prospect for a government intervention through lockdowns and hence more economic pessimism over the outlook of the economy.

That being said, this is not a thorough nor a comprehensive answer to your question. Looking forward to seeing more answers on this very interesting question.
For my own purposes, I am looking into government effectiveness through indicators through moving averages of the number of cases and deaths. This bears some resemblence to technical analysis of stocks, although, this techniques is not widely respected among the academic and economic circles.


Shutting off production in short term could you help me to solve the task, please? The task is following.
Total costs of the сompetitive firm are $TC = Q^3 +6$ (Q in thousands \$). If the production is stopped then monthly costs are 4000\$. At what prices the company that maximising profit should shut off the production?
I know that if $P < minAVC$, then the company should stop producing.
So $VC = Q^3$ then $AVC = \frac{Q^3}{Q} = Q^2$ and $minAVC = 0$
So I get $P<0$ that sounds stupid. And I don't even know how to use that 4000\$.
The answer should be $P<3$
Could you help me to find out how to solve this?
Thank you in advance.

I think I understand the problem now, your AVC(Q) is wrong. Your fixed costs are 4000, because it's what the firm will pay after it stops production. VC=TC-4=Q^3+2. Thus AVC=Q^2+2/Q. Now you should use your calculus in order to find where AVC has local positive minimum (because it doesn't have global minimum due to its hyperbolic nature).


A question on the accuracy of economic forecasts I apologise if thi's question appears dumb or boring, but I am asking it as a lay person. The context is that I am always arguing with friends that they should trust the economists view that Bexit (Britain leaving the EU) is bad for Britain. They counter by saying that economist get their predictions wrong. I even saw a documentary that suggested this, which I don't believe. I tried googling my questions but could not find helpful answers.

So my questions are:
What is the truth about economic forecasts, and are economic models able to accurately predict the economic  effects of Brexit?

Are there any good links to sources showing  the relavant models and how accurate they typically are at making predictions. It would be great if I could just say;: here's the evidence!

Again, I apologise if these are dumb questions to an expert. But my motivations are positive in that I am trying.to get people to trust the expert's,  i e  economists.

Regarding Forecasts in General

Economic forecasts as any forecasts can be sometimes wrong, however that does not mean they are always wrong and many times people just don’t really understand how to properly evaluate if forecast was wrong. For example if mean forecast of GDP growth is 4% but 95% confidence interval is 2%-6% you cannot say forecast is wrong unless it’s outside the bounds and unless further forecasts from the model give wrong predictions significantly more than 5% of the time. Normally in literature to evaluate forecasts people compute some forecast accuracy metric like root mean squared error (or even more fancier ones) which check how the actual forecasts performed against real observations and while still imperfect many forecasting models are good enough so that you can reasonably take them in account when making some (policy) decisions.

Furthermore, also many people confuse forecasts with predictions. For example, even if we wouldn’t be able to forecast how UK GDP changes after brexit we can make predictions based on our understanding of the economy. For example, based of our understanding of international trade a country seceding from a trade arrangement and not replacing it with a better one will experience some negative shock - we need forecasting to estimate the size of the shock, but just to predict there will be a shock requires just knowledge of general economic models and their implications.

Regarding Brexit Forecasts

Forecasting effect of something like brexit is very difficult because effects of brexit will depend on many contingencies like UK’s post brexit trade arrangements. If post brexit UK will become some beacon of free trade and somehow would manage to get the same access to EU market as it had before then the impact would be of course completely different than if UK will become some protectionist island.

Hence in case of brexit you get different forecasts depending on what assumptions you are willing to make about UK post brexit trade arrangements as well as its macroeconomic and monetary policy which can try to accommodate brexit shocks more or less successfully.

Because of that, adding to the uncertainty, most serious organizations or scholars making forecasts for brexit are working with different scenarios. For example, OECD which is well respected and non-partisan world organization estimated that depending on various scenarios brexit would in terms of GDP cost UK about 3% in short term and in long term between 3-7% (see here) However, those are just mean estimates taking some baseline scenarios. For a nice overview of brexit predictions by different organizations as well as further explanation why it’s hard to forecast effects of brexit you can look at this article from the economist.

However, the problem is that you can’t really evaluate how accurate the OECD or other organizations’ brexit forecasts are in advance. To really properly evaluate their accuracy we have to wait for brexit materializing and then making post mortem analysis because it’s a one-off event. A developed country seceding from economic union is totally unprecedented in modern history.

It would be possible to provide some measures of forecasting accuracy of the parts of brexit models in their previous non-brexit use but that would very laborious task. For example, the forecasts impact of brexit on UK GDP also depends on how brexit will affect UK trade openness which according to  estimation of Fournier et al. (2015) could be between 10-20%, then you have separate forecasts what would happen to labor supply etc. As you can imagine doing survey on forecasting accuracy of all these partial components would be very daunting task  (hence the reason why I did not do it here even though it was part of your question). If you really want to go that deep into weeds then you can just check all the sources for those individual models cited in the reports and then try to find on google scholar some evaluation or comparison of those models in different situations. Or if you are good with R or Python you can just check some basic forecasting evaluation criteria and then laboriously estimate all models and check their out of sample performance compared to some benchmark like random walk.


