What would cause the velocity of money (V) to increase / accelerate (or at least stop falling) Given that:

MV=PY

Or

P = (M)(V) / Y

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

Considering that the current rate of M2 is increasing at 7% per year over the last 12 months, and real GDP is now forecasted to decelerate from 1.9%/year to maybe as low as .4% by the end of Q4 2019, (according to the Atlanta Fed), am I correct to assume, going forward, that even the slightest sustained increase in (V) would rocket inflation from our current 1.7% per year to something resembling an inflation rate of over 7% in the very near future?

My primary question is this: what event(s) or scenerio(s) can you think of that would cause the velocity of money (V) to start increasing / accelerating again; or at the very least, stop falling like it has over the last 9 years?

Would V be expected to increase as a result of a mass exiting of the stock market (frigtened stock market investors liquidating their retirement holdings into cash and then spending it)?

For instance, the stock market starts falling and worried baby boomers start cashing out their retirement accounts and then start spending it on things like medical care, prescription drugs, on retirement housing, vacations, RVs, ect?

Or maybe baby boomers start dying and their children start taking the inheritance money and spending it all on consumer goods; buying sports cars, electronics, vacations, boats, ect?

[...] what event(s) or scenerio(s) can you think of that would cause the velocity of money (V) to start increasing / accelerating again [...]

That commercial banks stop using injected liquidities to "consolidate" their balance sheet instead of credit-stimulating demands. Extract from one of my previous answer, illustrated on Europe:

What I mean by "consolidate" is that the subprime crisis and its consequences have contaminated the Euro-zone's commercial banks through securitization, interrogating the default risk associated to their assets and liabilities. Injected liquidities have thus often been used by commercial banks to anticipate these potential defaults on the one hand, and to elevate their fractional-reserve ratios on the other hand so as to comply with the Basel III framework.

Indeed, there is a strong relation between fractional reserve banking (FRB) and the velocity of money, see, e.g. this.

Would V be expected to increase as a result of a mass exiting of the stock market (frigtened stock market investors liquidating their retirement holdings into cash and then spending it)?

I do not think so. Simply because I do not see stock market investors redirecting their capital toward commercial banks, i.e. toward FRB-to-velocity engines. That being said, why not (!). It all depends on their psychology.

For instance, the stock market starts falling [...] ?

The mechanism that you are so involving can only very indirectly change the velocity of money. According to me, this is not to be considered as key driver.


Bayesian Mechanism vs Prior-free Mechanism I have a double auction mechanism in which the valuations of the agents for the items are drawn from a known random distribution. To be precise, the valuations are the probability of each agent utilizing the items, i.e. in the range [0,1]. So I guess this is a Bayesian mechanism!

First: Why is it necessary to show that the mechanism is prior free?
Second: How could I prove that?

You may need to provide more information for a clear answer. How does the mechanism look like in detail? What is the goal you want to achieve?

Regarding your first question, it is not "necessary" to show that a mechanism is prior-free but it is a nice-to-have feature. Whether it is of first-order importance, as always, depends on the circumstances.

For example, Myerson's optimal (revenue-maximizing) auction requires that the seller allocates her object to the buyer with the highest "virtual valuation", $v_i - \frac{1-F_i(v_i)}{f_i(v_i)}$. This construction depends on $F_i$ (the cdf of $i$'s value distribution) and its derivative. That is, in order to design the optimal auction, the seller needs a prior about $i$'s value - and if this belief is way off, the designed auction can be far from optimal.

As another example, consider a bidder in a first-price auction. How should this bidder figure out an optimal bid if they have no clue about how the other bidders' valuations are distributed? Do they even know the mean or even the support of this distribution?

If a seller simply wants to allocate her good efficiently, i.e., to the buyer with the highest value, she can set a second-price auction without a reserve price. It is a (weakly) dominant strategy for each bidder to bid the true value and no knowledge about priors is required (for the bidders or the designer).

A participant in your double auction may know the support $[0,1]$, but what is the optimal price to be submitted if they don't know the value distributions? So what goal do you want to achieve with this double auction?

Mechanism designers refer to research weakening assumptions on common priors as following the "Wilson doctrine" (yeah...) because of this quote:

  Game  theory  has  a  great  advantage  in  explicitly  analyzing  the
  consequences  of  trading rules that presumably are really common
  knowledge; it is deficient to the extent it assumes other features to
  be common knowledge, such as one player’s probability assessment about
  another’s preferences or information.

  I foresee the progress of game
  theory as depending on successive reductions in the base of common
  knowledge required to conduct useful analyses of practical problems.
  Only by repeated weakening of common knowledge assumptions will the
  theory approximate reality. Wilson (1987)

Bergemann and Morris have done some nice research on this issue. Maybe you want to read this essay or get a copy of their book.


In which market structures does the producer employ price discrimination? I was recently reading up on the Price Discrimination, first second and third degree. Although the author has laid out the concept neatly, there are no connections established between this concept and the market structures. Therefore, I came up with the above-mentioned question.

In my opinion, the key criteria to exercise price discrimination is that the firms must have some price setting abilities. So Perfect Competition is definitely out. In Monopolistic Competition prices tend to be sticky so I think that this might be one market form where Price Discrimination is not heavily practiced. In a Monopoly, though the situation is quite different as the sole producer can charge as much as he likes and could therefore engage in Price Discrimination. I am not sure as to what would happen in Oligopolisitc Market Forms.

Market power required for price-discrimination?

In my understanding, no. I'm pretty sure that one can show this mathematically, but I'll just give you the intuition. Price-discrimination (PD) increases profits, because it incorporates different price-elasticities by having different prices. Therefore, a firm that incorporates PD should make, c.p. more profits than a firm that does not.

Perfect competition means that less profitable firms are forced out of the market. In this case, perfect competition will lead to firms that act with price-discrimination whenever they can.

Think about restaurants, where there is a lot of price-discrimination going on, either via lunch offers or menu pricing. Restaurants really shouldn't have market power, should they?


Real wages fluctuation as per classical economics I have just started studying Macroeconomics and have noticed that as per the Classical economics, the real wage level will always remain same because any change in price level in the market is subsidized by an equivalent increase in the wage level in the market. However a look at the USA's hourly real wages over years (https://en.wikipedia.org/wiki/Real_wages) shows that the wages are anything but constant.
Can classical economics explain the variation in the real wages or is this one of the shortcomings of the classical economics?

Classical economics is actually not taught at universities anymore (not since 19-20 century at least). You probably have in mind some Neoclassical model. I will presume that since you say you study macroeconomics and not only classical economics is now just part of history of economics, it for the most part did not dealt with macroeconomics.

You don’t mention in which model you observed this, but in general this has nothing to do with whether model is classical or neoclassical. For example, many business cycle models on purpose ‘turn off economic growth’ (which is what in long run drives also increases in real wage), implication of which is that also real wages remain same, and this holds for both Neoclassical or New Keynesian models.

This usually done on purpose so scientists and students can examine how economy behaves, for example during the business cycle, without having to track extra variables/equations and to also make math easier.

Going back to your question there are actually many Neoclassical models of economic growth where real wages increase. For example, in famous Solow-Swan  technological growth leads to increases in productivity and real output per worker and hence consequently also real wages.


Do consumers also invest? Definition of Investment that I have found:

Investment is the expenditure incurred on the procurement of such capital assets that would help in further production .

According to this, it means that investment is only made by producers.

Am I correct in saying that only producers invest? Or do consumers also invest?

It is true that we tend to think of Investment as something firms and businesses do, while consumers practice savings or "invest" in utility-enhancing assets (like a house to live in).

One could argue that when consumers buy shares of a corporation in the stock market they participate in productive investment, even though they do not control the decision-making process.

But exactly because they do not affect the decision-making process it is better to think of such "investments" also as saving, and retain the word investment for the purposeful and decided-upon transformation of resources into productive use.


How can the stock market keep growing indefinitely? It sounds like a dumb question, but there is only so much money in the world. Assets can grow, but money can only be printed. So if there is 400 trillion dollars worth of money in the world, and the stock market beats inflation by about 7% each year, eventually it will be projected to grow to be more than 400 trillion dollars, which should be impossible.

As mentioned in the other answer, the amount of money does not have to correspond to the total value of all assets in the economy. However, there is some correspondence that is not mentioned in the other answer so I will focus on that.
First, there should always be enough money in the economy so people can carry all the transactions they want. If that is not true the money market would not be in equilibrium. This can be formalized using the equation of exchange (see Mankiw, Macroeconomics 7th ed pp 86):
$$MV=P_TT$$
where $M$ is the stock of money, $V$ is the velocity of money (how many times is on average one bill used), $P_T$ are the prices and $T$ is the amount of transactions (which for the purposes of this answer can include asset transactions as well although normally this sort of model would be used only for goods and services).
We can learn several things from this formalization.
First, as the previous answer pointed out amount of money $M$ does not need to be equal to the value of assets, since the equation is $MV=P_TT$ not $M=P_AA$ (where $A$ would be assets). So the velocity of money matters as well. If you buy from me 1 stock of Apple for ${\\\$}100$ I can use the same ${\\\$}100$ dollar bill to buy other assets - so even though there is only single ${\\\$}100$ dollar bill multiple things can be purchased with it if it circulates fast enough. Moreover, because not all assets $(A)$ are always transacted $(T)$ there does not need to be correspondence between value of all assets and money as well.
Second the formula $MV=P_TT$ can be rearranged by decomposing the prices into aggregate price level $P$ and relative prices $P_r$ of the 'things' that are being sold on the market where the following equality would hold $P_TT=P P_r Q$  where $P_r Q$ would be the real value (i.e. inflation adjusted value) of $Q$'s  that are being sold (which we could also be in principle some asset). Lets also denote the real value of things being sold as $T_r$. So now the model would look like:
$$MV = PT_r$$
The equation above also shows us another thing. Even when $M$ and $V$ are fixed the real value of transactions $T_r$ can grow because prices adjust.
Ultimately what matters are real returns not nominal returns. When someone says that stock market returns beat inflation by $7\%$ that means that they real value increased by $7\%$ not that their nominal value is by $7%$ higher. For example, imagine that economy is experiencing deflation (negative inflation of $10\%$ and stock increases in value in real terms by $7\%$ per year. In such such situation if you invest ${\\\$}100$ dollars for one year in nominal terms at the end of next year your stock will be worth only ${\\\$}97$. However, real value of your asset (correcting for inflation or in this case deflation) is ${\\\$}107$ because deflation means everything in economy is getting cheaper and so you can purchase much more with ${\\\$}97$ than with ${\\\$}100$ year before.
The real value of asset  such as stock depends, very broadly speaking, on peoples' valuation of the underlaying companies. Constant improvement in technology and productivity on average leads to companies being more valuable on average over long time periods (of course, technological progress destroys some companies but it also allows other to flourish or completely new industries to rise up and we are talking about whole market here). Consequently, in real terms the only limit for how much stock market can grow are technological & resource constraints avaiable to humanity (with emphasis on the technology).
In addition, it is worth noting there is no limit on how many money there can be in the world. Nowadays most of money is not even printed it is just created at a keystroke virtually. In principle if central banks would be willing to they could always find a way to expand money supply to any size they desire, so in theory $M$ can be any non-negative real number you can think of.
Hence in conclusion, the premise in your question ignores the velocity of money and the fact that not all assets are always transacted so there does not need to be enough money to purchase them all. And secondly even if velocity of money and and money supply is fixed the prices can still adjust in a way that allows for the market to grow in real terms.


