Symmetric and asymmetric preferences I encountered a question where it was given that the consumers had asymmetric preferences. I couldn't find the definition of the term in any of the microeconomics book available to me.

Can anybody explain the terms and the difference between symmetric and asymmetric preferences? Please!

It is just a strict preference relation, an asymmetric (generic) relation $\succ$ is such that $a \succ b \implies \lnot b \succ a$.
With respect to symmetric preferences there are not really  pure symmetric ones in consumer theory at least, the only symmetric relation is total indifference ~ over the whole choice set. Clearly a ~b implies b ~a. A typical $\succeq$ preference relation is the union of an asymmetric and symmetric part.


Showing that production technology exhibits decreasing returns to Scale The Question
Suppose a firm has a production function given by
$$y=F(L,K)=L^{1/4}K^{1/4}$$
where L and K denote inputs used in the production of y units of output.
(a) Determine whether marginal products are diminishing
(b) Show that production technology exhibits decreasing returns to scale
My attempt
(a) So the marginal products, $MP_L$ , $MP_K$ are:
$$MP_L={\partial{F}\over\partial{L}}={1\over{4}}L^{-3\over{4}}K^{1\over{4}}$$
$$MP_k={\partial{F}\over\partial{K}}={1\over{4}}L^{1\over{4}}K^{-3\over{4}}$$
To determine if the marginal products are diminishing one needs to simply derive the equations again. Which would be:
$${\partial{MP_L}\over{\partial{L}}}={-3\over{16}}L^{-7\over{4}}K^{1/4}$$
and
$${\partial{MP_k}\over{\partial{K}}}={-3\over{16}}L^{1\over{4}}K^{-7\over{4}}$$
When both Marginal products are derived, their results are both are $<0$ which would imply that they are diminishing.
(b) This is where I get a little confused, is it not because we know that the Marginal products are diminishing, we know that the production technology exhibits decreasing returns to scale?

They are two different concepts I think.

Diminishing product means that holding other things fixed, one unit of extra input($K$ or $L$ here) yields less and less additional output, which you have known.

Meanwhile DRS is saying that if you multiply both $K$ and $L$ by some scalar $ t > 1$, the corresponding output would be less than $t$ times the original output.


Why doesn't the San Francisco Bay Area have two-story houses? The San Francisco Bay Area is an interesting place. Housing prices are through the roof (hehe) and increasing by an average of 5-20% per year for the past 20 years. This is largely driven by an increase in land values, as the SF Bay Area has very high incomes and rapid hiring, but geographically constrained area for settlement, leading to a supply and demand issue that has been driving up home prices to astronomical levels.
Interestingly, nearly all homes in the Bay Area are one-story, as opposed to the two-story homes so common elsewhere. I'm trying to square this with the relevant economic factors and I'm coming up just a bit short. Why would a land-dominant housing market lead to below-average construction of larger houses, when the relative cost of building a second floor is lower than it would be in a market where land is cheaper?

Areas such as San Francisco Bay Area have very strict zoning laws. In fact as this source shows in San Francisco Bay Area many houses are restricted to be single family houses. The source focuses mainly on Berkeley and Oakland but discusses also the situation of the wider area.
Adding an extra story just for your own family might not be economical even if there is housing shortage. Furthermore, there might be further restrictions on any such buildings (e.g. neighbors complaining to the zoning board that second story blocks their view/sun). Lastly, the housing shortage and exorbitant housing prices in cities such as San Francisco can actually itself be attributed (among other things) to the zoning laws themselves in the first place (see for example The Impact of Zoning on Housing Affordability Edward L. Glaeser, Joseph Gyourko).


When was fractional reserve banking introduced? According to Wikipedia's history of banking article:

  Modern banking practice, including fractional reserve banking and the issue of banknotes emerged in the 17th century.

The article on fractional reserve banking seems to suggest that the Bank of Amsterdam is the earliest example:

  In the past, savers looking to keep their coins and valuables in safekeeping depositories deposited gold and silver at goldsmiths, receiving in exchange a note for their deposit (see Bank of Amsterdam). These notes gained acceptance as a medium of exchange for commercial transactions and thus became an early form of circulating paper money. As the notes were used directly in trade, the goldsmiths observed that people would not usually redeem all their notes at the same time, and they saw the opportunity to invest their coin reserves in interest-bearing loans and bills. This generated income for the goldsmiths but left them with more notes on issue than reserves with which to pay them. A process was started that altered the role of the goldsmiths from passive guardians of bullion, charging fees for safe storage, to interest-paying and interest-earning banks. Thus fractional-reserve banking was born.

But it does not state that, nor does the article on the Bank of Amsterdam.

I imagine the exact details might be murky, but I'm looking for a summary of the recognized possibilities. What organizations are candidates for the earliest fractional reserve banking system, and when did they begin their fractional reserve banking?

I also realize that there may have been organizations which did so a long time before it became an established practice. If that's the case, please mention those organizations, but please also summarize who the early pioneers of our present system of fractional reserve banking are.

Fractional reserves banking is at least as old as the 1400's:

  A balance sheet from the London branch of the Medici Bank, dated
  November 12, 1477, shows that a significant number of the bank’s debts
  corresponded to demand deposits. Raymond de Roover himself estimates
  that at one point, the bank’s primary reserves were down to 50 percent
  of total demand liabilities. 60 If we apply the standard criterion
  used by A.P. Usher, this implies a credit expansion ratio of twice the
  demand deposits received by the bank. There is evidence, however, that
  this ratio gradually worsened over the bank’s life-span, especially
  after 1464, a year that marked the beginning of growing difficulties
  for the bank. The roots of the general economic and bank crisis that
  ruined the Medici Bank resemble those Carlo M. Cipolla identifies in
  his study of fourteenth-century Florence. As a matter of fact, credit
  expansion resulting from bankers’ misappropriation of demand deposits
  gave rise to an artificial boom fed by the increase in the money
  supply and its seemingly “beneficial” short-term effects.
  Nevertheless, since this process sprang from an increase in the money
  supply, namely credit unbacked by growth in real savings...

Page 73-74 of Money, Bank Credit, and Economic Cycles Jesus Huerta de Soto

The Wikipedia page on Scali Bank claims that the Austrian school or at least Soto believes that fractional reserve banking did in Scali bank in the 1300's but I couldn't find evidence for the claim in the citation.

Middle eastern banks were offering transaction accounts and loans in the  7th–12th centuries and this makes it likely that fractional reserve banking was occurring there as well.


Why is the rate of profit not important? I've been taking some time to read up on the history of economic thought and am wondering why the rate of profit (which was a measure heavily discussed up to the 1970s) seems to disappear out of economics education all together.
I have my own ideas for why it dropped out of economics education but am wondering if there is a reason why this metric is no longer discussed (for the most part) in mainstream economics.

I think it has to do with declining interest in Marxian economics. In the past the Marxian economics, especially the one in Sraffian tradition had much wider appeal.  The rate of profit was an important metric in Marxian economics, since Marxian economics makes several important predictions about the rate of profit in 'capitalist' economies (e.g. the  tendency of the rate of profit to fall (TRPF) hypothesis - see Marx Capital, Volume III).
If you look at the historical papers that discuss the rate of profit, they are very often connected to the TRPF hypothesis (although not necessarily from Marxian angle). In fact, if you just put rate of profit into google scholar now more than 1/3 of the searches relate either to Marxian economics of TRPF hypothesis. If you do the same with Palgrave dictionary of economics almost half of the results on first page are connected to Marxian economics or TRPF hypothesis. I realize this alone is not rigorous proof but it is at least bit suggestive.
In addition, I would challenge the idea that the rate of profit 'dropped from mainstream economics'. Rate of profit is often used synonymously with rate of return on capital (see Feldstein, Summers & Wachter, 1977). This is so because existence of profit is often (at least partially) attributed to the fact that firms typically own their capital, and indeed if you look at papers that try to measure rate of profit often they look at returns on assets as well such as the Feldstein et al paper above.
You will find rate of return capital to be mentioned far more often in the mainstream literature, and textbooks as well. Thus it is possible that the rate of profit was just abandoned due to the Marxist connotations.


How can I re-base monthly financial time series I have a monthly time series with 2015=100. I want it to be in 2010=100. How could I do so?
It is from 195901 to 201407.

I have a monthly time series with 2015=100. I want it to be in
  2010=100. How could I do so?

Unless I am misunderstanding your question, you need to multiply every entry by $$100/X_{2010}$$


Who invented these key notions in Finance? We often give credit to the origins of academic achievements. The Black-Scholes equation or the Gibbons Ross Shanken (GRS) test etc.

What about

Net Present Value (NPV),
Internal Rate of Return (IRR),
Duration of bonds,
Law of One Price (LOP),
Time value of money,
Stochastic Discount Factor (SDF) or pricing kernel?

These are fundamental things which are taught to undergraduates in one way or the other. But who first came up with these ideas?

Net Present Value (NPV) as a soft concept existed probably even in antiquity but it was formalized and made popular by Irving Fisher in his book the Rate of Interest.

Internal rate of return is basically a special application of NPV. It was also first formally introduced in Fisher's book although he called it 'rate of return over costs'.

Duration of bonds was introduced by Canadian economist Frederick Macaulay, but the concept was later greatly expanded by none other than Fisher together with Weil.

Law of One Price I was not able to trace this idea back to any single person. According to this article:

  The intellectual history of the concept can be traced back to economists active in France in the 1760-70’s, which applied the “law” to markets involved in international trade. Most of the modern literature also tends to discuss the “law” in that context.

But no exact names are mentioned. It might be that the original authors are unknown. As @Henry pointed out in his comment, these were most likely the French Physiocrats.

Time value of money this like the NPV, a vague notion that existed already in antiquity. You can find a lot of antique quotes that boil down to saying “time is money”, but more formally, it was introduced to the west by Martín de Azpilcueta of the School of Salamanca.