What does Eugene Fama mean "variance of price changes over multiple days should be less than the multiple of the variance over a day"? I transcribed A Symposium with 2013 American Nobel Laureates at Embassy of Sweden, Washington - YouTube starting at 54:45. Martin Karplus (Chemistry)  challenges Eugene Fama.

Look at how the stock market fluctuates over the last six months. It keeps going up and down like that [Karplus swings his left hand up and down.] Obviously these are short-term fluctutations. One day something happens in the government, and the stock market goes down by 200 points. Two days later, it goes up by 300 points. So  there is obviously some instability built into the stock market that if people were able to calculate it they would get very rich. But my impression is  very few people are able to do that. So what understanding of the stock market do you really have? IF ONE WANTS TO CALL IT A SCIENCE...If there are these...I mean I don't invest very much, but I see these fluctuations. They're unbelievable and they make zero sense to me. Maybe they make sense to you, and so it's a very unstable system.

Obviously Karplus is insulting the three economic Laureates and Dr. Fama in particular.
Fama responds quite elegantly

The empirical implication of your statement is the variance of price changes over multiple days should be less than the multiple of the variance over a day. That’s what you mean when you say price changes are volatile. But that's not true. So your presumption was factually incorrect.

The moderator, AAAS CEO Alan Leshner, then saves Karplus from what was about to be an utter thrashing by Dr. Fama.
I haven't done econometrics since 2013. Can someone pls explain Fama's rebuttal in simple terms?

Thanks whoever asked this at r/econometrics.

abcxyd 9 days ago
I don’t see how Fama’s reply relates to the initial comment at all. But what he means is if you calculate price changes over a longer horizon (e.g. a week), the variance of those price changes is not necessarily lower than the variance of daily price changes when the variances converted to the same frequency. I.e. the annualized variance of weekly price changes is not necessarily lower than the annualized variance of daily price changes. Here’s a well known paper that demonstrates this: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1540-6261.2012.01722.x.


What does Battigalli really mean by "Players can not choose strategies, they can only choose actions."? In this video (from 7: 30 to 9: 00)on Youtube, Battigalli mentions the state of world for a simple three-legged centipede game, which, in his own word, is

  "$\ldots$a description of everything matters, which in traditional theory, must include strategies that characterize Ann and Bob. I don't use the word 'Ann chooses a strategy'. The reason is very simple. The object of choice is action, not stategy. Players can not choose strategies, they can only choose actions. If Ann can choose strategies $(C, C^\prime)$, they are playing a different game."

What does Pierpaolo Battigalli really mean? If the actions for a player chooses has been specified, then it automatically specify a pure strategy. By this methodology, he seems to want to distinguish a game structure with commitment and a game without, but how?

Added: Here is the slides used in the video, and here is the corresponding paper.

The idea is precisely that players do not chose actions, but only chose one action at the time at every node at which they play, based on their beliefs about the way other players and themselves will play at future nodes in the game (where beliefs are conditional on the history that led to that node).

The interpretation is letting players choose full-fetched strategies is equivalent to letting players rely on a computer program to plays the game in their place. That is, they can commit via this computer program to playing a given action at each node.

Such games with commitment devices are in essence very different from games in which the actual players have to repeatedly chose an action at each of their decision nodes. When actual players play at nodes, players have to form beliefs about the way other players and themselves will play at future nodes, and these beliefs may depend on the history that led to future nodes.

For instance, in a Stackelberg game, the leader could believe that the follower will be rational (i.e., utility maximizing) if the leader plays "Low production", but will be irrational (i.e., non utility maximizing) if the leader plays "High production". Maybe the leader anticipates that the follower will be angry if the leader plays "High production", and that, blinded by her anger, the follower then then want to retaliate.

If the follower could have committed through a strategy, the game would have been completely different. Maybe the follower could have committed not to retaliate before she gets angry, and she cannot help her desire to retaliate anymore. But here the idea is that the actual follower has to choose an action later in the game given what the leader chose at the root node. Therefore, the behavioral rule through which the follower chooses an action at a node (e.g., utility max vs. non utility max), and the beliefs of the leader about these procedures may depend on the history that led to that node too.

This opens the way for many new outcomes of the game that would not have emerged from classical game theory. From a conceptual point of view, it also switches the focus from solution concepts to epistemic and behavioral assumption (i.e., from classical game theory to epistemic game theory). Instead of identifying a set of reasonable outcomes (e.g., Nash equilibrium outcomes) and look at the strategies that match these outcomes, one identifies reasonable properties of players' behaviors and beliefs (about each others' beliefs and behaviors), and derives the conclusions of these epistemic and behavioral assumptions for the outcome as the game unfolds.