What does this $(\gamma _{0.clothes} + \gamma _{1.clothes} * \ kids)$ term mean in my linear demand equation? I have the following demand equation system (expenditure ratio model):

$w_{clothes}= \beta _ {clothes} + \alpha_{clothes} * \ kids + (\gamma _{0.clothes} + \gamma _{1.clothes} * \ kids)* \ income + u_{clothes}$

$w_{food}= \beta _ {food} + \alpha_{food} * \ kids + (\gamma _{0.food} + \gamma _{1.food} * \ kids)* \ income + u_{food}$

...

$w_{other}= \beta _ {other} + \alpha_{other} * \ kids + (\gamma _{0.other} + \gamma _{1.other} * \ kids)* \ income + u_{other}$

where $\beta_i$ and $u_i$ denotes the constants and the residuals, kids is a dummy variable (1, if the consumer has got kids), and $w_{"product"}$ is the proportion of "product" consumption of the total expenditure.

My question is, how can I interpret the term, for example, $(\gamma _{0.clothes} + \gamma _{1.clothes} * \ kids)$? Is this a dummy variable, or interaction or other? It looks like an other regression's coefficients in this equation. I have no idea, please help.

Thank you for your time and help.

If you multiply out any one of the equations,

$$w_{clothes}= \beta _ {clothes} + \alpha_{clothes} \cdot \ kids + (\gamma _{0.clothes} + \gamma _{1.clothes} \cdot \ kids)\cdot\ income + u_{clothes}$$

$$=\beta _ {clothes} + \alpha_{clothes} \cdot \ kids + \gamma _{0.clothes}\cdot  income + \gamma _{1.clothes} \cdot \ kids\cdot\ income + u_{clothes}$$

it is evident that you have "kids" and "income" as regressors, plus an interaction term


Determining cost from production function, wage, and rental rate So I have a production function $Q=2K + 20L^{1/2}$ and I suppose the wage is $w=5$ and the rental rate is $r=9$.  I want to find the long-run cost of production, which I know is constrained by $\frac{MP_{L}}{MP_{K}}=w/r$ and therefore

$$\frac{10L^{-1/2}}{2} = 5/9$$

Which implies $L=81$.  However, I don't see how to find my quantity of capital, $K$.  Any help would be appreciated.

What's tricky is that the problem has a kink. Below a certain production value no capital is used. The demand functions for $k$ and $l$ are as follows:

If $Q \leq 180$
$$L(Q) = (Q/20)^2$$
$$K(Q) = 0$$

If $Q > 180$
$$L(Q) = 81$$
$$K(Q) = (Q - 180) / 2$$

Which you can get from thinking about what happens to the marginal cost of producing with labor just below and above $L=81$ (goes from below 4.5 to above 4.5) and comparing it with the the cost of producing a marginal unit with capital (which is always 4.5).

Why the split at $Q = 180 / L = 81 $?
 $$\frac{MP_{L}}{MP_{K}}=w/r \leftrightarrow  \frac{10L^{-1/2}}{2} = 5/9 \rightarrow L = 81$$
Note that $ Q(k=0,L=81) = 180$


What is the difference betwene a partial default and having debts partially written off? From The Daily Telegraph:

  The new Syriza-led government has demanded some form debt write-off on the country's €317bn liabilities, two-thirds of which are owned to official creditors in the form of the EU and the IMF.

From BBC News:

  New Greek PM Alexis Tsipras says his country will not default on its debts.

A default is, according to Wikipedia:

  In finance, default is failure to meet the legal obligations (or conditions) of a loan, for example when a home buyer fails to make a mortgage payment, or when a corporation or government fails to pay a bond which has reached maturity.

Which leads me to the question:

What is the difference between some form of debt write-off (demanded by the Greek government) and a partial default (denied by the Greek government)?

"Some form of debt write-off" means usually, mutually agreed (between creditor and debtor) elimination of a portion or the whole of debt.

"Partial default": I had the contractual obligation to pay EUR $100$ on Monday, but I paid only EUR $80$. Technically speaking, this is not always (or immediately) considered a "default", but a "credit incident" (alternatively it is characterized as "default on a payment" and not "default on the loan").

Then the reason why I haven't paid the remaining EUR $20$ is crucial: Do I recognize my obligation but I am unable to fulfill it because of financial inability? Or do I deny my obligation, questioning the validity of the underlying contract of the debt from which the obligation to pay the remaining EUR $20$ came?

In the first case, the issue is whether this financial inability is deemed as "temporary" or "permanent". If it is deemed "permanent" (usually by a court decision), then in some countries the debt is officially written off by necessity, while in other countries the creditors retain the right to seek payment whenever the debtor acquires assets in the future (so the creditors may be monitoring you). If it is deemed "temporary", then the issue is to make an attempt to restructure the debt.  For Public Debt, the inability is never officially considered "permanent" so the issue is always to restructure (which of course may include a mutually agreed partial write-off, which essentially means a recognition that there exists a "partial" permanent inability to pay).

We could call the second case, where we question/deny the validity of our obligation, a "unilateral debt write-off", which of course is rarely if ever accepted by the creditors, and so whether it should be called a "write-off" is questionable in turn.


Whats the rationale for using taylor series in economics? I've been reading about the translog production function and know its really just a log-log production function approximated using a first order maclauren series.

Why not just leave the function as is? What economic interpretation or use does taking taylor series do for us?

You will gain in flexibility and generality by adding more terms and avoid to impose restrictions on substitution between inputs and returns to scale, that are usually rejected (when tested).


Why consider non-farm payrolls? Why does the US consider non-farm payrolls when looking at employment levels? What are the reasons for not including farms? Are the workers too transitive, does it not contribute in a certain way to economy which is undesirable to measure? Other countries seem to have similar ways to measure employment levels which suggests farms payrolls are problematic.

Here is a link to a blog post aiming to answer your question.

Also, I am not sure if you mean the NFP is problematic or if general payroll estimations are problematic. I would say the later is, and the blog post highlights some reasons why.


log returns in finance Why are log returns used in finance? For example to calculate a stocks performance. There are a lot of articles on that topic yet I don't find them very helpful. Could somebody please explain step by step? Maybe also with pros and cons.

Thanks in advance.

Why are log returns used in finance?

It really is about compactness when devising models. The mathematical property of logarithms $$log(S_{t+n}/S_t)=log(S_{t+n})-log(S_t)$$ makes log returns more convenient for modeling than the traditional $$\frac{ S_{t+1}-S_t}{S_t}$$ because the former allow the modeler to think in terms of subtraction.

The only "con" for using log returns is that logarithms are more difficult to compute or approximate "by hand" than a subtraction and division. However, with our widespread access to computers, that is not really a drawback for practical purposes.


Papers on Game Theory and the Housing Market Professor George Fallis in his book "Housing Economics" writes:
(Chapter 4 pg. 78)

The (home)owners will establish a pricing strategy depending on how they believe demanders are behaving; and the search strategy of demanders will depend upon the pricing behaviour of the (home)owners. The elegant separation of the demand side and the supply side is no longer possible. The modelling of such a market will be extremely complex, and the idea of equilibrium will have to be rethought.

This being said there is one thing that comes to mind when wanting to model house pricing based on this reality: Game Theory.
My Question:
Is there any (famous or otherwise) papers which discuss the nature of Game Theory in the housing market?
(Papers with computer simulations of the housing market are additionally helpful!)

-Game Theory and Real Options:
Analysis of Land Value and Strategic Decisions
in Real Estate Development- Chun Kit So ( Timothy So )

https://dspace.mit.edu/bitstream/handle/1721.1/84171/867636352-MIT.pdf?sequence=2

-Course blog for INFO 2040/CS 2850/Econ 2040/SOC 2090

Using Game Theory to Understand the Housing Crisis of 2008

https://blogs.cornell.edu/info2040/2017/09/11/using-game-theory-to-understand-the-housing-crisis-of-2008/

-Why housing price in Hong Kong is so high? An explanation in game theory
Ho-Yin Yue1* • King-Tai Leung 2 • Lee-Kei Fung - Economics and Business Letters


Heteroscedasticity and weighted least square estimator "In presence of heteroscedasticity, OLS estimators are unbiased but inefficient"

Showing the unbiased part is relatively easy. Some authors have explained the inefficiency with the help of new variance of the least square estimator.  However, I was asked to show the same thing using the variance of weighted least square estimator ($\hat{\beta^*}$). I proceeded in the following way:-

Consider the model, $Y_t=\alpha+\beta X_t+u_t$   where $u_t$'s are  heteroscedastic.

