Why do celebrities get high wages? In the youtube video Why We Look down on Low Wage Earners the author argued: "economics states that wages are determined [...] by the number of people willing and being able to do a given job that others won't do." (video at 1:00). While this explains much of the variance in the wages of different jobs, it does not give in my opinion a good explanation, why celebrities earn high wages.

Take for example actors. There are a lot of people working in this field and there are many more wanting to become an actor or actress. Due to the quoted theory the wages in this field should be low which is not the case for celebrities. The theory does also not explain the variance of the wages inside this field (compare the median hourly earning of actors / actresses with those of celebrities).

My question: How do economics explains the outliers in the wages in form of the high earnings of celebrities? How does popularity exert an influence here? (Do celebrities get much money because they are popular or are they popular because they are rich?) How does economics explains the different wages for a certain kind of job?

If you ask yourself how much a potential employer would have to pay you to convince you to work for him, the answer is probably something like "at least as much as I could earn by doing the same job for another employer". So, provided there are several employers competing to hire workers, you can think of employers as bidding against each other for the best employees. But how much will firms bid? Each employer would be willing to pay up to the difference between its profit if it hired this particular worker and its profit if it took the next best alternative.

This is why the supply of alternative employees matters. If there are many people capable of doing the same job then a firm's profit if it hires you will be almost the same as the profit if it hire someone else. So why should it 'bid' a lot to hire you? An unskilled factory worker who asks his employer for a significant pay rise will likely be refused because virtually any worker doing the same job would have equivalent productivity.

Celebrities are a different story. Just as factory workers are hired to produce goods for the factory owner, actors are hired to produce movie ticket sales for the studio. But viewed in this light, Tom Hanks or Angelina Jolie are not close substitutes for as yet unknown actors at all. Indeed well-known actors are considerably better at producing ticket sales than unknown talent. Studios are willing to bid a lot to attract top actors because having a star in your cast is worth millions of dollars in extra ticket sales.


Balanced budget and change in taxes Consider a simple Keynesian economy in which the government expenditure ($G$) exactly equals its total tax revenue: $G = tY$ where $t$ is the tax rate and $Y$ is the national income. Suppose that the
government raises $t$. Then what happens to $Y$?.

My working: With the balanced budget multiplier in effect $Y$ becomes equal to $\frac I {(1- c) (1 - t)}$

However without the balanced budget in effect ( when taxes are increased over government expenditure), $Y$ becomes equal to $\frac {I + G} {1 - c(1-t)}$
Is the working right ?. How should I proceed in order to come to a solution ?.

Here's my take, which could be wrong.  We assume a closed economy, so net exports, imports and exports themselves are all zero.

We have Y = C + I + G
Suppose we have the simple consumption function C= k +c*(Y-T).  We are only allowed to consume out of disposable income or have autonomous consumption.

Then Y = k+c*(Y-T) + I + G
This goes to

Y*(1-c) = k - c*T + I + G

You take T = t*Y.  So this is

Y*(1-c) = k - ctY + I + G

Subtract ctY from both sides.  Then we have

Y*(1-c*(1-t)) = k + I + G

The solution in the absence of the balanced budget would be

Y = [k + I + G]/(1 - c*(1-t))

Now have G = t*Y - the balanced budget

Y*(1 - c*(1-t)) = k + I + t*Y  or

Y*((1-t) - c*(1-t)) = k+ I or

Y*((1-t)*(1-c)) = k + I

or

Y = [k + I]/((1-t)*(1-c))

So my take is that the multiplier is right, in both cases, but that there is or will have to be some autonomous consumption expenditure in the economy, and that's what's left out.  You can say, "I don't need autonomous expenditure!"  But just try coming up with a Keynesian cross to settle output in nominal terms without one!


Does the Federal Reserve have bank accounts for banks? Banks are constantly transferring electronic dollars to each other. There must be an entity that tracks how many digital dollars each bank has.

Does the Federal Reserve have "accounts" for banks? In general, do national banks have accounts for banks that use their currency?

The exact details of payment systems vary from country-to-country. The payments systems handle the multitude of transactions.

But if we are willing to simplify away the complexity of payment processing, private banks do have an account at the central bank, and transfers between banks are effectively transfers between those accounts. The central bank is a bank, and this is exactly how banks will handle transfers between its own customers.

These balances are generically referred to as settlement balances, but in a country with reserve requirements (like the United States), these will be refered to as bank reserves. It is fairly easy to find discussions of bank reserve operations on the internet.


Why should marginal cost be equal to the price an item is sold at? My interpretation of the condition $P=MC$ is that a firm's cost of producing one additional good should be equal to the firm's price. This means that the next item a the firm produces won't yield any profit to the firm.
What's the point of producing this additional unit? Do you have a hands-on explanation?

You should keep in mind that the definition of profit in economics is not the same as in accounting. In particular, economists always deduct opportunity cost from accounting profits, and the price = MC formula has to be interpreted in this way.

For example, let's say you are a self-employed web-developer and you may make a profit in an accounting sense. Economists will subtract from this accounting profit the opportunity cost of not working elsewhere. Looking at it this way, the profit of a self-employed web-developer is just a wage he pays to himself.

The same is true for larger firms. Those firms usually pay out accounting profits to their shareholders. Economists would interpret this as the cost of using the equity capital provided by owners.


Do German Goverment bonds usually include (or included) a condition that the debt will not be serviced in case of trade imbalance? Today the Spiegel ran an article on a proposal to end the Euro Debt Crisis.
That article made the claim given in the title

Syriza will eine sogenannte Wachstumsklausel für jene Schulden einführen, die nach dem Schuldenschnitt übrigbleiben. Im Falle Deutschlands handelte es sich damals um eine "Außenhandels-Einnahmen-Klausel", der zufolge der jährliche Schuldendienst drei Prozent der Exporteinnahmen nicht übersteigen durfte. Für die Gläubiger Deutschlands hieß es also: Kauft deutsche Produkte, wenn ihr euer Geld zurückwollt.
Syriza wants to establish a so called growth-clause for the debt left after the haircut. In the case of Germany there was the "Außenhandels-Einnahmen-Klausel" (Foreign-trade profit condition) which states that the amount of serviced debt is not allowed to be higher than 103% of export profit.
For the debtee that meant: If you want your money back you have to buy German products.

As the article mentions the London Debt Agreement of 1953 I assume that the statments given in the past tense refer to that agreement. However the term Außenhandels-Einnahmen-Klausel does not appear in those documents and on a cursory overview actually doesn't seem to include those conditions.
The only google hits for that exact term are that very article.
And the proposal also doesn't mentions foreign trade or export.
So, has this clause existed or even still exists today?

The answer is somewhat. Those terms were not part of the original bond but were added by the Debt Agreement

  The Conference recognised the principle that the transfer of payments under the Settlement Plan implies the development and maintenance of a balance of payments
  situation in which those payments, like other payments for current transactions, can be financed by foreign exchange receipts from visible and invisible transactions so
  that more than a temporary drawing on monetary reserves is avoided. (Final Report of the Conference on German External Debt 1952: paragraph 21)

That quote is NOT part of the official agreement (As seen by it's absence in the British  and the Swiss copy) - however the "One made it out of the debt trap" study claims it was accepted by the British and the French.


Why are vacancy rate and unemployment rate negatively correlated? Why is this the case?

Since Vacancy rate is defined as following,

let $A,Q,U$ denote number of vacancies in the economy, labor force, unemployed respectively.

$$\frac{A}{A+Q-U}$$

Here we can see that if unemployed increase vacancy rate would go up?

Why is there a negatively correlation then? Take the beveridge curve as an example :

https://en.wikipedia.org/wiki/Beveridge_curve

Adopting your notation, the vacancy rate at any given time is defined as $A/Q$. There is no mechanical relationship between the unemployment rate $U/Q$ and vacancy rate (A/Q).

They are negatively related because when vacancy rate is high, it means there are many unfilled job openings, and they are unfilled probably because most people already have a job, thus lower unemployment rate. And vice versa.


Rosen's unique equilibrium conditions: Multi dimensional strategies? I was wondering if the uniqueness of equilibrium conditions in n-person games as published in Rosen's 1965 paper (J. B. Rosen. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 1965) are for single-dimensional strategy spaces only? It says in the paper that the strategy of each player can be a vector, but the rest of the conditions seem to be derived for one-dimensional strategy spaces. Can the results be generalized to multi-dimensional spaces as well? Thank you.

These results can indeed be extended to a more general setting. In this case, define the $\nu$-th player's strategy vector $x^\nu \in R^{n_\nu}$ and so $x=(x^1,\dots,x^N)^T$ of a size $n_1+\dots+n_N$ for a $N$ player game.

In this context, $\nabla_\nu \varphi_\nu(x)$ is a vector of size $n_\nu$.

The pseudo-gradient (denoted $g(x,r)$ in the paper) is still the vector concatenated by all the gradients of $\varphi$ i.e. $g(x,r)=(\nabla_1 \varphi_1(x),\dots,\nabla_N \varphi_N(x))^T$. In this general case, the positivity constraint in the definition of diagonally strictly concave means that each component of a vector is positive.

Now, the reasoning of Rosen can be followed in the exact same way with the notations above.


Why does the same parameter estimate change in multiple regressions? I have a set of results from a multiple regression table with four columns. In each column, a new variable is added. Why, however, is the initial variable coefficient different in each column? Is it due to the coefficients being jointly estimated?