Stochastic Discount Factor - as in its modern mathematical representation can be traced back to the works of Harrison and Kreps (see 1), and Hansen et al (see  [2-5]). However, as pointed out in @Michael +1 comment, the concept can be already traced back all the way to Arrow-Debreu and Radner. Of course, on this subtopic, the list of sources is not exclusive.

1 Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets.
Journal of Economic Theory 20, 381-405.

[2] Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators.
Econometrica, 50, 1029-1054.

[3] Hansen, L. P., & Jagannathan, R. (1991). Implications of Security Market Data for Models of Dynamic
Economies. Journal of Political Economy 99(2), 225-262.

[4] Hansen, L. P., & Richard, S. F. (1987). The role of conditioning information in deducing testable
restrictions implied by dynamic asset pricing models. Econometrica 55(3), 587-613.

[5] Hansen, L., & Singleton, K. (1983). Stochastic Consumption, Risk Aversion and the Temporal Behavior
of Asset Returns. Journal of Political Economy 91(2), 249-265.


In what way is the labor participation rate useful for tracking unemployment? I'm trying to do some research on unemployment and labor participation rate in the US to figure out what people are talking about.

For instance, the Civilian Labor Force Participation Rate for Sept 2016 is 62.9% (FRED 1). My attempt to control for retirement would be to look at the 25-54 age group series, which puts the labor participation rate at 81.7% (18.3% unparticipation) (FRED 2), but I'm guessing there a number of things wrong with that approach. The Bureau of Labor Statistics says the U-6 unemployment is

  Total unemployed, plus all persons marginally attached to the labor force, plus total employed part time for economic reasons, as a percent of the civilian labor force plus all persons marginally attached to the labor force

and gives the Oct 2016 number as 9.5% (BLS 1). This sounds like an all-inclusive definition, or what people "really" mean when they talk about unemployment, but that differs from the 25-54 labor participation rate by quite a bit (9.5% vs 18.3%).

Question

In what way is the labor participation rate useful for tracking unemployment? It seems there are a large number of people included in labor participation that shouldn't be included when trying to measure unemployment, for example, the number of people retired and choosing not to work.

(side question: is there a number of people retired series on FRED? I'm not seeing one...)

There's a very fine point that needs to be mentioned:

The participation rate is the percentage of adult population of a country that is capable of work and wanting to work, individuals who are capable and wanting to work are the labor force.

Now when unemployment is measured, it is typically the percentage of individuals in the labor force who actually have the kind of employment (in terms of time worked) that they desire.

The importance of the participation rate is the following: when some individuals are unemployed for a long period of time, they eventually stop looking for work (the "willing to work" part is no longer valid) either because they've given up, or their skills are too outdated to be useful to the market. These individuals are dropped out of the labor force.

Assuming all else is constant, these unemployed individuals leaving the labor force means there are less unemployed individuals as a percentage of the total labor force (lower unemployment rate), but now the participation rate is lower (smaller labor force divided by same total adult population).

Therefore, unemployment numbers aren't really telling you the whole story if you assume that people dropping out of the labor force would actually want to work if they had found work, and thus unemployment rates alone may give a better picture of how workers are actually doing.

In short:

Unemployment rate = total employed/ labor force

Participation rate = labor force/adult population

As for the retired, I believe those are considered outside the labor force.

Example:

Assume a coal miner has no other job market skills than the ability to mine coal. Assume country X bans coal mining. All coal miners are left without a job but will not search for a job because they can't do any other job. The unemployment rate is unchanged, but the participation rate drops.

Very generally:

Unemployment rate rising, participation rate rising => not creating new jobs fast enough to absorb growth in labor force
Unemployment rate rising, participation rate falling => long term recession
Unemployment rate falling, participation rate falling => people are leaving the labor force
Unemployment rate falling, participation rate rising => high job creation


During QE what prevents the banks from selling government debt to invest in the stock market instead of lending out the money? This is how QE is supposed to work:

The fed buys government debt from banks.
This lowers the long term interest rates and businesses and consumers borrow more, which is good for the economy.
But what if the banks instead of lending out money put most of their money in the stock market?
They know that somewhat later the money will get to the general population.
And some of the general population make a good living. So good in fact that they save a lot of money in index funds, and in particular when the interes rates are low. The banks already know in advance that this will drive up the stock market.
Since they can buy the stocks before the money has reached the general population they can buy the stocks at a lower price.
As a more detailed example assume the investment bank G. Gecko own 1e6 10 years treasury bonds at USD 1000 per bond.
The bonds have a coupon rate of 10 USD, resulting in a yearly return of 20 USD = 2%. Now the Fed starts buying up 10 year treasury bonds and the price of these rises to 2000 USD. Now the return rate of these bonds are only 1%. This is not enough so G. Gecko sells it bonds. Now it has doubled its money but it need to invest these somewhere. So it buys Apple stocks.
Another bank also sell treasury bonds but use the new money to lend out.
This improves the economy and some of the general population gets more money.
Some of this they use to buy Apple stocks. However this drives up the price of the Apple stock. Let us say it doubles. Now G. Gecko have turned their initial 1e9 USD into 4e9 USD. Apple does not benefit directly from the rise in its stock price? The general population seem to benefit from the money trickling down from the other bank but the big winner here seems to be G. Gecko.

During QE what prevents the banks from selling government debt to invest in the stock market instead of lending out the money?

Nothing. Depending on which country we are talking about there might be a regulation preventing/limiting some banks investing in a stock market, in order to make banking sector less prone to collapse. For example, Basel rules mandate that banks have to keep certain level of capital buffer for their investments in stock market in order to make them resilient (see discussion about that here). This is very context dependent, there is actually no such thing as just a bank, there are commercial banks, investment banks, retail banks etc - all are regulated slightly differently and it is beyond scope of an SE answer to provide detailed overview rules for all individual institutions.
Besides that the only thing that would restrict them from doing so is that at some point it would not be profitable, especially if there is sufficient demand for loans.  Both equity and credit prices are subject to supply and demand forces.

But what if the banks instead of lending out money put most of their money in the stock market?

Ceteris paribus, this will stimulate economic activity the same way as issuing a loan would. From a macro perspective there is a little difference between bank buying from a firm A a bond with face value 1000USD with 10% coupon rate, versus bank buying 1000USD worth of stock expected to pay 100$ yearly dividend. What stimulates economic activity is firms getting the money (no matter whether as a loan or in exchange for equity) which allows them to increase investment.
If anything buying equity could potentially stimulate economy more, since there is some evidence that debt overhangs make firms invest less (e.g. see this Fed St. Louis explainer). Consequently, in situation where firms are already overleveraged such action would likely stimulate economic activity even more than just increase in borrowing.


Marginal Cost Calculation issue I calculated the Marginal cost for the below question. But it seems the results are wrong

After coming up with an innovative idea for a new product, you paid 4000 to an industrial designer to draw the blueprints and found a factory in China that agreed to produce the product for you for $3 per unit (the price includes the shipping cost from China to you).

Since this is a totally new and unique product, you have no idea how the demand for it would be. Therefore, before you start pricing the product and ordering large amounts from the Chinese factory, you decide to run an experiment (or a pilot study): you talk to Target and they allow you to sell your product at 11 different Target stores for 11 different prices (a different price at each store). These stores are located in areas whose residents have similar average income, so you can be certain that price (and not income) is the only factor varying among these stores.

I took the fixed cost as 4000
The variable cost was taken as 3.

When the MC was calculated, it was given as 3. I feel this is not correct and there is something not correct here.

Can someone kindly point it out.

Is the fixed price taken was incorrect? or the variable cost incorrect?

The marginal cost is the cost added of producing an additional unit of product. In this case the company is paying a factory in China \$3 per unit to produce the product. Assuming you have no other variable costs (i.e. costs that vary with level of output) then the cost of producing an additional unit is indeed $3.


Is 10 years monthly data enough for forecasting? I want to forecast demand for the cement industry. I have data for 10 years- Monthly data. Is that desirable for forecasting?

In your situation (after reading the comments) I would use the 10 year data over the 2 year company specific data, unless you can identify some reason why your specific company is especially atypical for the industry.

Considering the length of business cycles we typically see in the developed world, about 5 years, any 2 year period may not be reflective of the future, near or distant. The effects of independent variables like interest rate and inflation rate will not be accurately calculated because there is a strong possibility they will be very similar over a 2 year period (such as in the last two years in the United States), and therefore the data will not be sufficient to measure the difference these factors make.

Longer periods of time will solve this problem. There is no number of data that someone can point out and say "10 years is not sufficient but 10 years and 1 month is". In other words there is no cutoff, but longer periods of time, or in general larger sample sizes, are better and in this case outweigh the benefits of more specific data (although this should be decided on a case by case basis).


Basic microeconomics: supply, demand and substitutes in production The question is: explain the change in the market for skim milk, if demand for ice cream rises.

I'd say these two are unrelated in consumption (saying they're substitutes is kind of stretching it), but complements in production: you extract the cream from whole milk to make ice cream, and the rest becomes skim milk. (Right? Please correct me if I'm wrong.)

Based on this assumption, my answer is that the supply for skim milk will increase (the supply curve shifts right). As demand for ice cream rises, the demand curve for it shifts to the right, and assuming the supply curve for it remains still, this shift will increase both the price and quantity of ice cream. In turn, as ice cream prices rise, producers make more of it, and thus more skim milk.

The thing is, my textbook doesn't describe demand for a complement in production as a factor that shifts the supply curve. So I was wondering, is the reasoning above valid? Thanks.

Sounds pretty good to me. I think it would be more coherent to change the way you say this:

  As demand for ice cream rises, the demand curve for it shifts to the right, and assuming the supply curve for it remains still, this shift will increase both the price and quantity of ice cream. In turn, as ice cream prices rise, producers make more of it, and thus more skim milk.

I would change it to say this:

  As demand for ice cream rises, the demand curve for it shifts to the right, and assuming the supply curve for it remains still, this shift will increase both the price and quantity of ice cream. In turn, the increase in production will cause a upward shift in the supply of skim milk because skim milk and ice cream are "complements in production."

I make this change because you when you say that "this shift will increase both the price and quantity of ice cream" you have already said that the production of ice cream has increased (it increased along the supply curve).