Now, this is just to give some meat and intuition to Battigalli's framework, and it is does not do justice to the richness of the framework (in part because I don't know much about his work other that the video you linked to). If you haven't done it yet, I strongly recommend that you watch the whole video. I think Battigalli does a great job at making his framework accessible. He also present helpful and intuitive examples to connect his epistemic approach to "classical" game theory by identifying simple conditions on players beliefs and behaviors that allow to recover classical solutions to games such as backward induction.


Intuition for effect of interest rate changes in New Keynesian model I am trying to understand the intuition behind the effect of an interest rate change in a simple New Keynesian model (or really in any sticky price model).
As a simple example, I take (roughly) the model in https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxnYXV0aWVnZ2VydHNzb258Z3g6MTA1YTg1NTljNjE4ZjJhNg. In this model, a fraction $\gamma$ of firms sets their price optimally for that period, and the remaining firms index their price to last period. I have the following (log-linearised) equations:

Euler equation: $\hat{c}_t = E_t\hat{c}_{t+1} - \frac{1}{\sigma}\left(\hat{i}_t - E_t\hat{\pi}_{t+1}\right)$
Labour supply: $\hat{n}_t =\frac{1}{\phi}\left(\hat{w}_t - \hat{p}_t - \sigma \hat{c}_t\right)$
Optimal pricing: $\hat{p}_t^*-\hat{p}_t = \left(\hat{w}_t-\hat{p}_t\right) - \hat{a}_t$
Inflation: $\hat{\pi}_t = \frac{\gamma}{1-\gamma}\left(\hat{p}_t^* - \hat{p}_t\right)$
Output: $\hat{y}_t = \hat{a}_t + \hat{n}_t$
Goods market clearing: $\hat{y}_t = \hat{c}_t$

There is some redundancy because I am looking for intuition. The solution to this system is
$$
x_t = E_t x_{t+1} - \frac{1}{\sigma}\left(\hat{i}_t - E_t\hat{\pi}_{t+1} - r_t^n\right) \\
\hat{\pi}_t = \kappa x_t
$$
where $x_t = \hat{y}_t - \hat{y}_t^n$ is the output gap, $\hat{y}_t^n = \frac{1+\phi}{\sigma + \phi}\hat{a}_t$ is the natural level of output, $r_t^n = -\sigma\left(\hat{y}_t - E_t\hat{y}_t^n\right)$ is the natural rate of interest, and $\kappa = \frac{\gamma}{1-\gamma}\left(\sigma + \phi\right)$.
Now suppose the central bank reduces the nominal interest rate. Assume also that there is no change to the net supply of government bonds (which are the vehicle for borrowing and saving). I know that the outcome will be a positive output gap and increased inflation. I am trying to understand how that occurs.
The standard story is that there is consumption demand by the Euler equation, so firms have to increase output, which raises their costs. The firms that can do so will raise their prices. As a consequence, there is inflation and a positive output gap.
If this is the correct intuition, where does the increased demand faced by firms actually come from? Individuals do want to consume more (Euler eq, 1), but they cannot all borrow and they are already at their optimal intratemporal margin (labour supply, 2). Individuals can't actually consume more until their incomes/output is higher. They won't work more unless real wages rise. Firms won't increase output, wages, or prices unless there is more demand. What is the mechanism?
Thanks!
Edit - I clarified that individuals borrow and save via trading in government bonds, and that the net supply of government bonds is held constant.

Yes the 'standard story' you reference is the correct intuition here. Lower nominal interest rate encourage consumption which puts pressure on both output and prices.
Household can actually save and borrow in the model. However, because it is a representative household model in equilibrium there would not be any borrowing - the interest rate should just adjust in order to make agent's indifferent between consuming today and in the future - but the intertemporal consumption choice still depends on $i$ with higher $i$ incentivizing  future consumption at the expense of the present one.
Also, even if in the description provided in question this is not shown the Euler equation has its micro foundation in model where households are allowed to save and borrow - otherwise the interest rate would not be part of the Euler equation in the first place, and I am not sure how it would even be modeled if there would be no link between present and future. For example, see the treatments of IS-LM models in lets say Woodford (2003). Interest and Prices. You will see that in dynamic models the Euler equation is typically derived from model of household behavior where households have access to saving/borrowing.


Are Preference Relations Robust to Aggregation This is more a question of putting the theory into practice, or at least clarifying the theory in practice. The question has to do with the application of preference relation axioms and aggregation. Take the transitivity relation for example;

$\forall (x,y,z) \in X,$ if  $  x \succ y \wedge y \succ z \iff x \succ z $

Suppose I have a set of data on the preferences of $n$ consumers $C_1,C_2,...,C_n$ over products $a, b,$ and $c$ such that;

$C_1$ prefers $a \succ b \succ c$

$C_2$ prefers $a \succ c \succ b$

$C_3$ prefers $c \succ b \succ a$

and so on until consumer $n$, each with a respective WTP for each product.

