How can the Swiss exchange rate be very biased in a free market? In 2002, when Germany, France, Italy and Austria adopted the Euro currency, the exchange rate with Switzerland was 1.60 CHF (Swiss Franc) = 1€ (Euro).
The prices and salaries in Switzerland were slightly higher than in its neighbours, but reasonably so.

Since then the Swiss franc has been more and more valuable and today reaches the rate of 1.04 CHF = 1€. The prices and salaries in Switzerland are over two times higher than in the neighbouring countries.

Depending on the way of computing this (price of food, price of housing, prices of insurances, lower range salaries or median salaries), the purchasing power parity exchange rate should be between 1.80 CHF and 2.50 CHF for 1€.

Since the exchange rate is so biased, in a free market it should be easy for Swiss people to buy stuff in neighbouring countries for cheap prices, and re-sell them at a more competitive prices in Switzerland. That would have the effect of lowering prices, creating deflation, and equalizing prices with neighbouring countries.

So my question is : Why doesn't such a regulation of the exchange rate happen? What actually happens is the opposite : The price bias becomes wider and wider, leading to a ridiculous situation where for example a piece of bread costs over 2 times more in one side of the border than on the other side, with all the side issues this causes.

Swiss people do shop outside of their border, exactly as you think they should:

  "Even the Swiss are staying away from their local stores and products—they would rather buy from neighbouring countries and take advantage of the situation. Switzerland is bound by Germany, France and Italy, and most of its big cities are located just at the border. It is relatively easy for Swiss residents to do their shopping elsewhere and get high value for their money, but it also means that the Swiss supermarkets and downtown stores have lost huge shares of the consumer market." (Source: http://www.forbes.com/sites/realspin/2015/03/30/currency-wars-the-swiss-case/)

Currency is like any other commodity in the sense that its price (i.e. the exchange rate) is higher when demand is high relative to supply. For the exchange rate to remain high even when large sections of the population are selling Francs to get the Euros they need to shop in Germany, it must be that somebody else is buying up a lot of Francs and thus providing a large source of demand for the currency.

That someone else appears to be foreign investors, who are desperate to put their money into a safe and stable environment. In 2013, investors put 101bn Francs more into Switzerland than they took out (an amount equal to 22% of Switzerland's GDP!). In 2014, this figure fell dramatically, but there was still a net inflow equating to 7.5% of GDP.

On top of investors putting money into the country, Swiss companies are also net exporters. In 2013, Switzerland exported 65bn CHF more of goods and services than they imported–15% of GDP. Every time a Swiss company sells a product to someone in the US, dollars need to be changed into Francs (either because the Swiss company sets prices in Francs, or because it gets paid in dollars and then wants to repatriate the money in domestic currency).

These two sources of money flowing into Switzerland (respectively known as the capital account and the current account, and collectively known as the balance of payments) provide a robust source of demand for Swiss Francs and ensure that the value of the currency remains high.

The source for the numbers quoted above is here: http://snbchf.com/euro-zone-swiss-macro/swiss-balance-payments-2014/


Overlapping Generations model: Social Planner solution Assume we have a model of OVG where there are 2 overlapping generations, youngs and olds, the agents are two period living. The utility function is logaritmic, and the production function is Cobb-Douglas.

I have to show that the solution for the social planner does not coincide with the equilibrium from the market.
The social planner solves:
$$\max  \ln(c_t^y)+\beta \ln(c_{t}^o)$$
$$s.t.$$
$$c_t^y+\frac{c_t^o}{1+n}+k_{t+1}(1+n)-k_t=f(k_t)$$
Where the units are expressed in per capita terms and $n$ represents the population growth rate.
 The FOC for the social planner is
$$\frac{c_{t}^o}{c_t^y}=\beta(1+n)$$
We know that in steady state the level of consumption is actually constant i.e.
$c_t^o=c^o$ and $c^y_t=c^y$.
What I am not getting is if I should replace this on the constraint in order to obtain the values of S.S. or if I need to take the FOC with respect to the $k$.
I am a little bit lost, since I've already solved the problem for the market economy but I am having a hard time figuring out how to proceed.
Any hint will be greatly appreciated.

