How does one prove the convergence of a trajectory in the Ramsey model? Consider the Ramsey-Cass-Koopmans model in discrete time. Specifically, consider the following phase diagram.

For simplicity, let's consider the trajectory marked A which is in the northwest corner of this diagram.

In this location, supposedly $K_{t+1}<K_t$ and $C_{t+1}>C_t$. But how does one show this? Up to this point, all I have seen is that "supposedly" this trajectory veers off, but I don't see how it necessarily does so.

Let $$C_t = K_t^\alpha + (1-\delta)K_t - K_{t+1}$$

My Quesiton

Can someone explain why A veers off towards the NW direction? Specifically, why must $K_{t+1}<K_t$ and $C_{t+1}>C_t$?

See Romer (2006, Sec 2.3) for details of notation.
Dynamics are given by
\begin{align}
\dot k &= f(k) - (n+g)k - c\\
\dot c &= \frac{c}{\theta}(f'(k) - \rho - \theta g)
\end{align}

Presume you are located somewhere on the $\dot k = 0$ locus. Now if we increase $c$ one gets
\begin{align}
\frac{\partial \dot k}{\partial c} = -1 < 0
\end{align}

That is, if we are above $\dot k = 0$ capital decreaes over time. Hence at point $A$ we move to the left.

Now presume you are located somewhere on the $\dot c = 0$ locus. Now if we increase $k$ one gets
\begin{align}
\frac{\partial \dot c}{\partial k} = \frac{c}{\theta} f''(k) < 0
\end{align}

That is, if we are right of $\dot c = 0$ consumption decreaes over time. Hence at point $A$ we move up in addition (left of $\dot c = 0$).


How does paying off debt to the bank work? So, I understand that banks create money by making loans which end up as deposits. But what I don't get, is how paying off debt works in the big picture. Let me explain.
Let's say Jim got a loan of \$100 from the bank. He now owes the bank \$100 + \$10 interest. Where is he getting the money to pay off the loan? All of the money in the economy is created by the bank. So in this simplified example does he get it from someone else who took out a loan? Multiple people? Let's say he sold apples to Sarah and Bob for \$60 each. He would be able to pay the \$110 he owes to the bank. But Sarah and Bob would have had to take out loans, so they would also be in debt to the bank. Where would they get the money to pay off their debt?
Does the economy depend on a majority of people being unable to pay their debt? But if that was the case, how would the bank make money? I must be missing something here.

The total nominal income of the domestic economy is equal to nominal GDP growth. This chart shows nominal GDP growth for the U.S.: link to FRED graph.
If you dig into the numbers, we see that nominal GDP growth is often higher than most interest rates. So total income is growing faster than interest costs.
You cannot look at one loan in isolation and hope to make sense of total flows of income. At any given time, new loans are continuously made, while old loans are paid down. Mortgages are typically the largest household sector debt in aggregate. New buyers get large mortgages, while existing homeowners slowly pay down debt. The net change is normally positive, which effectively finances construction. Construction in turn adds to GDP and hence incomes. This story is repeated in different forms across all types of debt.


How can consumption taxes be made progressive? Consumption taxes (VAT, sales tax) are mostly applied at a flat rate. Some countries have exemptions or lower ratings for essential goods. But even with that, the tax is much less progressive than other taxes, like income tax.
There have been some suggestions that countries should move away from income tax and corporation tax and generate most revenue from consumption taxes. I just mention this as background, I know there's no clear consensus, and my question is not about that.
If consumption taxes were used more than income tax, how could these be made progressive?
Edit: I did some searches for progressive consumption tax and found this article that is most promoting a book and presupposes knowledge of terms like Flat Tax. Wikipedia on X Tax is interesting but brief. Further elaboration would be informative.

This answer simply points out what is, I think, an important part of 1muflon1's answer. There are two ways to think of consumption taxes: One is to tax certain consumption goods with a VAT. Making this progressive is an uphill battle and will cause a lot of distortions that have little to do with distributional concerns. On the other hand, you can simply tax the money spent on consumption, and this can be done in a progressive way. Income equals consumption plus saving. So by making savings tax-exempt, you turn a progressive income tax into a progressive consumption tax.


FDI - Foreign Direct Investment If foreign direct investment (FDI) in a sector is not stable, for example, if it increases dramatically one year and then declines the following year. If the fluctuation continues over ten years, what can FDI say about that sector? Its development, its problem, etc.

If a respective sector’s foreign direct investment (FDI) is not stable  then this will create uncertainty which is a general deterrent  to international investment.   Because a recipient country can affect investment decisions policies may need to change for a particular industry/sector.

Investment requires a stable economic environment and changes in the economic cycle, currency fluctuations, and changes in business confidence creates uncertainty, which is a general deterrent to international investment.

Possible Problems:

Transport costs would be increased as less firms having factories (manufacturing plants) overseas within consuming industries.   This is especially important for bulk increasing products, such as motor vehicles.
Investors will have a difficult time accessing to a countries markets thereby spending less on FDI resulting in  decrease in GDP for an industry resulting in decrease aggregate GDP.
more trading blocks forcing firms to deal with more barriers to trade such as tariffs.

Developments:

Less production growth and less productivity for a sector.

In a working paper by Robert Lensink and Oliver Morrissey (2001) titled "FOREIGN DIRECT INVESTMENT: FLOWS, VOLATILITY AND GROWTH IN DEVELOPING COUNTRIES"

When unstable FDI is introduced into their model the results have a negative effect on growth.

They stated that there are a number of reasons why volatility of FDI inflows may be negatively associated with growth.

One of them are that the volatility of FDI undermines investment (R&D [ If FDI inflows are uncertain, costs of R&D are uncertain, which negatively affects incentives to innovate.]), and thus has an adverse effect on growth and productivity.

Another finding, stated in their paper, is that they found increases in the volatility of FDI negatively affects growth as it decreases the certainty equivalent value of FDI and consequently increases set-up costs and decreases the rate of return on assets (page 10).


Why would a central bank buy government bonds? E.g. the Bank of Japan buying Japanese government bonds.

Because this is how the "government issues new money" in the era of (quasi) independent central banks: instead of directly issuing new money, the government in the narrow sense borrows from the central bank (which has been awarded the "printing privilege") so this new money is recorded as debt burdening the government (plus interest), which then is accountable for this debt burden and how it affects the balance of public finances.


How does a country devalue its currency? I recently read an article in the New York Times that talked about China devaluing its currency (which I believe is held to a peg against the US Dollar). My question is: specifically what tools does a central bank of a country employ to devalue its currency artificially and what effects does it have on its foreign trade?

Typically, a devaluation is achieved by selling the domestic currency in the foreign exchange market and buying other currencies. Suppose China sells one trillion Renminbi and buys 157 billion US dollars. From the point of view of the market, it is as if the supply of Renminbi just increased. As in any competitive market, an increase in supply will cause the price (i.e. the exchange rate) to fall: one Yuan will be worth less than before.

Devaluations are good for a country's balance of trade. Companies based in China ultimately care about how many Yuan they end up with. Suppose that the value of the Renminbi is 10 Yuan = \$1US. That means that a Chinese product priced at 10 Yuan would cost an American \$1 to buy. Now suppose that the value of the Renmimbi falls by half: 10 Yuan = \$0.50. Now the same product, still priced at 10 Yuan, will only cost an American 50 cents. It's as if everything China exports just got cheaper! This fall in the apparent price of Chinese exports will make people in other countries want to buy more Chinese products so that China will experience an increase in its exports. The argument also works in reverse: to a Chinese person, the devaluation makes it look as if American products got more expensive, so Chinese will demand fewer American (and British, and German, etc.) products and China will import less. Together, these two effects mean that China's balance of trade (i.e. the difference between exports and imports) will improve as a consequence of the devaluation.


Easy to understand explanation of deflation and what causes it This pretty much went over my head:http://en.wikipedia.org/wiki/Deflation

Is there something a bit easier to digest than this? For a non econ student?

Krugman's classic story of a babysitting co-op never uses the word "deflation" but describes it perfectly. Go read it first.

Basically, if you think of money as a thing that has a price level, just as other things have prices, it's possible to imagine that price level falling relative to other goods (inflation) or doing the reverse (deflation). Inflation is, for some reason, easier for people to understand— it means that if you hold on to a $100 bill for a year, that bill will buy you less stuff next year than it'll buy you right now.

In contrast, if you're in a deflationary world, the money in your wallet will be able to buy more stuff a year from now than it can today, giving you an incentive to hang on to your money and wait to spend it. The problem is, if everyone does that, then the fact that everyone is trying to hold on to cash means that the value of cash continues to go up relative to goods (more deflation), which is known as a liquidity trap.


What are the constituents of a country's inflation If we assume a country where only demand pull inflation holds, that is no imports cost inflation or currency fluctuations are a risk, then we can assume that inflation is determined by:

Consumer spending (for example for the US this should be the most important part of the economy)
Government spending

Are retail sales and house sales included in the consumer spending figure?

Aside from that, are there other economic indicators (that are neither consumer spending nor government spending) that influence a country's inflation?

The components of aggregate demand are government consumption, consumption, investment, net exports.

While people typically assume there is a relationship between demand shocks and inflation, this does not mean that inflation will necessarily go up whenever consumption goes up, because consumption depends not only on demand shocks but also many other things that will not necessarily affect inflation in the same way. For example, if consumption goes up because labor productivity and incomes increase, inflation may even go down. On the other hand, if the central bank decreases the interest rate, demand will increase and this will cause an increase in inflation.


Spence's Job Market Signaling Game I have a little doubt in the Job Market Signalling Game. I am referring to A Primer in Game Theory: Gibbons, Chapter 4, Signaling Games
The attached paragraph refers to a Separating Equilibrium case wherein, the High Ability type player chooses to signal $e_s>e^*(H)$, so that the Low Ability type has no incentive to mimic High Ability type, since he/she will mimic only when $e$ is between $e^*(H)$ and $e_s$.
I understand the reasoning behind this. However, I cannot seem to understand why a High Type player would choose to signal thus is he/she gets a lower payoff by doing so (since it is not optimal). Is it the case that the 'loss' due to Low Ability Type mimicing him/her is greater than the 'loss' ny not playing optimal action? Does this have anything to do with sequential rationality?

I'm sure I'm missing something. Please help me understand the concept and what I'm wrongly inferring. Thank You!