Understanding the Zellener-Revankar Production Function I took out a book from my university library called Econometric Modelling with Time Series: Specification Estimation and Testing in an attempt to understand the importance of MLE in Econometrics.

There is a small note mentioning a production function I've never seen before called the Zellener-Revankar Production Function (ZRPF). Its a non-linear production function relating to output, capital and labor defined as:

$$\ln y_t+\alpha y_t=\beta_0+\beta_1 \ln k_t+ \beta_2 \ln l_t + u_t$$

The left hand side makes sense, however the right hand side seems odd. What kind of production it is trying to represent and more fundamentally, how this is mathematically considered a function give that there are two dependents on the left hand side?

Ive looked at the relevant paper work namely:

  Estimation of Zellner-Revankar production function revisited
  SK Mishra,
  Department of Economics,
  North-Eastern Hill University
  Shillong (India)
  ALTERNATIVE FUNCTIONAL FORMS FOR PRODUCTION,
  COST AND RETURNS TO SCALE FUNCTIONS
  by
  Arnold Zenner and Hang Ryu

Any help would be appreciated in terms of understanding what type of process this is coming to represent would be helpful.

Caution: Heavy citing

"In his doctoral dissertation Revankar (1967) expounded his generalized
production functions that permit variability to returns-to-scale as well as elasticity of substitution. In contrast with the production functions that (rather unrealistically) assume the same returns to scale at all levels of output, Zellner and Revankar (1969) found a procedure to generalize any given (neoclassical) production function with specified constant or variable elasticities of substitution such that the resulting production function retains its specification as to the elasticities of substitution all along but permits returns- to-scale to vary with the scale of output. Their Generalized Production Function (GPF) is given as
\begin{equation}
\ Pe^{\theta P} = c^h f^h
\end{equation}
where f is the basic function (e.g. Cobb-Douglas, CES, etc) as the
object of generalization, c is the constant of integration and θ, h
relate to parameters
associated with the returns-to-scale function. In particular, if the Cobb-Douglas production function is generalized, we have
\begin{equation}
\ Pe ^{\theta P}= AK^{\rho\alpha} L^ {\rho (1- \alpha )}
\end{equation}. This function is interesting
from the viewpoint of estimation also. It has to be estimated so as to maximize the likelihood function since the Least Squares and Max Likelihood estimators of parameters do not coincide. The return to scale function is given by
\begin{equation}
\rho (P) = \rho /(1 + \theta P)
\end{equation} . Depending on θ the sign of θ , the returns-to-scale function monotonically increases or decreases with
increase in P. However, as we know, the returns to scale first increases with output, remains more or less constant in a domain and then begins falling. This fact is not captured by the Zellner-Revankar function since it gives us a linear returns-to-scale function."

from A Brief History of Production Functions by SK Mishra 2007

So, I would guess, the  \begin{equation}  \alpha  \end{equation} parameter
in your log-linearized function would have something to do with returns-to-scale.

Regarding estimation, I'm way too much of a newb. But this might be something at least similar to what you are looking for: https://link.springer.com/chapter/10.1007/3-540-28556-3_2
Variable Elasticity of Substitution and Economic
Growth: Theory and Evidence by
Giannis Karagiannis,
Theodore Palivos,
and Chris Papageorgiou,
2005


Textbook for macroeconomics (advanced undergrad) I find that many contemporary macroeconomics textbooks are too applied, filled with examples, case studies and intuitive illustrations, often at the expense of quantitative rigour and therefore the depth of the understanding they convey.

Is there a canonical, quantitative textbook for central macroeconomic concepts and models? This should be preferably readable at an advanced undergraduate level.

Advanced Macroeconomics by David Romer, now in its fourth edition. Link contains TOC and a sample chapter.

The presentation consists of formal theory models, but with lots of intuition too, followed by light empirical applications.


Textbook on the mathematics of RBC/DSGE models? I'm reading David Romer's Macroeconomics. However, what I don't like is that he doesn't go at all into detail about the mathematical underpinnings of RBC/DSGE models. When it comes to the central mathematical parts of these models, such as how to derive and solve an expectational recurrence equation in a mathematically rigorous way, Romer instead treats it very hand-wavy and skips over steps.

Perhaps that is fine for some people, but I would like more mathematical rigour.

However, the problem is that every textbook I've found so far that is about mathematical economics only treats deterministic dynamic models.

So my question is: Is there a good textbook that treats stochastic dynamic models in a mathematically rigorous way? Note I am NOT talking about the econometric estimation of these models, but merely the purely theoretical treatment of dynamic stochastic models.

The mathematical theory behind DSGE models can be found in any textbook on stochastic dynamic optimisation.

One common reference that economists use for this is Stokey, Lucas and Prescott. Of course, they focus exclusively on recursive methods, but (perhaps) the lion’s share of dynamic problems in economics are solved in this way.

There is also a treatment of dynamic optimisation (including non-recursive and/or continuous-time methods) in Acemoglu.


homothetic functions in economics Are there any results in economics that require function to be homothetic? The textbook I am using (Essential Mathematics for Economic Analysis) says that function is homothetic when " $f(x)=f(y)$ and $t>0$, then $f(tx)=f(ty)$". It also mentions that there are homothetic functions which are not homogenous like $F=xy+1$.
But then all economic examples in the  book where homothetic function is used turn out to work with homogenous functions too. Then why are they special? Is there some economic example where having homogenous function would not be enough so there must be homothetic function for it to work?

In the theory of production (and similarly for consumption), a homothetic production function is compatible with the occurrence of fixed costs, while a homogeneous production function is not.
In both cases (in standard notations), the production can be written as $$y=F(h(x)),$$ with $h$ linearly homogeneous. It is also common to impose $h(0)=0$. Then, the cost function inherits the form $$c(w,y)=g(w)F^{-1}(y).$$
When the production function is homogeneous of degree $k$ it turns out that $F^{-1}(y)=y^{1/k}$ and so $c(w,0)=0$. For homothetic production functions however, $c(w,0)=g(w)F^{-1}(0) > 0$ in general.
A further advantage of the homothetic case, is that the degree of returns to scale can depend on $y$, while it is constant for the (degree $k$-) homogeneous technology.


Interpreting wedge between MP and wage I am an econ master student and I need a bit of help understanding an issue, for my thesis. I have two related questions.

Assume a firm producing a good with labor and capital, $Y=F(L,\bar K)$. Capital is fixed, so the firm optimizes only labor. Consider two alternative scenarios:

1) Workers have monopsonistic power in the labor market: the supply of labor is $w(L)$, upward slopping, with elasticity $\eta$. In this case, profits are:

$$ \Pi(L) = pY - w(L)L - rK $$

It can be shown that optimal labor is given by:

$$ \frac{\partial Y}{\partial L} =  \left(1+\frac{1}{\eta}\right)\frac{w}{p} $$

If the elasticity of supply is infinity (competitive market), there is no wedge between MP and wages. If the elasticitity is below infinity (for example 2), there is a positive wedge (term is 1.5) so workers are paid LESS than their competitive wage. This is counterintuitive. Why can the firm pay LESS than competitive wage, if workers are the ones with the power? This is question 1. It is also strange that if supply is perfectly inelastic ($\eta=0$), the term is infinity, which means competitive wage is zero? I am lost. Now to question 2.

2) Firms have monopolistic power in the product market: the demand for output is $p(Y)$, downward sloppoing, with elasticity $\epsilon$ (which is negative)

$$ \Pi(L) = p(Y)Y - wL - rK $$

It can be shown that optimal labor is given by:

$$ \frac{\partial Y}{\partial L} =  \frac{1}{\left(1+\frac{1}{\epsilon}\right)}\frac{w}{p} $$

Here I am very very lost. So, in the case of competitive markets ($\epsilon=-\infty$), workers are paid their MP. If the elasticity is between negative infinity and -1, the wedge is positive. However, if the elasticity is $\epsilon=-1$, the wedge is infinity. What does this mean? What is so special about $\epsilon=-1$? Even worse, if the elasticity is between 0 and -1, the wedge is negative!! What the heck does this mean?

Thanks for taking the time to read this question. If you have any further question, let me know.

Bob.

You are right that for $|\epsilon|\leq1$, you would have issues with the wedge. However, this cannot occur in equilibrium, so it is not a problem.

Both your questions stem from the same issue. I will illustrate it for monopolists, but it is analogous for monopsonists.

First note, elasticity is not constant (except in the rare case of a constant elasticity of demand function). The elasticity of demand varies across the points on the demand function. In some regions it is $|\epsilon|>1$ and in others it is  $|\epsilon|\leq1$.

Second, note that the monopolist chooses the point on the demand curve, that she operates in, unlike under perfect competition.

It is a well known result that monopolists optimally only choose to operate in the elastic region of demand. This is because, if they are in an inelastic region, then in response to a price increase, demand is reduced proportionally less than the price increase. In such a case, the monopolist can increase its profits, so that cannot be an optimal price. The profit maximizing price chosen by the monopolist is always in the elastic region of the demand curve.

This means that $|\epsilon|>1$ always holds for a profit maximizing monopolist and the wedge is always positive.


Compare taxes Cobb-Douglass and more Let a utility function for a consumer be defined as $u(x_{1},x_{2})=x_{1}^{1/2} x_{2}^{1/2}$. With the budget $x_{1}p_{1}+x_{2}p_{2}=m$. With values $p_1=p_2=1, m=32$. The state now adds a tax of unit 3 on $p_{1}$ (pr. Unit $x_1$)
How does it effect utility? What does the state earn?

I got the utility before to be 16 and after to be 8 with taxes correlating to 12 pr unit $x_1$

The state now considers an income tax such that the income is now $m-T$ How much will the state earn with the new system whilst keeping the consumer indifferent? Which system is better?

I figured that i solve for the Tax in the utility function under optimal demand conditions so that i kepy utility equal to 8. This gave me 16 units of income tax.

How does one do the last part mathematically. I figure the income tax is better for the consumer but how can i show it mathematically?