Yes, it is because they are estimated jointly and the point estimates are conditional on other point estimates and also because of omitted variable bias. To be more specific, contrast an example of  univariate OLS with bivariate OLS, both of which are estimated by minimizing the sum of squared residuals, but resulting formulas for estimated coefficients are different.
In univariate OLS by minimizing squared residuals we get
$$\min_{b_0,b_1}\sum e^2 = \sum (y_i-b_0-b_1x_{1i})^2 \implies \hat{b_1} = \frac{\sum (x_{1i}-\bar{x_1})(y_i-\bar{y})}{\sum (x_{1i}-\bar{x_1})^2}$$
In a bivariate regression the result will be different
$$\min_{b_0,b_1, b_2}\sum e^2 = \sum (y_i-b_0-b_1x_{1i}-b_2x_{2i})^2 \implies \hat{b_1} = \frac{\sum (x_{2i}-\bar{x_2})^2\sum (x_{1i}-\bar{x_1})(y_i-\bar{y})- \sum  (x_{1i}-\bar{x_1})(x_{2i}-\bar{x_2})\sum  (x_{2i}-\bar{x_2})(y_i-\bar{y})}{\sum (x_{1i}-\bar{x_1})^2 \sum (x_{2i}-\bar{x_2})^2- \sum  (x_{1i}-\bar{x_1})(x_{2i}-\bar{x_2})}$$
Hence we can see that the difference is that in the second expression the calculation of $b_1$ critically depends on what the covariance of $x_1$ and $x_2$ is (i.e. $\sum  (x_{1i}-\bar{x_1})(x_{2i}-\bar{x_2})$), what variance of $x_2$ is (i.e. $\sum (x_{2i}-\bar{x_2})^2$ and also what covariance of $x_2$ and $y$ is (i.e. $\sum  (x_{2i}-\bar{x_2})(y_i-\bar{y})$) and hence $\hat{b_1}$, hence including additional variable will change the $b_1$ (and also other coefficient) formula. This will extend to multiple variables as well with formula getting progressively more complex.
Moreover, the coefficients will change substantially especially if there is some omitted variable bias present. If we assume that the true model is given by:
$$y= \beta_0 + \beta_1 x_1 +\beta_2 x_2 + u$$
but you will try to fit univariate model regardless of the above.
$$\hat{y} = \hat{\beta_0} + \hat{\beta_1} x_1$$
In such conditions it can be shown that even though we fit univariate regression the expected estimated beta will be (see Wooldridge Introduction to Econometrics):
$$E[\hat{\beta_1}]= \beta_1 + \beta_2 \frac{\sum  (x_{1i}-\bar{x_1})(x_{2i}-\bar{x_2})}{\sum (x_{1i}-\bar{x_1})^2}$$
Where the second term is the omitted variable bias. The intuition here is that if there is any covariance between $x_1$ and $x_2$ and if $y$  actually depends also on  $x_2$ (i.e. $\beta_2 \neq 0$) then if you apply univariate regression on bivariate relationship the estimate of $\beta_1$ will be biased as it partially captures the relationship of $y$ and $x_2$. For example,  if $\beta_1=0.1$, $\beta_2= -2$ and $cov(x_1,x_2)=0.5$ and $var(x_1)=2$ then if you estimate univariate regression the estimated $\hat{beta_1} = -0.4$ whereas in bivariate regression it would be $\hat{\beta_1}=0.1$ and $\hat{\beta_2}=-2$
Hence to sum up, the coefficients are different because they are in multivariate regression calculated conditional on other coefficients and also if you are omitting an relevant independent variable its effect will be 'hidden' in the estimates of non-omitted variable (if they are correlated).


Is the equity lending involved in naked short-selling structurally equivalent to fractional-reserve banking? Fractional-reserve banking consists in banks lending out more money than they
actually possess. This can also be seen as "money creation", or at least "money
substitute creation"-- the claim on the bank (e.g. checking account deposit)
is practically equivalent to cash-in-hand.
A short-seller borrows shares in a stock, sells them on the market, buys them
back later, and returns them to the lender. This becomes a "naked short" if the
borrowed shares "do not exist", i.e. are "share substitutes" credited to a
short-seller's account without being backed by specific shares. Thus
naked-shorting relies on a practice of "fractional-reserve brokerage".
Fractional-reserve banking is widely accepted while naked-shorting is widely
considered unethical and is in most cases illegal. This confuses me because,
per the above logic, they seem to be the same practice, just with a different
asset class. In both cases, an abstract financial asset in the form of a claim
on a backing asset (bank cash reserves or broker-held equities) is "created
from thin air". In both cases, the existing stock of the asset in devalued by
the creation of extra units, i.e. inflation.
Am I missing something? Are fractional-reserve banking and fractional-reserve
brokerage, for lack of a better term, "structurally equivalent"? If not, what
are the important differences in their economic effects?

There’s no inconsistency between allowing fractional reserve banking and banning naked short selling. Banks generally lend out money that they borrow (setting aside capital lent), and if one lends out a stock that one has borrowed, that’s not a naked short position, it’s just a plain short. What’s illegal about “naked” shorting (in the U.S.) is selling a stock that one hasn’t either borrowed or determined that one can borrow within the delivery timeframe (currently two days for equities).
The restrictions around money are actually in quite a bit tighter— if a bank were to enter into a transaction that required that it deliver funds and it failed to do so because it couldn’t borrow enough money, it would not be acceptable for the bank to say “oops we thought we could borrow the money sorry” and just pay a small fee (as with equities, where one pays a fails charge). It would instead be an event of default(1), which is more or less the end for a bank.
(1) “Generally, a bank is closed when it is unable to meet its obligations to depositors and others.”


Will a Free Software Society ever become a reality? I have gone through this question regarding the economic sustenance of the GNU Software and I think it is the foundation of my question.

Below is a small excerpt from the GNU Website which states the four principles
the Free Software Foundation lays its foundation on.

The freedom to run the program as you wish, for any purpose (freedom 0).
The freedom to study how the program works, and change it so it does your computing as you wish (freedom 1). Access to the source code is a precondition for this.
The freedom to redistribute copies so you can help your neighbor (freedom 2).
The freedom to distribute copies of your modified versions to others (freedom 3). By doing this you can give the whole community a chance to benefit from your changes. Access to the source code is a precondition for this.

A program is free software if the program's users have the above four essential freedoms.

I believe the above principles will :

lead to better transparency regarding how the software works.
fuel new ideas, which will lead to better customized software.

I couldn't ,however, think of the economic hindrances for :

Setting up a Free Software Society.
If set up, the survival of such a society.

A society where all the players abide by the above FSF principles is
what I call a free software society. Well, this is my terminology indeed.

Any suggestions are appreciated.

Your questions asks:

  A society where all the players abide by the above FSF principles

It won't ever happen for all players. As a counter-example, consider an engineer who invents software that can predict when a jet engine needs maintenance. It's worth millions to the airlines, who will happily pay him for the software. He has no incentive at all to release this software as open-source. The same principle applies to all sorts of specialist software.

In contrast, open-source works well for common building blocks. For example, there are all sorts of companies who need an operating system for their product - cloud providers, home network kit, super computing, all sorts. While they could build their own, it is much more efficient to have a common pool, like the Linux kernel. This environment means that companies can put paid engineers on open-source projects, and still run a profitable business.


Technological unemployment I am doing a project on technological change in the job market, that is the substitution of routine occupations and increasing demand for high-skilled jobs.
I have done some research on this and now I am seeking extra sources of advice. I was wondering if anyone could recommend me a model which would be applicable to present technological change or job-market flows with?
Thank you in advance!

It would be helpful if you could let us know the papers you found, some of the background experience you have, and some more specifics.

This might be a useful paper nonetheless.


What is the purpose of the local non-satiation assumption in the first welfare theorem? The profit maximization assumption implies
$$\text{if } x_i \succ x_i^* \text{ then } p_ix_i > p_i w_i$$

Okay so this just says if the agent is utility maximizing / rational, then if he doesn't choose a bundle strictly preferable to his bundle then it must not be affordable.

Why is the local non-satiation assumption needed to then say

$$\text{if } x_i \succeq x_i^* \text{ then } p_ix_i \geq p_i w_i$$

Why isn't this just automatic from the profit maximization assumption? If we know $x_i \succ x_i^* \implies p_ix_i > p_i w_i$, isn't it obvious that $x_i = x_i^*  \implies p_ix_i =  p_i w_i$ and so $$\text{if } x_i \succeq x_i^* \text{ then } p_ix_i \geq p_i w_i$$

The assumptions are different. First one states that if a bundle is better than the optimal one the consumer cannot afford it. The second one states that if a bundle is as good (not necessarily better) than the optimal one it has to cost as least as much, not less.

Consider a space with just one type of good, $x$, and a utility function $U(x) = 0$. Let the endowment of the consumer be $w = 1$. While
$$
\text{if } x_i \succ x_i^* \text{ then } p_ix_i > p_i w_i
$$
is still true,
$$
\text{if } x_i \succeq x_i^* \text{ then } p_ix_i \geq p_i w_i
$$
isn't, because $x^* = 0$ is both optimal and feasible, thus
$$
x^* \succeq x^* \text{ AND } p x^* < p w.
$$
More complicated examples (multiple goods, global non-satiation fulfilled) may also be constructed.


Is there a standard for job sectors? Is there any sort of recognised standard (e.g. ISO) for grouping jobs into job sectors e.g. 'technology', 'emergency services'?

I asked this on StackOverflow here and they suggested this SE.

Would this be as close as I'm likely to get?

NAICS seems to be what you're getting at (http://www.census.gov/eos/www/naics/). This is the industry classification mechanism in North America. If you are interested in groups of workers' tasks as opposed to groups of establishments, you might be interested in occupation, which is the Standard Occupation Classification (SOC) system (http://www.bls.gov/soc/).


Boots' Theory by Pratchett Consider the following quote from the book, $\textit{Men at Arms}$ by Terry Pratchett.

  “The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money.

  Take boots, for example. He earned thirty-eight dollars a month plus allowances. A really good pair of leather boots cost fifty dollars. But an affordable pair of boots, which were sort of OK for a season or two and then leaked like hell when the cardboard gave out, cost about ten dollars. Those were the kind of boots Vimes always bought, and wore until the soles were so thin that he could tell where he was in Ankh-Morpork on a foggy night by the feel of the cobbles.

  But the thing was that good boots lasted for years and years. A man who could afford fifty dollars had a pair of boots that'd still be keeping his feet dry in ten years' time, while the poor man who could only afford cheap boots would have spent a hundred dollars on boots in the same time and would still have wet feet.

  This was the Captain Samuel Vimes 'Boots' theory of socioeconomic unfairness.”

With what Pratchett wrote, I was thinking about a car-buying decision by a newly wed couple.

Consider two cars:
1. Durable Car: sturdy, long-lasting, and safe for even kids when they are born. Looking ahead for about 10-15 years usage wihtout too much maintain break downs.
2. Cheap Car: inexpensive, easy for commute, but expect maintenance cost to be high and possibly totaled withint 6-9 years.