Suppose ${\sigma _u}^2$ be the constant variance of $u_t$'s under the homoscedastic assumption.

Let $Var(u_t)={\sigma _t}^2$ be the variance of the disturbances under the heteroscedastic assumption.

In Particular, suppose ${\sigma _t}^2=k_t {\sigma _u}^2$, $k_t$'s being some non stochastic constant weights.

Now, consider the above model in deviation form

$y_t=\beta x_t +u_t$, where $y_t=Y_t-E(Y)$, $x_t=X_t-E(X)$

$\Rightarrow \frac{y_t}{k_t}=\beta \frac{x_t}{k_t}+\frac{u_t}{k_t}$

$\Rightarrow \frac{y_t}{k_t}=\beta \frac{x_t}{k_t}+v_t$
where $v_t$ has constant variance ${\sigma _u}^2$

Now, the weighted least square estimator is $\hat{\beta^*}=\frac{\sum \frac{y_t}{k_t}\frac{x_t}{k_t}}{\sum \frac{{x_t}^2}{{k_t}^2}}$

which would eventually give us $Var(\hat{\beta^*})=\frac{{\sigma _u}^2}{\sum \frac{{x_t}^2}{{k_t}^2}}$

Now, under the heteroscedastic assumption, we have $Var(\hat{\beta})=\frac{\sum {x_t}^2{\sigma_t}^2}{(\sum {x_t}^2)^2}$

Now, $$\frac{Var(\hat{\beta^*})}{Var(\hat{\beta})}=\frac{{\sigma _u}^2}{\sum \frac{{x_t}^2}{{k_t}^2}}\times \frac{(\sum {x_t}^2)^2}{\sum {x_t}^2{\sigma_t}^2}$$
$$\Rightarrow \frac{Var(\hat{\beta^*})}{Var(\hat{\beta})}=\frac{{\sigma _u}^2}{\sum \frac{{x_t}^2}{{k_t}^2}}\times \frac{(\sum {x_t}^2)^2}{\sum {x_t}^2{k_t\sigma_u}^2}$$
$$\Rightarrow \frac{Var(\hat{\beta^*})}{Var(\hat{\beta})}=\frac{(\sum {x_t}^2)^2} {\sum \frac{{x_t}^2}{{k_t}^2} \sum {x_t}^2{k_t}}$$

However, before I could proceed further, my instructor asked me to check it again. He was insisting that I should get something like  $\frac{\sum (a_t b_t)^2}{\sum {a_t}^2 {b_t}^2}$, so that I can use Cauchy-Schwartz inequality  resulting in $Var(\hat{\beta^*})<Var(\hat{\beta})$. This would eventually prove the  *inefficiency *  part.

Since I am not getting that form, I think I have made mistakes. I would be happy if somebody can point it.

Let $\hat{\beta}$ be the OLS estimator of $\beta$ in
$$y_t = \beta x_t + u_t$$
Let $\tilde{\beta}$ be the OLS estimator of $\beta$ in
$$\dfrac{y_t}{\sqrt{k_t}} = \beta \dfrac{x_t}{\sqrt{k_t}} + \dfrac{u_t}{\sqrt{k_t}}$$
$\text{Var}(\hat{\beta}) = \dfrac{\sum x_t^2\sigma_t^2}{\left(\sum x_t^2\right)^{2}} $

$\text{Var}(\tilde{\beta}) = \dfrac{\sigma^2_u}{\sum \dfrac{x_t^2}{k_t}} $

So, $\dfrac{\text{Var}(\tilde{\beta})}{\text{Var}(\hat{\beta})} = \dfrac{\left(\sum x_t^2\right)^{2}}{\sum \dfrac{x_t^2}{k_t} \sum {x_t^2}{k_t}} $.

Let $a_t = \dfrac{x_t}{\sqrt{k_t}}$ and $b_t = {x_t}{\sqrt{k_t}}$, and we can rewrite the ratio of variances as

$\dfrac{\text{Var}(\tilde{\beta})}{\text{Var}(\hat{\beta})} = \dfrac{\left(\sum a_tb_t\right)^{2}}{\sum a_t^2 \sum {b_t^2}} \leq 1 $ [By Cauchy-Schwarz inequality]


Real world production-possibility frontier example? I'm reading an economics textbook and trying to make sense of PPF (or PPC) concept. All examples I could find are like producing computers vs food. I can't understand how it can be evaluated and applied to real life situation. Do you know any practical example of PPF?

In the 1940's the RAND corporation put together a series of simulations about war between the USA and the USSR. In the end, they came out with a series of two "good" possibilities, degree of victory and number of crew lives saved.

  The US Air Force asked RAND to apply systems analysis to design a
  first strike on the Soviets. ....  Paxson and RAND were initially
  proud of their optimization model and the computing power that they
  brought to bear on the problem, which crunched the numbers for over
  400,000 configurations of bombs and bombers using hundreds of
  equations. The massive computations for each configuration involved
  simulated games at each enemy encounter, each of which had first been
  modeled in RAND’s new aerial combat research room. They also involved
  numerous variables for fighters, logistics, procurement, land bases,
  and so on. Completed in 1950, the study recommended that the United
  States fill the skies with numerous inexpensive and vulnerable
  propeller planes, many of them decoys carrying no nuclear weapons, to
  overwhelm the Soviet air defenses. Though losses would be high, the
  bombing objectives would be met. While RAND was initially proud of
  this work, pride and a haughty spirit often go before a fall. RAND’s
  patrons in the US Air Force, some of whom were always skeptical of the
  idea that pencil-necked academics could contribute to military
  strategy, were apoplectic. RAND had chosen a strategy that would
  result in high casualties, in part because the objective function had
  given zero weight to the lives of airplane crews.

Retrospectives: The Cold-War Origins of the Value of Statistical Life

  RAND quickly backpedaled on the study, and instead moved to a more
  cautious approach which spelled out a range of choices: for example,
  some choices might cost more in money but be expected to have fewer
  deaths, while other choices might cost less in money but be expected
  to have more deaths. The idea was that the think tank identified the
  range of choices, and the generals would choose among them. But of
  course, financial resources were limited by political considerations,
  and so the choices made by the military would typically need to
  involve some number of deaths that was higher than the theoretical
  minimum--if more money had been available. In that sense, spelling out
  a range of tradeoffs also spelled out the monetary value that would be
  put on lives lost.

The Origins of the Value of a Statistical Life Concept

Maybe that's too much like the two input story of Aerandal. Depends on if you consider the saved lives a "savings" or a "good". For a clearer example of the guns vs. butter tradeoff, consider another example from WW II.

  In February 1942, Fisher Body completely stopped making auto bodies
  and began assembling the famous M-4 "Sherman" tank in its No. 1 plant
  in Flint. The operation eventually moved to Grand Blanc and would turn
  out 11,358 tanks by 1945.

  Buick tackled the manufacture of ammunition, churning out 75,000
  casings per month for the duration. By the war's end, the division had
  supplied more than 12.5 million casings.

  Buick also retooled to meet the demands of making engines for the B-24
  bomber. At first, they talked of about 500 engines a month, but the
  government doubled its order by the time Buick had its tooling in
  place. By 1944, Buick's Melrose Park factory was regularly turning out
  2,000 engines a month....

  In all, more than 113,000 employees left GM to serve while the company
  churned out $12.3 billion in aircraft, tanks, vehicles and arms.

  When it was all counted up after the war, GM had produced 854,000
  trucks (including the legendary DUKW, or "Duck" amphibious vehicles),
  198,000 diesel engines, 206,000 aircraft engines, and 38,000 tanks,
  tank destroyers, and armored vehicles, not to mention vast quantities
  of guns and ammunition.

How GM's Divisions Tackled the War Effort


What are FOCs and SOCs? I keep seeing the terms first-order conditions and second-order conditions used in my undergrad economics class on production functions, monopolies, etc but I have no idea what these terms mean. It seems like a completely ambiguous term. What kind of conditions?

Can someone explain what these terms mean? If it is context dependent, provided some of them most elementary meanings you associate with the term.

Suppose you have a differentiable function $f(x)$, which you want to optimize by choosing $x$. If $f(x)$ is utility or profit, then you want to choose $x$ (i.e. consumption bundle or quantity produced) to make the value of $f$ as large as possible. If $f(x)$ is a cost function, then you want to choose $x$ to make $f$ as small as possible. FOC and SOC are conditions that determine whether a solution maximizes or minimizes a given function.

At the undergrad level, what is usually the case is that you need to choose $x^*$ such that the derivative of $f$ is equal to zero:
$$f'(x^*)=0.$$
This is the FOC. The intuition for this condition is that a function attains its extremum (either maximum or minimum) when its derivative is equal to zero (see picture below). [You should be aware that there are more subtleties involved: look up terms like "interior vs corner solutions", "global vs local maximum/minimum", and "saddle point" to learn more].

However, as the picture illustrates, simply finding $x^*$ where $f'(x^*)=0$ is not enough to conclude that $x^*$ is the solution that maximizes or minimizes the objective function. In both graphs, the function attains a zero slope at $x^*$, but $x^*$ is a maximizer in the left graph, but a minimizer in the right graph.

To check whether $x^*$ is a maximizer or a minimizer, you need the SOC. The SOC for maximizer is
$$f''(x^*)<0$$
and the SOC for minimizer is
$$f''(x^*)> 0.$$
Intuitively, if $x^*$ maximizes $f$, the slope of $f$ around $x^*$ is decreasing. Take the left graph, where $x^*$ is a maximizer. We see that the slope of $f$ is positive on the left of $x^*$ and negative on the right. Thus, around the neighborhood of $x^*$, as $x$ increases, $f'(x)$ decreases. The intuition for the case of minimizer is similar.