The intuition you have is correct. Mathematically you can show it by first deriving the optimal choices with the lump sum income tax. So you will set up the following lagrangian:
$$\mathcal{L} = x^{1/2}_1 x^{1/2}_2 - \lambda [x_1p_1+x_2p_2 - m + T] $$
This gives you 3 FOC's the budget constraint and:
$$ 0.5x_1^{-0.5} x_2^{0.5} = \lambda p_1 \\
0.5x_2^{-0.5} x_2^{0.5} = \lambda p_2$$
Solve for optimal $x_1^*$ and $x_2^*$:
$$ x_1^* =  \frac{m-T}{2p_1} = \frac{32-T}{2} \\
x_2^* =  \frac{m-T}{2p_2} = \frac{32-T}{2}$$
Where here the second equalities take advantage of the assumptions that $p_1 = p_2=1$ and $m=32$.
Now  you can just plug this into the utility function and assuming you made no mistake equate this to the utility with the consumption tax on $p_1$ so you will have:
$$ 8 =  \left( \frac{32-T}{2}\right)^{0.5} \left( \frac{32-T}{2}\right)^{0.5} \\
T =16$$
So under the income tax regime government gets $T=16> t=12$ while consumer still has the same utility as under the consumption tax, meaning the income tax is better. The intuition for that is that income tax does not distort the relative prices only has an income effect whereas consumption tax has both income and substitution effects.


What major monetary policy actions were taken during the Great Recession (2007-2009)? What major monetary policy actions were taken during the Great Recession (2007-2009)?

Quantitative easing and unconventional policy actions such as asset purchases and "forward guidance". I think I'm missing some things.

First, the interest on reserves and the fed funds rate changes:

Source: FRED

Second, we can roughly see the pattern of the QE actions by looking at the balance sheet of the Fed.

Source: FRED

For details on the timing of quantitative easing actions, see Figure 2 from Fawley and Neely (2013):

Source: Four Stories of Quantitative Easing


Pure Exchange Economy I need help drawing the Pareto Set for an Edgeworth economy. I know how to find the contract curve given an allocation, and I think that ends up being the competitive equilibria, but drawing the Pareto line is much harder than anticipated.

We are given 2 goods and 2 agents, with log utility $(\alpha_i > 0)$:

$$u_i(x_i) = \alpha_i \ln x^1_i + \ln x^2_i$$

We get the tangency condition:

$$\alpha_1 \frac{x_1^2}{x_1^1} = \alpha_2 \frac{x_2^2}{x_2^1}$$

And combine with the resource constraints:

$$x_1^1 + x_2^1 = r^1$$
$$x_1^2 + x_2^2 = r^2$$

A lot of algebra:

$$\alpha_1 \frac{x_1^2}{x_1^1} = \alpha_2 \frac{r^2 - x^2_1}{r^1 - x^1_1}$$

$$\implies \alpha_1 (x^2_1 r^1 - x^2_1 x^1_1) = \alpha_2 (x^1_1 r^2 - x^1_1 x^2_1)$$

$$\implies \alpha_1 x^2_1 r^1 - \alpha_2 x^1_1 r^2 = (\alpha_1 - \alpha_2) x^1_1 x^2_1$$

$$(\alpha_1 \cdot \frac{1}{x^1_1} \cdot r^1) - (\alpha_2 \cdot \frac{1}{x^2_1} \cdot r^2) = \alpha_1 - \alpha_2$$

Which gets us:

$$\boxed{x_1^1 = \frac{\alpha_1 r^1 x_1^2}{\alpha_1 x_1^2 - \alpha_2 x_1^2 + \alpha_2 r^2}}$$

For our Pareto Set. (You could also solve in terms of $x_1^1$.)

As denesp notes, if $\alpha_1 = \alpha_2 - r^1 = r^2$, then $x_1^1 = x_1^2$.

The question is, how would I draw this for different values of $\alpha$? What is the intuition behind the slope of it?

As you note in your question the (inner points of the) Pareto set are defined by
$$
x_1^1 = \frac{\alpha_1 r^1 x_1^2}{\alpha_1 x_1^2 - \alpha_2 x_1^2 + \alpha_2 r^2}
$$
In order to better examine this curve, let us treat it as a function. Let
$$
f(x) = \frac{\alpha_1 r^1 x}{\alpha_1 x - \alpha_2 x + \alpha_2 r^2}.
$$
As I stated in my comment
$$
f(0) = 0 \mbox{ and } f(r^2) = r^1,
$$
so the set indeed goes from one corner to the other. In between you have
$$
\frac{d \ f(x)}{d x} = \frac{\alpha_1\alpha_2r^1r^2}{\left(\alpha_1 x - \alpha_2 x + \alpha_2 r^2\right)^2}
$$
and
$$
\frac{d^2 f(x)}{dx^2} = 2 \cdot \frac{(\alpha_1\alpha_2r^1r^2) \cdot (\alpha_2-\alpha_1)}{\left(\alpha_1 x - \alpha_2 x + \alpha_2 r^2\right)^3}.
$$
The first derivative is always positive because $r^2 > x$ and all other parameters are positive. For the same reason, the sign of the second derivative depends on the sign of $\alpha_2-\alpha_1$.  Thus the Pareto set will be a strictly increasing curve, which is convex if agent 2 values good 1 'relatively more', concave if agent 1 values good 1 'relatively more', and a straight line if they value it 'relatively equally'.


How do we determine if wealth will be created or destroyed (and how much) when we want to provide (quasi)public goods? It seems quite simple under framework of free market, when there are no taxes or subsidies,price celling or price floors, etc, that can mess up the market: if there is profit (or will be, according to forecast of expert), then wealth was created (or will be created). If profit is negative (i.e. we have loses) then wealth was destroyed.

But what if we have public goods provided by the State? There will be no profit, so this metric is dead in this case. Normally people don't buy things from the State, they are taxed.

Using opinion of an expert seems too fragile strategy to see if wealth is created or destroyed. Probably we could survey people with questions like "How much would you contribute to additional street lighting if there was crowdfunding campaign?", but I'm not sure if it's how it is done in practice.(Please confirm if I right). Ideally it would give us demand curve.

You are right, given that it is not possible for markets to provide public goods this is often done by the state and surveys are one way of establishing the amount desired. Such surveys could establish individual demand curves. Note that, due to the non-rivalry of public goods constructing a demand curve for society as a whole requires vertical addition of the individual demand curves. This is known as the Samuelson rule.

There are however all kinds of problems associated with such surveys. Given that tax levels depend upon your answer you may want to understate your true willingness to pay. Survey respondents may also find themselves in a public goods game where it is individually rational to understate WTP even though as a group they would want the public good.

Of course we are not surveyed all the time in practice, but we approve or disapprove of further increases or decreases in public goods provision by voting for certain parties (of course that is not the only consideration when voting but it may be part).

Depending on the public good in question sometimes other tools are available. For example a large recreational spot or natural area that is freely available for recreation is also a public good, provided it doesn't become congested. The demand curve can then be constructed by estimating the travel costs that people incur to travel and recreate in that spot. That is called the travel cost method.

Also, sometimes we can construct demand curves for public goods by observing the premium people are willing to pay in terms of house prices for a nice view in their house, or the reduction because they live in a highly polluted area (pollution is often an example of a public bad). Those are hedonic methods.


Why are lower cost retailers going bankrupt but premium chains are not? In recent months, there has been a lot of talk of a "retail apocalypse". The increasing purchases on the internet have (supposedly) put pressure on storefront retailers. Payless is declaring bankruptcy and Sears has made public statements that suggest they may be facing bankruptcy shortly.

Nevertheless, luxury retailers like Nordstrom and the Hudson Bay Company, exactly the kind of companies I would expect to be most affected by internet sales cutting into their business, seem to be doing well.

Why would this be the case?

Note that my impression that higher-income consumers are more likely to use is the internet is born out by statistics (Pew Research report on internet use by income level.)

I think your anecdotal evidence is not enough to support your generalisation. In many markets there are just a few big firms (well-known to many), and many small ones (lesser-known). You could imagine a distribution of firm size being left-skewed (like a Chi-Squared or Beta distribution). Actually, this is a table showing the distribution of size by employment for 2014 for the US:

(Source here)

Thus, even if some big companies are closing down, what about the so many other smaller ones? Maybe some of the are also closing down, but this is less salient because they are less known (and less big thus less "important").

Now, if your claim were to be true, several factor could contribute to it. Most of shoppers in mass-market stores want quality, but also cost-efficiency. Conversely, luxury chains rely particularly on the value of brands. Their shoppers want quality, but also status. Consumers of the former are mainly worried about cost, and therefore loyalty to brand/stores is more or less inexistent. If they can buy cheaper online many would do so. Thus, internet has certainly increased competition for these stores. Conversely, consumers of exclusive shops care about store experience, relations, visibility, things which Amazon cannot give. There might even be an issue of power. You would not spend \$5,000 on a dress buying it online. You would go to the store, where others can see you, and buy it, so other can see your purchasing power.

Greater inequality might be a factor too. Inequality in the US went up since the 1980's. This has been "driven" particularly by a stagnation of income for most of households and a fast increase in top 10 and top 1% income shares. You can imagine that this means great pressure on prices for mass retailers, without an equivalent effect for exclusive retailers.

Finally, big (ergo popular) stores and small (ergo exclusive) stores are not direct competitors. Since brands are precisely a mean of differentiation, many luxury goods face lower competition than mass-market oriented goods (I am sure you can name more brand of cars directly competing with Ford than with Aston Martin). This, together with the status element mentioned earlier, mean that luxury producers (and retailers) are likely to face a higher price-elasticity of demand. Under this setting, they can change higher markups than standard goods producers. This increases the profitability of their business, giving their brand/company higher life expectancy. That is why they are less likely to go bankrupt.


What is the effect of redirecting government tax intake to a consumer retirement saving incentive? In New Zealand we have a retirement saving scheme called Kiwisaver.

The scheme is opt in. If a consumer opts in, they must save at least 3% of their income, which they can't access until retirement. (They can also withdraw it to buy a first house).