I don't have a copy of Gibbons handy, so I cannot speak to the specific model presented there, but only generally. The intuition of the conclusion is based on the combination of the following factors:

Whenever the firm can tell the high and low types apart, it's willing to pay a high wage to high type and a low wage to low type
If the firm cannot tell the two types apart, it will pay both types the same wage equal to their average productivity
Low type will try to pretend to be high type whenever possible to get a higher wage (note that even the average wage is higher than the low wage)
High type, in order to get the high wage as opposed to the average wage, will try to distinguish themselves from the low type whenever possible

Hence, if $e^*(H)$ is a sufficiently small cost for the low type to pay to pretend to be high type, then the high type choosing $e^*(H)$ will only result in them getting the average wage instead of the high wage.

As a consequence, high type would be willing to pay a bigger cost $e_s>e^*(H)$ --- a cost so big for the low type that they won't find it profitable to pay to get the average wage, but at the same time small enough for the high type so that their gains from getting the high wage instead of the average wage outweigh such a cost --- to distinguish themselves from the low type.

The key here is to take into account the presence of the low type (and asymmetric info). They are the ones who cause the reduction of the high type's wage to the average level at cost $e^*(H)$.


Substitutability vs complementarity of efforts Suppose $n$ players are in joint production to produce a common output $v(a_1,a_2,...,a_n)$ with their individual actions $a_i$. Does the convexity or concavity of $v(a_1,...,a_n)$ in the actions say something about the substitutability or complementarity of their actions?

In problems like this, complementarity and substitutability are often defined with respect to the cross-derivatives.

Write $v_i(\cdot)$ for the derivative of $v$ with respect to its $i$th argument. Thus, $v_i(a_1,\ldots,a_n)$ measures how much output increases if $i$ increases his effort slightly.

Now let's think about the derivative of $v_i$ with respect to $a_j$: $v_{ij}(a_1,\ldots,a_n)$. If $v_{ij}>0$ then an extra unit of effort from $i$ yields more output when $a_j$ is high (and vice-versa). We say that $i$'s and $j$'s efforts are complements because extra effort from $j$ makes $i$'s effort more effective (and vice versa).

Conversely, if $v_{ij}<0$ then extra effort from $j$ makes $i$'s effort less effective, and this is often taken as a definition of substitutability.


LEN-Model equivalency Starting position is a principal-agent-model with incomplete information (moral hazard) and the following properties:

Agent utility: $u(z)=-e^{(-r_az)}$
Principal utility: $B(z)=-e^{(-r_pz)}$
Effort levels $e\in \Bbb R  $
Outcomes $x\in \Bbb R, x\sim N(\mu(e), \sigma), \mu'(e)>0, \mu''(e)\le0$
Contract: $w(x)=a+bx$,

where $r_A$ and $r_P$ is the Arrow–Pratt measure of absolute risk-aversion for the agent and the principal respectively.

I am looking for the optimal contract for the principal to offer to the agent when the agent's effort is not visible. The principal's utility can be written as follows:

$$U^P(e,a,b)=\int_{-\infty}^\infty-e^{(-r_P((1-b)x-a))}f(x\mid e) \, dx$$

I want to show that the following equivalence holds, meaning that the maximization of the principal's utility can be written as the RHS of the following equivalence:

$$\max_{\rm e,a,b}\int_{-\infty}^\infty-e^{(-r_P((1-b)x-a))}f(x\mid e) \, dx \Leftrightarrow \max_{\rm e,a,b}(1-b)\mu(e)-a-\frac{r_P}2(1-b)^2\sigma^2$$

where $f(x|e)=\frac{1}{\sigma\sqrt{2\pi}}e^{(-\frac{1}2(\frac{x-\mu(e)}\sigma)^2)}$ is the density function of a normal random variable $x\sim N(\mu(e),\sigma)$, with expected value $\mu(e)$ and variance $\sigma>0$.

I tried to use the explicit form of $f(x|e)$ in the LHS, manipulate it a bit and then itegrate but could not get the equivalence.

The main point is that the principal's expected utility from a payoff $z$ conditional on a certain level of effort $e$ can be written as

$$ \text{E}[{z}|e] - \frac{r_p}{2}\text{Var}(z|e).$$

In other words, since wealth is normally distributed, exponential utility has a simple `mean-variance' representation. For a derivation, see here.

I take it that the principal's payoff $z$ equals $x - w(x) = (1 - b)x - a$. It is then straightforward to compute the (conditional) mean and variance of $z$:

$$ \text{E}[z|e] = (1 - b)\text{E}[x|e] - \text{E}[a] = (1 - b)\mu(e) - a,$$

$$\text{Var}[z|e] = (1 - b)^2 \text{Var}(x|e) - \text{Var}(a)= (1 - b)^2\sigma^2. $$

It follows that the principal's expected utility can be written as

$$ (1 - b)\mu(e) - a - \frac{r_p}{2}(1 - b)^2\sigma^2.$$


The efficient frontier in mean variance criterion The efficient frontier is the portfolios with the minimum of variance ($V$) at a given mean ($E$) or a maximum of mean at a given variance，Why do the optimal portfolios in the effcient frontier, is the efficient frontier consistent with the maximum of expected utility?
For example, assume a logarithmic utility function U=log(1+R), through Taylor series expansion and keep the first three terms,  we can get the expected utility $EU=E-(E^2+V)/2$, from this equation, take the partial derivative of $E$, it is not monotonical increase, it is the same with $V$, it seems the efficient frontier does not lead to the maximum of expected utility.
I understand if the utility function is expoential, the expected utility $EU=E-\lambda V$, which is exactly consistent with the efficient frontiers. I just do not know the other form of utility function, like the logarithmic form as above.
Any help would be appreciated.

Using $\mathbb E$ for the expected value symbol, $E_R$ and $V_R$ for the mean and the avriance of returns $R$, for a utility function of the form
$$U(R) = \ln(1+R)$$
the second-order Taylor expansion gives (ignoring the remainder)
$$U(R) \approx \ln(1+E_R) + \frac{1}{1+E_R} (R- E_R) -\frac{1}{2(1+E_R)^2}(R-E_R)^2.$$
Then
$$\mathbb E[U(R)] \approx E_R + 0 - \frac{V_R}{2(1+E_R)^2}. $$
We then have
$$\frac{\partial \mathbb E[U(R)] }{\partial V_R} = -\frac{1}{2(1+E_R)^2} < 0$$
so decreasing the variance always increases expected utility, while
$$\frac{\partial \mathbb E[U(R)] }{\partial E_R} = 1 + \frac{V_R}{(1+E_R)^3} <0$$.
The reason why this derivative is always positive, is that even with negative returns, by construction "returns" cannot fall below $-100\% = -1$.
So increasing mean returns always increases expected utility.
I don't see where the problem is. What am I missing?


Access to the markets for a country What does it mean for a country to have access to the markets. E.g: There is an ongoing discussion when Greece will follow a prosperity path in order to enter again the "markets".

When a country loses access to markets they mean access to debt markets. Here is a quote from a paper if you need a citation:

  Greece lost access to credit markets when debt exceeded 130% of GDP,
  whereas Belgium successfully handled identical debt relative to GDP.
  What determines the highest debt that a country could repay, defined
  as “fiscal limit?” Can we estimate the fiscal limit for a country
  which has never lost access to markets? We use historical data on
  primary surpluses (surpluses excluding interest payments) and debt
  relative to GDP for six high-debt, developed countries, two of which
  lost access to markets after the 2008 global financial crisis, to
  estimate the behavior of the primary surplus in response to changes in
  debt. The high-debt countries include Belgium, Canada, France, Greece,
  Italy, and Portugal.

Predicting Sovereign Fiscal Crises: High-Debt Developed Countries (Daniel and Shiamptanis (2015))

Specifically, "closed" means that that the sovereign can no longer raise funds from capital markets. Depending on the specific situation, some entities within that country can continue to raise external funds. A business with significant assets or good prospects may be able to continue to raise funds even when the country cannot. In Greece, at least until recently, this was the case. See the article Greek companies get back on the road, with help from bonds.


Value of money (incomes) question - what is the "r" here? I would like some help with a fairly basic "value of money" question. (I'm very much a beginner in this field so please bear with me.)

I'm writing about income changes throughout a decade (2010-2019). And I would like to convert a bunch of random incomes (lump sums) from different years to their "2020" value.

I found the formula for the present and future value calculations. My problem is that I do not know what to put in place of the "r" and if I'm using the right formula.

Suppose that I have an amount of $3000, and this amount is an income in the year 2011. Now do I understand it correctly that I need to use the FV formula if I want to know its value for the current year (2020)?

So it would look something like: FV = 3000 x (1+r1) x (1+r2) ... x (1+r9), right? (9 because 2020-2011 = 9, that's why I wrote 9, correct me if I'm wrong please)

Similarly, with another example, would $5000 from 2019 look like this for 2020: FV = 5000 x (1+r1) ? So just one r.

But what exactly is r? Is it simply the inflation for each year? Do I just take the yearly inflation rate of my country in each year from 2011 to 2019 and use it as r1, r2, r3 etc.?  Or from 2012 to 2020? IF it really is just the inflation rate, then for r1 do I start with the inflation rate of 2011 or 2012? If I'd like to see the value of a 2011 lump sum for 2020, then r1 should be the inflation rate of 2012? Or what do I put in the place of r if not this?

OR do I have to do something entirely different to get the results I need?

Thanks in advance, any help is very much appreciated!!

This question implies to me that you want to convert historical incomes to “2020 dollars”. The standard way to do that is to use the consumer price index (CPI). Note that this is the level, not the rate of change (“inflation rate”).

The formula for a year T is straightforward:

(Income in “2020 dollars”) = (income in year T) *(CPI index in 2020)/(CPI in year T).

For example, if the income was \$100 in a year where the CPI was 60, and the 2020 CPI is 110, the income in 2020 dollars is \$100*(110/60).

If you wanted to convert future incomes to 2020 dollars, you would need to create an assumed inflation rate. You would either use the PV formula, or use the above formula with an extrapolated CPI. How the future inflation rate is determined is your decision.


Infinitely repeated game: prisoners' dilemma I have done most of the legwork, but I have fallen short at the final hurdle.
Could you please correct my mistake(s)?

Given the condition $x>0$ I need to consider the infinitely repeated game where the above strategic form is the stage game. The discount factor: $\delta=\frac{1}{2}$.

I need to find a further condition on the game, such that we have a subgame perfect equilibrium in which both players "cooperate" in each period.

What I have done so far

The profile of strictly dominated strategies $(u,r)$ constitutes the cooperative strategy where $x>0$ and $x \ne 1$.