So the question is, if the data were aggregated over $n$ consumers we would achieve an aggregate WTP for whichever preference dominates. Lets say that the aggregate data reveals $a \succsim b \succsim c $. Does this result violate transitivity and completeness since the individual consumer $C_3$ prefers $c \succ b \succ a$. Do individual and aggregate preferences have to be consistent.

I presume you mean to take the total (or average) willingness to pay for each alternative to be the social willingness to pay. $WTP_{soc}(a)=WTP_{1}(a)+WTP_{2}(a)+WTP_{3}(a)$ Then $WTP_{soc}$ is a representation of a social preference relation $a\succsim b \Leftrightarrow WTP_{soc}(a)\geq WTP_{soc}(b)$. This preference is transitive and complete. Individual and aggregate preferences are consistent in the sense that they satisfy the Pareto criterion and the independence axiom of Arrow's impossibility theorem. The way we have tricked the impossibility theorem is that we have taken an ordinal preference relation and turned it into a cardinal concept (WTP).

The question is whether the mean willingness to pay is a meaningful concept in any way. For example, a poor person's willingness to pay for a good may be relatively low, but the marginal utility very high. For a discussion of interpersonal comparisons of utility, see the following article:

Harsanyi, John C. Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Springer Netherlands, 1976.


How can a crypto currency crash affect liquidity? To the best of my knowledge, no bank will allow a borrower to provide crypto as collateral for a loan.  So, if the price of crypto crashes to zero, there shouldn't be any liquidity issues because no fiat backed by crypto had been created.

All that would happen with a crash would be a redistribution of wealth: the people who sell first get the most, and the people who sell last get nothing.

So, why are bankers claiming a crash would cause liquidity problems for the financial sector?

As an initial note, I have not seen any plausible claims that a crypto crash would cause liquidity problems for the financial system. As a reult, I would need to guess to the mechanism.

I do not think “liquidity” is what anyone should worry about right now. For a firm we need to distinguish between illiquid and insolvent.

Illiquid: the firm does not have enough short-term assets (“cash”) to meet short-term liabilities.
Insovent: the net worth (equity) of the firm drops below zero.

A bank loan is an illiquid asset. As a result, loan losses do not directly cause illiquidity; they cause insolvency. Of course, people will not normally lend short-term to an insolvent bank, so it will be illiquid later. (If the concern is about money creation, impaired deposit growth would only be a consequence of insolvency.)

Can a crypto crash cause a general wave of insolvencies? That is difficult to answer, but we can look at the possibilities.

The credit risk at the time of writing appears to from individual investors borrowing to buy cryptocurrencies. The only business borrowing that I am aware of is by the crypto exchanges - they borrow to support customer borrowering. Such loans are covered by two parties - the customer, and the exchange. We cannot double-count these debts as a result.

As for customers, banks either lend against collateral, or cash flow.

No sensible bank would lend against most crypto-currency collateral: most of the cryptocurrencies are designed so that authorities cannot seize them. Unless there is an exchange-traded fund (which can be used for margin debt), such crypto-based lending will be negligible.

Banks could lend against other collateral, such as a second mortgage. However, such loans are backed by both the home as well as household cash flow. People take out second mortgages to go on vacation or to fund small businesses (which mainly fail); there is always a safety margin for the banks in such lending.

Unsecured lending is lending against income. The recent wave of banks blocking cryptocurrency purchases via credit cards is a sign that some are getting uncomfortable with such risks. However, losses would only materialise if the involved investors are cash-flow impaired (lose their job in most cases). Although such cases will happen, any losses need to be looked at in the context of other sources of loss, such as those caused by medical emergencies in the United States.

In order for these losses to pose a systemic risk, it would probably require large job losses, which by itself poses a risk.


How does the Monetary base, Narrow money and Broad money affect inflation? In a lot of countries (e.g. Hungary) the M0, M1, M2 and M3 all doubled, tripled or even quadrupled in the past 10 years. How does this directly affect inflation?

Since just because M2 doubles, it doesn't mean that the Hungarian Forint is worth the half of what it did before. What is the relation between money supplies and consumer price indexes?

The relationship between money supply and price level (inflation is just change in the price level) is as follows:

$$P=\frac{MV}{Y}$$

Where  P the price level, M is the money supply, V velocity of money and Y is the real output.

So price level is  increasing in money supply and velocity of money, but decreasing in real output.

If everything else would be held constant price level would actually grow at the same rate as money supply, but in real life of course ceteris paribus condition is not satisfied. Real output continuously changes either due to economic growth or due to the boom/bust cycle, seasonal effects etc. Velocity of money is often though to be more or less constant, but it can change as well and in fact at zero lower bound, in a liquidity trap, changes in velocity can often offset increase in money supply preventing inflation.