Economic Impact of A Student Loan Bubble Popping? A few pundits have been stating that we have a student loan bubble, and this bubble will pop, similar to housing.

I'm struggling to imagine the economic impact of what this would look like if these pundits are right, outside the obvious bailout or student loan forgiveness.  Hypothetically, let's say a scenario where 15% of students are unable to pay back their loans occurs, and the government bails them out (or forgives their loans), how would that be a negative economic event?  Would it create inflation?  Would it cost in terms of productivity, in that students would spend more time borrowing money and staying in school than working and producing?

If, as you say, 15% of student loan borrowers were to default and the government were to forgive their loans, that would simply be a transfer of wealth from the government to those borrowers (on the order of about 15% of \$1.3 trillion, or about \$200 billion). What happened from there would depend first on whether the government funded that transfer by cutting other spending or by issuing debt. Inflation is a basically unrelated issue— the monetary authority (the Federal Reserve) is independent of the fiscal authority (Congress and the Treasury), and as they say, the monetary authority acts last.

Student loan payments are generally not due until some time after a student leaves school, so as a practical matter, forgiveness on defaulted loans would not generally affect whether students remained in school versus being in the workforce, unless you assumed that students started borrowing more with the intent of defaulting (a "moral hazard" scenario). I'll ignore this possibility just to keep things simple and to keep the focus on the fiscal and monetary impact.

In all scenarios, borrowers who received loan forgiveness would be better off, as their wealth would increase by the amount of the forgiven debt. They would, as noted, likely already be working or seeking work. Because they had already stopped paying their debt, we would not assume that they would experience improved cash flows. Work on structuring modifications to defaulted mortgages suggests that households are more sensitive to changes in cash flows than changes in net wealth, so we would only expect these individuals to increase their consumption modestly, but we would in fact expect this side of the ledger to result in increased consumption and economic growth.

However, if the government financed this debt forgiveness by reducing its consumption, it would probably be a net negative to GDP in the short run, as it would remove \$200 billion in government spending, which would not be made up by the slight increase in consumption by borrowers. Government consumption expenditures are currently equal to about \$3.2 trillion annually, which equaled about 18% of GDP in the most recent quarter, so... the direct impact would be a reduction of about 1% of GDP. You can make assumptions about consumption multipliers for government consumption and come up with different results, but this is the direct impact in that scenario.

If the government financed the debt forgiveness by issuing its own debt, it would increase the stock of outstanding US government debt by \$200 billion, or about %1. This would have little impact on debt markets, so there would be no concern about "crowding out" private borrowing, and because it was debt-financed, there would be no reduction of government consumption. As a result, the only real effect on GDP would be the small net positive contribution from increased private consumption.

With respect to inflation, even if the monetary authority bought all the additional debt issuance, it'd only increase the amount of money in the financial system by a negligible amount. For comparison, the Federal Reserve's aggregate increase in holdings of Treasury securities in response to the financial crisis and through its quantitative easing program was close to about \$2 trillion, or ten times the size of this hypothetical debt issuance. Inflation during that period has generally remained below the Fed's 2% target. So currently, the effect on inflation would likely be negligible.


Is it possible to imagine humanity without a modern understanding of money? Of course we can't just take money from current world order and give nothing back.

In theory, can an advanced civilization exist without money at all?
May be this is an utopic idea because of... what? Intraspecific aggression? Our education system? Our history or heritage?
What stops us to do so or to go in that direction?
Is it good or bad in long term?

You need stuff – you take it. You don't need "golden toilet" because of marketing don't try to sell it to you, because "business minds" will be busy to solve problems (or to coordinate other minds to do so), not to make more businesses and make more markets.

The main purpose of this question is to understand what fundamental economics and/or cultural (historical) problems tasks do we need to solve to use more science and less marketing in our lifes.

I have an opinion that we need so much things to buy, sell and choose because of culture, lack of education and a lots of marketing around us.

Marketing needed for business, but not for humanity. We, as a species, spend so much resources of our brains and planet to solve small things (not all of us, of course). And this stops us from doing really BIG things.

The rather famous political economist Marx claims that the wage labour relationship contains within itself the transcendence of that relationship. This is in part as the only socially productive property a worker has consists in the giving away of themselves for a mess of postage.  This suggests a non-engagement with owning socially productive property and instead an emphasis on usufruct. Similarly the commodities of the wage are used (consumed) rather than hoarded.

In Marx’s suggestion that the proletariat can abolish itself, the wage, profit, Capital—in general “the value form”—the abolition of money as we understand it in Marx or contemporary use would necessarily be abolished. Movements of socially useful stuff and services would somehow work on the basis of capacity and need. There might be a mediator, but it wouldn’t have the current functions of money.

Apart from a few very short term instances during revolutionary crises, and generally without ordinary productive activity, there’s no empirical evidence for these relationships; and, there isn’t sufficient material to move beyond large weak concepts like “love,” or “solidarity.”


Difference between "Level" and "Flow" in the Z.1 Fed data The Z.1 Fed data can be found in FRED.

I notices that many similar data sets are labelled "Flow" or "Level". For example,

Financial business; total liabilities, Flow
Federal government; total liabilities, Level
Financial business; total financial assets, Level

And sometimes, the Level version for a Flow series doesn't exist or vice verse.

What is the difference?

Say you have a balance sheet that measures a country's total stock of financial assets and liabilities for a given year. If you have a bunch of these balance sheets for several years, those data points are the actual levels of total assets/liabilities.

Now suppose you decide to subtract the levels that correspond to year $t-1$ from the levels that correspond to year $t$. That's what the Fed is doing with these data series -- the flows are the first-difference of the levels.


Non-uniqueness of iterated elimination of weakly dominated strategies? In the lecture, my professor said "when we eliminate weakly dominated strategies, you might end up with different equilibria depending on
the order of deletion!"

Can anyone give me an example?

Consider the game below.

$$
\begin{array}{|r|c|c|}
\hline
&L&R\\\hline
U&5,1&4,0\\\hline
M&6,0&3,1\\\hline
D&6,4&4,4\\\hline
\end{array}
$$

Both $U$ and $M$ are weakly dominated by $D$.

If we start by deleting $U$. This would lead to the removal of $L$ in the next step. Then $M$ would be deleted. The solution would be $(D, R)$.

However, if we start by removing $M$, then $R$ would be removed next, and then $U$. The solution from deleting in this order is $(D, L)$.


Why are allocation and distribution important consequences of the second welfare theorem? I'm reading Intermediate Microeconomics: A Modern Approach by Hal Varian.
On page 606, he states:

  The Second Theorem of Welfare Economics states that as long as preferences are convex, then every Pareto efficient allocation can be supported as a competitive equilibrium.

He then states on 604,

  The Second Welfare Theorem implies that the problems of distribution and efficiency can be separated...Prices play two roles in the market system system: an allocative role and a distributive role. The allocative role of prices is to indicate relative scarcity; the distributive role is to determine how much of different goods different agents can purchase. The Second Welfare Theorem says that these two roles can be separated: we can redistribute endowments of goods to determine how much wealth agents have, and then use prices to indicate relative scarcity.

My Question:

How does the second remark follow from the first?

The First Welfare Theorem essentially says

  price equilibrium with transfers => Pareto optimal

The FWT hence solves the "problem of efficiency" i.e. If we let the market work through prices, we will achieve Pareto efficiency.

The SWT, on the other hand, states

  Pareto optimal => price quasi-equilibrium with transfers*

It assures us that any Pareto optimal point can be achieved via the market.

Note that distribution and inequality are normative problems which must be addressed through say, the political process, rather than economics. The concept of Pareto efficiency does not tell us anything about distribution. Oftentimes in a 2x2 model, giving Agent 1 all the resources and Agent 2 none of the resources counts as Pareto optimal.

Therefore the SWT addresses the "problem of distribution" by saying that "Ok, society has decided that a certain Pareto optimum is the most desirable outcome. We know that we can achieve this by redistributing endowments/incomes and then letting the market work."

*PQWT is a weaker definition of PEWT


Does my research prove market inefficiency? The long story short, I have developed an index based on a certain distribution. Then I aligned NYSE stocks according to this index i.e. the stocks with the best fit are first and the worst are last. The index is irrelevant with economic theory.

Afterwards, I created a group of portfolios with equal number of stocks and equal observations and then I calculated the minimum variance per portfolio.

The result suggests that the portfolios with better fit have lower variances than the ones with "bad" fit. Does this prove market inefficiency assuming that it didn't occur just by chance?

Edit: According to efficient market hypothesis, asset prices reflect all information given and "patterns" should not occur. However, according to the results, patterns occur and they are independent to the information given.

The efficient market hypothesis does not imply that there are no patterns!

As Eugene Fama pointed out decades ago, any test of market efficiency is a joint test of market efficiency and an asset pricing model. The EMH on its own is not a testable theory.

If I understand your statement properly, you're claiming that forecasting variance would violate market efficiency? For that to be true, you would need to assume an asset pricing model where variance is not forecastable. That's a strange claim. It would imply that risk free government bonds must have the same volatility as small biotech firms (otherwise, I can forecast volatility based upon whether a security is a stock or a bond).

It well known that volatility is forecastable, both in the cross section and in the time series. For example, there is the widely used GARCH model and all kinds of other stochastic volatility models. Forecasting volatility is interesting, but it in no way constitutes a per se violation of market efficiency.

This answer of mine goes into greater depth on what the efficient market hypothesis actually says and how to test it.

References

Fama, Eugene F., 1991, "Efficient Capital Markets: II," Journal of Finance


what are some unique features of heterodox economics? I've been reading up a bit on heterodox economics as well as watched some of the lectures online and quite frankly, I'm having a hard time figuring out whats are the unique features of this school of thought.

Meaning that it seems to me (as of now) one can learn about uncertainty from standard economics textbooks and read up on Marxian economics and seemingly find little to be gained from this approach.Though I could be not very open minded in this regard.

This all being said, what are some of the unique features of heterodox economics that one wouldn't necessarily be exposed otherwise?