The prescription (cooperative strategy) will therefore be $(u,r)=(x+1,x+1)$

The grim trigger is $(d,l) = (x,x)$

Payoff from obeying the prescription:

$(x+1) + \delta(x+1) + \delta^2(x+1) +\delta^3(x+1)+... = \frac{x+1}{1-\delta}$

Payoff from deviating (here comes the mistake):

$2x + \delta x + \delta^2 x +\delta^3 x +... =\color{red}{\frac{2x-\delta(x+1)}{1-\delta}}$

The part in red should apparently be:

$$\frac{(2-\delta)x}{1-\delta}$$

I don't understand why I am wrong, could you please explain?
My understanding was that if a player deviates in period 1 in order to obtain $2x$ then both players would have to play the grim trigger profile $(d,l)$ from period 2 to perpetuity. As a result, the players would be missing out on $\delta(x+1)$.  The payoff numerator would therefore be $\color{red}{2x - \delta(x+1)}$ instead of $\color{blue}{(2-\delta)x}$.

Given that the correct numerator is $\color{blue}{(2-\delta)x}$, I can easily finish the question:

$$\frac{x+1}{1-\delta} \ge \frac{(2-\delta)x}{1-\delta}$$

Therefore, we would have a subgame perfect equilibrium iff $x \le 2$.

The problem is that my mistake lies in:

  $2x + \delta x + \delta^2 x +\delta^3 x +...$
  $=\color{red}{\frac{2x-\delta(x+1)}{1-\delta}}$

But, I'm not sure why. I would like to know why I am wrong and why $\color{blue}{(2-\delta)x}$ is the correct numerator.

Thanks.

the payoff from play the trigger strategy will be:
$$ \sum_{i=0}^{\infty}(x+1) \delta^i=\frac{x+1}{1-\delta}$$

if I deviate and I play $l$ or $d$ the payoff will be
$$ 2x + \sum_{i=1}^{\infty}x \delta^i = 2x+ x\frac{\delta}{1-\delta}=\frac{2x(1-\delta) + x\delta}{1-\delta}= \frac{x(2-\delta)}{1-\delta}$$

then, the condition is $$ \frac{x+1}{1-\delta} \geq \frac{x(2-\delta)}{1-\delta}$$

I hope that this will help you ;)


Was there resistance, historically, to the idea that human behavior deviates from rational decision making theory? I have edited this question considerably to narrow the focus.

A recent New York Times article was published on the Nobel Prize for Economics. The article discusses that Nobel laureate Richard Thaler was responsible for a push to account for human behavior in economic models:

  ...He showed that people depart from rationality in consistent ways,
  so their behavior can still be anticipated and modeled.

What is the historical context of resisting including these data in older models and what has influenced the paradigm shift?

More broadly, I am most interested in the question of why there was resistance historically in economic models when there is empirical evidence (cognitive neuroscience, psychology) going back for decades indicating that humans, in certain contexts, make decisions that may deviate from various definitions of "rational" choice. If this is not out of scope for this site (as pointed out in the comments) I would also like this to be a part of the answer to my question.

I would recommend reading Thaler's Misbehaving, which chronicles the development of behavioral economics as a field and its struggle to gain recognition by mainstream economists. Several of its chapters (particularly, 6, 17-20) would directly answer your question regarding the historical context and partly the "why".

I share my own personal view below.

I believe the "as if" argument as advanced by Milton Friedman in his Essays in Positive Economics plays an important role in countering the move towards a relaxation of the rationality assumption. In a nutshell, the argument says that a theory should be judged by the accuracy of its predictions, not by the realism of its assumptions. Therefore, while the assumption of a rational decision-maker is not entirely realistic, the theory is doing a good job as long as it generates sufficiently accurate predictions (in the sense that they match what actually happens in the real world) based on such an assumption. Friedman describes a simple of model of billiard players that I think nicely illustrates his idea:

  Consider the problem of predicting the shots made by an expert
  billiard player. It seems not at all unreasonable that excellent
  predictions would be yielded by the hypothesis that the billiard
  player made his shots as if he knew the complicated mathematical
  formulas that would give the optimum directions of travel, could
  estimate accurately by eye the angles, etc., describing the location
  of the balls, could make lightning calculations from the formulas, and
  could then make the balls travel in the direction indicated by the
  formulas. Our confidence in this hypothesis is not based on the belief
  that billiard players, even expert ones, can or do go through the
  process described; it derives rather from the belief that, unless in
  some way or other they were capable of reaching essentially the same
  result, they would not in fact be expert billiard players.

Thaler, and Kahneman and Tversky before him, mounted copious evidence that people  consistently deviate from the behavioral benchmark set by the homo economicus. But to people like Friedman, this is not a sufficient cause for a change of paradigm, unless one brings conclusive evidence to show that the predictions made by rational choice models are wrong. It didn't help that experimental economists like Vernon Smith were successfully showing that (in the market context) people's collective behavior leads to outcomes consistent with rational choice theory. (In this regard, it does seem a bit ironic that Smith would share a Nobel with Kahneman).

Another reason against the paradigm shift could be in the interest of parsimony. Including more realistic behavioral foundations in economic models inevitably makes the models more complex. But if the simpler, albeit less realistically-founded, rational choice model can get things right just as well, there is a philosophical reason for favoring the latter. In a way, this is similar to the if-it-ain't-broke-don't-fix-it mentality.

Eventually, however, rational choice theory were found to fail to predict a lot of phenomena. For example, Nash equilibia are notoriously inaccurate in predicting how people actually behave in many games (e.g. Prisoners' Dilemma, ultimatum game, public goods game, and so on). And adding behavioral assumptions/relaxing the rationality assumption seemed like a natural way to "fix" existing models to increase their predictive power. Hence we have the rising popularity of behavioral economics these days. Still, these "behavioral patches" are often met with skepticism from of many traditional "rationalists". See this post for example.


Slutsky equation with marshallian demand We have marshallian demands for goods 1 and 2:

$x_1^* = \frac{I}{2p_1}$  and $x_2^* = \frac{I}{2p_2}$
where $I$ is income and $p_i$ is price.

We need to solve the slutsky equation for income effect and substitution effect as such:

$\frac{D (x_i)}{D (p_j)} = \frac{D(H^i(p1, p2, i))}{ D(p_i)} - x_j*\frac{D(x_i^*)}{D(I)}$

So in balance marshallian demand is the same as the compensated demand.

I solved the left hand side of equation and got a result of $0$.

Then I moved on to the income effect and got the following result:

$-\frac{I}{2p_j}*\frac{1}{2p_i} = -\frac{I}{4p_jp_i}$

Substituting the results from above in to the slutsky equation gives a positive result for substitution effect. I thought that that the substitution effect is always negative. Can anyone help me out?

The first term on the RHS of the Slutsky equation (as you write it) should be $\frac{\partial h_i(p_i,p_j,I)}{\partial p_j}$, not $\frac{\partial h_i(p_i,p_j,I)}{\partial p_i}$.

So your subsequent algebra is fine but you're conflating cross-price substitution with the own-price substitution: when you let $i \neq j$ in the Slutsky equation, the first term on the RHS $\left(\text{again, }\frac{\partial h_i(p_i,p_j,I)}{\partial p_j}\right)$ measures the cross-price substitution effect of an increase in the price of $j$ on the (compensated) demand of $i$. You found it to be positive, so goods $i$ and $j$ are net substitutes (the cross-price partials of $h_i$ and $h_j$ cannot be oppositely signed -- this follows from Shephard's Lemma).

If you let $i = j$, however, you will then find that the Slutsky equation implies that the own-price substitution effect is negative for both goods, which you correctly note should be negative:

$$
\begin{align}
\frac{\partial h_i(p_i,I)}{\partial p_i} &= \frac{\partial x_i}{\partial p_i} + x_i \frac{\partial x_i}{\partial I} \\
&= -\frac{I}{2p_i^2} + \frac{I}{2p_i} \left(\frac{1}{2p_i}\right) \\
&= -\frac{I}{4p_i^2} < 0.
\end{align}
$$


What would happen if corporations can only make a maximum profit of 10% per product I have learned in accounting that companies can add any amount of profit on their products as they want. That can be 10 - over 500 %.

I also think that international corporations like Coca Cola, Nestlé definitely make more than 200 % profit for each of their products (does anybody know how much).

I don't know much about what is done with that profit, as every cost the company has is already included in the price. That is not the question here.

My question is: What would happen if by law EVERY company on this planet can only make a maximum profit of 10 % for each product. When answering please ignore potential legal loopholes or anything similar.

Prices would definitely decrease but what about wages for workers. They would stay the same, because the profit doesn't affect them. Only the wage for managers and CEOs would decrease. But what about international economics. Would it remain stable.

And the most important question: Can a law like that (if valid in every country) actually work on long-term? This is a similar question as "Can communism/socialism work?" but It is also a little bit different.

I also think that international corporations like Coca Cola, Nestlé definitely make more than 200 % profit for each of their products (does anybody know how much).

How are you defining profit?

Coca Cola, first quarter 2018
Net income:  \$1.37 billion
Revenue:  \$7.6 billion
Profit:  18%
Percentage markup:  22%

Nestle was higher in the second half of 2017, around 49.9% profit or 98% markup.

I don't know which, but if you are getting 200+%, I think that you are leaving out a lot of costs.  If you enforced that standard, companies would go out of business, because you aren't leaving enough for operating expenses.

If all companies, even the risky ones, could only have 10% profit, their product prices would tend to swing greatly.  Because when their costs are high relative to their revenues (e.g. in a recession), their prices would go up.  When costs are relatively low, their prices would be restrained.  So they would be cutting prices in good markets and increasing them in bad markets.

Companies would also have trouble financing through equity, which is rewarded by profits.  They would have to borrow, as that would show up as costs.  But it's hard to borrow unless a company is already profitable.  So no venture capital startups.

Companies would also tend to become bigger.  Because it is easier for a company that does many things to make sure that some are not so profitable.  And of course they wouldn't have to worry about startups stealing their business.

Companies would take few risks.  Because the maximum return is 10%, they have no incentive to pick the riskier choices.  They might just as well pick the safe choice, as it has the same return.  Progress would slow.

To engage in things like pharmaceutical development or oil discovery, companies would basically write off the upfront costs (to minimize profit).  Then if they actually succeeded, they'd have to engage in a flurry of additional costs so as to get full value for their products.  So the companies engaging in such behavior would expand revenues quickly.  And only companies that are already profitable could undertake the most profitable activities.

This encourages companies to out and out waste money.  Higher costs means a higher base, so the 10% is bigger.


Why could boasting oil during the current drop in oil demand be good for Saudi Arabia? According to Bloomberg :

  Saudi Arabia is one of the few countries in the world that can boast crude production that’s profitable in the current environment. But the kingdom’s economy is at risk, too, as Riyadh needs much higher prices to fund its budget. So does Russia.