Also, the above monetary formula is bit of an simplification because in more complex models not just the actual changes in these quantities but also expectations of these changes matter.


Constant elasticity proof for log-linear demand curve From Perloff 2008e solved 2.2:

Q: Show that the elasticity of demand is a constant e if the demand function is log-linear, ln Q=ln A+e ln p.
A: Differentiating with respect to p, we find that (dQ/dp)/Q=e/p.

Where did 'dQ/dp' come from in the numerator?

$\frac{dlnQ}{dp}=\frac{dlnQ}{dQ} \frac{dQ}{dp}$ thus:

$\frac{dQ}{dp}=\frac{dlnQ}{dp} \frac{dQ}{dlnQ}$

Since we know that if $f(x)=lnx \Rightarrow f'(x)=\frac{1}{x}\Rightarrow \frac{1}{f'(x)}=x$

We replace $\frac{dQ}{dlnQ}$
by $Q$. You get:

$\frac{dQ}{dp}=\frac{dlnQ}{dp} Q$

It is readily found that
$\frac{dlnQ}{dp}= \frac{e}{p}$

So our expression for the derivative of $Q$ wrt $p$ now reads:

$\frac{dQ}{dp}=\frac{e}{p} Q$

Divide both sides by $Q$ and you get $\frac{dQ/Q}{dp}=\frac{dQ/dp}{Q}=\frac{e}{p}$

Elasticity is now found by simply multiplying both sides by $p$, you get:

$\frac{dQ}{dp} \frac{p}{Q} \equiv \eta=e$


Whether a good is a Giffen good should be based on circumstance? The textbook example of a Giffen good is the potato during the Irish Potato Famine. It is characterised by a positive income effect that is larger than the negative substitution effect when the price of the good increases. During the famine, the increased price of potatoes counterintuitively led to an increase in the quantity consumed of potatoes. This was because potatoes were likely one of the only available staples for the peasants and that alternatives may have been significantly more expensive. Hence, the increased consumption of potatoes and a diversion away from more expensive foods was observed during the famine. This makes sense in the context of the peasants having very low, limited incomes and that other staples or foods were either unavailable or far more expensive.

If the circumstances were changed and say, rice or noodles, were cheaper than potatoes, I am certain that there would be a drop in the quantity demanded for the potatoes given the increase in price. Hence, I would like to ask if it is possible to assert that a good can be considered a Giffen good only under the appropriate circumstances? That is, the income and substitution effects would play out differently given different circumstances and under certain circumstances, these effects would be opposite with the income effect being larger.

In fact, if you think about it, given a sufficiently large increase in the price of potatoes, the quantity demanded would have to decrease as it really becomes unaffordable and the peasants may have to resort to consuming less of it and find some other substitute. Hence, the Giffen good behaviour would only be observed for a particular price range and not below or above that.

Yes, whether a good is a Giffen or inferior good depends on "the circumstances", or to be more narrow, it can depend on the income and price levels.

Claim 1. Being an inferior good is a local attribute.

Proof. Suppose a good $x$ is inferior for all income levels $I$ and all price vectors $\mathbf{p}$. Trivially demand for $x$ at $I = 0$ is 0. If $x$ is inferior for all income levels, then for any $I > 0$ demand for $x$ is also 0. This contradicts the strict definition of inferior good, which specifies that as $I$ increases $x$ should decrease.

Claim 2. All Giffen goods are inferior goods.

This is covered in some detail in textbooks, usually in a chapter that mentions the "Slutsky-equation".

Combining the two claims we have that being a Giffen good is also a local attribute; as being Giffen everywhere would imply being inferior everywhere, and we have shown that that is not possible.


Best instruments for "years of schooling"/"education" As an answer to question “Seminal papers that later were proven to contain errors”, @snoram mentioned Angrist and Krueger (1991), and there use of quarter of birth as an (exogenous) instrument for education.

@snoram illustrates using (Buckles and Hungerman, 2013) how quarter of birth is in fact correlated with important characteristics of the mother.

In a comment, @snoram write:

  “For the record I think Angrist and Krueger's work is amazing, but
  today we know better than to use quarter of birth (in the us at least
  and for this purpose) as an instrument. Science advances.”

My question : which variables are know to be better than quarter of birth as instruments for, say, “years of schooling” (or more generally “education”)?

Check out
Estimating the Return to Schooling: Progress on Some Persistent Econometric
Problems by David Card (2001) ECA

I know distance from school has been used in the past as an IV..although it has been criticized.


Selling price of a widget at competitive equilibrium Let's suppose that it costs producers a minimum of y dollars to produce a widget (it may actually cost more, depending on the producer, but that is the bare minimum). In a competitive equilibrium, where there are several producers of this identical widget, would the selling price of the widget be $y?