Among the references in the paper hinted by indigo_luc, there's one (Mearman, 2011), which [was apparently the first that] has surveyed some (43) self-styled heterodox economists and applied factor analysis as well as cluster analysis to their ideas:

  [The first factor is addressed in the next para.] The second
  factor has high loadings on class, power, labor, gender and (negatively)
  markets. Factor 2 might thus be called a “radical” (or perhaps
  Marxist-feminist) grouping. Factor 3 might be an “Austrian” grouping,
  associating uncertainty, individualism and fallibilism. Factor 4 is
  perhaps a “Post Keynesian” group that stresses money and history.
  Factor 5 suggests an “ecological economics” group that stresses natural
  systems, but also the use of mathematics.

  Factor 1 might be called a mainstream factor. Significantly, this
  factor groups rational, equilibrium and scarcity. This may reflect a bias
  within heterodox economics as to what constitutes the mainstream:
  i.e., if heterodox economists associate scarcity, equilibrium and rationality
  with the mainstream, they may reject them more easily. The
  finding also partly supports Davis’ (2009) definition of the mainstream
  in terms of equilibrium, rationality and individualism. However, the
  adoption of individualism by Austrian economists means that the
  adoption of individualism alone cannot be a definition of the mainstream;
  it also complicates the division between mainstream and
  heterodox. Further, the mean scores for “mainstream concepts,”
  although consistently lower than heterodox concepts, are consistently
  non-zero. Also, although there was a significant negative correlation
  between mainstream and heterodox, the correlation coefficient was
  only |0.438|, meaning that many respondents regard themselves
  mainly as clearly defined heterodox economists—yet with an important
  element of mainstream economics thrown in. Heterodox economists
  are a mixture of concepts and influences. An alternative
  interpretation is that heterodox and mainstream are overlapping categories.
  This would be significant given that treatments of mainstream
  and heterodox often treat them as strictly distinct. The other clear
  finding for this group is that in terms of concepts, heterodox economics
  remains a concatenation of ideas (echoing Lee’s (2010) term) and
  groupings of individuals.

As for cluster analysis:

  Cluster A, the largest, is
  characterized by a rejection of the label “mainstream” and to some
  extent of mainstream concepts (apart from individuals and markets).
  The second feature of cluster A is an acceptance of the label as
  heterodox and pluralist and a matching acceptance of general heterodox
  concepts such as class, uncertainty, fallibilism, power, money and
  history. It could be argued that this cluster exemplifies the recently
  developing picture of heterodoxy as being non-mainstream but pluralist,
  with a concern for methodological issues. Almost all of the
  female respondents to the survey are in this group, although it is far
  from clear why this would occur.

  Cluster B is different, exhibiting
  much stronger rejection of the mainstream and its concepts, maximum
  scores for class and labor and much lower scores than the other
  clusters for uncertainty and fallibilism. Methodologically this group
  scored much higher than cluster A on the need for maths in
  economics. Cluster B seems like a Marxist group and indeed its cluster
  members are self-identified radicals.

  Cluster C is different from clusters A and B in that it does not
  reject the label of being mainstream, whilst accepting the labels of
  heterodox and pluralist. This cluster is similar to cluster A but more
  pluralist. The members of this cluster reject the strict distinctions
  between the three categories. Further, although this cluster accepts
  many of the traditional heterodox concepts such as power, labor
  and class, it also accepts mainstream notions such as rational, equilibrium,
  positive, maths and crucially, scarcity. Above, when factor
  analysis was conducted, a factor was extracted that was labeled
  “mainstream” whereas the view of cluster C suggests instead this use
  of mainstream concepts alongside heterodox ones is another exhibition
  of pluralism. Unfortunately these individuals are difficult to
  identify from the information gleaned so it is difficult to draw too
  many conclusions. It should also be noted that in the dendrogram,
  arguably cluster C might have been split into two, so perhaps not
  too much coherence should be expected.

  Cluster D is in some ways
  the most interesting cluster because it contains most of the cases
  identified as peripheral. The cluster score for mainstream is similar
  to cluster C, but the score for heterodox is lower. Accordingly,
  scores for core heterodox concepts such as class, power, gender
  and particularly labor are clearly lower than for the other clusters.
  As a corollary, cluster D’s scores for individuals, markets and rational
  are much higher than for the other clusters. Looking at the
  cases who are members of this cluster, they appear to be
  members of underrepresented elements of heterodox thought, such
  as behavioral economics, Austrian economics and American
  institutionalism.


Why is railway electrification in North America far less common than in Europe? Why is railway electrification in North America far less common than in Europe?  I suspect that the answer has something to do with the economics of electrification.  In Europe, railway electrification varies a lot between countries, ranging from 3% in Ireland to 95% in Luxembourg (not shown: 100% in Switzerland):

Source: European Commission: Mobility and Transport.
In the USA, less than 1000 km is electrified, or less than 0.5% of the network length.
One might expect the answer to be related to population density, but electrification rate is 76% in Sweden, 55% in Finland, and nearly 50% in Russia, three countries with lower or much lower population densities than the USA.  The US network is primarily freight whereas the European network is dual-use, but many freight-heavy railway lines in Europe (and Asian Russia) are electrified as well.  The Trans-Siberian railway electrification completed in the 21st century.  Why is it, then, that railway electrification is apparently economical in Europe, but not in the USA?

Essentially, the question of electrification is a trade-off: electrified railways are more energy efficient, the engines often supply more power and they are quieter and without local emissions while at the same time requiring a large up-front cost and additional maintenance. The benefits of electric railways are best played out when running many trains on the same line, especially if they have many stops and accelerate often.
On the other hand, while diesel is less energy efficient, has slightly higher running costs and a different complexity of moving parts, there is no additional up-front cost other than laying the rails, acquiring and distributing the fuel is easy and there are no problems with different standards if the network has multiple owners.
Electrification of (sub)urban and underground railways as well as electric tramways date back to the 19th century. At the time, the principal technology was steam; the main reasons for experimenting with electric systems was probably noise complaints and air quality (the latter is of particular concern in tunnels such as the London Underground). The advantages of electric traction over coal-powered steam engines were, however, quickly noticed and attempts to extend the technology of urban railways to main lines were made early. The first electrified full railway in Germany (and possibly the world) was opened in 1905 (it had run on steam for the previous five years due to lack of operating permission and the initially developed system being insufficient) between Murnau and Oberammergau. This line did not touch any major population centres but the landscape is rather hilly so the power advantages of electric traction could be exploited.
By the way, this is a pattern in Europe: most early electrifications were in hilly or mountainous areas, where large amounts of power were needed to climb, a situation that steam engines struggled with. On the other hand, these areas often provide ample opportunites for hydroelectricity which became the primary power source of many railways – especially in Switzerland which wanted to be more independent of coal (and later: oil) imports. In areas where electrification provided less of a benefit because less power was needed, it often progressed far slower or stalled altogether as coal was cheap overall.
After the Second World War, diesel traction started becoming a thing that would eventually displace steam traction on all non-electrified lines typically by the 1970’s. Diesel provided immense benefits over steam (no reliance on water, greater power output, only one person required in the cab all the while at a similarly cheap price as coal) while being able to use the same infrastructure – most notably, it also does not require any power lines to be built or catenary to supply the power to the engine. Now, the trade-off outlined above began to really matter: while coal was more obviously inferior in everything except price of the raw material and ease of construction, diesel could actually challenge electric traction on equal grounds, each having a use case where they are superior.

After all this backdrop, the actual answer follows here.
The mostly freight-only railways in the United States use most of the advantages diesel provides to the fullest. They typically run very long trains with lots of cargo (maximising profit per train while minimising driver cost). They tend to use more of the airspace above (e.g. double-stacking of containers, larger cars) as they have essentially unlimited clearance in most places. They tend to run fewer trains per line and the trains tend to run very long distances. There are many different lines that criss-cross the US (more than one might expect when looking at the Midwest’s population density), typically each belonging to a different company that will run trains along its own line. As the lines are mostly freight-only, the frequency of service doesn’t matter as long as there is sufficient capacity.
If these were electrified, that would mean they could either not use as much vertical space (or would need far taller pantographs). Each company would have to electrify its own lines at a high cost but the return in fuel savings would be far lower as there are not as many trains that can benefit. The power needs to be generated somewhere and distributed to the line; this is a significant problem in the sparsely populated Midwest. Finally, they would likely have to agree on some kind of standard as interoperability across companies exists in the current diesel-based system.
Contrast this with Europe: Most railways are or were nationalised allowing for a single national standard. A nationalised company has an easier time investing large sums for a slow return as electrification would provide. Most lines are primary passenger-oriented; the benefits of electrification for passengers are much higher than for freight (acceleration, noise and pollution are all more important). Thus, freight tends to be handled a little bit as an afterthought and has to follow passenger rail requirements rather than vice-versa. In addition, most freight runs along a smaller number of key trunk routes that are used by all freight companies; meaning that the single investment generates a return at a much faster rate. Finally, due to the more densely populated nature of most of Europe (Germany has almost 20 times the average population density Kansas has; even Lower Saxony still has 10 times the density of Kansas) pollution is more of a concern and electric infrastructure is more widespread.
A similar line of reasoning applies to Russia: the Transsiberian is the one single trunk railway that connects European Russia to Siberia and the Far East. The electrification of this one single line benefits so many trains including probably 50 % of long-distance and freight trains. The benefits are enormous and train density is large. Furthermore, the Transsiberian not only connects the major cities of Asian Russia but also actively developed the areas it was built through, leading to a string of higher population density all through the country which not only means more accessible infrastructure but also a greater ease of electrification.


If Lebanon has a shortage of dollars, are USD donations meaningless? I was reading about the dollar crisis in Yemen the other day, which mentioned that even people who owned dollars couldn’t withdraw them.
If the situation with Lebanon’s currency is similar, what effect does that have on donations of USD to Lebanese organizations that don’t bring in new paper currency?