Why is boasting oil production in the pandemic-driven drop in demand of oil profitable for SA? I just don't get it.

The same article  next states:

  Russia argued at the time that it wasn’t willing to keep sacrificing production at its companies to prop up prices while shale explorers in the U.S. benefited from the cuts without contributing to them.

Follow up (I have to admit)

Why do shale explorers benefit from the current situation?

The country's funding costs are very low in comparison:

at an average of  25 per barrel (in comparison: Russia  is funding for 45, the fracking, which is mainly carried out in the United States, costs $ 75 per barrel). So the earnings are above average anyway.

The USA, which has become a serious competitor, should give up market share. Today the United States produces almost as much oil as Saudi Arabia. The Middle East is fighting back with a crowding-out competition.

With state reserves of $ 750 billion, the desert state can easily cope with lower oil revenues over the years.


Limit of random walk auto correlation function Given the random walk process $y_{t}=y_{t-1}+e_{t}$, the auto correlation function is given by $corr(y_{t}, y_{t-h})=(\frac{t-h}{t})^{1/2}=(1-\frac{h}{t})^{1/2}$, which tends to 0 as t tends to infinity. What is the intuition behind this result?

Hi: The expression tends to 1.0. The intuition is that, as $t$ gets larger and larger, the $h$ lags that seperate the two processes become more and more negligible and the processes begin to look the same. This happens because, as $t$ gets larger and larger, the proportion of observations common to both processes becomes larger and larger.


Is there any article or paper that describes what Thomas Sargent thinks of New Keynesian economics/models? Is there any article or paper that describes what Thomas Sargent thinks of New Keynesian economics/models?

I am asking this question, because we all know what Thomas Sargent thinks of Old Keynesian economics, but I can't find what he thinks of New Keynesians that involve sticky price (well, Calvo/Rotemberg/etc. methods) and imperfect competition.

This journal article (Oct 29-2011,) has parts from a telephone conversation of the journalist with Sargent:

http://www.nytimes.com/2011/10/30/your-money/thomas-sargent-nobel-winner-rejects-philosophical-slogans.html

Although none of it mentions "New-Keynsian", there are some interesting points, like

  "Professor Sargent said he felt insulted by people who call him
  “non-Keynesian” or “right wing,” terms that, he said, are based on a
  misunderstanding of his thinking... He’s a Democrat, he said, “a fiscally conservative, socially liberal Democrat,” adding, “I
  think that budget constraints are really central.”"

On Keynes?

  "The “non-Keynesian” label irks him particularly. “That’s just off
  base,” he said. “Keynes was a very good economist. He was brilliant.
  He had wonderful insights. His work has inspired me many times.”"

So are we to believe that Sargent is a "Keynesian"?

  "Today, Professor Sargent says that in some ways he actually is a
  Keynesian, but he qualified that claim, too. “I’m happy to say I am a
  Harrison-Kreps-Keynesian,” he said, citing work by two scholars at
  Stanford, J. Michael Harrison and David M. Kreps. They developed a
  theory of speculative investor behavior and stock-bubble formation
  that subtly modifies rational expectations “in a beautiful way” and
  “captures Keynes’s argument, makes it rigorous, and pushes it
  further,” he said."


Is it possible to sell a rival and non-excludable product? The context pertaining to which I have asked this question is same as that of the question linked below

  Rival and non excludable products

In the linked question, a few examples of rival and non-excludable products were given like fish in ocean. But fish is a natural resource and nobody is selling fish to the fishermen. So my doubt is that whether it is possible to sell a rival non excludable product(not a service)?

A good is excludable if people can be prevented from using it. If one person is using any rival good then this good won't be available for others. You asked about rival and non-excludable good such as Common-pool resources. Examples of Common-pool resources is fisheries, forests, groundwater basins, oil fields and so on. Unlike pure public goods, common-pool resources face the problem of overuse (the tragedy of commons).
Let's see the case of fisheries you talked about. Generally, fishermen are free to fish in the sea. The tragedy of the commons problem tells us that each of the fishermen will try to catch more fishes as they are rival goods, unlike public goods. Therefore, this common pool resource of sea fishes will be vulnerable to get extinct or get empty due to overuse. To reduce the chances of this happening, government or any common group will be given authority to manage it and reduce the overuse of it. Nobel prize winner economist, Elinor Ostrom noticed this and talked about collective-choice arrangements and effective monitoring of common-pool resources.
Coming to your doubt, CPRs may or may not be sold. Talking about Sand in the river basin (another example of  CPR) there is an example of selling of rights to mine or excavate sand. Also, there is a prohibition of fish mining from the area where fishes are endangered species.  due to over mining or preserving the bio-diversity.
Therefore, it depends on the situation whether Common pool resources can be sold or not.


First paper to introduce the "principal-agent problem" The principal-agent problem is to some extent an intuitive thing that even ancient kings must have thought about.

But what is the first journal paper that has introduced the term "principal" and "agent", and made the first formal economic analysis of the principal-agent problem as a general phenomenon?

The term principal-agent problem is due to Ross (1973) (per Stiglitz, 1989). Other early contributions to this literature include Mirrlees (1974, 1976) and Stiglitz 1974, 1975).


Does anybody knows where I should look for a proxy for consumption to estimate a two factor C-CAPM? Has anybody seen, any textbook recommendation that refers to the proper proxy for consumption. I am trying to estimate a two factor consumption CAPM, namely we I add a second factor apart from consumtion in the model. But the paper that I read, it only refers to non-durable goods and services as a proxy. I am wondering if there is some other type of proxy and any recommendation would be very helpful.

I would recommend you read Kroencke (2017). That paper dismantles the problem in a lot of prior (flawed) consumption-based asset pricing research as well as explaining some findings for what were seemingly better proxies. It is a fantastic bit of work and likely not yet in some of the texts you might encounter.


Lagrangian: How to understand the No-Ponzi Condition In http://www.uni-hamburg.de/fachbereiche-einrichtungen/fb03/iwwt/makro/slides2.pdf page 8, lagrangian is written as follow: $$L = E_0 \sum_{t=0}^{\infty}\beta^t\{U(C_t,N_t) + \lambda_t(P_tC_t + Q_tB_t - B_{t-1}-W_tN_t+T_t)+\psi_t(\lim_{T \to \infty} B_T)\}$$
where bond $B_t$ has solvency condition $\lim_{T \to \infty} B_T \geq 0$.

In page 9 then all first-order conditions are derived, but I don't see anything related to $\psi_t$ and solvency condition. Why can the first-order condition relating to $\psi_t$ be dropped?

The condition is mostly referred to as the No-Ponzi (-scheme) [NP] condition. It is one additional constraint, that prevents Ponzi-schemes: Paying debt with new higher debt, ad infinitum.

By the way: The NP condition is one condition, hence the associated multiplier should be $\psi$ instead of $\psi_t$. While certainly nothing is lost repeating the same condition over and over again (for any $t$), we don't need it more than once, and it is being imprecise.

Think about optimization for finite $T$ periods. Then, you have the condition that $B_T \geq 0$. The Lagrangian optimization gives you the local optimization between $0, 1, 2$... There are many solutions that are locally optimal, but you will only allow solutions that in the end lead to $B_T > 0$.

A simple example

Your example is much too messy to think about these core issues. Look instead at the problem

$$ \max_{\{c_t, a_{t+1}\}_t} \sum_t \beta^t U(c_t) + \lambda_t (a_{t+1} + c_t - Ra_t)$$

That is, a household that choses assets $a$ and consumption $c$ to maximize his utility. You can summarize the FOC as

$$ \beta^t U'(c_t) = \lambda_t \\
\lambda_t = R\lambda_{t+1}\\
\Leftrightarrow U'(c_t) = \beta R U'(c_{t+1})
$$

Look for a moment at the special case where $\beta R = 1$ (what does that imply?). With most preferences, this necessarily leads to $c_t = c_{t+1}$. This is the local optimization that I was referring to, which is what the Lagrangian gives you. There are, however, infinitely many solutions that satisfy $c_t = c_{t+1}$. Next, we try to use the budget constraint:

$$ a_{t+1} + c_t = R a_t\\
\Leftrightarrow R a_0 = \lim_{T\to\infty}\sum_{t=0}^T \frac{c_t}{R^t} + \frac{a_{T+1}}{R^T}$$

This is as far we get using the (infinite) set of local budget constraints, where I have used forward iteration (hopefully correctly), assuming any start date $t=0$.

Now, if the household also has to satisfy the NP condition, this boils down to

$$R a_0 = \lim_{T\to\infty}\sum_{t=0}^T \frac{c_t}{R^t}$$

which, as we showed $c_t$ to be constant, we can solve easily and receive a single budget constraint. The unique solution to the problem that satisfies the NP condition is the solution where $c_t$ is a constant and this last equation holds.


Scarcity in Relation to Free Goods This is a basic economics question about scarcity in relation to free goods. The hypothetical question is that if iTunes decided to have free streaming for all their songs, would there still be scarcity for songs and would the incentives change?

I'm fairly new to these definitions and principles as it is economics 101. My understanding leads me to believe that songs remain scarce, as not all consumers have access to computer and as such to iTunes, and the incentives do change, as more people seeking free tunes will buy computers for the additional factor of the unlimited, free streaming.

Am I correct?

No, all would be the same. Except that its will monetize the android and iOS networks to make money that way.

Like youtube's model, this is how iTunes might operate


How to show that GLS estimator is consistent in regression model? $$\mathbf Y=\mathbf X\beta + \mathbf U$$
$$\mathbf E[\mathbf U\mathbf U']=\Omega $$

$$\hat \beta - \beta=(\mathbf X'\Omega^{-1}\mathbf X)^{-1}\mathbf X'\Omega^{-1}\mathbf U$$

let $\mathbf X^{*}=\Omega^{-0.5}\mathbf X$, and $\mathbf U^{*}=\Omega^{-0.5}\mathbf U$. it is obviously that $\mathbf u^{*}_i$,which is the i-th element of $\mathbf U^{*}$, is iid follows the standard normal distribution, if we assume that $\mathbf U$ follows normal distribution. But $x_i^{*'}$, the i-th row of $\mathbf X^{*}$ is not necessarily independent, for it is the linear combination of all rows in $\mathbf X$ (which is assumed iid for they stand for observations from the same distribution).