Please explain your reasoning.

EDIT:

I have arrived at the selling price of $y based on this algorithm.

The long run equilibrium price should be $\$ y,$ however, in the short run, we only know that price must be higher that the minimum average variable cost (of which no info is given).

In the long run all production takes place at the minimum average cost. All firms with average cost higher than $\$y$ will either adapt their technology and reduce their costs or exit the market.


Bank maturity mismach So my question is about maturity mismatch and what is the appropriate method to calculate it. I have seen some simplified examples in academic books but, when I tried to approach it in a holdings bank, I could not really find a solution. Do I do a duration gap analysis? Cause for example in the balance sheet I am looking, the liabilities are less 1 year, between 1 and 5 years, and more than 5 years. Do I just look for the short term A-L ? Can you suggest me to an approach?

There’s two things of interest: interest rate risk, and liquidity risk.

For liquidity risk, you could compare short-term liabilities to short-term assets. This would be just a ratio. The long-term buckets (1-5) and (5+) aren’t going to add much information. Banks are in the business of rolling over 1-5 year term deposits, so that bucket will always be big. And since bank loans are often amortising, while the deposits have a bullet maturity, the mismatch between a 5-year deposit (bank liability) and a 10-year loan (bank asset) is much smaller than the maturity date suggests. This is why I would just look at ratios with the mid-long buckets merged.

For interest rate risk, the duration gap is what matters (plus interest rate shock simulations; see below). (Although I write duration, that is just habit. Technically, you need something like a DV01: how much money is gained/lost on a 1 basis point rise in yields? This can be inferred from an estimated duration.)

A part of the question is unclear - you are looking at a financial report of a real world bank? There might be a memo item buried in the notes on the financial statement that gives the exact mismatch. The bank and the regulators know what the mismatch is, it is unclear whether that is public information. Since it is sensitive commercial information, it is highly possible that the net duration information is not public. (I obviously do not know.)

You could try approximating the duration for each bucket of assets and liabilities, and then add them up. The problem is that this answer could easily be wildly incorrect, and the exercise is probably a waste of time.

It ignores the optionality of mortgages (for a US bank). So straight duration is somewhat misleading, you also need to look at large shifts in the yield curve (which is another standard stress test applied by regulators and the bank’s risk management.)
A bank can own or issue long-term floating debt. So even if the maturity is 10 years, the duration is at money market length.
It ignores the fact that banks use interest rate derivatives (swaps) to hedge their duration risk.

If you dig into the regulator’s documentation (obviously depends on the bank’s jurisdiction), they should publish the risk limits for interest rates that they allow. Obviously, the bank’s internal models will give a number within the limits, as even the most incompetent regulator would notice a deviation. It may be that the bank has some exotic interest rate risk that does not show up on those stress tests, but you would never know by looking at public information anyway.


Why is Pareto efficiency not always equitable or equilibrium? Just for information. I think we can agree on that a Pareto optimal allocation is where you cannot put someone in a better position without making someone else worse off. I know that any competitive equilibrium is Pareto optimal, but any other form of equilibrium is not always Pareto optimal. Why is that?

Given an example, if a firm's demand for labour is equivilant to the labour supply by consumer, there is an equilibrium. But is it not also Pareto optimal or does that depend on the equation of demand for labour and labour supply?

Graphically speaking; will an equilibrium between two factors be the intersection, whereas a Pareto optimal is when the slope is the same for both factors?

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

Partial equilibrum

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

General equilibrum in pure exchange economies

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

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

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

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

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

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


supply-demand imbalance I have a basic question

What are the different means/mechanisms available to address supply-demand imbalance?

The answers that come to my mind are :

Using pricing  (when demand > supply)
Using rationing (when demand > supply)
Preempting the imbalance by gathering precise demand information (when supply > demand)

Are there any other means available to address situations when demand > supply and supply > demand?

In order to cover the supply and demand imbalance following methods can be used in addition to the ones mentioned by you:
TO DEAL WITH THE IMBALANCE WHEN DEMAND > SUPPLY:

In the long-run period, Innovation of substitute goods
First come, first-served basis
Innovation of better production techniques which would increase the supply
Commodities are sold only to the frequent costumers of the producers
Better transportation and communication systems on the producers part to increase the supply and to meet excess demand.

TO DEAL WITH THE IMBALANCE WHEN DEMAND < SUPPLY

Decrease in the prices of complementary goods.
Better credit facilities (ex: lowering the bank rates)


Is it worth betting on this case? Let's imagine a coin-flip game, which uses an unbiased coin.
Starting with X dollars, your total increases 50% every time you flip heads. But if the coin lands on tails, you lose 40% of your total. You can play this game N times. On each turn, you must bet the total amount you had on the last turn.
Is it worth betting on this case? How can we formalize this in order to have this answer in the general case?
Is it easier to formalize this for a specific value of X and N? Let us assume, for example X = 100 dollars and N = 100 turns.
PS: This scenario appears in an article discussing some ideas of Ole Peters, a theoretical physicist who is claiming that Everything we know about modern economics is wrong.