Lebanon has had significant current account deficit (low level of exports versus imports). This was financed by capital inflows seeking to benefit from facilities given by the CEntral Bank. The Financial Times says:

Lebanon depends on imports and for years the central bank has helped to finance the trade deficit by offering high interest rates — sometimes more than 10 per cent a year — on dollar deposits from commercial lenders. The banks, in turn, passed those generous rates to their clients, helping to attract foreign currency from local depositors and the large Lebanese diaspora abroad.

The problem is that this suddently changed based on local instability. FT:

The system has helped Lebanese banks generate impressive profits. But last summer fragile investor confidence waned, the flow of dollars began to dry up and the system started to break down. Mass protests began in October, stoked by frustration with stark inequality, and eventually toppled the government.

The lack of USD means depreciation (in the black market particularly) of the local currency (which was overvalued).
Sending USD is equivalent to foreign capital inflow. It is one way to finance deficits and can help Lebanon. But it is clearly not a sufficieny nor sustainable solution. The problem is a depressed economy crippled with enormeous corruption (a problem running deep because of the ethnic and religious fault lines dividing society), lack of public investment and low productivity. It requires a deep clean of all the rotten political and elite class, which is on the "save yourselves" mode. Let's hope it doesn't descend into another civil war.


Proof for homogeneity of elasticities Throughout microeconomic literature i see the following restiriction placed on the nature of elasticities in demand system estimation.

This being for some arbitarary good $x$ we require price elasticities and income elasticities to be:

$$\varepsilon(x,p_x)+\varepsilon(x,p_y)+\varepsilon(x,I)=0$$

What is the proof for this? (I cant seem to find it).

Note that the Marshallian demand function $x^*(p_x,p_y,I)$ is homogeneous degree zero in $(p_x,p_y,I)$ (see here for a proof). According to Euler's theorem for homogeneous function, it follows that
\begin{equation}
\frac{\partial x^*}{\partial p_x}p_x+\frac{\partial x^*}{\partial p_y}p_y+\frac{\partial x^*}{\partial I}I=0\cdot x(p_x,p_y,I)=0
\end{equation}
Dividing both sides by $x^*$, you have
\begin{align}
\frac{\partial x^*}{\partial p_x}\frac{p_x}{x^*}+\frac{\partial x^*}{\partial p_y}\frac{p_y}{x^*}+\frac{\partial x^*}{\partial I}\frac{I}{x^*}&=0\\
\epsilon_{xx}+\epsilon_{xy}+\epsilon_{xI}&=0
\end{align}


Exchange rate and domestic money supply It seems an obvious fact (not explained by authors but stated) that when a Central Bank purchases foreign currency (to stabilise its own), the domestic money supply goes up.

It seems to me that the CB in question would use its domestic currency to buy foreign exchange but I don't see how this increases domestic money supply (I assume domestic money supply to be the amount of domestic currency in circulation in the domestic market).

This question can be answered once a few facts are realized.

The Central Bank has a monopoly on the production of currency;
The Central Bank can purchase foreign currency by using currency it has either already produced but stored in its vault or by producing new units of the currency;
The currency that the Central Bank has produced but stored in its vault or not produced yet are not in circulation;
By purchasing foreign currency the Central Bank brings its currency in circulation;
This currency can be brought out of circulation by the Central Bank purchasing this currency with assets such as foreign currency and destroying it afterwards or by anyone else doing exactly the same.

If we therefore define the domestic money supply as the currency in circulation, then purchases by the Central Bank of foreign currency will bring currency in circulation from either its vault or its press.


Why did foreigners keep buying Swiss francs at -41% (not a typo) interest rate in the 1970s? A Bloomberg (opinion) piece notes

  In January 1975, the Swiss government held an emergency meeting and then took the extraordinary step of slapping a 41% annual penalty on foreign deposits. But even this failed to stem the tide. The franc continued to appreciate against the dollar — a total of 70% in nominal terms between 1971 and 1975 alone.

I feel that something is missing in this story... What sane investor would put their money into an account earning -41%, even in the mid-70s?! So what explain this story, if it is actually accurate?

I am not sure if 41% is correct I wanted to double check it but could not find a reference to primary source for 41%, but the overall narrative seems to be true. For example, Reinhart, C. M., & Smith, R. T. (2002), in their paper that you can read here argue that

  Switzerland  in  the  late  1970s  in  which  substantial  capital  inflows  –  partly because  of  German  residents’  desire  to  escape  a  new  withholding  tax  in  Germany  –  prompted  the Swiss  National  Bank  to  impose  a  100%  reserve  requirement  on  non-residents’  bank  deposits  in Switzerland.  The  result  was  a  negative  nominal  interest  rate  on  foreign  deposits  in  Swiss  banks,  as these  banks  demanded  a  fee  to  accept  foreign  deposits.

The above quote already gives you a partial answer (it was German savers), but actually the second part of the original quote of paragraph you gave gives you hint at the rest of the full answer. CHF was appreciating really fast at the time. Standard monetary model for exchange rate tells you that exchange rate depends on fundamentals, output, money supply, price levels, interest rate and also based on future expectations of these.

Now consider western world in the 70s. Half of Europe was under uncertain totalitarian regimes, eastern Europe under iron curtain, Spain was still under Franco, even democratic regimes across the Europe seemed very uncertain. You had a lot of right or left wing radical terrorism across many democratic countries in Europe. Major developed countries like USA or Britain were hit hard with oil shocks. France and west Germany were not doing very good as well. Many countries were experiencing stagflation. Plus in 70s it was popular to have punitively high marginal tax rates and Switzerland always was good tax haven.

In such crazy world there were not that many options to invest your capital in so safe havens like Switzerland experienced unprecedented capital inflow. If you are faced with bad options a rational person picks the least bad option. It is like asking why did you got your arm cut. Well if other options involved you dying then suddenly loosing a limb is not so bad.

Investors expectations of fundamentals in all other countries were probably so bad that simply Switzerland came on the top even if you face negative nominal interest rates. They rightly expected large appreciation of CHF and also expected that their savings will be safe even in near-apocalyptic scenarios - after all if you saved your money in Switzerland during I or II world war you did not lost your money, but if you did so in many other European countries your savings could be often confiscated or wiped out by inflation. It is also the real not nominal interest which drives decision making and I am sure that must have been less negative or even positive. Some irrational exuberance could play role too. Once everyone is saving in Switzerland it sort of becomes self fulfilling prophecy, but in this case Swiss fundamentals seemed to be really strong so this was at the best just part of the story.


Are options a form of insurance? In my economics classes we have studied some really rudimentary concepts about insurance. I'm not really sure what qualifies as insurance to be honest.

I was wondering if options are considered a form of insurance? Is that the right way to think about options?

Perhaps a better way of phrasing the question is, "Is the primary purpose of options to provide insurance against changes in the stock's underlying value?"

No, the primary purpose of options is not to provide insurance against changes in the price of the underlying instrument: options don't have a primary purpose, they don't have an agenda, and they don't have a plan. They're just another tradeable instrument.

Some people buy them as means of insuring a position. Some people write them as a means of insuring a position.

And as Aurigae notes, in a crisis all correlations tend to one; so even if, in theory, your options insure the rest of your position, in reality, in a crisis, the counterparty risk can become very high, so the insurance is least available when it's most needed.


Comparative Statics on Balanced Growth Path It would be a silly question. In a model, I have found the BGP (balanced growth path) for all key variables.

As expected, these variables are constant variables ;

$$\mu^{BGP}=\frac{\alpha+\rho+\pi}{\epsilon\left(1+\pi\right)^{2}}$$

All paramaters on the right hand side are exogeneous constant parameters. Let's say $\mu$ is a variable for technological progress level.

For another variable, let's say capital accumulation $k$,I find a constant growth rate which is ;

$$g_{k}=\frac{\alpha\left(\rho+\pi-\delta\left(\frac{1-\alpha}{\alpha}\right)\right)}{1-\alpha}$$

The parameters on the RHS are again exogenous parameters.

My question is : Is it possible to see the effect of the variable $\mu$ on the growth rate of capital $g_k$ ?

My way of doing seems to me a little bit weird. I firstly put

$$\rho=\mu^{BGP}\epsilon\left(1+\pi\right)^{2}-\alpha-\pi$$

and replace it in $g_k$. So, I have

$$g_{k}=\frac{\alpha\left(\mu^{BGP}\epsilon\left(1+\pi\right)^{2}-\alpha-\delta\left(\frac{1-\alpha}{\alpha}\right)\right)}{1-\alpha}$$

After, I say that technological progress level at BGP affects positevly the growth rate of capital.

Do you think that it is correct to say that ? Making this kind of comparative statics analysis ?

Or any other way to do it in a more appropriate way ?

The approach is not correct, because $\mu^{BGP}$ is a result of underlying structural parameters. So to say "when $\mu^{BGP}$ increases..." immediately begs the question why it increases, which underlying parameter(s) has changed to cause such an increase... assume it was $\epsilon$ that decreased. But in this case $g_k$ is not affected at all, so you see that you cannot claim what you claim about  $\mu^{BGP}$ affecting positively $g_k$.

What is meaningful to do is to perform comparative statics for the exogenous parameters, and record whether $\mu^{BGP}$ and $g_k$ move in the same or the opposite direction (or don't move) in each case. It may not be a causal link, but co-movement is also a useful result, and testable.