Their employer must match up to 2% of the employee's income.

The government matches up to ~$500 a year.

My question is, what happens if the government, instead of giving a tax cut, increases its contribution to the retirement scheme?

e.g. The government cuts services, and so can afford to give taxpayers a 1% tax cut. Instead of simply giving the tax cut, they announce that they'll be instead matching an additional 1% on the saving scheme.

The effects I see are:

There is the effect of of reduced government spending.

There's also the effect that it will increase consumer participation in the scheme.

But there's also the effect that all this extra money has on the investment world. Would this simply be inflationary on existing stock prices? Or is it likely to increase new (risky?) investment?

If you've ever looked at the ratchet effects model, you might be able to glean insight from there? Basically, if a worker is paid in a piece rate $a + bq = S, for \space e(q)$, where e is the effort exerted by the worker, we know that it is the most efficient--normally--to set $b = 1$ (no deadweight loss of "taxation" of labor, so to speak), assuming that e is measurable. However, given the cost of effort, the firm will always try to guess what that ($C(e)$) is so that $a + be - C(e) = 0$, to minimize the salary $S$ that is paid out. Workers, anticipating this, ratchet their productivity downwards, since working hard will tell a firm that the job being done by the worker is very easy, and not worth much pay.

So this means the optimum is for the firm to set $b > 1$ in a two period model where you observe effort, and then set the piece rate pay in the second period. Imagine how this might work for employers. They know that the amount they put into the Kiwisave is dependent on how much they pay out to the worker, given some chance that the employee actually puts aside the 3%. So the firm will set pay lower than they normally would if the government raised their investment into Kiwisave. The question is, would firms lower $b$ or $a$. When you optimize a simple model like this, $a$ usually doesn't go into the FOC, so probably what will happen is $b < 1$.

I think that increased government spending wouldn't necessarily increase employer costs if more employees opt in. If employers only had to pay the 2% if employees successfully paid their share that is, 100% chance employees who opt in, then more government spending would do almost nothing, barring elasticity. Those who opt in would simply have their wage set lower by the firm.

All in theory.


How to add additional observations to panel data? this is my sample dataset

How can I add for each id a new observation for 2020 month 10 which would be the average of 2020 month 8 and 2020 month 9?
I have tried the following, however, it almost works but it does not assign category name to the corresponding id value and the average is not taken correctly
egen year_m_id=group(year month) /* 127 & 128 correspond to 2020 month 8,9 */
global id=r(levels)
foreach id of global id{
generate tmp=category if id==`id'
local 2020_9=_N+1
set obs `2020_9'
local 2020_9=_N
replace id =`id' if _n==`2020_9'
sum value if year_m_id===127|year_m_id==128 & id == `id'
replace value = r(mean) if _n==`2020_9' & id == `id'
replace year = 2020 if _n==`2020_9'
replace month = 2020 if _n==`2020_9'
replace category = tmp if _n==`2020_9' & category=="" & _n==`2020_9'
drop tmp
}

Not sure if this is on-topic, but I'll give a simple solution. It's perhaps not the most efficient, but should be easy enough to follow.
Assuming you also want to keep "category" and not just "id", how about something like the following:
use sample.dta, clear
tempfile month10
preserve
keep if month==8 | month==9
collapse value , by(year category id)
gen month=10
save `month10' , replace
restore
append using `month10'


Manufacturing economics book? I am interested in manufacturing economics - suppose I have to built an engine, I would like to learn a systematic approach to break down what the costs of building an engine would be and how I could eventually optimize the process. I am a complete beginner to this, and I would like to learn from a resource that is not math-heavy (but not totally void of it!) which prioritizes intuition and is generic enough to be applicable to many different scenarios (not just engines!).

The reason is I often hear people talk of fixed costs, variable costs, production costs, amortization, etc. I would just like to learn more about it to be able to "follow the discussion".

What good books could you recommend on this? I could not find any myself.

I think you are referring to Optimization, which is taught in both engineering, math, computer science, biology, and economics.   In engineering, it's taught in a general course on Linear programming, and in economics it would be taught in a class like Operations Research.   For both courses, I believe the standard introductory text these days is Winston, Wayne L. (2004), Operations Research: Applications and Algorithms (4th Edition).  You'll need to have a  background in linear algebra to digest this book.

But there is a ton of stuff on Youtube that will probably suffice.   Google "Linear Programming". Once you understand the basic principles of the Simplex Method, you can simply download some free software like LINDO or use Excel, and you'll cover 99% of the needs of most mere mortals.

You can also find good courses on Coursera.

That being said, Optimization can get very  complicated and require courses in advanced linear algebra and calculus. For example, convex optimization is taught in many universities, but at the graduate level or in pure Mathematics. See http://stanford.edu/~boyd/teaching.html for a taste of what some engineers work on when they build very complex "machines".


Are democracies more economically productive than autocracies? The book The Dictator's Handbook claims in several places that democracies are more productive than autocracies. It's central to their argument of lower taxation rate in democracies giving more wealth than higher taxation in autocracies.
They further claim that democratizing an autocratic nation will make everyone more productive, and increase wealth available in the country.
Is this true? Is it accepted among economists that democratization leads to wealth?

In economics, it is accepted that countries with good 'inclusive' institutions, such as strong property rights, are more productive and able to develop faster (or even develop at all) than countries with bad 'extractive' institutions, such as forced labor (see Acemoglu 2008, Acemoglu & Robinson 2000a, 2000b, 2001, 2006, 2008; Olson 1984, Bates 1981, 1983, 1989 and sources cited therein*)
Democracies do  adopt inclusive institutions more often than dictatorships but not always (e.g. see Lindert 2004, 2009 + sources from previous paragraph). Furthermore, the ability of country to develop and become more productive and prosperous, or fall of a country in terms of prosperity and productivity may not only depend on a single institution but rather whether country predominantly has inclusive or extractive institutions (although some inclusive institutions like property rights are more important than others).
Consequently, it would be fair to say that it is accepted that democracies tend to be  more economically prosperous, but it is all conditional on the institutions they adopt. For example, a Venezuela is de jure a democracy but in indexes that measure strength of property rights it gets very low scores (e.g. see evolution of their property rights index (0-100) between 1995-2020). On the other hand consider China that is clearly a dictatorship both de jure and de facto, but their property rights index score between 1995-2020 got better.
To sum it up, given the above it would be fair to say that the view that democratization leads to better economic outcomes**  has some merit but with caveats. It is not that democracies are more productive by virtue of being democracies, it is thanks to their better (inclusive) and more robust institutions and in principle dictatorships could adopt the same institutions, but they tend not to. This is because while the extractive institutions might be bad for a country as a whole, as their name suggest, they help political leaders to extract economic resources for themselves.

* Note this research is also summarised in Acemoglu & Robinson: Why Nations Fail? which is book that is written in a way that is more accessible to laymen readers than the papers mentioned above).
 ** Meaning, among other things, government can often in the end collect more revenue even with lower tax rates because tax bases critically depend on size of output being taxed (e.g. $10\%$ tax on tax base 1,000,000€ gives government more revenue than $50\%$ tax on tax base 1,000€).


Prove the budget correspondence is upper hemi-continuous Let $p \in \mathbb{R}_+^L$ be price vector and let $w \in \mathbb{R}_+$ be wealth of the consumer. Define the Budget correspondence $B(p,w) =\{x \in \mathbb{R}_+^L : p\cdot x\le w  \}$ . How to prove that this budget correspondence is upper hemi-continuous?

A correspondence $Γ:R_+^{L+1}+→R^L_+$ is upper hemi-continuous if, $(p_n,w_n)→(p,w) $ and $x_n \to x$ where for each $n$ it's true $x_n \in
\Gamma(p_n,w_n)$, will ensure $x \in \Gamma(p,w)$.

I've seen a possible solution using Bolzano–Weierstrass theorem by Mark Dean at the following link http://www.econ.brown.edu/fac/mark_dean/Maths_HW4_13.pdf. But I failed to understand the last step in his approach where he claims that if every sequence $x_m \in B(p^m, w_m)$ has convergent sub-sequence converging to a point in set $B(p^*, w^*)$, then we have hemi-continuity for budget set, aren't we supposed to show that $x_m$ converge to $B(p,w)$? Am I missing any theorem?

I am assuming that the following facts do not require proofs for the purposes of this question.

Fact 1: Let $h_n$ be a sequence in $\mathbb{R}^K$ such that $\lim_{n\rightarrow \infty} h_n =h\in \mathbb{R}^K$. Then, for each $i\in \{1,2,\ldots,K\}$, we have $h^i_n\rightarrow h^i$.

Fact 2: Let $z_n$ and $q_n$ be sequence in $\mathbb{R}$ such that $\lim_{n\rightarrow \infty} z_n =z\in \mathbb{R}$ and $\lim_{n\rightarrow \infty} q_n =q\in \mathbb{R}$. Then,

i) $\lim_{n\rightarrow \infty}(z_n\pm q_n)=z\pm q$

ii) $\lim_{n\rightarrow \infty}(z_n \times q_n)=z\times q$

Fact 3: Let $z_n$ in $\mathbb{R}$ such that for each $n$, $z_n\leq a\in \mathbb{R}$ and $\lim_{n\rightarrow \infty} z_n =z$. Then, $z\leq a$.

Definition: A correspondence $G:X\rightrightarrows Y $ is upper hemicontinuous at $x\in X$ if for any open neighborhood of $V$ of $G(x)$. There exists a neighborhood $U$ of $x$ such that for all $x'$ in $U$, $G(x')\subseteq V$.

Unlike the previous remarks, the following fact requires proof.

Fact 4: Let $G:X\rightrightarrows Y $ be a correspondence. If for every $x_n\rightarrow x\in X$ and $y_n\in G(x_n)$ there exists a subsequence $y_{n_k}$ of $y_n$ with $y_{n_k}\rightarrow y$ and $y\in G(x)$, then $G$ is upper hemicontinuous. Moreover, if $G$ is compact valued, then the converse is also true.