The game has positive expected value, so you should play (assuming constant utility of each dollar, which tends to break down somewhat for very large sums of money). If you start with \$X, after 1 round you have a 50% chance of having \$1.5X, and a 50% chance of having \$0.6X, for a total expected value of \$1.05X. That is, for every dollar you bet, on average, you'll win \$1.05. The amount of money and number of trials doesn't matter at all for this analysis - every round is effectively identical, so you should always bet.
In addition, there is absolutely no risk of "gambler's ruin" here, since you can never go bankrupt. In games where you can lose your entire wager, playing even a positive expected value game can lead to bankruptcy over time, since you'll eventually run into a losing streak that outstrips your bankroll. But here, since you will always have some amount of money on hand, you can keep playing forever no matter how bad of an unlucky streak you get.


Why, in supply and demand curves, does price go on the y-axis? I know it doesn't actually matter which axis is which, but it seems less intuitive me. When I see a supply and/or demand graph, I always have to flip it in my head to feel like I really get what's going on.

It just seems like if you have one variable (price) on which two other variables (supply and demand) depend, then the single variable should be on the horizontal axis. So why isn't this the convention?

As @KennyLJ points out I think the reason is partly historical. However it is a useful convention for several reasons.

Demand curves are frequently not functions but mappings, e.g. in the case of perfectly elastic demand. So you could not guarantee 'nice' functions anyway.
In this coordinate system the surpluses (producer's and consumer's) are areas under the curves. The explanation is more intuitive and it is somewhat easer to see which integral you have to take.


Solow model: Partial derivative of k* with respect to g Given the solow model
$sf(k)=(n+g+\delta)k$, written as
$$F=sf(k^\star)-(n+g+\delta)k^\star=0$$
I am trying to find the partial derivative of k* with respect to n
Here is what I've tried: I use the implicit function theorem such that I need to calculate $\frac{\partial k^\star}{\partial n}=-\frac{F_n}{F_{k^\star}}$. I've previously found that
$$F_{k^\star} = sf'(k^\star)-(n+g+\delta)$$
Next I want to find $F_{n}$. Taking the partial derivative and finding that $F_n=-k^\star$. However I am in doubt as to whether or not I should use the chainrule, as $k^{\star}$ is dependant on $n,g,s,\delta$. In that case I find that, because
$$\frac{\partial f(k^\star)}{\partial n}=f'(k^\star)\frac{\partial k^\star}{\partial n}$$
Then we have that $F_n=sf'(k^\star)\frac{\partial k^\star}{\partial n}-k^\star$. Thus we have
$$\frac{\partial k^\star}{\partial n}=-\frac{F_n}{F_{k^\star}}=\frac{sf'(k^\star)\frac{\partial k^\star}{\partial n}-k^\star}{sf'(k^\star)-(n+g+\delta)}$$
It seems odd to find the result of $\frac{\partial k^\star}{n}$ includes itself.

When you are using implicit differentiation along a level curve you will treat the variable with respect to which you are differentiating as a single variable, rather than function.  This is because the formula for implicit differentiation along level curve is already based previous derivation where you already solve for $y'$.
For example, for general function $F(x,y)=c$ where $y=f(x)$, we get by implicit differentiation:
$$v(x) = F(x,y) = c \implies v'(x) = F_x' + F_y' y' = 0 $$
Consequently we get the result that:
$$y' = - \frac{F_x'}{F_y'} \tag{1}$$
Hence, if you just apply formula given by 1 you will not use chain rule anymore, since it was already used in derivation of the formula. For example:
$$xy=5 \implies y'= -\frac{y}{x}  $$
so in your case the correct implicit differentiation along a level curve would yield:
$$\frac{\partial k^*}{\partial n}=  -\frac{F_n'}{F_k'} =\frac{k^*}{sf′(k^⋆)−(n+g+\delta)}$$
You could verify it by actually implicitly differentiating the original function which would yield:
$$\frac{\partial k^*}{\partial n}[sf(k^*)=(n+g+\delta)k^*] \implies sf'(k^*)\frac{\partial k^*}{\partial n} = k^* + (n +g + \delta )\frac{\partial k^*}{\partial n}$$
Solving for $\frac{\partial k^*}{\partial n}$ yields:
$$\frac{\partial k^*}{\partial n} =\frac{k^*}{sf′(k^⋆)−(n+g+\delta)}$$
so it clearly works.