Average ability conditioning on having accepted an offer There is a continuum of workers between 0 and 1. These have ability $\alpha\sim U[0,2]$. A firm offers them a salary $v$ and has profits
$$
\pi = (\rho \alpha-v) n(v)
$$
where $n(v)$ is the fraction of workers accepting the job at $v$ and $\rho>0$ is a productivity parameter.
Workers accept the offer if the salary is higher then the outside option $2\alpha^2$. Compute the expected profits of the firm.
I think share of people accepting the offer is (by uniformity of $\alpha$):
$$n(v) = \mathbb{P}[2\alpha^2 \leq v] = \mathbb{P}[\alpha \leq \sqrt{v/2}] = \sqrt{v/2}.$$
Expected profits are conditioned on acceptance and so is expected ability, hence:
$$
\mathbb{E}[\alpha \vert \alpha \leq \sqrt{v/2}] = \int_0^\sqrt{v/2}  \frac{\alpha f(\alpha)}{\mathbb{P}[\alpha \leq \sqrt{v/2}]}d\alpha = \frac{1}{4n(v)}\left[\alpha^2\right]_0^\sqrt{v/2}
$$
by definition of conditional probability.
I would like to double check that I am correct here and that average ability given acceptance is not simply the midpoint between $\sqrt{v/2}$ and 0 (i.e. ability is uniformly distributed between the proposed salary and 0). I think that this is incorrect, since acceptance is not uniformly distributed, conditioning on acceptance skews the distribution of ability observed after acceptance.

If $\alpha \sim U$, then how come there is no expectation in your profit function? The $\alpha$ is unknown and which $\alpha$-types the firm gets depends on salary $v$. This should be reflected in the profit function.
Next, your $n(v)$ seems to assume that $\alpha \sim U[0,1]$, but you set $\alpha \sim U[0,2]$. I assume this is a typo and I edited your question. Otherwise, you need to divide your $n(v)$ by two, because your density is $\frac{1}{2}$ instead of 1. This upperbound cancels out anyway.
For any uniformly distributed $\alpha<\widehat v$, you have
$$\mathbb{E}[\alpha \vert \alpha \leq \widehat v] = \int_0^{\widehat v}  \alpha \frac{1}{\widehat v}d\alpha = \left[\frac{1}{2\widehat v}\alpha^2\right]_0^{\widehat v}= \frac{\widehat v}{2} $$
And in your case, it's ${\widehat v}=\sqrt{v/2} \Rightarrow \mathbb{E}[\alpha \vert \alpha \leq \sqrt{v/2}] = \sqrt{v/8}$. If $\alpha \sim U[0,x]$ then the density is $1/x$, but you also account for $\alpha<\widehat v$ by dividing by $\widehat v/x$ such that $x$ cancels out.
Hence, your expected profit function is
$$\mathbb{E}[\pi(v)] = (\rho \sqrt{v/8}-v)\sqrt{v/2}.$$
Acceptance does not skew the distribution. All types below a cutoff accept, all others reject. Therefore, the distribution conditional on acceptance is uniform up to the cutoff.
If you replace your $n(v)$ by $n(v)/2$, taking account for the upperbound 2, you would get the same.


Preorder and multi-utility function Let $\succeq$ be a preorder, i.e., it is reflexive and transitive on $X$. Prove that there exists an index set $N$ and a multi-utility function $u:X \rightarrow \mathbb{R}^N$ such that $x \succeq y$ if and only if $[u(x)](n) > [u(y)](n)$ for all $n \in N$.

I know, for example, the relation $x \succeq y$ on $\mathbb{R}^2$ if $x_1 \ge y_1$ and $x_2 \ge y_2$ can be represented with $N= \{1,2\}$ and the multi-utility function defined by $u(x) = (x_1, x_2)$. But, I am unsure of how to do the general proof.

This seems like an interesting question but I am not sure I understand all the details here, so this is more a comment than an answer.
Because the preference relation is incomplete, we cannot have a real-valued utility function representing it (recall that indifference is different from indecisiveness because the latter is not transitive).

Moreover, I do not think that you can have an arbitrary set $X$ together with an arbitrary $\succeq$ being represented by a finite-dimensional $u$. To give a simple example, suppose that $X=[1,p_n]$ with $p_n$ being the $n-th$ prime and your preferences are $x\succeq y$ if $x\geq y$ and $x,y\in(p_k,p_{k+1}]$ for some $k<n$. There are $n$ subsets of alternatives, each with a well-defined preference order but alternatives are no comparable across subsets so that you need at least $f(n)$ (not sure about the exact $f$) dimensions in your vector-valued utility function. When $X=[1,\infty)$, the number of dimensions explodes.

An important example is the case of social choice. Suppose that you have $k$ individuals with preferences over $X$ and you want to aggregate them. The Pareto order then gives you $u(x)=(u_i(x))$ for all $i$ the (ordinal) utility of individual $i$ from alternative $x$. Indeed, if $u_i(x)>u_i(y)$ for all $i$, then $u(x)>u(y)$.

Finally, if $X$ was finite, then simply order the elements in some way $x^1,x^2,..,x^k$ and construct $u\in \mathbb R^k$ as follows:
$u_l(x^l)=1$, $u_l(x^k)=1$ iff $x^l\succeq x^k$ and $u_l(x^k)=0$ otherwise.

To see that this represents the preferences, notice that if $x^l\succeq x^{l'}$, $u_l(x^l)=1>u_l(x^{l'})$, $u_{l'}(x^l)=u_{l'}(x^{l'})$; if $x^m\succeq x^l$ it must be that $x^m \succeq x^{l'}$ so that $u_m(x^l)=u_m(x^{l'})$ and viceversa but if $x^l\succeq x^m\succeq x^{l'}$, then $u_m(x^l)>u_m(x^{l'})$; and if $x^m$ is not comparable with $x^l$ it cannot be worse than $x^{l'}$ so that $u_m(x^l)=u_m(x^{l'})=0$, while if it is not comparable with $x^{l'}$ it cannot be better than $x^l$.


Co-integration and Error correction This is a homework question:

$y_t = \alpha y_{t-1} + \beta_0 x_t + \beta_1 x_{t-1} + \epsilon_t , 0<\alpha<1, (t=1,...,T)$
where $x_t$ is an I(1) process independent from $\epsilon_t$ for all $s$ and $t$, and $\epsilon_t , t=1,...,T $ are i.i.d with mean zero and variance $\sigma^2$

Question

1) Suppose that $\beta_0 \not= -\beta_1$. Is it possible that $y_t$ is stationary?

2) Write down the error correction form of the model, showing the relationship between the new parameters and those in the original model.
Argue that $y_t$ and $x_t$ are co-integrated and write down the co-integrating vector

Any help/pointers would be great.

For question 1), take the expectation of both sides, assume that the expectation of Y is the same in both periods (the definition of stationarity) and see what conditions the coefficients on X must satisfy.

For question 2), try rearranging the equation to be in terms of X and see what determines its variation.

P.S. I am still getting the hang of the mathematical notation on here, but I figure too much working out would be giving it away anyway


Free market defense against anti-competitive behavior? One argument against a completely free market economy without "government" oversight is the tendency towards anti-competitive behavior. The argument is that government laws are needed to prevent anti-competitive behavior which could be used to create and solidify monopolies.

A typical example of this is the behavior of liquor distributors in the United States. In the United States it is (or was?) a common practice of liquor distributors to coerce retailers into selling only the brands of liquor that the distributor offered. Distributors carrying the major brands would inspect liquor stores and if they found the store selling any small company's liquor, they would threaten them: "Either stop selling this company's liquor, or else our deal is over and we won't supply you anymore." This is deadly threat, since liquor stores need big brands to stay in business. Because of this, it has been traditionally been difficult for small liquor distillers to survive without a deal with a major distributor.

The same kind of argument was floated at the turn of the century (1900). Oil companies would threaten pipelines: don't carry this small oil company's oil or we will drop you. This type threat caused small oil companies to get frozen out of pipeline distribution networks until legislation basically forced pipelines to carry all oil equally and made it illegal to prefer one company's oil to another.

Is it possible in a totally free market economy to combat anti-competitive behavior or is government regulation the only way to stop it?

Depends on what you mean by 'possible'. The liquor stores in your example could form a union, and collectively bargain with brands. Then if a brand breaks a contract with one of them, they all break the contract. This would greatly disincentivize the brands' strong arm practice.

In my opinion this is unlikely to work (it is very hard to organize), but it is 'possible'.


Are Cobb-Douglas preferences homothetic? Our lecture defined a preference to be homothetic, if the following is true:

$$(x_1, x_2)  \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$

Cobb-Douglas preferences can be displayed as some utility function of the following form:

$$u(x_1, x_2) = x_1^a \cdot x_2^b$$
Therefore:
$$(x_1, x_2)  \thicksim (y_1, y_2) \\
\Leftrightarrow x_1^a \cdot x_2^b = y_1^a \cdot y_2^b \\
\Leftrightarrow k^ax_1^a \cdot k^bx_2^b = k^ay_1^a \cdot k^by_2^b \\
 \Leftrightarrow (kx_1, kx_2)  \thicksim (ky_1, ky_2)$$

With this argumentation the Cobb-Douglas preferences should be homothetic.

The wikipedia article about Homothetic preferences however defined a preference to be homothetic, if they can be represented by a utility function  and the following is true:

$$ u(kx_1, kx_2) = k \cdot u(x_1, x_2)$$
And I am pretty sure, that this is not true for Cobb Douglas preferences:

$$ u(kx_1, kx_2) = (kx_1)^a (kx_2)^b = k^{a+b} x_1^a x_2^b \neq k \cdot u(x_1, x_2)$$

So what am I missing here? Are the definitions not equivalent? Did I calculate something wrong?

Note that the wikipedia article  is very specific:

  [...] defined a preference to be homothetic, if they CAN be represented by A utility function [...]

You chose a specific utility function to represent your Cobb-Douglas preferences. However there are infinitely many others. All monotonic transformations of your utility function represent the same preference. Take
$$
\hat{u}(x_1,x_2) = \left(u(x_1,x_2)\right)^{\frac{1}{a+b}} = x_1^{\frac{a}{a+b}} \cdot x_2^{\frac{b}{a+b}}.
$$
As $\hat{u}$ is a monotonic transformation of $u$, it represents the same preference. It is straightforward to check that $\hat{u}$ fullfils the condition set forth in the wiki article. So there is indeed such a utility function, that also represents the preference, hence the preference is homothetic.