Thus the followings are not necessarily true under independent Law of Large number and Central limit theorem:

$plim\frac{\mathbf X'\Omega^{-1}\mathbf U}{n}=plim\frac{\mathbf X^{*'}\mathbf U^{*}}{n}= plim\frac{1}{n}\Sigma x_i^{*}u_i^{*} =0$
$\frac{\mathbf X'\Omega^{-1}\mathbf U}{\sqrt n}=\frac{\mathbf X^{*'}\mathbf U^{*}}{\sqrt n}= \frac{1}{\sqrt n}\Sigma x_i^{*}u_i^{*} $, converges to normal distribution

I understand that when $\mathbf \Omega $ is a diagonal matrix then $x_i^{*}$ is independent and it is not a problem, what if when $\mathbf \Omega $ is not a diagonal matrix? What kind of dependent LLN and CLT can be applied here? should we make other assumptions?

If the regressors are strictly exogenous to the error term (which is the initial standard assumption made), meaning, if the error vector is mean-independent of the regressor matrix

$$E(\mathbf u \mid \mathbf X) = \mathbf 0$$

then consistency follows immediately. Set for convenience $\mathbf \Omega ^{-1/2} \equiv \mathbf C$. Then

$$\text{plim}\left(n^{-1} (\mathbf C\mathbf X)'\mathbf u \right)= \text{plim}\left(n^{-1}\mathbf X'\mathbf C'\mathbf u\right)$$

This is a $k \times 1$ matrix. What would a typical element will be, say the first?

The matrix $\mathbf C'\mathbf u$ is a $n\times 1$ vector,

$$\mathbf C'\mathbf u = \left(\sum_{i=1}^nc_{1i}u_i,..., \sum_{i=1}^nc_{ni}u_i\right)'$$

Mutliplied by the first row of $\mathbf X' = (x_{11}\;...\;x_{1n})$ gives

$$\left [\mathbf X'\mathbf C'\mathbf u\right]_1 =x_{11}\cdot \sum_{i=1}^nc_{1i}u_i\;+...\;+ x_{1n}\cdot\sum_{i=1}^nc_{ni}u_i$$

Now strict exogeneity comes into play: it is stronger and so implies that

$$E(\mathbf u \mid \mathbf X) = \mathbf 0 \implies E(x_{1i}u_j)=0\;\;\forall i,j$$

So the above sum of sums, scaled by $n^{-1}$ will tend to zero asymptotically, since all products in each sum will tend to a zero expected value. This proves consistency.

Note that strict exogeneity is really needed, for the case where the matrix $\Omega$ is a function of the regressors. In such a case, we would be looking at products of the form

$$x_{1i}\cdot h(\mathbf x) \cdot u_j$$

which would still go to zero in expected value terms, because mean-independence implies orthogonality between the error term and any function of the regressors.

If $\Omega$ does not depend on the regressors, then we could weaken strict exogeneity to the RHS condition, which is  stronger than "contemporaneous uncorrelatedness", the latter needed for OLS.

I  leave the case for asymptotic normality to anyone interested.


How to detect if Ergodicity, Stationarity and Martingale. dif. sequence are satisfied? I'm not sure, but I think I've read somewhere that because the Classical Linear Regression model assumes to have a random sample, when researchers think they might not be in presence of a sample with that property, they try to use some randomization technique to make sure the usual theory may be applied.

In Hayashi's Econometrics, chapter 2, he develops the OLS and studies its large-sample properties in a generalization of iid sample. He assumes that the sample is ergodic, and stationary, and that the regressors multiplied by the error terms (the same that define the orthogonality conditions) also follow a martingale difference sequence.

My question is, given a sample, is there a way to know if it satisfies ergodicity, stationarity, and martingale diff. seq.? Also, even if the sample does not satisfy it, is there a way to make sure that we are able to obtain such a sample, when randomization techniques are not possible to apply?

Any help would be appreciated.

P.S.:
This question is also posted in CrossValidated, but with a different intention. When posting it here, I'm looking more for a perspective of applied econometricians, not so much for formal mathematical explanation of the possible existing methods. But of course, if you're willing to formalize and going into depth I would also be very thankful.

Ergodic and strict stationarity are the essentially the weakest assumptions for which you have a LLN, i.e. can do large sample estimation. Given the very liberal way applied econometricians use laws of large numbers, ergodicity and strict stationarity is almost always assumed. If that is in question, you're simply not in business for consistent estimation.

Similarly, if one would like to have a CLT, i.e. do large sample inference, MDS is a general weak assumption. (There are other CLT's around but more technical. The MDS CLT and Lindenberg CLT are the two immediate generalizations of the classical CLT.)

The MDS assumption can be tested. An MDS is just a discrete-time martingale with mean zero. In particular, its increments are uncorrelated. (The martingale assumption is an intermediate condition between serially uncorrelated and independence.) So a rejection by a serial correlation test would also reject the MDS assumption.


Calculus and Indifference Curves in an Urban Economics Example I am reading the paper 'The Structure of Urban Equilibria' by Jan Brueckner.

It uses a monocentric city model, where all consumers earn income $y$ at the centre of the city. They buy $q$ housing for a price $p$ at distance $x$ from the centre, incurring transport costs $tx$.

Consumers have a utility function:

$v(c,q)=v(y - tx - p(\phi)q(\phi),q(\phi))=u$

where $\phi=x,y,t,u$

The budget constraint is:

$c = y - tx - pq$

The tangency condition implies:

$\frac{v_1(y - tx - pq, q)}{v_2(y - tx - pq, q)} = p$

where the subscript 1 denotes partial differentiation w.r.t. the first argument etc.

The paper then discusses how $p$ and $q$ vary with $x, y, t$ and $u$.

If $\phi=x,y,t$, we stay on the same indifference curve. I find it relatively straightforward to find $\frac{\partial{p}}{\partial{x}},\frac{\partial{p}}{\partial{y}}$ and $\frac{\partial{p}}{\partial{t}}$.

If $\eta$ is the slope of the income-compensated demand curve, then $\frac{\partial{q}}{\partial{\phi}} = \eta\frac{\partial{p}}{\partial{\phi}}$.

Now to allow $u$ to vary. The budget constraint swings out to meet a new indifference curve, determining the new $p$ and $q$.

I can find $\frac{\partial{p}}{\partial{u}}$. Totally differentiate the utility function w.r.t u:

$\frac{d}{du}[v(y - tx - p(\phi)q(\phi),q(\phi))= u] = v_1(-\frac{\partial{p}}{\partial{u}}q-p\frac{\partial{q}}{\partial{u}})+v_2(\frac{\partial{q}}{\partial{u}})=1$

Since, by the tangency condition $v_2=pv_1$:

$v_1(-\frac{\partial{p}}{\partial{u}}q-p\frac{\partial{q}}{\partial{u}}+p\frac{\partial{q}}{\partial{u}})=v_1(-\frac{\partial{p}}{\partial{u}}q)=1$

So $\frac{\partial{p}}{\partial{u}} = \frac{-1}{qv_1}$.

The paper then quotes:

$\frac{\partial{q}}{\partial{u}} = [\frac{\partial{p}}{\partial{u}}-\frac{\partial{MRS}}{\partial{c}}\frac{1}{v_1}]\eta$

I don't know how to derive this. I'm guessing the first term in the square brackets is a substitution effect and the second term is an income effect.

Please help me understand this last expression $\frac{\partial{q}}{\partial{u}} = [\frac{\partial{p}}{\partial{u}}-\frac{\partial{MRS}}{\partial{c}}\frac{1}{v_1}]\eta$ and how to derive it.

The utility function under consideration is $v(c,q)$ and then
$$MRS(c,q) = \frac{\partial v/\partial q}{\partial v/\partial c} = v_2/v_1$$
make the functional denpendency of on $u$ explicit then you have
$$\frac{\partial}{\partial u}MRS(c(u),q(u)) = \frac{\partial MRS(c(u),q(u))}{\partial c} \frac{\partial c(u)}{\partial u} + \frac{\partial MRS(c(u),q(u))}{\partial q} \frac{\partial q(u)}{\partial u} = \frac{\partial p(u)}{\partial u},$$
where the last identity follows because you know that $p = MRS$. Now simply rearrange the identity
$$\frac{\partial MRS(c(u),q(u))}{\partial c} \frac{\partial c(u)}{\partial u} + \frac{\partial MRS(c(u),q(u))}{\partial q} \frac{\partial q(u)}{\partial u} = \frac{\partial p(u)}{\partial u},$$
to get
$$ \frac{\partial q(u)}{\partial u} = \frac{\left[\frac{\partial p(u)}{\partial u} - \frac{\partial MRS(c(u),q(u))}{\partial c} \frac{\partial c(u)}{\partial u}\right]}{\frac{\partial MRS(c(u),q(u))}{\partial q} },$$
then use that Brueckner has defined $\eta := \left[\frac{\partial MRS(c(u),q(u))}{\partial q}\right]^{-1}$ in footnote(3) to get
$$ \frac{\partial q(u)}{\partial u} = \left[\frac{\partial p(u)}{\partial u} - \frac{\partial MRS(c(u),q(u))}{\partial c} \frac{\partial c(u)}{\partial u}\right] \eta ,$$
and finally apply the rule that $\frac{\partial c(u)}{\partial u} = \frac{1}{\partial v/\partial c} = 1/v_1$ to get
$$ \frac{\partial q(u)}{\partial u} = \left[\frac{\partial p(u)}{\partial u} - \frac{\partial MRS(c(u),q(u))}{\partial c} \frac{1}{v_1}\right] \eta.$$


How to determine the worth of a good I've searched around the web for awhile now and I'm beginning to think this might be an unanswerable question. I want to know if there is a theoretical way to determine the worth of a particular good, either cash or item, independently of average purchase price (ideal selling so exactly whoever wants one and can pay for it at the price will get it).

The specific case is a virtual economy such as a video game, where there might be no way to get real world cash into or out of the game, but you want to determine if the value of SuperSwords is right to buy and what those swords are likely to be worth in the future. Is there a general formula for this situation?

A secondary case that I also wish to know about is setting the price (in-game stores) of such items. While this may push the topic more towards video game design rather than economics, I think that the basis of a price is more heavily in the modeling an economy area than a game area. What will be the best way to adjust the pricing? The four factors controlled are price sold by the store, price paid by the store, how many the store can buy and how many the store can sell.

What you are after

The value of a good should be the highest possible utility that it would give anyone in the economy. If you care differently about different people, you are interested in the highest possible adjusted utility that it would give anyone in your economy, where you have adjust the utility with a weight that indicates how much you comparatively care about that person

It doesn't exist

This is almost what a price is: It is the highest possible utility that it would give anyone in the economy who can afford it, under frictions. These frictions could be informational (someone who benefits most from the new iPhone isn't aware of its existence) or other (some people/groups are restricted from purchasing a good, for example due to trade sanctions).