Their financing needs are:
1. Durable Car down payment: USD 10,000
2. Cheap Car down payment: USD 2,000

Their monthly leasing fees are:
1. Durable car monthly leasing fee: USD 200
2. Cheap car monthly leasing fee: USD 300

There are two newly wed couples: a financially affluent one, and a poverty stricken one.

Control all other factors such as credit score of both couples, financing terms and horizon, etc.

According to Pratchett, the poor couple would always resort to the cheap car option while the rich couple always resorts to the durable car option. Do you agree? What are your thoughts?

Rampini elaborates on your idea (and also the Pratchett quote) in his AER article "Financing Durable Assets". See the abstract:

  This  paper  studies  how  the  durability  of  assets  affects    financing.  We  show  that  more  durable  assets  require  larger  down  payments  making them harder to finance, because durability affects the price of assets and hence the overall financing need more than their  collateral value.  Durability  affects  technology  adoption,  the  choice  between  new and used capital, and the rent versus buy decision. Constrained firms invest in less durable assets and buy used assets. More  durable assets  are  more  likely  to  be  rented.  Economies  with  weak  legal  enforcement invest more in less durable, otherwise dominated assets and are net importers of used assets.

Similarly, Orhun and Palazzolo study this argument in "Frugality Is Hard to Afford" in the context of bulk buying large packets at low prices vs. only being able to buy small packets.

  Intertemporal savings strategies, such as bulk buying or accelerating purchase timing to take advantage of a good deal, provide long-term savings in exchange for an increase in immediate spending. Although households with limited financial resources stand to benefit the most from these strategies, they are less likely to make use of them. The authors provide causal evidence that liquidity constraints impede low-income households’ ability to use these strategies, above and beyond the impact of other constraints. Exploiting recurring variation in household liquidity, this study shows that when low-income households have more liquidity, they partially catch up to higher-income households’ ability to use intertemporal savings strategies. The findings provide guidance to marketing managers and researchers regarding targeted promotional design and measurement of deal-proneness. For policy makers, they suggest a new path for decreasing the higher prices low-income households have been documented to pay for everyday goods. Policies have traditionally focused on increasing financial literacy or access to supermarkets. Our work suggests that providing greater liquidity can help low-income households make better use of savings opportunities already available to them.


Log-Linearizing a Dixit-Stiglitz function In a New-Keynesian Model, the Consumption index

$C_t=\left(\int_0^1{C_t(i)^{1-\gamma} \ di}\right)^{\frac{1}{1-\gamma}}$

is log-linearized to

$\tilde{c_t}=\int_0^1{\tilde{c_t}(i)  \ di}$

where variables with tilde are log deviations from steady state and $i=[0,1]$ are varieties of the consumption good.

Even though I feel comfortable log linearizing other equations, I have no idea how to deal with the integral. How do you get to the result? And what would a second order approximation look like?

Thanks for the hint and the link! I think I now managed to find the solution.

Putting the exponent on the LHS and replacing

$C_t^{1-\gamma}$ with $C+(1-\gamma) C^{1-\gamma}C \tilde{c}$

and

$C_t(i)^{1-\gamma}$ with $C(i)+(1-\gamma)C(i)^{1-\gamma}\tilde{c}_t(i)$

i get (subtracting Steady State values):

$(1-\gamma) C^{1-\gamma}C \tilde{c}=\int_0^1 (1-\gamma)C(i)^{1-\gamma}\tilde{c}_t(i) \ di$

Assuming steady state values of $C(i)$ are constant across $i$, i can take all values out of the integral and simplify to get:

$\tilde{c}=\int_0^1 \tilde{c}_t(i) \ di$


Derivations of trade balance I am facing some problems in deriving the two equations for trade balance (from which we derive that the trade balance is zero within each country) in the article "A SIMPLE FRAMEWORK FOR INTERNATIONAL MONETARY POLICY ANALYSIS" (2002) that you can find here.
My objective is to derive equations 28 and 29 of that paper. In order to do that, I used the following equations:

Firstly, I tried to substitute the value of  given by equation 7a in equation 25, but what I got was not right:

Then I tried to get the value of  from equation 25 and substitute in equation 7, but this was not right either:

I also tried to substitute for gamma, but the results were not correct. I cannot think of anything else. How would you do that?
The equations that I am looking for:
Equation 28:
Equation 29:

Dividing equation 25 by $\gamma$ gives:
$$
Y_t = C_h + \frac{\gamma}{1-\gamma} C_h^\ast.
$$
Then using 7 and 7a to substitute for $C_h$ and $C_h^\ast$, we get:
$$
Y_t = (1-\gamma) \frac{P_t}{P_h} C_t + \frac{\gamma}{1-\gamma}(1-\gamma) \frac{P_t^\ast}{P_h^\ast} C_t^\ast.
$$
Then multiply both sides by $P_h$ and use $C_t^\ast = C_t$ to get:
$$
\begin{align*}
P_h Y_t &= (1-\gamma)P_t C_t + \gamma \left(\frac{P_t^\ast}{P_t}\frac{P_h}{P_h^\ast}\right) P_t C_t,\\
&= P_t C_t \left(1- \gamma + \gamma \left(\frac{P_t^\ast}{P_t}\frac{P_h}{P_h^\ast}\right)\right)
\end{align*}
$$
This is equal to equation 28 if:
$$
\frac{P_t^\ast}{P_t} \frac{P_h}{P_h^\ast} = 1.
$$
Now $\dfrac{P_t^\ast}{P_t} = \dfrac{1}{\varepsilon}$, which would require that:
$$
\frac{P_h}{P_h^\ast} = \varepsilon.
$$
Dividing 7 by 7a gives:
$$
\frac{P_h}{P_h^\ast} \frac{C_h}{C_h^\ast} = \frac{P_t}{P_t^\ast} = \varepsilon.
$$
So this means that $C_h$ has to equal $C_h^\ast$. I don't know if this makes sense (as I don't know the meaning of all these variables).
Similarly, you can show that 29 is satisfied if $C_f = C_f^\ast$.


Two interpretations of the Lagrange Multiplier A question about the second answer on this thread:
Help understanding Lagrangian multipliers?

If we have a standard utility maximizing problem
$$
\max_{x,y} U(x,y)
$$
with the constraint $p_{x}x + p_{y}y = B$, where $p_{x}, p_{y}$ are the prices of $x,y$, and $B$ is the budget/income. The Lagriangian would work as
$$
U(x,y) + \lambda(B-p_{x}x - p_{y}y)
$$
and we would proceed to take partial derivatives and find critical points. My question is on the interpretation of the Lagrangian function above and specifically the multiplier $\lambda$:

1) In what way is $\lambda$ the "price we pay for not obeying our constraint"? (as one of the explanations in the linked post has it)

2) Intuitively, not mathematically, how is this equivalent to the interpretation of $\lambda$ as a "shadow price"?  What exactly is a shadow price?

3) What difference does it make to $\lambda$ if our constraint was written as $p_{x}x + p_{y}y - B$ instead? (i.e. in reverse order)

If you would NOT obey the constraint and spend 1\$ more (or more precisely an infinitesimal amount more) your utility would go up by $\lambda$. As such $\lambda$ is what you give up for obeying the constraint, it is the price you pay indirectly and hence it is called the shadow price.

Writing the constraint in reverse has no effect other than changing the sign of $\lambda$, but that depends on the way you set-up your problem anyway (I.e. whether you add the constraint with a plus or a minus).


Generating profit by leveraging fluctuations I was writing some code akin to a sound limiter when it occurred to me that if you could find something fluctuating in price between two extremes (what and when those extremes would be isn't relevant I think, just the fact that between those extremes there exists a space where the "signal" would always return to) you could theoretically leverage that in a market setting.
If such fluctuations had sine-wave like properties you could write an algorithm that "buys" below zero and "sells" above zero and generate a profit this way. (I'm using quotes because I really don't mean to exclusively ask about financial markets or stocks, just any exchange that fits the description)
This raises some possibilities:

I'm the programmers answer to Einstein, I should have kept this to
myself and could have made billions.
The type of predictable fluctuations that are needed do not occur in reality ever. This is feels counter
intuitive to me, stocks go up and down, economies wax and wane?
This actually happens but the fact that it does
"closes the gap" so to speak, i.e. it leads to an equilibrium
because even the tiniest fluctuations are "used up" like this. If
so, is this a principle that has a name I could read up on?
This is, when talking about physical goods, entirely impractical because it
implies storage. Similar constraints exist for other kinds of
markets.
This is something very mundane, I'm just thinking about it
in the wrong way.
Something else?

What's going on here?
I've tried finding information on this subject but I'm having a hard time formulating a query. To me, this has all the hallmarks of something that would appear either as a game in game theory or as a problem category in computer science, however it seems to me that it is essentially an economics question, that's why I'm asking it here.
I've also tried asking on another site with an ill conceived practical example, but that never got me past 1, or at least the discussion never really went beyond the practical example.

Generally, it's a combination of 2 and 3.
You can't predict that a stock will go up and down in cycles. Stock prices move randomly. Let's say you're looking at one stock, and it goes down so your algorithm buys some and waits for it to go back up. What happens if it never goes back up higher than it started as? Then you lost money.
Even worse: Even if it does go back to where it started with, you still lost money. Stocks have an overall upward trend, so you have to make more than a certain amount of money, or otherwise you would've been better off by just buying random stocks!
Why do stock prices move randomly? According to the "Efficient Market Hypothesis", stocks move randomly because all non-random information is already being exploited by other people (point 3) until it stops being profitable to do so. Thousands of people might get a couple of cents each from the fluctuations.
When something has a regular fluctuation - like ice-cream prices perhaps - there's a reason. Maybe (hypothetically, if ice-cream prices fluctuated a lot) you could make money by buying ice-cream in winter and selling it in summer. You'd have to have a big refrigerated warehouse, and that would be a legitimate way to make money, it wouldn't just be a financial gain.


Help in interpreting data - Deficit I was looking at the deficit for different countries
http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=gov_10q_ggnfa&lang=en

How shall they be read?