When a country collects data for calculating the Gini index, do they usually neglect single household? OECD data for South Korea is based on the numbers provided by Statistics Korea, which does not count single household family income data in their statistics. I am just curious that neglecting single household is a general or traditional statistical method for getting sound Gini index so other countries use same way Or, it just happens in South Korea. Recently, The number of single households are growing fast, and usually their incomes are lower, so neglecting single household data leads lower Gini index, which means lower inequality. Do the other countries use the similar criterion for gathering data for Gini index? If the countries use different criterion , where could I find that?

I am not sure this is currently correct as http://www.oecd.org/els/soc/OECDIncomeDistributionDataReview-Korea.pdf says:

  Income distribution and poverty indicators for Korea are also available from:

  The  same  combination  of  Household  Income  &  Expenditure  survey  combined  with  Farm household economy survey from previous years, using different coverage of population

  Since 2006: all households (same series as OECD reference series)

  Since 2003: only for 2 and more non-farm household

  Since 1990: only for urban salary and wage worker, 2 and more household

which I intepret as saying that all households have been counted since 2006, while only households with 2+ people were counted from 1990 to 2005


Why doesn't the supply curve shift to the left in the following situation? Why do producers respond to the surplus by cutting their prices? I am reading "Principles of Economics" by N. Gregory Mankiw.
Why doesn't the supply curve shift to the left in the following situation?
Why do producers respond to the surplus by cutting their prices?

Suppose first that the market price is above the equilibrium price, as in panel
(a) of Figure 9. At a price of $5 per cone, the quantity of the good supplied (10 cones)
exceeds the quantity demanded (4 cones). There is a surplus of the good: Producers
are unable to sell all they want at the going price. A surplus is sometimes called a
situation of excess supply. When there is a surplus in the ice-cream market, sellers
of ice cream find their freezers increasingly full of ice cream they would like to sell
but cannot. They respond to the surplus by cutting their prices. Falling prices, in
turn, increase the quantity demanded and decrease the quantity supplied. These
changes represent movements along the supply and demand curves, not shifts in
the curves. Prices continue to fall until the market reaches the equilibrium.

Why doesn't the supply curve shift to the left in the following situation?

Because in order for a demand curve to shift demand has to change at any price. For example, let us suppose that the demand function is given by:
$$D_1 = 100 -P$$
If a firm changes price it chargers it does change quantity demanded  $D_1$ but does not shift the whole demand function $D = 100 -P$. If quantity demanded changes just because price varies, we call this movement along demand curve.
However, suppose now that there is some change in preferences of people so that demand function $D_1$ shifts and we will have new demand function $D_2$:
$$D_2 = 50 -P$$
Can you see the difference? Now at any price demand will be smaller compared to $D_1$. If price is $5$ the demand in $D_1$ will be $95$ but in $D_2$ only $45$, if price is $10$ then $D_1 = 90$ and $D_2 = 40$ and so on.  This is what we would call shift in demand (in fact if you would plot $D_2$ an $D_1$ you would see that $D_2$ is just $D_1$ shifted to the left.

Why do producers respond to the surplus by cutting their prices?

Because, within the bounds of a simple supply-demand model,  if there is a surplus of goods producers have two options:
A) throw the goods away and get nothing.
B) sell them at lower price.
selling them at lower price if you can is more rational then just throwing the goods away (at least it would be in a simple models, there might be some complex strategic interactions where it might be other way around, but you won't encounter such more nuanced and complex models in econ 101 textbook).


How is it possible that shipping of eBay items from China to US is 'free'? How is it possible that Chinese vendors are able to ship a small / light $3 part to a doorstep in the US for free?  When shipping items the opposite way via USPS it is often greater than the cost of the part making it cost infeasible to return.   Is shipping somehow subsidized?

The major reasons that I understand are that:

the Chinese government subsidizes shipping.
the US Postal Service, eBay China, and Hong Kong Post office have a trilateral agreement called the ePacket service which roughly speaking, allows shipping of small packages to the US at bulk pricing (instead of at the price for individual sales).

I don't think it's common for there to be "free" shipping though.

I'm retracting the part about China subsidizing exporters.


Is there unnecessary duplication for borrowing in this circular flow of income diagram? Here is a circular flow of income that I took from Krugman's macroenomics textbook.

We can see that when firms want to borrow they can go to the financial sector and borrow savings of national and foreign households. BUT, it seems like there is also another way for firms to borrow money: the factor market. Capital is a factor of production. And there are different kinds of capital, in our case we're interested in financial capital, specifically in financial capital that is basically a pile of money. And how can we, sort of, buy such financial capital? By borrowing it! So firms "buy" financial capital from households and then pay them interest (you can see that interest is paid to households from the diagram).

I don't get the purpose of this duplication. Why use financial sector for borrowing when we have the factor market? Or why use the factor market for borrowing when we have the financial sector? Is there some kind of important difference between them that makes both of them necessary in borrowing? Or did I make a mistake in my reasonings and firms can't get borrow money from the factor market? If yes, then why do households get paid interest from the factor market?

No because the financial markets do not provide firms with capital they provide them with funds to buy capital which is a difference. You can call those funds financial capital but it’s not capital in economic sense.

In common usage in English capital is often used as a synonym for money. For example in Oxford dictionary under the word capital the second entry is simply money (see here).

However, in economics capital, especially when we are talking about factor markets, is used in the following definition:

“The equipment and structures used to produce goods and services.”

The above definition is taken from Mankiw and Taylor (2014), Economics the 3rd edition. In different textbooks the exact wording may change but to my best knowledge no conventional textbook would include money as it’s definition.

Also generally money is not considered a factor of production in itself hence it’s a tautology that factor markets should provide only factors of production.

Moreover, generally financial markets are often considered quite distinct from other economic activity. In fact often you can hear economists speak of ‘real’ economy and financial markets separately. This is due to the classical dichotomy which makes sharp distinctions between real and monetary (nominal) variables. Factor markets are considered to be part of real economy, where real goods, services, and factors circulate, while financial markets are part of monetary sector which covers the circulation of money and other financial goods and services.

In comment @user161005 asks additional question of why the arrow going to factor markets includes interest, since answer to this might be of interest (no pun intended) to other users who skip comments I put the answer also here:

In economics the income derived from labor is called wages, the income from land rent, and income derived from capital interest.

The last often confuses students because many textbook models call the interest earn from capital $r$ instead of $i$ but this is because $i$ is already used widely in other macroeconomic models.

The profit is what is left after the wages are paid to the labor, rent to landowners and interest to capital owners. Profit is considered to be the reward for entrepreneurship which can be considered as another factor of production.

A good entry level explanation of this is provided in this FED St. Louis podcast that you can listen to (or read transcript to) here.


How to calculate the ideal maintaining time of a machine? I have a question regarding a cost calculation problem:
I have the following curve, which shows, that with increasing number of tasks without maintaining a machine, the error probability for the produced parts increases.

The x-Axis represents the counter of tasks without maintaining the machine. This means the point (10;0.2) says: When the machine wasn’t maintained the last 10 cycles, the error rate is 20%.
Maintaining the machine costs, let’s say 1000 € and one error 15 €. Now I need to find out the perfect maintaining counter, when to maintain the machine.
I thought about multiplying the curve with 15€ and then integrating the function, to take into account the already increased probability of the previous cycles at a specific count. However, I am not sure about this integration step.
Maybe anyone else has any idea how to handle this problem.

Suppose the probability of an error in the $n$th cycle since the most recent maintenance is
$a+bn$, and let the number of tasks (cycles) between maintenance be $x$. I'm assuming here that the tasks can be treated as discrete.
The way I would approach the optimization is to calculate both the total maintenance cost and the expected total error cost over some fairly large number of cycles - say 1,000.  What number is chosen here is arbitrary, but I find it more intuitive to think of total costs in that context than averages per cycle, although each should lead to the same result.
Total maintenance costs are:
$$\frac{1000}{x}\times 1000=\frac{1000000}{x}$$
Expected error costs between two successive maintenance events, using the triangle number formula to sum the $b$'s, are:
$$\sum_{n=1}^x 15(a+bn)=15\Big(ax+b\Big(\frac{x(x+1)}{2}\Big)\Big)$$
Hence total expected error costs are:
$$\frac{1000}{x}\times 15\Big(ax+b\Big(\frac{x(x+1)}{2}\Big)\Big)=15000\Big(a+\Big(b\frac{x+1}{2}\Big)\Big)$$
Total costs $TC$ (including both maintenance and expected error costs) are therefore:
$$TC = \frac{1000000}{x} + 15000\Big(a+\Big(b\frac{x+1}{2}\Big)\Big)$$
Setting the first derivative equal to zero to find the minimum:
$$\frac{dTC}{dx}=\frac{-1000000}{x^2}+15000\Big(\frac{b}{2}\Big)=0$$
$$-2000000+15000bx^2=0$$
$$-400+3bx^2=0$$
$$x=\sqrt{\frac{400}{3b}}$$
To confirm this is a minimum:
$$\frac{d^2TC}{dx^2}=\frac{2000000}{x^3}>0$$
Putting (as approximately suggested by the chart) $a=0.18, b=0.001$, this yields:
$$x=\sqrt{\frac{400}{0.003}}\approx365$$
Note that in this case $a+bx=0.18+(0.001\times365)=0.545 < 1$.  The formula would need modifying should the values imply a probability of error exceeding 1 before reaching the next maintenance event.
Addendum 3/11/2020
In response to your comment re integration, if the tasks are taken to be discrete then integration does not give an exactly correct formula for the total expected error costs.  The integral needed is:
$$\int_0^x 15(a+bn)dn=15\Big(ax+\frac{bx^2}{2}\Big)$$
This has $x^2$ where the calculation above has $x(x+1)$.  However, this difference vanishes on differentiating TC since:
$$\frac{d(bx)}{dx}=\frac{d(b(x+1))}{dx}=b$$
Thus this approach leads to the same optimum value for $x$.