Now, let's go back to your question. Let $(p_n,w_n)$ be a sequence in $\mathbb{R}^{L+1}_{++}$ such that $\lim_{n\rightarrow \infty} (p_n,w_n) =(p,w)\in \mathbb{R}^{L+1}_{++}$. Moreover, let $x_n\in B(p_n,w_n)$ for all $n$.

Let $w^\ast = \sup_n w_n$. Since $w_n\rightarrow w\in \mathbb{R}_{++}$, it must be true that $w^\ast \in \mathbb{R}_{++}$ because otherwise we could have created a subsequence $w_{n_k}$ of $w_n$ for which $w_{n_k}\rightarrow\infty$ which would contradict with $w_n\rightarrow w$. Similar arguments would imply that $p^{\ast} = \min_i( \inf_n p^i_n)>0$ since $p^n\rightarrow p\in\mathbb{R}_{++}^L$.

The previous observations imply that for all $n$ and for all $i$ we have $x_n^i\leq w^\ast/p^\ast$. Therefore, the sequence $x_n$ is bounded. By Bolzano-Weierstrass Theorem, $x_n$ has a convergent subsequence $x_{n_k}$ with $x_{n_k}\rightarrow x$. From here onwards, we will suppress the subscript $k$.

Since $x_n\in B(p_n,w_n)$, we have $\sum_i p_n^i\times x_n^i-w_n\leq 0$. Let $c_n = \sum_i p_n^i\times x_n^i$. By fact 1, we have $p_n^i\rightarrow p_i$ and $x_n^i\rightarrow x_i$ for each $i$, and by fact 2, we have $c_n=\sum_i p_n^i\times x_n^i\rightarrow p\cdot  x$.

By fact 2, $c_n-w_n\rightarrow (p\cdot  x-w)$. Fact 3 implies that $(p\cdot  x-w)\leq 0$, which in turn implies that $x\in B(p,w)$. This concludes the proof that the budget correspondence is upper hemicontinuous.

Original (incorrect) Answer

The following answer has been posted earlier. However, I realized that there is a mistake with this one. I am keeping this here since the original question had been wondering specifically about how Bolzano-Weierstrass theorem is relevant to the question and comparison of this incorrect answer and the correct version shows why we would need this theorem.

Definition: A correspondence $G:X\rightrightarrows Y $ is upper hemicontinuous at $x\in X$ if for all sequences $x_n\in X$ with $x_n\rightarrow x$, for all $y_n\in G(x_n)$ with $y_n \rightarrow y \in Y$, we have $y\in G(x)$.

Now, let's go back to your question. Let $(p_n,w_n)$ be a sequence in $\mathbb{R}^{L+1}$ such that $\lim_{n\rightarrow \infty} (p_n,w_n) =(p,w)$. Moreover, let $x_n\in B(p_n,w_n)$ for all $n$, with $x_n\rightarrow x$.

Since $x_n\in B(p_n,w_n)$, we have $\sum_i p_n^i\times x_n^i-w_n\leq 0$. Let $c_n = \sum_i p_n^i\times x_n^i$. By fact 1, we have $p_n^i\rightarrow p_i$ and $x_n^i\rightarrow x_i$ for each $i$, and by fact 2, we have $c_n=\sum_i p_n^i\times x_n^i\rightarrow p\cdot  x$.

By fact 2, $c_n-w_n\rightarrow (p\cdot  x-w)$. Fact 3 implies that $(p\cdot  x-w)\leq 0$, which in turn implies that $x\in B(p,w)$. This concludes the proof that the budget correspondence is upper hemicontinuous.


Is there any index which relates population growth rate with food production growth rate? I would like to know if there is an index which shows if food production growth is keeping pace with population growth worldwide. I know there are population growth rates available, for example for population there is a figure of 30% population growth rate for the period 1990-2010 worldwide from UN. Food production is harder to find , so I'm not sure if they are well known. I found here
Food production growth that USDA economists estimate global agricultural TFP growth averaged 1.4 percent per year between 2000 and 2007, but that doesn't help to compare it with the 1990-2010 period of population growth. So, is there any organization which keeps track of both figures or makes an index to compare both food production growth worldwide with population growth worldwide?

Here there is a very good summary of existing information. Key variables are daily intake of calories/proteins/fat per person (so it is not so much about tons of food but their nutrient content). An example:

Notice that most of the data is taken from the FAO, which is available online here.


Did I calculate the expected value and the variance correctly? I have the following assignment to solve but I'm not sure if I solved it correctly.

Questions

  Let the stochastic process $(Y_t)_t$ be defined by $Y_t = \mu + Y_{t-1} + \varepsilon _t$ with $(\varepsilon _t)_t\sim \mathrm{WN}(0,1)$.

  a) Calculate the expected value and the variance of $(\Delta Y_t)_t$.

  b) Prove that $(\Delta Y_t)_t\sim \mathrm{MA}(1)$ and calculate the autocovariance function of $(\Delta Y_t)_t$.

My solutions

a) \begin{eqnarray}
Y_{t+1} &=& \mu + Y_t + \varepsilon_{t+1}\\[1ex]
\implies \Delta Y_t = Y_{t+1}-Y_t &=& \mu +\varepsilon_{t+1}\\[1ex]
\mathrm E(\Delta Y_t ) &=& \mu + \mathrm E(\varepsilon_{t+1}) = \mu \hspace{6cm} \\[1ex]
\mathrm {Var}(\Delta Y_t) &=& \mathrm{Var}(\varepsilon _{t+1}) = 1
\end{eqnarray}

b) \begin{eqnarray}
(\Delta Y_t)_t &=& \mu + \varepsilon_{t+1} + 0\cdot \varepsilon_t \\[1ex]
\implies \mathrm{ACV} &=& \mathrm{Cov}(\Delta Y_t, \Delta Y_{t-h})\\
 &=& \mathrm{Cov}(\varepsilon_{t+1}, \varepsilon_{t-h+1}) = \left\{\begin{array}{ll}
1 & h=0 \\
0 & \text{otherwise}
\end{array}\right.
\end{eqnarray}

What do you think?

He who formulated the exercise is wrong, and this is why I am posting a full answer to a homework question.
This is a classic example where manipulating recursive relations can lead to different representations that may appear "different" and with different properties.

$$\Delta Y_t \equiv Y_{t}-Y_{t-1} =  \mu + Y_{t-1} + \varepsilon_{t} - \mu - Y_{t-2} - \varepsilon_{t-1}$$

$$\implies \Delta Y_t = \Delta Y_{t-1} - \Delta \varepsilon_{t} \tag{1}$$

At the same time

$$Y_t = \mu + Y_{t-1} + \varepsilon _t \implies \Delta Y_t = \mu +\varepsilon _t \tag{2}$$

The right hand side of Eqs. $(1)$ and $(2)$ represent the same process.

In any case, neither of these are $MA(1)$.

Moving forward, which one to choose?

A soft adoption of Occam's razor indicates that eq. $(2)$ is the simplest. A bit more specifically, we note that the manipulation resulting in $(1)$ hasn't "saved" us from the existence of a unit root and non-stationarity in a clear way.

Both therefore suggest to adopt $(2)$, that says that  $\{\Delta Y_t\}_t$ is the sum of constant and a $WN$ process.


Code finding all stable matchings in one-to-one problem Do you know of any publicly available code in python or R (or any other free high level language) that returns all the stable matchings for any one-to-one matching problem?

Note: This is related but different from Available code for computing solutions to matching algorithms?.

In this other question, I asked for code implementing famous mechanisms such as the deferred acceptance mechanism. Some of these mechanisms find one stable matching among others. Here I am looking for code that finds all stable matchings.

I have inspected the packages recommended in the answers I got to Available code for computing solutions to matching algorithms? and did not find anything that would do the job.

Patrick Prosser has some great java code at http://www.dcs.gla.ac.uk/~pat/roommates/distribution/ which, among other things, can compute all the stable matchings in roommate problems.

The code is for roommates problems, but Patrick's code allows preferences over roommates to include unacceptable roommates. To implement a two-sided market, just make sure any roommates on one side of the market views any other roommate on the same side of the market as unacceptable, and you're good to go.

If (like myself) you are not used to java, you might struggle a little to get the code working. Here is a little tutorial for Mac OS, which worked for me as of today.


on the FRED website where do i find definitions of the variables they give charts of? eg M3?
how can we see precisely how it is defined, measured?

https://fred.stlouisfed.org/series/MABMM301USM189S?fbclid=IwAR1lwaCbKUX16L1meOk6iZvloYOW0F7pIjmq9I4sb5VfvhhLhj8lsVTlpxg

The bottom of these indicator/series pages on FRED always lists the source. In this case, it's the OECD. If you dig around a bit on their site, and find where they host the data, there is always some meta-data attached to these that explains pretty much everything you would be looking for normally. Otherwise, they also list an email and you can ask them directly--which I've done on occasion.  They're slow to respond, but get back.

For your specific question, for example, if you go to https://stats.oecd.org/, click on the 'Finance', 'Monthly Financial Statistics', 'Monthly Monetary and Financial Statistics' and the select 'Monetary Aggregates - Broad Money M3', it pulls up all the M3 data. On the right-hand side, there is a window you can expand that has all the metadata that answers your question.


Time Value of Money Question For the following Question

The Answer is

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

I think that , there is about 3% interest

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

This is a very poorly written question.

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

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

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

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


Why Chinese GDP does not correspond to Chinese GDP growth rate? Hi all. According to google we have:
China GDP 2017=12.24 trillion USD
China GDP 2016=11.19 trillion USD
Therefore
China GDP 2017 growth rate=(12.24-11.19)/11.19=0.0938 that is approximately 9.4%
However according to google China GDP growth rate 2017 is equal to 6.9%
Why those numbers do not correspond?

Google's figures for China's GDP are simply taken from the World Bank's "GDP (current US\$)" (NY.GDP.MKTP.CD):

2016: 11190992550229.5 USD -- Google rounds this off to US\$11.19 trillion.
2017: 12237700479375 USD -- Google rounds this off to US\$12.24 trillion.