Why is the prime rate typically 3% higher than the fed funds rate? What is the right framework to think about the prime rate in relation to the fed funds rate?
Idea 1: A bank is safer to lend to than even trustworthy institutions so there's a premium on prime rates. Why is this true though? I could imagine several institutions with great credit could be safer than some banks. Is there something that makes a loan to a bank safer?
Idea 2: A bank can borrow at the fed funds rate. So banks could borrow at fed funds and lend to customers at higher rates. If their borrowing rate changes, their lending rate changes with it to reflect their cost. Perhaps though this is uncommon because lending on borrowed capital would inherently have a smaller margin than lending on unborrowed capital, so it would be hard to compete with borrowed capital.
Basically the causality can come from the fact they can lend at the fed funds rate or borrow.

The Prime Rate in the US is supposed to represent the rate at which banks make loans to customers.  For many years is has been set at Fed Funds+300bp, whereas the rate at which banks actually make loans varies a lot depending on the creditworthiness of the borrower.


Why did the price level of government consumption increase in the United States? From The Penn World Tables (PWT7):

Before 1970, the price levels of the three GDP components had been going in parallel. In the late 60s, the price level of government consumption went up (the Nixon Shock + Vietnam War?), and then it steadily increased since after 1980. Investments also behaved differently since then.

Is this price behavior due to the budget deficit (for government consumption) and trade deficit (for investment deflation) or there're some other important factors?

The price level of government consumption (education, parts of health care, police etc.) consists mainly of wages.

Since the productivity (as we measure it) of government production often does not increase too much, the price level increases about as much as the level of wages. This, contrary to the price level of consumer expenditure which is driven down by productivity, increases in manufacturing as well as cheap imports.

The price level of investment goods might have gone down because of 'hedonic'calculation, i.e. statisticians calculate the dollar price of one unit of computing power instead of the price of one computer. In the new national accounts, military equipment is however also (and rightly so, IMO, as many military items have a clear second hand value and a well developed second hand market exists) considered to be an investment good, this gear may have another pattern of development than computers.

In a general sense, I suspect that the investment price level shown is only valid for machinery and the like. Most investment is however in land related items like dwellings, roads, bridges and other buildings as well as the prices of these and of the land itself, have not gone down that much (to the contrary, even, though there are quite some differences between the pre- and post-2008 period).

Here is some useful background information for the EU which shows that price levels of investment goods (broad definition) can differ up to 400% between countries.


Is there any research, theory, or anything which shows how much of a market has to be in power of a few companies to be a force against free market? According to Free market

  a free market is a system in which the prices for goods and services
  are determined by the open market and by consumers. In a free market,
  the laws and forces of supply and demand are free from any
  intervention by a government or other authority and from all forms of
  economic privilege, monopolies and artificial scarcities

Being monopolies and oligopolies a force against free market, is there any study, theory or anything which shows how much of a market has to be in power of a few companies for them to be able to alter the free market laws/rules?

The quote in the question isn't really rigorous about what a free market is, but it talks about monopolies and artificial scarcities, so I am interpreting the efficient outcome with price equal to marginal cost as being one necessary feature of what they understand as a free market.

Let's look at the cournot model of competition. There are $n$ firms, each with idiosyncratic marginal cost $c_i$. Each firm simultaneously chooses its output (supply) quantity, $q_i$. Given consumers' demand, this results in some market price $P(Q)$, where $Q=\sum_{i=1}^n q_i$ is the total industry output. We would expect the demand curve to be downward sloping: $P'(Q)<0$.

Thus, a firm's profits are
$$\pi_i(q_i,\mathbf{q}_{-i})=\left(P(Q)-c_i\right)q_i.$$
The first-order condition for maximisation of profit is
$$\frac{\partial\pi_i}{\partial q_i}=P(Q)-c_i+\frac{\partial P(Q)}{\partial q_i}=0.$$
Noting that $$\frac{\partial P(Q)}{\partial q_i}=\frac{\partial P(Q)}{\partial Q},$$
the first-order condition can be re-written as
$$\frac{P(Q)-c_i}{c_i}=-\frac{\partial P(Q)}{\partial Q}\frac{Q}{P(Q)}\frac{q_i}{Q},$$
$$\frac{P(Q)-c_i}{c_i}=-\frac{1}{\eta}m_i,$$
where $\eta$ is the price elasticity of demand and $m_i=q_i/Q$ is firm $i$'s market share.

The left-hand side measures a firm's price-cost margin, or its market power. We can compute the average market power in the industry by weighting each firm by its market share:

$$\text{avg market power}=\sum_i m_i \frac{P(Q)-c_i}{c_i}=-\frac{\sum_i m_i^2}{\eta}.$$

Note that $\sum_i m_i^2$ is the HHI index for the market. So this equation tells us that the average market power in an industry will be positively related to the HHI. For any positive HHI, there will be a positive mark-up and the market will deviate from the perfectly competitive outcome in which artificial scarcities do not exist. Put differently, only if there is an infinite number of firms, each controling an infinitely small share of the industry do we obtain the textbook perfect competition outcome.