There is no other objective way that we are aware of. At the cost of sounding dogmatic, this is the superior part of capitalism compared to other economic systems: Allowing prices to judge the value of goods.

In alternative systems, you need committees or similar to do this job. While there is no theoretical reason why human's couldn't do a better job than prices do (unless you allow for hand waving the system is too complex), it turns out they don't.

Do you need real world cash for prices?

There is three properties of money: It is

a storage of value
a unit of exchange
unit of account

Introduction of money into your economy doesn't need to connect it to real world cash, but you need to make it valuable. Connecting it to real world cash at some rate would immediately determine its value. Say, if you allow modwizdollar at 1-to-1 rate to the USD, your dollar has immediately the same value as the dollar, and also its inflation rate.

In Diablo, players find gold and items over time, as they kill enemies. Therefore, the objective value of gold is the time it takes a player to earn that much gold, devalued by how much that time is worth to the player. The more time it takes for players to find items, the more valuable these are. For money to be work as a store of value, it is sufficient to keep finding modwizdollars costly in terms of time.

How to set prices

It depends on what your goals are, and I suppose people could write Bachelor papers on the complexity of these systems, and in fact, an economist of late publicity did exactly that for Valve.

One simple way to set up prices

One simple way would to allow the measure of goods (items) grow constantly over time. This would imply a new supply of a specific item $i$ of $S_i$. Let time be denoted by $t$.

Compute, at any time, the actual demand for goods by players given the current prices $D_i(p_{i,t})$. Given initial $p_{i,t}$,

Increase $p_{i,t+i}$ if $D_i(p_{i,t}) > S_i$
Decrease $p_{i,t+i}$ if $D_i(p_{i,t}) < S_i$

How much you want to increase or decrease these depends on many things, and I can't possibly spell out the whole model for you. Assuming that demands are stable over time, you could try a bijection.


Why couldn't the Karush-Kuhn-Tucker optimization find the solution? I have the following utility maximization problem:
$$\max (xy)$$
$$(x+y-2)^2 \leq 0$$
Conditions:
$$y-2\lambda (x+y-2) =0$$
$$x-2\lambda (x+y-2) =0$$
$$\lambda(x+y-2)^2=0$$

When I set $\lambda>0$, I get:
$$(x+y-2)^2=0 \Rightarrow (x+y-2) = 0$$
$$y-2\lambda (x+y-2) = y = 0$$
$$x-2\lambda (x+y-2) = x = 0$$

But the obvious solution is $x=y=1$.

When I set $$\lambda=0$$ that's not a case with a valid solution either. Is the constraint too low? What is the explanation to this?

I would greatly appreciate your help.

As @user32416 pointed out the first order stationarity conditions are not enough. Specifically it seems that you violate Slater's condition, which states that "the feasible region must have an interior point". There are no $x,y$ for which
$$(x+y-2)^2 < 0.$$

If you rephrase the problem to
$$\max (xy)$$
$$x+y-2 = 0$$
$$x,y \geq 0$$
Slater's condition is met (for linear conditions no interior points are necessary) and you can apply Karush-Kuhn-Tucker.


price elasticity of output, makes sense? I was wondering, in a log-log model of output, labour and commodity price where output is the depedent variable, does it make sense if the coefficient on the price variable is interpreted as the "price elasticity of output"? Assume output is measured in constant monetary unit.

Let's say $log(gdp_t) = \beta_0 + \beta_1log(labour_t) + \beta_2\log(commodityprice) + \epsilon_t$

I've not seen $\beta_2$ being defined as the elasticity of output with respect to price. But, could this be correct at all?

I use some abbreviations and drop the index t.

$\ln(G)=\beta_0+\beta_1\ln(L)+\beta_2\ln(P)+\epsilon$

Taking both sides as an exponent of e

$e^{\ln(G)}=e^{\beta_0+\beta_1\ln(L)+\beta_2\ln(P)+\epsilon}$

$G=e^{\beta_0+\beta_1\ln(L)+\epsilon}\cdot e^{\beta_2\ln(P)}$

$e^{\beta_0+\beta_1\ln(L)+\epsilon}=C$ is a constant if you differentiate w.r.t $P$.

$G=e^{\beta_0+\beta_1\ln(L)+\epsilon}\cdot e^{\ln(P^{\beta_2})}$

$G=e^{\beta_0+\beta_1\ln(L)+\epsilon}\cdot P^{\beta_2}$

$\frac{\partial G}{\partial P}=e^{\beta_0+\beta_1\ln(L)+\epsilon}\cdot \beta_2\cdot P^{\beta_2 -1}$

The elasticity is $\large{\epsilon}\normalsize{=\frac{\partial G}{\partial P}\cdot \frac{P}{G}}$

$\large{\epsilon}=\normalsize{e^{\beta_0+\beta_1\ln(L)+\epsilon}\cdot \beta_2\cdot P^{\beta_2 -1}\cdot \frac{P}{e^{\beta_0+\beta_1\ln(L)+\epsilon}\cdot P^{\beta_2}}}$

=$C\cdot \beta_2\cdot P^{\beta_2 -1}\cdot\frac{P}{C\cdot P^{\beta_2}}$

You can finish by simplifying the term.

In general it is true that

$\large{\epsilon}=\normalsize{\frac{\partial \ln(G)}{\partial\ln(P)}}$

Thus the short way is to differentiate $\ln(G)$ w.r.t $\ln(P)$.


A government running like a literal business Hopefully this doesn't get partisan, but I wanted to see where a thought experiment would go where a government stopped collecting taxes and instead fund itself by running businesses (selling products and services) alongside other private businesses out in the free market.

This is an extremely implausible scenario.  The conditions for it to work would be extremely demanding:

The government would need to run businesses in which it has the
potential for a sustainable competitive advantage, giving it the
opportunity of earning profits on an ongoing basis. That might be
based on a natural resource endowment (cf Saudi Arabia and oil) or
on a technology which others are, for whatever reason, unable to
copy. For most countries, such opportunities are limited.
The government would need to run the businesses efficiently, so as
    to realise those profits. This would be challenging due to:
    a) political necessities conflicting with efficiency; b)
    rent-seeking behaviour by managers and workers in the businesses.
The profits realised would need to be sufficient to fund the
        government's expenditure.  For a typical developed country with high
        government expenditure on education, health, welfare, defence, etc.,
        this would require improbably large profits.  To give an idea of scale, UK government spending in 2015/16 was £772 billion. By contrast, the world all-time largest corporate earnings (Vodafone in 2014) were less than 10% of that at £59 billion.


Differences between Slope of budget line and MRS? Slope of budget line= change in y/ change in x and also  Marginal rate of substitution= change in y/ change in x. If the definitions are same of both then what is the difference between the two? I mean 1. Slope of the budget line will be number of units of good y that the consumer is willing to sacrifice for an additional unit of good x. 2. The marginal rate of substitution (MRS) is the amount of a good that a consumer is willing to give up for another good. Here both definitions means the same, right?

Not really, you're right in that (loosely speaking) the MRS is the amount of one good someone is willing to give up in order to get an additional unit of another good. However, the slope of the budget line measures the amount of one good someone has to give up in order to get an additional unit of another good.

In the first case, only preferences matter, whereas in the second only prices are relevant.


Financial markets, money demands How can an increase in the interest rate make bonds more attractive and reduce their price?

The question as posed doesn't make sense to me. An increase in the market interest rate will reduce the price of current bond holdings precisely because they become less attractive since there are now more profitable alternatives in the market. Market forces will lower the price of the bonds in response to the increase in expected future coupon streams from these alternatives.


Does the Labor Theory of Value hold in the long term in competitive markets? Most criticisms of the Labor Theory of Value I have come across go something like this quote from Carl Menger:

There is no necessary and direct connection between the value of a
good and whether, or in what quantities, labor and other goods of
higher order were applied to its production. A non-economic good (a
quantity of timber in a virgin forest, for example) does not attain
value for men since large quantities of labor or other economic goods
were not applied to its production. Whether a diamond was found
accidentally or was obtained from a diamond pit with the employment of
a thousand days of labor is completely irrelevant for its value.

This is perfectly obvious and Marx even mentions this:

A commodity, such as iron, corn, or a diamond, is therefore, so far as
it is a material thing, a use value, something useful. This property
of a commodity is independent of the amount of labour required to
appropriate its useful qualities.

But putting aside the natural resource example for a moment, in the long term in a competitive market isn't it the case that if there is a situation where someone is able to sell something for more than the cost of the labor that went into it, someone else should be able to step in and sell that thing for a lower price? Eventually prices will go down until they are stopped by another constraint. That constraint being the cost of all the labor required to produce the product.
In situations where this doesn't happen isn't it an indication of some anti-competitive force?
Monopoly of a natural resource, monopoly of a technology through a patent, externalities that result in a small number of large companies, cooperation between large companies to set prices, etc...
So is it fair to say that in the long term in competitive markets the labor theory of value holds?
If the theory is "at any point in time a commodity is worth as much as the cost of labor that went into it" then it is obviously wrong and I can't imagine any classical economist would have believed it.
But if the theory is "over time the cost of a good will tend towards the cost of the amount of labor that went into it assuming the market is competitive" then it still seems plausible.

No it does not for several reasons. Labor theory of value (LTV) central tenant is that there is some intrinsic component to value determined objectively by labor  (see Brue and Grant History of Economic Thought  7ed). This implies that there exist some unit of labor in which every value could be measured. In addition, it means that the value ($V$) is some sort of function labor $L$ i.e. $V=f(L)$. As stated by Adam Smith in Wealth of Nations who first developed the LTV (and as mentioned in the comments as well):

"The value of any commodity ... is equal to the quantity of labour which it enables him to purchase or command. Labour, therefore, is the real measure of the exchangeable value of all commodities.

Hence, at the core of labor theory of value is proposition that all value can be somehow objectively measured by labor, and that it should depend on labor.
Well there are several problems with that proposition:

What about things that require great labor inputs but are worthless (which is situation that can and empirically does arise even in competitive markets as preferences and tastes change and something that was once desired might be trash today)?

The LTV actually has no good answer for that. Adam Smith tried to
answer this objection by distinguishing between value in use and
value in exchange. As Smith further writes in his Wealth of Nations:

The word value, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and sometimes the power of purchasing other goods which the possession of that object conveys. The one may be called "value in use"; the other, "value in exchange." The things which have the greatest value in use have frequently little or no value in exchange; and, on the contrary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarce anything; scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it.