(As you point out, the growth rate from the above figures should be ≈9.4%.)

Google's figure of 6.9% for China's 2017 GDP growth is simply taken from the World Bank's "GDP growth (annual %)" (NY.GDP.MKTP.KD.ZG). Which, as you point out, is a discrepancy with our computed 9.4%.

But look at the "Details" on the last linked page, which explains:

  Annual percentage growth rate of GDP at market prices based on constant local currency.

That is, the growth rate is calculated from the World Bank's "GDP (constant LCU)" (NY.GDP.MKTP.KN), for which we have these China figures:

2016: 73521858296478.3 CNY
2017: 78594866518935.4 CNY

And now we do indeed get the figure of 6.9%.*

The lesson here is that when making GDP comparisons across time or space, there are some adjustments that one can choose to make. What adjustments one makes can lead to different results.

*A little strangely, the 6.9% is exactly precise. Which suggests that instead of calculating the growth rate using estimated GDP figures, the World Bank's GDP figures for China are calculated using the estimated 6.9% growth rate.

In general, with national income and product accounts (NIPA), there is a great deal of crude estimation and sausage making. You shouldn't take too much faith in any numbers past the first one or two significant figures. This is especially the case for China where, in addition to measurement difficulties faced everywhere, economic data are manipulated for political purposes.


How does one graph indifference curves for a set of Lexicographic preferences? Two Questions:

Since Lexicographic preferences are not continuous, is it still appropriate to use $\Bbb{R}^n_+$ to define my coordinate axes when drawing Lexicographic preferences? If not, what should I use instead?
Since the indifference sets for Lexicographic preferences are singletons, how do I draw them? What's the convention? Will a single point do?

(related to this question)

You can draw discontinuous functions in a standard $R^2$ space. For example when you draw a floor functions (a discontinuous function), the standard coordinates are still appropriate. Just make clear what to what part the discontinuous point belongs to.
Usually, for lex. preferences, one draws only the preferred set. Here you can find a graph of this kind (page 2).
Yes, each point is an "indifferent singleton" (if we may say so, as your set has only one element, and of course you're indifferent between the same thing).
The infinity number of points is not a problem. When you draw a preference map (for standard preferences), there are an infinite number of possible indifference curves. The idea is just to know how many you need to make your point. If you're using a software, you can plot with colors instead of a huge number of lines...


Books to self-study applied econometrics I'm a student and I'm interested in focusing on the application of econometric theory to "practical" situations. It would be great if you can suggest freely available books along with those that are not. The best thing would be books with explained examples of applications to real data. Also, a good and solid theoric book would be appreciated (maybe with a practical approach to the theory). All the above, whether it would be possible, may consider econometrics in general and macroeconometrics (in this area, along with the general topics, also some specific suggestion on forecasting would be great).
Summing up, the books I would like you to suggest me has to refer to these arguments:
- econometric theory
- applied econometrics
- macroeconometric theory
- applied macroeconometrics
- forecasting
- applied forecasting
I know that's a huge question and every suggestion would be strongly appreciated.

As properly suggested I add that for the applications any of Stata, Eviews and R is ok. About my background I think I can say to have a good graduate preparation, but it is fair for you to suggest books that starts from the basics concepts.

Experts can provide better suggestions if you give more information about your background, preferred programming language, etc. An absolute beginner myself, I am trying to learn Stats and Econometrics, and their applications using R language, the lingua franca among stats community. So far I have consulted primarily Springer's Use R series and free resources available on CRAN. I found the following particularly useful:

Introductory Econometrics: A Modern Approach by Jeffrey M. Wooldridge
Applied Econometrics with R by Kleiber & Zeileis

These are rather elementary books. Have a look at CRAN Econometrics Taskview to learn about applications of more advanced topics and even most recent Econometrics research.


Central banking in Saudi Arabia People say that central bank with autonomy is needed to avoid political business cycle but then how do we explain the existence of central bank in arab oil exporting countries like saudi arabia where government has no election to run periodically?
Why can't the government do the work of central bank in such countries ?

Government (meaning here executive branch of government since in most countries central bank is already government institution just independent like courts) could do that, in fact in many dictatorships/monarchies central banks are not properly independent so governments are de facto doing it if not de jure. In many such places central bank as an institution exists only nominally the same way as many dictatorships hold elections or have parliaments.

This being said historical experience shows governments are very bad at managing money supply because there ultimately complicated monetary decisions are being made made by people who don’t understand them at all. Historically, politically independent central banks perform much better at keeping prices stable and also actually better job at stimulating economy exactly when it’s needed. Hence to the extend that dictators care about having good monetary policy they would opt to have independent central bank. Although let me again reemphasize that in most dictatorships/monarchies central banks are not really independent and they are de facto controlled by dictator/monarch.


Why should $dp_2=dm =0$ in this problem? I am studying Essential Mathematics for Economic Analysis and in chapter 12 problem 10 there is a problem that I can solve but I do not understand why the solution works.
The problem asks us to differentiate the following system from consumer demand theory:
$$U'_1(x_1,x_2) = \lambda p_1 \\ U'_2(x_1,x_2) = \lambda p_2 \\ p_1 x_1 + p_2x_2=m $$
where system defines $x_1, x_2$ and $\lambda$ as differentiable functions functions of $p_1,p_2$ and $m$. We are asked afterwards find expression for $\partial x_1 / \partial p_1$.
Now I have no problem with the first step - the differentiated system will be:
$$U^{''}_{11}(x_1,x_2)dx_1 + U^{''}_{12}(x_1,x_2)dx_2 = \lambda dp_1 + p_1 d\lambda   \\ U{''}_{21}(x_1,x_2)dx_1 + U{''}_{22}(x_1,x_2)dx_2 = \lambda dp_2 + p_2 d\lambda \\ p_1 dx_1 + x_1 dp_1 + p_2 d x_2 + x_2 dp_2=dm $$
Now my first attempt was to solve 2nd equation for $dx_2$ substitute it into the first and solve for $d x_1 /dp_1$ but I got wrong result. Afterwards in the solution in the back there is a hint that says that to solve this we should put $dp_2=dm=0$ after I follow this hint I get the correct solution:
$$\partial x_1 / \partial p_1 = \frac{[\lambda  p_2^2 + x_1(p_2 U^{''}_{12}-p_1U^{''}_{21})]}{(p_1^2 U^{''}_{22} -2p_1p_2U^{''}_{12} + p_2^2 U^{''}_{11})}$$
But I don't get why we can simply assume $d p_2 = dm = 0$ that seems so arbitrary, how come that  is necessary  to find the correct solution?

The assumption $dm =0$ says that we examine the behavior of the consumer under a fixed nominal income, and this is something interesting to study, because it aligns to a large degree with the observed reality of many people that have approximately constant income.
The assumption $dp_2=0$ assumes away general equilibrium effects, since we are looking at changes in $p_1$ which is price in one market, while $p_2$ is the price in another market, presumably of a different good. So while formally the justification here is that "we do partial equilibrium analysis", the vindication of partial equilibrium analysis is that the effects from changes in one goods market to another goods market take some time to materialize, so partial equilibrium analysis has relevance to the real world.
So we see that the assumption $dm=dp_2=0$ is not "necessary to find the correct solution" (there is not one correct solution, but solutions each consistent with the corresponding assumptions made). But it is neither an "arbitrary" set of assumptions, on the contrary, it has a specific logic and purpose for which it is imposed.
The OP asked in the comments

"Then why not also assume that $d\lambda=0$"?

But the optimal value of lambda is endogenous to the model, and it summarizes aspects of the consumer's optimal behavior. So whether it changes or stays constant is for the model to tell us.


Perfectly functioning credit markets and consumer saving Today in my Macroeconomics lecture, while covering the Real Intertemporal Model with Investment (Chapter 11 of Williamson's Macroeconomics), my professor proponed that a key assumption to not make consumer saving a central choice variable is the existence of perfectly functioning credit markets. This left many students and I slightly confused. Can somebody please help me get a good grasp of this? Thanks!

I did some quick research online and think I understand better. My basic understanding is that credit market imperfections restrict a consumer's capacity to borrow or to lend, thus his or her saving ceases to be a "neutral"/"fully" endogenous variable. (Rather than being a means to an end--maximize lifetime wealth--it becomes more and more of an end in itself?)


Strong monotonicity and weak monotonicity We say $\succsim$ represents weak monotonic preferences if $$x,y \in X, \,\, y >> x \implies y \succ x $$

where $y >> x$ means that every element of $y$ is greater than every element of $x$.

And we say $\succsim$ represents strong monotonic preferences if $$x,y \in X, \,\, y \geq x, y \neq x \implies y \succ x$$

where $y \geq x$ means that at least one element of $y$ is greater than an element of $x$ and all others are equal.

My question is: do strong monotonic preferences imply weak monotonic preferences?

My answer: yes. The reasoning is as follows:

Since the set $A = \{ x,y \in X: y >> x \}$ is a subset of $B = \{x,y \in X: y \geq x, y \neq x \}$, then if $B \implies y \succ x$ it must also be true that $A \implies y \succ x$ and thus strong monotonic preferences imply weak monotonic preferences.

In plain English, if a bundle with more of one commodity and the same of all others is preferred, then a bundle with more of every commodity must also be preferred.

Is my reasoning correct?

Thanks!

Let $x,y\in X$. Suppose $y \gg x$ (so that in particular, $y\geq x$ and $y\neq x$). By assumption, $\succsim$ satisfies strong monotonicity; and so, $y\succ x$.

(We've just shown that for any $x,y\in X$ such that $y \gg x$, we have $y\succ x$. Hence, $\succsim$ satisfies weak monotonicity.)

The argument you've given above is correct and roughly the same as the proof I've just given. The only problem is that your argument is somewhat indirect, convoluted, and unclear.


Comparing relative change for different base value I need to compare change in employment size for a sample of companies. I could use percentage change, however, the problem with it is that when the base is small, a small absolute change result in a large percentage change.