For instance Greece had a -15% in Q4 of 2015 and +0.5% in Q2 of 2016.
Does this datum refer only in that specific period? I mean in Q4 of 2015 Greece had a 15% unbalance, but this is not on annual basis.
If we want the yearly data we shall sum up the 4 quarters?
Following this path in the entire 2015 Greece had a total annual deficit of 30%? Isn't it too high?

It is the difference between total general government revenue and total general government expenditure defined in the National Accounts system.  You can find some sort of explanation at http://ec.europa.eu/eurostat/statistics-explained/index.php/Government_finance_statistics_-_quarterly_data#Government_revenue_and_expenditure

For Greece, Eurostat's underlying figures look like this

UNIT    NA_ITEM/TIME            2015Q1  2015Q2  2015Q3  2015Q4  2016Q1  2016Q2  2016Q3
M euro  Total GGov revenue      16,945  19,711  19,970  27,484  18,430  20,598  23,780
M euro  Total GGov expenditure  20,925  21,336  20,796  34,290  20,222  20,368  20,982
M euro  Net lend(+)/borrow(-)   -3,980  -1,625    -826  -6,806  -1,792     230   2,798
% GDP   Total GGov revenue        42.0    44.5    43.3    61.3    46.2    46.3    50.9
% GDP   Total GGov expenditure    51.8    48.1    45.1    76.5    50.7    45.8    44.9
% GDP   Net lend(+)/borrow(-)     -9.9    -3.7    -1.8   -15.2    -4.5     0.5     6.0

The percentages are of quarterly GDP.  If you wanted exact annual percentages then you should add up the four quarterly figures in Euros and divide by the sum of the four quarterly figures for GDP in Euros (from a different Eurostat table), but you will get a close approximation if you take the average of the four quarterly percentages.  So for Greece it might represent a government deficit of around 7.7% in 2015

Be aware that the numbers are not seasonally adjusted: it looks as if a lot of Greek government revenue and expenditure comes in Q4.


How do the Government, Firms and the Foreign sector pay their debts in this circular flow of income? Here is a circular flow of income that I took from Krugman's macroenomics textbook.
Please notice, in this diagram households just give their savings to banks (which are part of the financial sector) and everybody else seem to just take these money, not returning them. For an example, Government transfers to households are just good old welfare, not payment for money that the government borrowed from households. Besides, the financial market gives access not only to savings of national households, but also to savings of foreign households. So there should be a separate outward flow from the Government and Firms specifically to the finanical market and specifically for paying their debts. As for the Foreign sector, it needs to add "payment for debts" to its out outward flow to the financial market. But even without the Foreign sector normally debts are paid to banks, rather than directly to people who keep their money in banks.

Do I read the diagram wrong? If yes, how do then Government, Firms and the Foreign sector return money that they borrowed from households according to this diagram? If no, then why does this scheme NOT include any flows for returning borrowed money? I understand that it's all simplification of real life, but presenting borrowing in way that is indistinguishable from charity seems like an OVERsimplification, I don't see reasons why to present borrowing like this. Please enlighten me if you understand why borrowing was presented like this, like a charity.

For the households it would through the savings arrow. Borrowing from macroeconomic perspective can be and in most advanced textbooks (such as Romers advanced macroeconomics) is often treated as a negative saving.

Hence when the households and businesses borrow they incur negative saving and when they repay debts it can be viewed as a positive increase in saving (which for people who borrowed would be negative).

This can actually be clearly seen from the diagram since savings arrow goes to the financial market and from financial market you get the borrowing.

It’s not that the financial markets lend people money - people lend money to each other through financial markets and then pay it back from the savings.

Saving is the difference between your income and consumption so in order to pay any debt you have to save (if you consume all your income you cannot pay your debts).

When it comes to the government it technically pays back by public savings which occurs when taxes are larger than spending so there in principle you could argue there should be another savings arrow from the government. However, I think that Krugman decided to include this in the transfer arrow. If you buy a government bond and your government is paying you back interest you could consider it as transfer.


Does segregation make economic sense? A central tenet of libertarianism is the notion of free association–being able to socialise and enter into contracts with people of your choosing, with the corollary of being able to refuse to do those things too. The obvious criticism of this would be that one could then refuse to sell to people based on their skin colour, sex, orientation, etc., which has a historical precedent pretty much all over the globe. Does this make economic sense, though, or does it represent a market failure?

To my non-economist eyes it looks pretty cut and dry. Say Alice has a widget store and decides to only sell to people in group A. Bob also has a widget store and sells to both groups A & B. Surely Bob should have a significant economic advantage here, allowing him to lower prices and stay competitive with Alice? Even if some group A customers would refuse to shop at Bob's, presumably more would be attracted to Bob's store for its lower prices?1

Even if social or legal pressures meant everyone had to segregate, would this not present a gap in the market to be filled by group B store-owners, who would then sell to the underserved group Bs, with prices presumably more in line with group B incomes (if they are also economically disadvantaged compared to group A), and with the profits more likely to be redistributed amongst other group B businesses?

It's a cliche that the libertarian answer to everything is that 'the market will fix it', but this does seem like a sitation where that should happen, unless government pressure countered market forces (e.g. if it was made illegal for group Bs to even open their own stores or buy stock from wholesalers willing to sell to them). Would the libertarian counter-claim be, then, that the existence of economic segregation can only occur when backed by state force?

1 However, this paper does suggest that '[d]iscriminators are on average willing to forego 8 percent of their earnings to avoid a coworker of the other ethnic type'.

In many models, we assume that firms simply want to maximize profits, and there are no externalities. If these assumptions are true, then a free market will be racism-free, gender-blind etc, etc. However, this is not the case in the real world. People that own and operate firms not only want to maximize profits, often they also have all kinds of biases, including social biases like racism, sexism, etc; as well as cognitive biases, for example when they want to make the firm as big as possible even if that is not profitable. In all cases, this biases necessarily mean forgoing profits. For example the paper you cite. Ross Levine has other papers on the topic.

However, the question of segregation is broader than this. For some type of relationships, "segregation" can make economic sense. For example, if you have a common resource, like a lake that provides some fishes, limiting who has access to such lake to only people who take care of the lake and does not overfish it, can have clear advantages, and be socially efficient.

In short, segregation can be the result of a friction, like cognitive or social biases. This is not a market failure, properly speaking, but it entails some inefficiencies, so in that sense, it does not make "economic sense". But you can also have segregation, being the optimal response to a situation that involves externalities (like in the example of the lake). This segregation can make "economic sense" in that it is individually rational, and it may or may not be socially efficient.

Consider an example where it is likely not socially efficient. Suppose there is a big proportion of people who are racist, and you own a restaurant. Let's assume you are not racist and you only care about maximizing profits. It is perfectly reasonable to think that you will deny service to people based on race if that will make your racist costumers more likely to visit your restaurant. This segregation makes "economic sense" even though it might not be socially efficient in some way or desirable (the social welfare can be measured in many ways). Notice that I needed to assume that your other customers somehow have negative externalities from you selling to racial minorities.


Can logarithm and polynomial transformation be included in the same equation Is it allowed to include logarithm and polynomial tranformations in the same econometric model.
For instance :
$$Y = x_1 + \log(x_2) + x_3 + x_3^2$$

I didn't find any interdiction however it seems to be not used in practise.

Thank you !

Yes it is "allowed". Econometrically it is not a problem. The real question is how useful such a model is for your setting and that will depend on your exact research question, variables and data.


How does the Austrian School view land rents? I have come across these publications:
The Spatial Market Process. Advances in Austrian Economics Vol. 16.

In “An Austrian Theory of Spatial Land,” Fred E. Foldvary addresses
the disregard of spatial issues in basic Austrian economic theory as
formulated by Carl Menger (1871) and elaborated upon by Ludwig von
Mises (1940). Foldvary shows that Johann Heinrich von Thünen (1826)
and Henry George (1879/1884), in particular, serve to fill these gaps
in the classical Austrian theory of the market process.

Henry George and the Austrian Economists (Oscar Johannsen, 2003)
This article states that Rothbard had a Lockean view of property in land:

every man has the absolute right of property in his own self and in
the previously unowned natural resources which he finds

From what I heard, Austrian economics is descriptive, not prescriptive; for example, being an Austrian economist and a communist may not be a contradiction. However, the following represents the view of an average Austrian economist on land rents, based on my experience.
Land can be acquired by property transfer or by homesteading. Homesteading is mixing land with labor. Property rights to land can be lost by property transfer or by abandonment. Same as with any other property, the owner of land can rent to others.


What is the difference between Margin and Markup? Please clarify the difference in meaning behind markup and margin. Why would I use one or the other?

Markup = (Price - Cost)/Cost

  useful for examining how much actual profit is made on each sale.

Margin = (Price - Cost)/Price

  useful for helping ensure that a sale generates a profit.

Sources:

https://www.linkedin.com/pulse/margin-vs-markup-two-sides-same-coin-steve-raye/.
https://www.inflowinventory.com/blog/calculate-margin-vs-markup/

Markup is how much the seller is adding to the cost to get the price of sale.

Margin is how much of the sale price is available for overhead and profit.

You would tend to use markup when you are more concerned with costs than the sale price.  You would use margin when you are more concerned with the sale price than costs.

$$\frac{\text{markup}}{\text{margin}} = \frac{\frac{\text{Price}-\text{Cost}}{\text{Cost}}}{\frac{\text{Price}-\text{Cost}}{\text{Price}}} = \frac{\text{Price}}{\text{Cost}}$$

Since cost is generally less than price, markup will generally be larger than margin.

Profit (both accounting and economic) will be no more than margin.  So if you want to talk about profit, you might start by considering margin.

$$\text{markup} = \frac{\text{Price}}{\text{Cost}} - 1$$
$$\text{margin} = 1 - \frac{\text{Cost}}{\text{Price}}$$

One reason you might use markup rather than margin is that you may not know the price.  If you have something that costs one unit and you want 100% markup, then you find out that the price is two units.

$$\text{Price} = \text{markup}\cdot\text{Cost} + 1$$


Greece default and why are US States not seen defaulting? Reading various articles, it is clear that Greece is in the situation simply due to the fact that they have indulged in overspending on their national budget for over a decade, and with the 2008 financial crisis this have have worsen as they have lost additional revenue.

Every US state and city is also responsible for their own budgets, and making sure that they are kept in balance -- while a handful of US cities have gone bankrupt, there have not been any news about US state getting into a crisis of the same scale as Greece has.