This is basically the argument that Marx repeats (although he had different name for it), as mentioned above (indeed I am always surprised that Marx is often quoted regarding LTV given he did not do virtually any original work on the LTV and just took it from Ricardo and Smith).
The problem with this is that it is already quite scientifically undesirable as it is essentially a cop-out. Labor is the source of value, well, except in cases where it isn't because the object is not useful. So already LTV from the get go admits it is not a theory that can explain all value, which is scientifically undesirable as we want to generalize as much as possible. Now, if we would not have alternative theories of value this could be forgiven but given we do have them and they can explain more this in itself is argument for ditching LTV (e.g. we can safely ditch Newtons theory of gravity in favor of relativity as the latter is more general, but even though theory of relativity can't explain everything we cannot ditch because there is no other competing theory that can).
With regards to your main question, already this point 1 proves that in competitive markets LTV does not need to hold as it is completely valid outcome under perfect competition that value of produced good will be 0 (or indeed even negative like with oil futures).

How to measure value in labor (the problem of transformation)?

One of the central tenets of labor theory of value as mentioned
above is that labor must be some sort of real measure of value of
all commodities. However, due to the problem mentioned in point 1 it is also necessary to argue that value of labor will not correspond exactly to the  price.
Hence, this gives raise to the question how to actually establish some correspondence between prices and labor which is also known as the problem of transformation (see Samuelson; 1971). This was in fact a problem that Ricardo devoted considerable amount of time to solve, although he was ultimately unsuccessful.
Samuelson argues there is no general solution to the problem, and although there are some scholars claiming to solve it  there are no generally accepted solutions.
In regards to your question, assuming competitive market does not provide solution to the above problem and without the above being possible it is very hard to sustain claim that value can be somehow objectively measured by labor.

Empirically value seems to be orthogonal on labor inputs and this hold regardless of how competitive industry is.

There simply does not seem to be any relationship between value and labor inputs. Relative prices fluctuate widely even when labor inputs stay same. This can occur both in theoretical models of perfect competition (e.g. consider two perfectly sectors two goods model with some idiosyncratic demand shocks), and frequently occurs in reality.
Now even if there would be a discrepancy between price and the value of labor that went into producing the product, if there is any objective value determined by labor then you would at the very least expect relative prices to depend on relative labor inputs but they do not and there is no indication that they start doing so in competitive industries. Hence $V \perp L$.
This also connects to the previous point, but for LTV to hold it is simply not enough to just show that something that was produced with labor is happens to have value - the value of it should depend on labor input and ultimately be measurable.  What even more it should be the  measuring stick of the value. But this is clearly inconsistent with observation that relative prices change and fluctuate widely even when labor inputs do not.


What is the difference between the Classical and Keynesian models? I have read something about the short and long run aggregate supplies, but I don't know what the main difference is about these two models. Does someone know the difference(s) between these two models?

In the classical model, aggregate supply curve is vertical (price level on the y axis), meaning that output is fixed, constrained by technology and inputs. Prices are flexible. So that if the demand curve changes, the effect will be entirely on price level and not on output.

In the keynesian model, aggregate supply curve is horizontal at some price level. If demand changes, the effect will be entirely on output.

So the main difference lies on price flexibility and the power of increasing output through aggregate demand stimulus.


What would happen if stock markets were open 24 hours? Suppose you are a broker or a trader, and the stock markets will be open 24 hours a day.

What would be the implication for you as a broker in this scenario?
I mean:

How will your strategies change?
Will it be more difficult or easier to trade?
What algorithms that you know that would have to be adjusted in this scenario?

You would have trading teams who work shifts like any other 24-hour business areas.

The power market is open 24-7; many companies have around-the-clock trading teams. A lot of analysis and other work that can be done in the daytime is still done in the daytime.

A major source of income during nighttime - in the power market - is just being there and executing trades - when other people are not there. I think that is the main change, that liquidity would shrink and give more arbitrage opportunities.


Is a country in economic downturn if its growth rate is negative, but improving? As I understand it, economic downturn means that economic growth is significantly slowing down or entering into recession. (If anyone wants to correct me, please do so). i.e. Growth rate is decreasing.

But what if the country is already in recession, but its growth rate is increasing? i.e. -5% one year, -3% the next, -2.5% the next, etc. Is this still classed as downturn (since the economy is still shrinking) or is it not since the growth rate is actually increasing despite being negative?

I'm no macroeconomist, so other will correct me if I am wrong, but I would use the following definition:

More formally, if $Y(t)$ is GDP at time $t$, one could express this as

Recession: $Y'(t)<0$ for 6+ months

downturn: $Y''(t)<0$

recovery: $Y''(t)>0$.

The definition of recession (2 quarters of negative growth) is widely standardised. I think the definition of downturn and recovery is less standard, and therefore more subject to debate.


Is there an intuitive explanation for the tax incidence formula from elasticity? You're probably familiar with the formula for tax incidence (in a standard Principles framework) from elasticity. Specifically, that the consumer share is

$$\frac{\varepsilon_S}{\varepsilon_S+|\varepsilon_D|}$$
and the producer share is
$$\frac{|\varepsilon_D|}{\varepsilon_S+|\varepsilon_D|}$$

I had always assumed that this was just a byproduct of linear supply/demand and therefore not of much interest, but just now have proven to myself that it's not with a few nonlinear supply/demand forms that also produce this result.

Is there an intuitive reason why the tax incidence takes this particular functional form, or is it just a common mathematical happenstance? This isn't the only functional form that satisfies what I think of as the intuitive tenets of the tax incidence solution (consumer + producer shares add to 1, increase in your side's elasticity increases your side's burden). Another form that satisfies this, but is not in fact a calculation of incidence share, is $$\frac{(|\varepsilon_D|/\varepsilon_S)}{(|\varepsilon_D|/\varepsilon_S)+(\varepsilon_S/|\varepsilon_D|)}$$

I suppose an alternative explanation is that the counterexamples I happened to test this with satisfy some condition necessary to have those be the shares, and it's not actually universal.

Ah, never mind, got there.

Both supply and demand share the same change in quantity as a result of the tax, so

$$\Delta Q_S = \Delta Q_D$$

The amount by which the quantities changed is the derivative of that quantity wrt price, times the change in price that side experienced

$$\frac{\partial Q_S}{\partial P_S}\Delta P_S = \frac{\partial Q_D}{\partial P_D}\Delta P_D$$

Multiply both sides by the equilibrium P/Q

$$\frac{\partial Q_S}{\partial P_S}(\frac{P^*}{Q^*})\Delta P_S = \frac{\partial Q_D}{\partial P_D}(\frac{P^*}{Q^*})\Delta P_D$$

which of course is the formula for elasticity at the equilibrium

$$\varepsilon_S \Delta P_S = \varepsilon_D \Delta P_D$$
$$\frac{\varepsilon_S}{\varepsilon_D}\Delta P_S = \Delta P_D$$

So then the producer's share is

$$Incidence_S=\frac{P^*-P_S}{T}=\frac{|\Delta P_S|}{|\Delta P_S|+|\Delta P_D|} = \frac{|\Delta P_S|}{|\Delta P_S|+|\frac{\varepsilon_S}{\varepsilon_D}\Delta P_S|}$$

the price change cancels out and you get producer's share as

$$Incidence_S=\frac{1}{1+|\frac{\varepsilon_S}{\varepsilon_D}|}=\frac{|\varepsilon_D|}{|\varepsilon_D|+\varepsilon_S}$$

So it all comes from the fact that this is the unique formula that produces the price-change ratios that generate identical quantity changes in both sides of the market. Probably not any intuition that can come down to a principles course level but makes a lot more sense than it did before!


How would increase labor productivity lead to improved living standards of people in an economy? I would like to know more about the mechanisms through which higher labor productivity would translate into higher living standards for a population in a given economy.

In economics we measure living standards by the amounts of goods and services people can consume. Increasing labor productivity allows us to produce more goods and services and thus also consume more goods and services, hence it improves the living standards.

For example consider classic Cobb-Douglas production function:

$$ Y = K^{\alpha} (AL)^{1-\alpha}$$

in this production function $A$ can be viewed as a productivity of labor (or technology that makes labor more effective). In the equation above $Y$ is income or output (i.e. amount of goods and services) $K$ capital and $L$ labor supply.

Even if everything stays constant (meaning economy does not have more capital or people dont work more hours and so L is also constant), but the labor productivity increases ($A$ goes up) the output of economy goes up as well. Higher output means that there are more goods and services for people to enjoy and in economics we would count that as an increase in (material) living standards.


Does Average Total Cost (ATC) include implicit opportunity costs? Does the average total cost include opportunity costs? If so, are these opportunity costs considered fixed costs or variable costs? How are they calculated.

Generally, ATC does include implicit costs unless otherwise specified by regular accounting


Could the Troika's economic plan work for Greece? There are a number of things that are confusing me about the current Greek financial crisis.  The first is this.

  Is it plausible that if Greece did everything the Troika asked then
  the Greek economy would revert to high growth and high employment in a
  small number of years?

The short answer is "No", if by "small number" we mean something no more than "five".

The two characteristics you mention are rather different: "high growth" describes a rate of evolution. Now, it is standard corporate speak to say "we are in an excellent position to grow" to express in a diplomatic way the fact that you have hit rock-bottom. Given the unprecedented fall in Greece's GDP, to obtain some positive growth rate it is not that hard, since the base has shrunk so much.

As for "high employment", if by that we mean reverting back to the country's "natural rate of unemployment" (which was $7-8\%$ for decades), to do that in $10$ years, back-of-the-envelope calculations show that one would need $50$ billion euros additional investments yearly for $10$ years in a row to achieve that. This represents a $128\%$ increase in yearly investments from current level, or almost "two times and a half more" than now. Yearly.

From a structural point of view, what is required is a massive increase in Greek exports, or a massive increase in import-substituting economic activities. These things do not happen "in a small number of years".  The first has to deal with international competition, the second requires extended geographical and sectoral relocation of productive resources.

But Greece returning to "high growth-high employment" was not and is not the main concern of the creditors -not unsurprisingly, and perhaps rightfully, since it should be the main concern of the Greeks and their (our) political system.

As to whether the approach taken by the creditors do indeed serve their own interests, is a totally different question, and a very complex to answer -because we would have first to clearly identify "their interests".


Why are different currencies able to purchase different amounts? I am baffled by this for so many years! Kindly, explain this in layman's terms (i.e. to a guy who never studied economics at a university):

  I  can purchase one dozen of eggs for €3.52 in Frankfurt, Germany but for ₹66 in New Delhi, India.

If I am living in India, I am in double trouble:

Why is the price of goods higher in India than that of Germany with reference to people's income level?
An employer is paying me such an amount of money (say,₹10,000 ≈ USD 152.52) which apparently looks larger, but in actuality, I am earning much lesser than that of a German guy (say, €1000 ≈ USD1173.96). Why am I earning less?