For instance, company A and B employment is 10 and 10,000 respectively. assuming both company increase their employment by 5. the percentage increase is 50% for A and 0.05% for B.

I recall reading somewhere that there are some measures that take into account the different initial value when measuring changes (e.g., multiplying relative change by a function of absolute change). However, I can't recall where I read it or the name of the indicator.

Anyone is aware of such indicator or is able to propose a solution?

TIA

https://en.wikipedia.org/wiki/Relative_change_and_difference
Törnqvist, Leo; Vartia, Pentti; Vartia, Yrjö (1985), "How Should Relative Changes Be Measured?", The American Statistician, 39 (1): 43–46, doi:10.2307/2683905


Government Ownership vs Private Ownership In a debate concerning long term economic strategy, a representative of a left party was trying to support that privatisation and Small Government which minimizes its own activities is not a viable direction in a Global Economy, i.e. it will lead to a further loss of sovereignty in a sense that a country applies its policies mostly via the public sector, which if minimized will have insignificant impact. Then the opponent asked a simple, but intriguing question:

"Is there an example where a government owned company1 has a product that is competitive with a product of a private company?"

After a brief research I really couldn't find such example. Is there such an example and if not, what counter argument there could be presented against the above question?

1. Without the trivial and most frequent example of a monopoly.

Yes, there are lots. Several state-owned energy companies succeed in international competitive markets, for example.

EDF is majority-owned by the French State, and is a successful competitor in energy markets in other countries; e.g. GB electricity retail.

DONG is majority-owned by the Danish State, and is a successful competitor in energy markets in other countries; e.g. UK offshore windfarm installation.


How to derive a marginal cost curve Provide a mathematical proof for the general result that, given a linear average curve, the corresponding marginal curve must have the same vertical intercept but will be twice as steep as the average curve

That comment said, I can provide an answer here.

Take an average cost function:

$$f(x) = mx + b$$ where x is output, b is the intercept, and m is the gradient.

So total cost is:

$$C(x) = x(mx + b) = mx^2 + bx$$

And that makes marginal cost the derivative of this function:

$$C'(x) = 2mx + b$$

Best of luck with your homework.


Interpretation of a 2SLS Coefficient - Civil War Determinants I am a bit confused because of the interpretation of a coefficient in my analysis. I am using 2SLS in two different subsamples with economic growth as endogenous variable. It is instrumented by a variable for natural disasters. The outcome variable is a measure of civil conflict onset. The first stage shows that if natural disasters increase, economic growth decreases. The second stage then provides a positive coefficient for one subsample, while it produces a negative coefficient in the other subsample.
Does a positive coefficient in the second stage mean that a decrease in economic growth (as a consequence of increased natural disasters) decreases the risk of conflict onset?
I am confused because I do not know how to interpret the coefficients since the instrument is negatively correlated to the instrumented variable. If natural disasters would increase economic growth, then the interpretation would be easier since the direction is the same.
Below, you find my LaTeX Output Table. I hope this will help. The coefficients I am interested in are on the one hand -0.0312 and     0.0210 on the other hand.
I know, there is no F test and no control in the analysis. This analysis is not supposed to be sophisticated, it is basically just a means to understand the interpretation of those coefficients.

\begin{table}[t!]\centering
\begin{threeparttable}
\renewcommand{\arraystretch}{1.2} % Default value: 1
\def\sym#1{\ifmmode^{#1}\else\(^{#1}\)\fi}
\begin{tabular}{l*{3}{c}}
\hline\hline
            &\multicolumn{1}{c}{(1)}&\multicolumn{1}{c}{(2)}&\multicolumn{1}{c}{(3)}\\
            &\multicolumn{1}{c}{GDP growth p.c.}&\multicolumn{1}{c}{Onset of Conflict}&\multicolumn{1}{c}{Onset of Conflict}\\
\hline
GDP growth p.c.&                     &    -0.0312\sym{**}&     0.0210\sym{**}        \\
            &                     &     (-2.01)         &      (2.00)         \\
Natural Disasters&      -18.02\sym{***}&     Instrument&              Instrument       \\
            &     (-3.39)         &              &                     \\
\hline
Observations       &        3894         &        3894         &        3894         \\

\end{tabular}
\end{threeparttable}
\end{table}

The code produces following table:
$$
\begin{array}{|l|c|c|c|}
 \hline
   & \text{(1)} & \text{(2)} & \text{(3)} \\
   & \text{GDP growth p.c.} & \text{Onset of Conflict} & \text{Onset of Conflict} \\ \hline
\text{GDP growth p.c.} & & -0.0312^{**}  & 0.0210^{∗∗} \\
 & & (-2.01) & (2.00) \\
\text{Natural Disasters} & -18.02^{***} & \text{Instrument} & \text{Instrument}  \\
 & (-3.39) & & \\ \hline
 \text{Observations} & 3894 & 3894 & 3894 \\ \hline
\end{array}
$$

You have a model
$$(1)\  y = x \beta + e,$$
where $x$ is endogenous $\mathbb E[xe] \not =0$. This is the structural model in the sense that the parameter you are interested in is $\beta$ interpreted by its appearance in (1). In your case

y is civil conflict onset
x economic growth

suggesting that you are interested in examining how economic growth affects propensity for civil conflict. So positive $\beta$ means economic growth increase propensity for civil conflict.
Using 2SLS you get an IV-estimate of $\beta$ which we can denote $\hat \beta_{IV}$. When $\hat \beta_{IV}$ is positive it suggests that $\beta$ is positive and hence  economic growth increase propensity for civil conflict.
Interpretation is independent of $Cov(z,x)$ where $z$ is the instrument. Which in this case is

z is natural disaster.

For instrumental regression instruments must be relevant which in the simple univariate case reduces to $Cov(z,x) \not = 0$, but the sign is irrelevant (you can try to use $w := -z$ as instrument then $Cov(z,x) < 0 \Leftrightarrow Cov(w,x) > 0$ but the 2SLS estimate $\hat \beta_{IV}$ will be the same).


In which situation does the demand and supply curve both shift? In which situation does the demand and supply curve both shift? My professor told me for the demand curve,  the income of the consumers changes etc. will shifted the demand curve; For the supply curve, the changes technology etc will shift the supply curve.

So is this statement true: Only the types of situation with some factors causes the demand curve shift along with some other separate factors causes the supply curve shift may had both curve shift simultaneously, but in fact there is no single one factor that could shift both curve simultaneously.

No, this case is not true.

A factor which both shifts supply and demand curves at the same time is an increase or decrease in population.

This both adds consumers (increase in demand) to the economy and increases the workforce (increase in labor force, thus producing more and increasing quantity supplied).


Find high resolution market data for a single ticker? I'm doing my dissertation at the moment and for it, I need high-resolution market data. The only problem is I'm a student and haven't got much money. A lot of sites I have seen want monthly subscriptions or big upfront fees, I do not have this.

What's the cheapest way I can get 6/3 months of Tesla market data at say 1-second resolution?

Thanks.

Many universities have access through WRDS to the NYSE Trade and Quote (TAQ) data. Despite the name, TAQ has " intraday transactions data (trades and quotes) for all securities listed on the New York Stock Exchange (NYSE) and American Stock Exchange (AMEX), as well as Nasdaq National Market System (NMS) and SmallCap issues."

Quandl has intraday data, but only at a minute level frequency. Tesla is a member of the NASDAQ 100 and so is one of the minute by minute firms available through Quandl via AlgoSeek. The pricing for an individual user for the whole year is \$800 (as of 2/2/17).


Have countries ever tested economical measures at city level? Countries all the time takes measures at national level, and several times they create disasters. For example, they believe adding or removing a new tax will be positive for the overall economy, and it turns out to be bad and it causes a big problem. Are there examples of countries taking measures at city level, to see if that measure could succeed or fail nation wide? For example, trying how a tax affects economy in a small town first, if it impacts positively, trying it in a city, if it fails, restore the town's economy to its original state (since it is a small town a country with all its resources can fix economical mistakes in a town) and if it goes well scalate the measure, after the town, trying in a city, later in a county or deparment, later in a province or state, to finally reach nation wide. Do countries ever do things like that, is there any example of a country doing such thing?

Yes, there are lots of examples of countries piloting new economic measures before they are rolled out nationwide.  A couple of recent examples are of Finland piloting universal basic income and the UK piloting universal credit in 12 local authorities, which was then extended nationwide in a number of stages.


What are some good books and articles about the principal-agent problem? What are some good books and articles about the principal-agent problem? I'm looking for introductory academic books/articles or "popular-science" kind of ones.

In my PhD program everyone was using The Theory of Incentives: The Principal-Agent Model by Jean-Jacques Laffont and David Martimort. It offers a formal and relatively complete treatment without being too technical. I haven't read any other book on the topic, so unfortunately I cannot compare.

If you want to avoid any mathematical formalism, a good introductory article and literature review on the topic is Incentives in Principal-Agent Relationships by David E.M. Sappington, in the Journal of Economic Perspectives (1991).

Finally, I would also recommend that you have a look at the Nobel lectures by Hart and Holmström on contractual relationships inside organizations.


What exactly is a trust? In my history class, we're studying the Industrial Revolution and how Rockefeller came to dominate the oil industry with his Standard Oil company. According to our textbook, a man named Samuel Dodd (who was Standard Oil's attorney) came up with the trust in 1881. But our textbook does a very poor job of explaining what exactly a trust is or why it helped Rockefeller to monopolize his business and basically dominate the oil industry. I've done a bit of research myself, and I'm not really good with economics. Could someone please explain, in very simple layman terms, what a trust is and what it does?

Wikipedia has an article worth reading.

An American trust was typically a combination of companies operating effectively as an entity with dominant market power, so perhaps somewhere between a cartel and a monopoly.

Trusts originally took their names from the use of trust law to establish them, but later the term was used for all large companies and groups of companies which used their market position to take advantage of their suppliers and customers and to drive competitors out of business.  The most famous was Standard Oil.

This meant that when the US legislated to regulate or dismantle trusts, it call this antitrust law, where in Europe it would be called competition law.