Is there a difference between how a national budget is run in the Euro Zone versus how a US State budget is run with respect to oversight where a US State cannot get insolvent to the same degree as Greece before the US Fed steps in?

What are the lessons from the US model which would need to be implemented in the Euro Zone to prevent another Euro Zone member to end up in a similar situation?

EDIT

Specifically; Are there any specific laws in the US which allows the Feds to step in before a state defaults?

Two reasons:

The United States has a capable federal government that takes care of social insurance transfers and countercyclical economic policies. The American states spend less.
The American states have stronger anti-tax sentiments, and increasing public spendings face opposition from business and rich people.

Take the 2008 crisis for example.

As for 2008, all developed countries, including Greece, had a lot of bad debt in the private sector and a subsequent recession due to the credit crunch. The United States immediately approved two things in response: a $700 bn stimulus and the Fed's QE programs. They cleared bad debt and supported business in 2009.

These measures was done at the federal level. It's the federal government that took additional debt. And the debt looked like this:

(McKinsey - 2012 - Debt and deleveraging)

The EU was slower. And its recovery fund lent money to European countries (as if the US fed government lent money to the states), so increasing their debt-to-GDP levels. This is how the EU, IMF, ECB happened to be the holders of all Greek bonds and a demanding creditor, as for now.

In short, US states got their federal stimulus for free, while Greece had to buy the stimulus on its own.


Why would the economy return to equilibrium at full employment after a supply side shock? As far as I'm aware, in the absence of any changes in the long run aggregate supply LRAS, any changes in the level of aggregate demand AD or short run aggreagete supply SRAS should eventually in the long run see the economy return to full employment, as per monetarist theory. How does the economy return to full employment when there is a change in the SRAS, when, for example, SRAS decreases?

I guess it depends on the model you are considering, but in the basic AS-AD model it should happen via adjustment in the labour market: if $Y_t > \bar{Y}$, then there will be upward pressure on the nominal wages (employment is higher than equilibrium employment, therefore workers ask for higher wages), to which firms respond by increasing prices, inducing an increase in inflation. As inflation expectations adjust, the SRAS shifts leftward. The adjustment stops when workers' real wage demands are met by firms (which is, when inflation expectations are realised) and output is back at $\bar{Y}$.


Could robots replace humans as consumers? Could it ever be economically viable, once technology allows, to create robot consumers to replace humans if demand was so low because of automation and reduced spending power/unemployment or is there simply no way to make robot consumers pay?

I am envisaging a future in which elite consumption has risen, but not enough to offset a huge decline in mass consumption. In that scenario, I was wondering if robot consumers could keep capitalism afloat? I am trying to check out for something I am writing whether such a thing could work economically ie whether there could be a profit in it for the producers and owners of the robots, I don’t think they could ever be economically autonomous because of the build and running costs. But could robot demand be sold or rented for example by the producers/owners to other companies to consume their products? There might be some state investment as well under the banner of demand stimulation? Or is it as the first reply argued, that this is just an economically illogical premise because the maths (profit) just can’t work because of cost of building and maintain the robots?

Short answer

Perhaps your concern about stimulating demand is explained by the broken window fallacy. The fallacy is the belief that there is a social benefit to income that is concomitant with a loss in a stock of wealth.  Instead of using a stone to break a window you want to use a robot.

Longer answer

You said "demand was so low because of automation". I think automation increases valuable output so it increases income so it increases demand. I think you suggested a nonsensical premise.

I think current day robots are economically viable since there is a market for them. As @Fizz correctly says they use spare parts and they also use energy, usually electricity. Presumably they produce more value than they consume, otherwise nobody would buy one. What is a robot and what is the owner of the robot are hard to separate since robots do not have what I might call autonomy under the law. They are chattel. As chattel, you might say it is the combined unit of the owner plus robot that is the consumer and the producer. The owner might be a corporation. Robots can mechanically pay for goods and services but since it's not an autonomous individual it is really the owner that is paying, using the owner's money. The robot itself does not own money.

If the law changes to recognize robots as autonomous individuals, not chattel, not slaves, then their individual output would add to GDP and their individual consumption of goods and services would add to aggregate demand. They already do add to these economic measures, but as part of a combined unit of owner plus robot.

You asked if robots can replace human consumers. Yes, robots as autonomous individuals can replace humans as consumers of goods and services. When a robot as an autonomous individual consumes a rival good, a human cannot consume the same. I think this is easy to understand if we consider electricity. If a robot as an autonomous individual runs, swims, and bicylces a triathlon, it will use energy that a human could not have used to air condition their condominium.

Link to a description of rival goods.

ADDENDUM

You have edited your question so I am posting an addendum. In this addendum I will assume that the law changed to recognize robots as autonomous individuals.

If elite consumption increases by one dollar and consumption by non-elites decreases by two dollars, aggregate consumption will decrease but that is a transitory problem. The lower level of consumption will soon be matched with a lower level of output. Nobody will persist in producing goods that will obviously fail to sell. I sense your question is about permanent effects and you did not specifically express a concern about transitory problems. One reason it is transitory is because when people stop producing goods that do not sell they switch to producing something that does and when that happens the economic recession comes to an end. Consider that there is the "permanent" phenomenon of productivity improvement which will eventually cause income and consumption to increase for elites and non-elites and so the lower level of non-elite consumption is temporary.

You asked if a robot consumer will "keep capitalism afloat". If the non-elite, motivated by a temporarily lower living standard, desire to vote to switch to a non-capitalism regime I think the robot consumer producer has an uncertain effect in that aspect. The robot consumer will consume some rival goods while also producing some rival goods. In the long run the robot producer consumer will be powerful and it will produce much and consume much. They will be part of the elite. Under a progressive tax system human elites and robot elites will be taxed at a higher rate than non-elites. It might be the progressive tax system, not as much the existence of robot consumer producers, that helps the non-elite.

Since I am assuming robots are recognized as autonomous individuals I will not answer the questions involving owners of robots and robots being sold and rented.

You seem very concerned about the cost to build and operate robots. These costs are always decreasing because of the permanent phenomenon of technology improvement.

You seem to persist in being concerned about stimulating demand. I refer you to the beginning of my answer that said low demand because of automation is nonsensical. We do not need robots to stimulate demand of rival goods. The destruction of rival goods is sufficient to stimulate demand.


Why do banks take deposits if they do not need them to make loans? I have taken some economics courses in university, where I was introduced to fractional-reserve banking. From my understanding, in fractional-reserve banking, the bank has motivation to encourage deposits from depositors, because a large part of these deposits can then be lent out as loans. A small part of the deposits have to be retained as "reserves" (hence the term "fractional-reserve banking"). The bank profits by earning more interest on the loans than it has to pay to the depositors.
However, I read several articles that contradict my understanding. In an article from the Quarterly Bulletin of the Bank of England - Money creation in the modern economy:

The reality of how money is created today differs from the description found in some economics textbooks ... Rather than banks receiving deposits when households save and then lending them out, bank lending creates deposits.
[...]
In reality, neither are reserves a binding constraint on lending, nor does the central bank fix the amount of reserves that are available.
[...]
While the money multiplier theory can be a useful way of introducing money and banking in economic textbooks, it is not an accurate description of how money is created in reality.

In light of this, I am forced to re-evaluate my understanding of fractional-reserve banking. The most pressing question I now have is: if banks do not need deposits to create loans, why do they take deposits? What motivates retail banks to allow retail customers to deposit their money if banks have no need for deposits to make loans?

I think there are a few separate issues here.
First, semantics: if an institute doesn't let you deposit money into your account, I think we'd be hard-pressed to call it a "bank".
This really doesn't matter to the fundamental aspect of your question, but I think it's of some use. Because a "bank" has to allow deposits (at least by a naive definition, if not a legal one), you're artificially limiting yourself to institutes that do so.
If we broaden the scope of the question to include more than just "banks", we start to get to the meat of the problem.
Second, the real question: why would an institute let you deposit money into their possession to begin with?
I'm sure a hundred super-smart, very educated experts on the subject will give you a hundred and five different answers that are all the absolute, only truth in all the universe.
But the gist of it is that people are willing to pay the bank to safeguard their money. Money in the bank is insured against theft and heavily guarded, so many people would rather have large sums of money in the bank than in their house.
In return, they might pay for the service directly or through microtransactions related to the account. Many banks charge fees for various things, such as cashier's checks, notary services, or financial advice, services you might not bother with if you aren't already in possession of a checking account.
Further, banks can take the money in your checking account and invest it elsewhere (an obvious form of investment being loans to other people). A single, smart person investing a thousand people's money can make enough profit to be worth their while without being directly paid a cent. Scale that up and you get large banking corporations.
Banks often make money off credit card transactions, even if you make payments before any direct interest is due. They also make money off overdraft fees (a form of lending with very high "interest" rates), interest on the credit card (more lending), and so forth.
And, of course, they hope that if you need to borrow money, you'll do it through them.
Third, the side question: do institutes need deposits to make money off loans?
No, they absolutely do not.
Payday loan establishments don't take deposits, instead relying on high-interest, low payback period lending to make their money.
Pawning an item is a form of payday loan with physical collateral: you leave the collateral with the pawn shop and get paid for it, then if you return on time you get most of your money back, with the difference being the shop's fee for the loan. Pawn shops make a lot of money through simply buying low and selling high, but they still make money off pawned items and don't take deposits.
That said, you can only lend money if you have it, so having a large amount of cash sitting in your vault from deposits allows you to lend more money than if you only lend from your own finances. There's more risk involved, but when you start getting thousands and millions of account holders, the aggregate risk goes way down and you can start treating random statistical values like static rates.
Because bank deposits allow the bank to loan more money, it raises the interest they earn on the loans, so it's a good incentive to allow people to deposit into bank accounts.
Fourth, the question not asked: what does the quoted article mean?
I'm not an expert here, but from my reading it's basically just a way of twisting around the semantics to describe how things can be treated in an opposite fashion to common convention, but doesn't actually prove the convention wrong.
The article claims that lending money "creates" that money. This is true to a degree, but is meaningless in the big picture. When a modern bank gives you a loan, they don't actually hand you any physical thing that's worth money. They just write a number on a (probably digital) ledger that says you "have money".
But they can only get away with that because they own assets that are worth real-world value equivalent to the amount they've "created", and because, in the long run, you will give them the amount of money they've lent you, balancing the sheet yourself.
A bank can only get away with "creating" money for a borrower if they can afford to transfer that money to whomever the borrower is trying to buy something from. It does no good to have fictional money if you can't actually spend it, and you can't spend it if the bank doesn't have a commodity the seller's bank wants.
In practice, the commodity transferred is often virtual money established by digital ledgers, but that commodity is very real, and very controlled, and therefore has actual, real-world value. As such, when a bank "creates" money out of thin air, it's doing so by spending a real-world commodity it only regains if you pay back your loan (or they sell your collateral after taking it back).
There's a particularly egregious bit of word-twisting the article makes. It claims:

Bank deposits are simply a record of how much the bank itself owes its customers. So they are a liability of the bank, not an asset that could be lent out. A related misconception is that banks can lend out their reserves. Reserves can only be lent between banks, since consumers do
not have access to reserves accounts at the Bank of England.