So, what factors make this difference?

Let EUR 1 = USD 1.17. Also, let INR 1 = USD 0.015 (these are the actual figures reported by Google on 10/2/2017)

Before we can make any meaningful comparison, we need to express the values of the dozen of eggs in a common currency. For simplicity we choose as that common currency the USD.

A dozen of eggs in Frankfurt cost USD 4.142
A dozen of eggs in Delhi cost USD 0.99

How did we get the USD equivalent prices?

It's straightforward: we multiplied the price of the commodity (dozen of eggs) denominated in some currency (EUR or INR) with the price of that currency denominated in USD.

Therefore, the price of a dozen of eggs is lower in Delhi than it is in Frankfurt, when the common currency in which the prices are quoted is the USD.

Let's turn now to the compensation figures:

wages of INR 10,000 are equal to USD 152.58
wages of EUR 1,000 are equal to USD 1,170

A employee in Germany can afford to buy 282 dozens of eggs while an employee in Delhi can afford to buy 154 dozens of eggs (divide the wage figure in USD by the price of the eggs again denominated in USD).

Therefore, if we are quoting wealth in terms of dozens of eggs that can be bought, then the employee in Germany is 1.8 times wealthier than the corresponding employee living in Delhi.

What are the contributing factors to this unequal distribution of wealth (measured in dozens of eggs-potentially-bought)?

There are three factors in play, namely

the price of the commodities quoted in domestic currency (ie the
price level in eg Germay or India)
the price of the currencies quoted in USD (the common currency we
used as a common measure)

and lastly
the level of the compensation quoted in domestic currency that each employee can command, in different countries


Suitable terminology for the inverse elasticity? In many microeconomic applications (e.g. monopoly price-setting) the inverse elasticity appears. Explaining such relations to laymen is often awkward because inverse proportionality is not as intuititve as direct proportionality.

In physics, there are often separate terms for inverses of important concepts (e.g. electrical resistance and conductance are each other's inverse).

Question: is there a commonly used term for the inverse elasticity? If not, what would be a suitable term that is easily grasped by laymen?

Economists generally call it the "inverse elasticity". But note
$$\frac{1}{\eta}=\left(\frac{\partial Q}{\partial P}\frac{P}{Q}\right)^{-1}=\frac{1}{\left(\frac{\text{% change in quantity}}{\text{% change in price}}\right)}=\frac{\text{% change in price}}{\text{% change in quantity}}$$

Thus, whilst the price elasticity of demand can be interpreted as (roughly)

  The percentage change in quantity sold that would follow a one percentage point increase in the price.

the inverse elasticity (the "demand elasticity of price") could be explained as

  The percentage change in price necessary to achieve a one percentage point increase in quantity.


Conditional Mean and Linearity The conditional mean of $Y$
  given $X$
  is:$$E[Y|X]=\int yf(y|x)dy$$
  What is the relation to the linear model? I have read somewhere that when X
  and $Y$
  are normal (their marginal distributions), then the conditional mean of $Y$
  becomes a linear function of $X$.
  How can I see this?

If X and Y are normal, then the distribution of X conditional on Y is:
$$ X | (Y = y) = N(\mu_x + \rho \frac{\sigma_x}{\sigma_y}(y - \mu_y), (1-\rho)^2 \sigma^2_x )$$

Therefore, $E[X|Y = y] = \mu_x + \rho \frac{\sigma_x}{\sigma_y}(y - \mu_y) = (\mu_x - \mu_y (\rho \frac{\sigma_x}{\sigma_y})) + (\rho \frac{\sigma_x}{\sigma_y})y $ which is linear in $y$.
Symmetrically:
$$E[Y|X = x] = (\mu_y - \mu_x (\rho \frac{\sigma_y}{\sigma_x})) + (\rho \frac{\sigma_y}{\sigma_x})x   $$
which is also linear in $x$


Can higher working hours reduce productivity? Are there studies about the impact on per-hour output (productivity) of increasing the number of hours worked each week by employees? If every employee works 3hrs/week longer (from 41 to 44hrs), does productivity  increase or decrease?

Edit
About who and how much; if every worker works 3hrs more. So there is more time spent on building machines with the same amount of money. But my hypothesis is, that the more time demotivation overcompensates this marginal plus.

The closest study I could find was that by John Pencavel titled 'The Productivity of Working Hours.'

Abstract:

  Observations on munition workers, most of them women, are organized to examine the relationship between their output and their working hours. The relationship is nonlinear: below an hours threshold, output is proportional to hours; above a threshold, output rises at a decreasing rate as hours increase. Implications of these results for the estimation of labor supply functions are taken up. The findings also link up with current research on the effects of long working hours on accidents and injuries.


Log-linearization of the market clearing condition I am dealing with a paper of Walsh & Ravenna.

www.banque-france.fr/fondation/gb/telechar/bourses_recherche/Welfare-based_Ravenna.pdf

I am kind of confused by the euqation (19) on page 33.

The market clearing condition goes as follows:

$$Y_{t} = C_{t} - w^{u}(1 - N_{t}) + \kappa\upsilon_{t}$$

Log linearization around the steady state yields

$$\hat{y}_{t} = \frac{\bar{C}}{\bar{Y}}\hat{c}_{t} - w^{u}\hat{n}_{t} + \left( \frac{\kappa\bar{\upsilon}}{\bar{Y}}\right)(\hat{\Theta}_{t} + \hat{u}_{t} )    \;\;\; \mathbf{(19)} $$

I don't know how this formula (19) is derived?
Isn't there something missing? From my basic understanding of log linearization it ought to look like this:

$$\hat{y}_{t} = \frac{\bar{C}}{\bar{Y}}\hat{c}_{t} - \left( \mathbf{\frac{\bar{N}}{\bar{Y}}} \right) w^{u}\hat{n}_{t} + \left( \frac{\kappa\bar{\upsilon}}{\bar{Y}}\right)(\hat{\Theta}_{t} + \hat{u}_{t} )$$

with
$$ Y_{t}\;\;...\;\; output $$
$$ C_{t}\;\;...\;\;  consumption $$
$$ w^{u}\;\;...\;\;  wage\;of\;unmatched\;workers $$
$$ 1-N_{t}\;\;...\;\;  unmatched\;workers $$
$$ w^{u}(1-N_{t})\;\;...\;\;home\;production$$
$$ \kappa\;\;...\;\;  cost\;of\;posting\;vacancy $$
$$ v_{t}\;\;...\;\;  vacancies $$
$$ \hat{v}_{t} = (\hat{\Theta}_{t} + \hat{u}_{t} ) $$
$$ \omega = \frac{v_{t}}{u_{t}}\;\;...\;\;measure\;of\;labour\;market\;tightness$$
$$ \hat{\cdot}\;\;...\;\;log\;deviation\;from\;steady\;state\;value$$
$$ \bar{\cdot}\;\;...\;\;steady\;state\;value$$

Small letter with a hat: log deviation of a variable arount its steady state.
Big letter with a bar: steady state value.
K: cost of posting a job vancancy.
w^u: "wage" of unemployed workers.

I've read the paper and the appendix aswell, read both the papers in the bibliography of this one aswell as later ones basing on this publication, but I could not find a helpful hint.

Is there any special relationship between N and Y in the steady state that explains why this whole term vanishs? Or do I have a wrong understanding of log-linearization?

I have to apologyze for my rusty English. I am already taking care of this problem. But for the above mentioned I would like to have your help. Does anyone has a decisive hint?

We have:

$$y_t = c_t − w^u(1 − N_t) + \kappa v_t$$

We take the log of both sides:

$$\ln y_t = \ln \left[ c_t − w^u(1 − N_t) + \kappa v_t \right]$$

And then linearize around the steady states:

$$\begin{align}
\ln \bar{y} + \frac{1}{\bar{y}}(y_t - \bar{y}) & = \ln \left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right] + \frac{1}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}(c_t - \bar{c}) \\
& + \frac{w_u}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}(N_t - \bar{N}) \\
& + \frac{\kappa}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}(V_t - \bar{V})
\end{align}
$$

Cancel $\ln \bar{y}$ and $\ln \left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]$

$$\begin{align}
\frac{1}{\bar{y}}(y_t - \bar{y}) & = \frac{1}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}(c_t - \bar{c}) \\
& + \frac{w_u}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}(N_t - \bar{N}) \\
& + \frac{\kappa}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}(V_t - \bar{V})
\end{align}
$$

Multiply the first term on the right hand side by $\frac{\bar{c}}{\bar{c}}$, and similarly for the other terms:

$$\begin{align}
\frac{1}{\bar{y}}(y_t - \bar{y}) & = \frac{\bar{c}}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}\frac{(c_t - \bar{c})}{\bar{c}} \\
& + \frac{w_u \bar{N}}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}\frac{(N_t - \bar{N})}{\bar{N}} \\
& + \frac{\kappa \bar{V}}{\left[ \bar{c} - w^u(1-\bar{N}) + \kappa \bar{V} \right]}\frac{(V_t - \bar{V})}{\bar{V}}
\end{align}
$$

And we simplify, taking advantage of the fact that $\hat{v}_t = \hat{\theta}_t + \hat{u}_t$, to get what you have:

$$\hat{y}_t = \frac{\bar{C}}{\bar{Y}}\hat{c}_t + w^u \frac{\bar{N}}{\bar{Y}} \hat{n}_t + \left( \frac{K\bar{V}}{\bar{Y}} \right) (\hat{\theta}_t + \hat{u}_t) $$

I don't think this derivation is wrong. But you can see that $y_t$ and $N_t$ are directly proportional to each other. It's definitely plausible that $\frac{\bar{N}}{\bar{Y}} = 1$, but I've pored over the equations in the setup for 3 hours to no avail at showing that rigorously. It's probably something silly that I don't understand. I'll look back later and if nothing else, I'll turn this answer into a community wiki so anyone who has the right idea can edit it.


Where to find the face value in a US treasury bond announcement I am learning about the auction and bidding process of US 30 year treasury bonds. I am unable to locate the face (par) value of the bonds in official announcements (PDFs). For reference, here is a link to a recent 30-year bond announcement - PDF announcement, dated Feb 8, 2018

The entry “offering amount” is the total par value that is being auctioned. (In the example given, this is a reopening of an existing issue, so it is the increase of par value for the issue.)

From the perspective of a bidder, the “par value” is what they are awarded, which will only be a portion of the total par value of the issue. (There is a maximum bid size specified, which prevents a single bidder from taking down the entire offering.)