It's true that reserves themselves can't be lent. That's the definition of the required reserve. But it's also irrelevant. Only 10-12½ % of deposits are required reserves (Bank of England, relevant to the article; other banking systems will have other reserve ratios). The other 87½-90 % of deposits are free to be lent out as desired to make money for the bank. Deposits are absolutely an asset for the bank to lend out in the normal sense of the word. They're also liabilities in a strict sense, but they're liabilities that earn the bank a lot of money.
Imagine you loan me £1000 of tools. I owe you either the tools, in good shape, or £1000, or some equivalent combination. Additionally, I'm probably paying you a fee, say £100 a month, to borrow them. Financially, that's a "liability".
But I'm able to use those tools to earn £5000 a month doing something like construction or automotive repair. In normal speak, the tools are an enormous asset, not a liability. I just need to make sure I can return the tools and borrow other tools if you want yours back.
So while the text is "true", it's also completely misguided in rebuking common "misconceptions". In short, it's using smoke and mirrors to make you think you're wrong about something even though you really aren't.
Summary
Institutes don't require deposits to make money off lending, nor do they require lending to make money off deposits, but the two functions synergize very nicely with each other to create what we would typically think of as a bank.
The article you're quoting is mostly just using some hand-waving semantics to explain how modern banking uses a different mindset to approach the same thing we've been doing for millennia, with virtual currencies replacing physical bases for value.
But there's no epiphany behind the hand-waving; the fundamental nature of what's going on behind the layers of bureaucracy and pedantry hasn't changed since a caveman borrowed one sheep from his neighbor and gave back two sheep the next year.
Note
Most everything I've said is actually written in the quoted article. It talks about how a home loan that "creates" money is then balanced out by the bank paying the home seller's bank. It talks about gaining deposits so the bank can afford to lend more money. It talks about needing to pay interest to the central bank to maintain the assets upon which the commercial bank's finances are based.
The article isn't really bad or inaccurate. It just makes a few over-reaching, semantic claims that don't hold up under scrutiny in an attempt to make you think about banking a bit differently. And those are the claims that threw you off.
It also throws in the concept of growing the aggregate amount of money in the country (the "broad money"), a process typically called "inflation", to maintain a stable, thriving economy. So in that sense, banks do "create" money (though ultimately the central bank does the creation by effectively forgiving tiny amounts of debt here and there through carefully-controlled interest rates as well as simply handing out newly-printed notes), but that's really an entirely different topic that's muddying the issue.


Literature Recommendation: Advanced Undergraduate Economics I come from a strong quantitative background and am going to law school in the fall. I'm interested in financial product regulation and competition law. I have taken an introductory course in economics, but my exposure to economics stopped there.

I was wondering if you had reading suggestions in micro, macro, and financial markets. Although I don't have an issue with calculus, lin alg, or probability, I tend to prefer learning by the use of examples, e.g. "too many chefs in the kitchen" to explain diminishing returns.

I really don't like jargon and so far I seem to come across a lot of online resources (especially regarding financial products) that seem to use a lot of jargon with little reference to basic concrete examples. I tend to be very detailed oriented, so I prefer texts that lay out their variables and constants clearly. Something lighter and shorter tailored for independent study would be best.

I would suggest Mankiw and EconTalk (despite my Keynesian leanings).

Specifically Mankiw's text "Principles of Economics" is a great math-light introduction that covers both Macro and Micro. I recommend this edition particularly because you can get it new off Amazon for under $20, though of course the latest edition is best, but the field hasn't changed that much that I'd spend 15x as much to get it.

Additionally Stiglitz, Piketty, Buchanan, and Fama (particularly Fama, given your interest in finance), are all great authors, and in my opinion fairly accessible (in book, not in paper, they're each just as jargonated in paper as any one else).

Hope that helps.


Optimal population allocation layout over the Earth Does exist some model of optimal people occupancy over whole our planet?

Something accounting for climate, resources (with and without existing settlements) availability, progress and grows perspectives and so on.
I would like to find it in form of heat map.
All I can find is just studies about cities layout or population size and density.

I came to the question thinking about advisability of my little hometown existence and ways to improve it - may be the game is not worth the candle.

The closest I can find to what I believe you’re looking for would be the biocapacity map of the Global Footprint Network. They don't seem to publish granular spatial data, i.e. where in a country its biocapacity is located.
Note, however, that actual economic activity does not correspond to local biocapacity because high density stock energy (fossil fuel) can be transported to population centres. (Source)


Measuring Subjective Beliefs I am starting on a research project that requires the measurement of subjective beliefs of subjects around uncertainty. Since I'm new in this field I'm looking for references that can help me get started. In this project we can survey the subjects but bringing them to lab might not be possible. I'll appreciate any leads in this direction. Thanks for your help.

you can do a belief elicitation.
See more on this here:

Rauhut, H., 2013. Beliefs about lying and spreading of dishonesty: Undetected lies and their constructive and destructive social dynamics in dice experiments. PloS one, 8(11), p.e77878.

and here:

Gächter, S. and Renner, E., 2010. The effects of (incentivized) belief elicitation in public goods experiments. Experimental Economics, 13(3), pp.364-377.

If you don't want to invite them into the lab, you can use Amazon mTurk and oTree.


How does the money supply grow in the long term? For inflation to happen at roughly 2%/yr and for people to trade the same (or higher) volumes of goods, people must be trading more money. For such a trend to exist in the long term, there must be more actual units of currency that exist (right?) which means actual currency must be being created by the central bank (right?). When does the central bank create this money (or am I wrong in inferring the central bank must be creating cash...)?

Central banks often do not create cash.  For example, in the United States, it is the Treasury department that prints cash.

What a central bank does most often that has the effect of creating money is to engage in open market operations.  In an open market operation, it does one of two things:

Sell an asset that it is holding, usually a government bond.
Buy an asset, again usually a government bond.

If it sells, it takes money out of circulation.  Obviously it does this less often, as overall the money supply is growing.  More often, it buys.  This transfers money from its account to someone else's account.  Most of the time, this is a purely electronic transaction.  While the central bank may track its account balance, there's nothing keeping it from being negative.  As it grows more negative, we call this money creation.  But again, this is an electronic transaction.  No actual cash needs to change hands.

Now, someone may go to the bank and ask for the money.  The bank hands that person cash, which it has to replenish.  The bank may ask the central bank to ship it some actual cash.  If the central bank had none, it would have to go to whomever prints the money to get some.

Because of the way that fractional reserve banking works, most money is actually created by the banks.  The way this works is that someone deposits money in the bank.  Let's say it's \$10 and the reserve fraction is 10% (as in the US).  The bank keeps \$1 or deposits it with the central bank as a reserve.  The other \$9 it can loan out to someone else.  That entity either spends it or banks it.  If it spends, then someone else faces the same decision.  Eventually all of that \$9 is deposited.

In the new deposit, the bank (which may be a different bank or the same one) has to reserve \$.90 but can loan out the remaining \$8.10.  But now we have two deposits of the same money.  So there's \$19 of deposits with only \$10 of money.  \$9 was created by the banks.  The process repeats until there is \$10 of reserve and \$90 more (10% reserve fraction).  So for every \$10 created by the central bank, regular banks can create up to \$90 more.

Most of this money will never be exchanged as cash.  People will write checks or use credit cards.  The money will never exist physically.  It only exists as accounting transactions.

It's not even necessary to involve banks.  Let's say I sell you something for \$10.  But you tell me that you have no cash.  I loan you the money implicitly by allowing you to take the item.  I've implicitly created \$10 of money.  When you pay off the loan, you are implicitly destroying that \$10 by closing the loan.

In summary, central banks often don't print any cash.  But regardless of who prints cash, most money in the money supply is never printed.  Most money only ever exists as accounting transactions, and most money is generally created by regular banks rather than the central bank.


Question regarding to Government Debt in Williamson Textbook I am using the Williamson Macroeconomics textbook to look over a chapter on Monetary Policy and Banking (Chapter 12, 5th Edition).

For a bit of context, the author specifices the government budget constraint as:

$$PG+\left(1+R^{-}\right)B^{-}=PT+B+M-M^{-}$$

wherein it can be understood as a flow budget constraint. The term $PG$  is the amount in dollars of government purchases, and the term $(1+R^{-})B^{-}$  is the payment due on outstanding government debt. The LHS therefore corresponds to government outlays. The RHS consists in nominal terms, government recepits. The first term $PT$ measures nominal taxes, $B$ denotes government bonds, and the final term $M-M^{-}$ deenotes change in nominal money supply.

The question relates to what would happen the nominal money supply increased (the last term $M-M^{-}$ increased).

The explanation on page 455 is as follows: because both sides have to be equal, and one part of the RHS has increased, something has to give way. That means either $PT$ has decreased or $B$ has decreased or both to preserve equality. In the case that $PT$ does not change, the author explains that the government could reduce the quantity of bonds $B$ that it issues during the current period. This is an open market operation wherein the fiscal authority issues debt, and the monetary authority purchases some of this debt by issuing new money. In essence, the author argues that $M-M^{-}$ increases as $B$ decreases. This does not make sense to me, however. If the fiscal authority were to issue more debt, would $B$ not increase? That is, the quantity of bonds in the market would go up in this open market purchase. Am I missing something obvious?

Many thanks!

Given the clarification from the OP in the comments, there appears to be a mix-up here.

We learn that the author explains as follows:

  This is an open market operation wherein the fiscal authority
  issues debt, and the monetary authority purchases some of this debt by
  issuing new money.

This sentence describes a situation where the monetary authority is separate from government. But if this were so, we could not have in the same budget constraint both inflows from bond issue and from increase of the money supply.

Namely, the budget constraint describes a different situation, one where the government is a single entity that has three options to finance itself:
1) Collect Taxes from the private sector
2) Issue bonds that are purchased by the private sector
3) Issue new money by fiat

In such a case, with fixed outlays in the left-hand side, more money issuance allows indeed for less debt.

I note the the author writes "the monetary authority purchases some of this debt". This complicates things a bit, it means that part of the debt is bought by the private sector, and then we could have a partial substitution effect, but then we would have to distinguish between "debt held by the monetary authority" and "debt held by the private sector", etc.


Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion? We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$.

Are there intuitive interpretations of the numerical values of these coefficients? Let's say that someone has $R_a=5$ or $R_r=3$ for certain wealth level $W$, how would we interpret that number?

Yes, there is such an interpretation in Section 3 of the original paper by Pratt:

  Pratt, J. (1964). Risk Aversion in the Small and in the Large.
  Econometrica, 32(1/2), 122-136.

Under some regularity conditions, the coefficient of absolute risk aversion approximates the risk premium divided by half the variance for a small actuarily fair gamble. In Pratt's words, "$r(x)$ is twice the risk premium per unit of variance for infinitesimal risks". A similar interpretation holds for relative risk aversion, see Section 10.


Volatility and the stock market In general, it is known that market volatility increases during bear markets while it decreases during bull markets. Why is this the case? It seems strange that volatility is linked to the the general direction of price movements. Volatility is a measure of how much fluctuation there is in stock prices. During the bear market, prices go down and during a bull market, prices go up. There seems to me no relationship between the general direction of price movements and market volatility.

There seems to me no relationship between the general direction of
  price movements and market volatility.

Clearly the market disagrees with you. As the saying goes, "markets go up in an escalator and down in an elevator"---just take the recent mid-March correction and subsequent rebound
of, say, the S&P500 index.

Price and its properties are outcomes of market participants' trades.
Direction of price movement is determined by direction of trade and volatility by size of trade.
It is a consistently observed fact that when traders perceive that their positions are in danger of being wiped out (the perception possibly spurred by some exogenous event), they head for the exits en masse and quickly. This can also be seen during a "short squeeze", where shorts scramble to close their positions, or a bank run (e.g. the margin calls faced by Lehman Brothers, and subsequent liquidation of its positions, during the precursor to the financial crisis).
In comparison, a crowded trade usually becomes crowded gradually.

The economic explanation for this market behavior is risk-aversion.

Much of finance is built on the equilibrium relationship between the first and second moment of prices, i.e. expected price movement and volatility.
What matters is not just expected return $\mu$, but risk-adjusted return---this is precisely the Sharpe ratio $\frac{\mu - r}{\sigma}$ that arises in CAPM, where $\sigma$ is volatility.
This is because risk aversion leads to market participants putting more weight on the downside than upside. Therefore high risk (volatility) means market demands high risk premium.

The flip-side of this coin is that, in a bull market, it's the upside that is being priced and risk-premium demanded by the market is low. Therefore volatility is low and price escalates up gradually.
On the other hand, when perception of market risk changes, traders reduce their holdings as prevailing expected excess return falls short of required risk-premium.
As more and more market participants exit their long positions, this cascades and becomes a self-fulfilling phenomenon.

Price becomes more volatile on the down-leg because the market is expecting more volatility, and vice versa.

(To be slightly more technical, the Sharpe ratio $\frac{\mu - r}{\sigma}$ is proportional to the degree of risk-aversion. Assuming the degree of risk-aversion remains constant, then expected excess return $\mu - r$ is proportional to $\sigma$. Therefore, low volatility, low return---escalator. High volatility, high return---elevator.
If people become more risk-tolerant during bull market and more risk-averse during bear market, this would exaggerate the escalator/elevator contrast even more.)

The change in market perception of risk---implied volatility---can be large compared to (already dramatic, during a crash) change in price.
See, for example, the comovement of the S&P500 and VIX indices during the mid-March episode.
The drop in S&P500 is tame compared to the increase in VIX.

Further Comments

In economic theory, the fact that agents "put more weight on the downside than upside" is reflected by the stochastic discount factor (SDF). This is a standard object in asset pricing. The SDF is basically agent's state-dependent marginal utility, up to a multiplicative factor. Because of risk-aversion, in bad states of the world where consumption is low, marginal utility is high. Therefore agents put more weight on bad states than good states. A closely related object in mathematical finance is the risk-neural measure. The risk-neutral density and SDF differs by a discount factor.
VIX is the volatility of S&P500 implied by the Black-Scholes formula (one example of risk-neutral pricing). High VIX means market expects high volatility, as reflected by options prices.
The typical "volatility smile" is skewed towards the put side---one such example here. Put options  are more expensive relative to calls, i.e. it is more expensive to buy insurance against price falling than betting on price rising. This again points to the fact traders put more weight on the downside.
In a world where market participants are risk-neutral, what you say would be true. But, as discussed above, the market tells us otherwise.


Can the US government selectively cancel debt held by the Federal Reserve? Sort of a follow-up to this question on the Politics SE, which asked about the US government cancelling debt held by China.
From the answers to that question, this kind of selective default is not much better than a full default, because the entity being defaulted on (China in this case) can seize US assets abroad as "payment" for the debt. How would this work if the US government decided to only cancel bonds held by the Federal Reserve? Since the Fed is part of the US government, presumably the government can decide not to seize its own assets (does that even make sense?) or retaliate in any way, and there'd be no consequences other than the fact that there's no more interest payment on debt.
Can the US government selectively default on debt held by the Federal Reserve? If yes, what are the possible consequences? I'm especially interested in economic consequences.
Related: What would happen if the US defaults on its debt? which deals with a wholesale default.

The total federal debt equals intragovernmental holdings plus debt held by the public. Technically the federal debt held by the Federal Reserve System (Fed) is considered to be debt held by the public. However by law the Fed covers its operating costs and then returns to the federal government almost all of the interest payments it earns from holding the debt of the federal government.
If Fed is treated as the monetary authority of the federal government, despite its political independence, then the Fed balance sheet can be consolidated with the Treasury balance sheet for the federal government. Note the Treasury keeps an incomplete balance sheet because the value of land and natural resources is not considered in the national accounts.
If one consolidates the Fed and Treasury balance sheet positions then this reduces the debt held by the public by the amount of debt held by Fed. Also it eliminates the Fed liabilities due to Treasury. But it would not reduce the Fed liabilities held by the public. So the public holds a mix of Fed and Treasury liabilities issued to manage fiscal policy and monetary policy on behalf of the federal government.
The federal government issues debt to implement fiscal policy and authorizes Fed to implement monetary policy in large measure by the purchase and sale of Treasury debt in the open market. So there is nothing to be gained in terms of fiscal or monetary policy objectives even if the government tried to cancel debt owed to Fed.


Should the government regulate the price of bananas? Diclaimer: This is not a homework question. Every word of it was written originally by me.

Hypothetical Scenario

Alice is shopping for groceries and thinks the current price of bananas at $0.79/lb is a little too high for her budget. Alice calls Bob, her local legislator, and asks Bob to sponsor a bill that regulates the price of bananas to cost no more than $0.50/lb in the grocery store so Alice can afford to buy them.

Bob thinks this is a great idea because it will help more people (especially the poor and those on a fixed income) afford to buy more bananas — a very nutritious food.

Question

Is this bill to regulate the price of bananas really a good idea? What would be the impact of such a law if it were to pass?

(source: dineshbakshi.com)

As you can see in the graph, price controls policies create excess demand, therefore you will end up with shortage or you will import more bananas.

I'm not a banana expert, but I assume bananas are pretty inelastic. Also, banana supply is inelastic in the short run (they have already planted bananas), therefore the excess demand will be less than the graph shows.

Whatever the case, price control policies generate deadweight loss and it depends on the elasticities who loses more (consumer vs supplier). This market is no longer efficient and that impacts the welfare negatively.


Show a compound function is increasing and supermodular given its components If $f:\mathbb{R}^n \to \mathbb{R} $ is twice continuously differentiable, has a non-negative gradient, and is supermodular, and $g: \mathbb{R} \to \mathbb{R}$ is twice continuously differentiable and convex, then $g(f(x))$ is increasing and supermodular

To show increasing I think we can just show $\displaystyle \frac{d}{dx} g(f(x)) > 0$

$$ \displaystyle \frac{d}{dx} g(f(x) = g'(f(x)) f'(x) $$

Since $f(x)$ has a non-negative gradient $f'(x) \geq 0$, but I'm not sure how to show $g'(f(x)) > 0$ as given convex tells us $g''(x) > 0$

For supermodularity, let $l, l' \in \mathbb{R}^n$; $g(f(x))$ will be supermodular if the following inequality holds:

$$ \displaystyle (g \circ f)(l \vee l') + (g \circ f)(l \wedge l') \geq (g \circ f)(l) + (g \circ f)(l') $$

I think if we had $l_i \leq l_i', \; \forall i$, then we will have equality as $(g \circ f)(l \vee l') = (g \circ f)(l') $ and $ (g \circ f)(l \wedge l') = (g \circ f)(l)$, but don't know what to do for the other cases.

I don't think this proposition holds without assuming that $g$ is also increasing.
Take $f(x_1,x_2)=x_1x_2$ (actually any supermodular function) and $g(z)=-z$ (decreasing and convex). Then, $g(f(x_1,x_2))=-x_1x_2$ which is neither increasing in its arguments or supermodular.

If you assume also that $g$ is increasing, you get $g'(f(x))\geq 0$ straightforwardly.

You can easily show supermodularity using the conddition on the second derivatives. Denote $x=(x_1,...,x_n)$. Supermodularity is equivalent for function f to $$\frac{\partial^2 f}{\partial x_i \partial x_j}(x)\geq 0$$ for any $i\ne j$.
If you twice-differentiate $g \otimes f$ ($\otimes$ is the compound operator),
$$
\frac{\partial^2 g \otimes f}{\partial x_i \partial x_j}(x)=\frac{\partial^2 f}{\partial x_i \partial x_j}(x) . g'(f(x)) + \frac{\partial f}{\partial x_i}(x) .\frac{\partial f}{\partial x_j}(x) .g''(f(x))
$$
You can check that $\frac{\partial^2 g \otimes f}{\partial x_i \partial x_j}(x)\geq 0$ so that $g \otimes f$ is supermodular since $f$ is supermodular, $g$ is increasing and $g$ is convex.


Economic models failing to predict inflation In this video here Warren Mosler states that all economic models fail to predict inflation ("All their models show it's indeterminate"). I am looking for some references to support that claim... Or is Warren plain wrong?

Depends on what the author meant by:

  All their models show its indeterminate.

If you would want to take this in a literal sense then no. An easy counter example would be some bachelor level monetary model or Philipps curve.

However, there is a famous indeterminacy problem in macroeconomics which is real in many models. The problem is that in many (but not all) macroeconomic models forward looking monetary interest rates setting rules such as Taylor rule with finite horizon may lead to real indeterminacy which means that when you shock your system there might be many different paths that will make real variables return to the long run equilibrium, and consequently also to indeterminacy in the rate of inflation.

But there are also mainstream models outside MMT that solve this problem. For example, even in this paper from ECB authors show that just change in interest rate setting rule can resolve this issue. Moreover, again this is definitely not issue in “All economic models”.

However, if the author was exaggerating and by that meant that there is a serious indeterminacy issue in many models based on simple finite horizon interest rate setting rules, which is still an active research topic in mainstream macroeconomics then in that sense the statement would be accurate.


Best-responding to a stochastically higher distribution of bids In Auction Theory, Krishna writes that:

  a bidder who faces a stochastically higher distribution of bids–in the
  sense of reverse hazard rate dominance–will bid higher

(This follows the proof of proposition 4.4 in the section 'Weakness Leads to Aggression'.)

Supposedly, this is 'easy to see' - however, I am having trouble seeing it! I would be grateful if someone could explain why this is true.

My (unsuccessful) efforts so far:

If I bid $b$ when my valuation is $v$, then (under risk neutrality) my expected utility is

$$(v - b)F(b)$$

where $F(b)$ is the cumulative distribution function of all the bids apart from mine (and thus the probability that I win the auction).

Maximising my expected utility with respect to $b$, we obtain the first order condition

$$(v - b)f(b) - F(b) = 0$$

Which implies that

$$b = v - \frac{F(b)}{f(b)}$$

A distribution $G$ is stochastically higher than a distribution $F$ in the sense of reverse hazard rate dominance when, for every $b$

$$\frac{g(b)}{G(b)} > \frac{f(b)}{F(b)}$$

Now, if $f(b)/F(b)$ and $g(b)/G(b)$ do not depend on $b$, it is obvious from the first order condition that I will bid higher when facing a stochastically higher distribution of bids. However, it is not clear to me what happens in the general case where the 'hazard rates' may depend on $b$.

Many thanks in advance!

Bonus question: When my bids increase, will my new distribution of bids 'stochastically dominate' my old distribution (in the sense of the reverse hazard rate)?

Here is a sketch of an answer.

As noted in the question, the optimal $b$ must satisfy

$$b = v - \frac{F(b)}{f(b)}$$

Let us define the function $h(b) = v - F(b)/f(b)$. Our problem is to find the the fixed points of the function $h(b)$, i.e. the $b$ such that

$$b = h(b)$$

What can we say about $h(b)$? Assuming there is a unique optimal bid, it crosses the 45 degree line exactly once. Moreover, assuming that bids cannot be negative, i.e. $F(b) = 0$, it follows that $h(0) = v$. Thus, assuming that $v > 0$, the function $h(b)$ starts off above the 45 degree line.

Now, when the opponent bids are 'stochastically higher', the function $h(b)$ moves upwards in the sense that the 'new' function lies everywhere above $h(b)$. It thus seems reasonably clear that the unique fixed point must increase, though admittedly I lack a conclusive proof of this fact.

I am also unsure about the bonus question (whether my new bids seem stochastically higher in the sense of the reverse hazard rate).


Can I get a more detailed explanation of the Weak Axiom of Profit Maximization? In Hal Varian's Book "Microeconomic analysis" on page 35 he gives the following description of a profit maximising firm.

"...If the firm is maximising profits, then the observed net output choice at price pt must have a level of profit at least as great as the profit at any other net output the firm could have chosen. We don't know all the other choices that are feasible in this situation, but we do know some of them-namely, the other choices $y_s$ for $s=1,...,T$ that we have observed. Hence, a necessary condition for profit maximisation is that
$p_ty_t≥p_ty_s$
for all $t$ and $s=1,...,T$.

"We will refer to this condition as the Weak Axiom of Profit Maximisation (WAPM)."

I dont understand this can I get a more detailed drawn out explanation as if I'm five, or a reference to where I can further information on this?

You don't need more detail, you need less:

Suppose a firm could make production choice A, or production choice B.  Suppose the firm chooses A, and is maximizing profits.  Then, this implies that the firm is making as much or more profits as it would make if it had chosen B.


What limits central banks from setting highly negative interest rates? What limits central banks from setting highly negative interest rates if needed? Is it only that people can take out a lot of cash and put it in a vault, or are there other reasons?

If we had removed cash and only had electronic money, could central banks set interest rates highly negative, for instance, -10%? Could they set it to -20%? Or would people just have started to use other means of value, like foreign currencies, crypto currencies or gold?

Since this is a question about central banks... they would not want to do this because it would push many ordinary people to put their savings in highly speculative assets, potentially destabilizing the economy. It is/was already a bit of a concern even with near zero, never mind mildly negative interest rates. There's a fine line between "kickstarting the economy" and setting up a large portion of the population to speculate in the junk bond market and/or housing.

Also, wealth inequality will probably go up faster as well (in the long) as more smaller investors get wiped out, although that's seldom a concern for central banks, given their usual mission.

As for hoarding cash in such an environment... that's not without risk either, because the authorities could decide to counter that with some kind of demonetization (see India, and numerous other historical examples.)

Also, in a democracy, weird stuff might happen, like the Swiss left- and right-wing populist parties threatening to put to a referendum a redistribution of the central bank profits into the pension funds (who blame the central bank for their losses.) That would basically negate the effect of the negative interest rates, as far as the pensions funds are concerned. In fact, it would act like a redistribution from others to said pension funds, ultimately.


Difference between automated and living labor pertaining to surplus value In the Marxist concept, animals, machines and slaves are incapable of producing surplus value. They only produce as much as they have to in order to function, and no more. Doesn't this also describe the condition of "wage-slaves"? I have heard that the difference is that the wage-slave sells his labor. But I fail to see how a machine that sells its labor for fuel and spare parts would suddenly be able to produce surplus value. Explain please.

This question is oddly phrased.

The main marxist thesis about profit is that firms can't profit from technology, but ultimately profit comes from exploitation of human labor, i.e. by extracting surplus value from workers.

In marxism, profit always comes from "living labor", in the sense that the price of a commodity both reflects the technology used to create it and also the human labor congealed in it. However,  a firm can't "pay less" machines because machines have fixed values while a living human being can be paid less than their value of their labor if the value of their labor exceeds the value the worker needs for subsistence (e.g. sufficient for their bills, calories, leisure etc).


How to calculate standard deviation of a portfolio? So i have this information:

Suppose that 60% of your portfolio is invested in Johnson & Johnson (JNJ) and the remainder is invested in Ford. You expect that over the coming year JNJ will give a return of 8% and Ford, 18.8%.

Then I know that expected return on the portfolio is simply a weighted average of the expected returns on the individual stocks:

Expected portfolio return = (.60 × 8) + (.40 × 18.8) = 12.3%

However, then the book says:

We said earlier that if the two stocks were perfectly correlated, the standard deviation of the portfolio would lie 40% of the way between the standard deviations of the two stocks.

There have been no other calculations on the book and only after this statement should i start the calculations in order to understand the portfolio risk.

Can somebody please tell me where this 40% is coming from ? Thanks!

You could say the return on Johnson & Johnson is a random variable $R_J$ with expected value $\mu^{\,}_J$ and variance $E[(R_P-\mu^{\,}_P)^2] = \sigma^2_J$, and on Ford is $R_F$ with expected value  $\mu^{\,}_F$ and variance $E[(R_F-\mu^{\,}_F)^2] = \sigma^2_F$

$R_J$ and $R_F$ perfectly correlated means $\frac{\mathbb E[(R_J-\mu^{\,}_J)(R_F-\mu^{\,}_F)]}{\sigma^{\,}_J\,\sigma^{\,}_F}=1$ so $\mathbb E[(R_J-\mu^{\,}_J)(R_F-\mu^{\,}_F)] = \sigma^{\,}_J\sigma^{\,}_F$

Now consider your portfolio $60\%$ Johnson & Johnson and $40\%$ Ford.  It has return $R_P= 0.6 R_J +0.4 R_F$ with expected value $\mu^{\,}_P= 0.6 \mu^{\,}_J +0.4 \mu^{\,}_F$ by linearity of expectation, so the actual return and expected return are $40\%$ of the way from the corresponding figures for Ford to the figures for Johnson & Johnson

Now consider the variance of the return on the portfolio $$\sigma^2_P = \mathbb E[(R_P-\mu^{\,}_P)^2] \\= \mathbb E[(0.6 (R_J-\mu^{\,}_J) +0.4 (R_F-\mu^{\,}_F))^2] \\ = 0.6^2 \sigma^2_J +2\times  0.6 \times 0.4 \sigma^{\,}_J\,\sigma^{\,}_F + 0.4^2 \sigma^2_F \\= (0.6 \sigma^{\,}_J + 0.4 \sigma^{\,}_F)^2 $$
so taking square roots gives $\sigma^{\,}_P = 0.6 \sigma^{\,}_J + 0.4 \sigma^{\,}_F$, i.e. the standard deviation of the return on the portfolio is  again $40\%$ of the way from the corresponding figure for Ford to the figure for Johnson & Johnson