Start by writing the Lagrangian (as it sounds like you have already done):

$$L=\sum_{t=0}^{\infty} \{\beta^t(\ln C_t^y + \ln C_t^o) + \lambda_t (C_t^y +\frac{C_t^o}{1+n} +k_{t+1}(n+1)-k_t-f(k_t))\}.$$

First order conditions are given by
$$\frac{\partial L}{\partial C_t^y} = \frac{\beta^t}{C_t^y} +\lambda_t = 0$$
$$\frac{\partial L}{\partial C_t^o} = \frac{\beta^t}{C_t^o} +\frac{\lambda_t}{1+n} = 0$$
$$\frac{\partial L}{\partial k_{t+1}} = \lambda_{t-1}(1+n) -  \lambda_t(1 + f'(k_t)) = 0$$
$$\frac{\partial L}{\partial \lambda_{t}} = C_t^y +\frac{C_t^o}{1+n} +k_{t+1}(n+1)-k_t-f(k_t)=0.$$

First notice the first two equations give us
$$\frac{C_t^y}{C_t^o} = 1+n.$$
Also notice that the first equation implies $\lambda_t = -\frac{\beta^t}{C_t^y}$. Substituting this into our third equation gives
$$\frac{\beta^{t+1}}{C_{t+1}^y}(1+n) = \frac{\beta^{t}}{C_{t}^y}(1+n)(1 + f'(k_t)$$
or equivalently
$$\frac{\beta C_t^n}{C_{t+1}^y} = (1 + f'(k_t)).$$

Finally, we can write our system of four equations with three equations, having removed $\lambda$ from the system:
$$\frac{C_t^y}{C_t^o} = 1+n$$
$$\frac{\beta C_t^y}{C_{t+1}^y} = (1 + f'(k_t)).$$
$$C_t^y +\frac{C_t^o}{1+n} +k_{t+1}(n+1)-k_t-f(k_t)=0.$$

Dropping time subscripts, i.e. applying the steady-state condition, gives
$$\frac{C^y}{C^o} = 1+n$$
$$\beta = (1 + f'(k)).$$
$$C^y +\frac{C^o}{1+n} +nk-f(k)=0.$$

Hence, you are left with a system of three equations with three unknowns $C^y$, $C^o$, and $k$. Solve the system to arrived at a steady-state solution.


Preferences over lotteries Can anybody give me a hint how to solve the following problem?

*One way to construct preferences over lotteries with monetary prizes is by
evaluating each lottery L on the basis of two numbers, Ex(L), the expectation
of L and var(L), L’s variance. Such a procedure may or may not be consistent
with vNM assumptions.

Show that u(L) = Ex(L) − (1/4)var(L) induces a preference relation that
is not consistent with the vNM assumptions. (For example, consider
the mixtures of each of the lotteries [1] and 0.5[0] ⊕ 0.5[4] with the
lottery 0.5[0] ⊕ 0.5[2].)*

I am especially not sure about how to compute the variance in this case.

A lottery is essentially a probability distribution. So the variance of a lottery is the variance of the probability distribution it represents, which is given by the formula
\begin{equation}
\mathrm{Var}(L)=\sum_{i=1}^np_i(x_i-\mathbb E(L))^2,
\end{equation}
where $p_i$ is the probability that outcome $i$ occurs, $x_i$ is the monetary value of outcome $i$, and $\mathbb E(L)$ is the expected value of the lottery.

Take the lottery $L_2=0.5[0]\oplus0.5[4]$ for example. We can easily verify that $\mathbb E(L_2)=2$. By the formula above, then,
\begin{equation}
\mathrm{Var}(L_2)=0.5(0-2)^2+0.5(4-2)^2=4.
\end{equation}

I'll leave you to finish the rest of the question.


Guess 2/3 of the average with integers - mixed strategy equilibria? The "Guess 2/3 of the average" game (Wikipedia) is a game in which n people guess what 2/3 of the average of their guesses will be, and where the numbers are restricted to the integer (in this case) numbers between 0 and 100, inclusive. The winner is the one closest to the 2/3 average.

By iterated deletion of weakly dominated strategies, it is easy to show that all integers but 0 and 1 vanish because it is possible to rule out iteratively those numbers who cannot be 2/3 of the average of the played numbers. For example, the first step is to eliminate all the integers above 66 because even though everybody will play 100, 2/3*100 = 66.67, thus this is the maximum value the right number could reach.

Now, my question is which are the pure and mixed strategy Nash equilibria of this game?

Winning the game gives a payoff of 1, losing a payoff of 0. If there is a tie, the payoff is distributed uniformly among the winners. The pure NE should be playing 0, while I am totally lost about the mixed strategy one.

Does anybody know how to proceed?

Quick note: in pure strategies for sufficiently many players, shouldn't all 1 be NE as well?

Onto mixed strategies:

To have a mixed strategy Nash equilibrium, each player needs to be indifferent between the strategies they are mixing and they must prefer all those strategies to the ones they never play.

That means players must mix only between strategies between which they have an equal probability of winning (when given all other players' strategies). I suspect you can use this to show that players must mix between 0 and 1. Then it remains to solve for whatever mixed strategies give which players indifference between 0 and 1.


What am I doing wrong in the derivation of Bass diffusion model? I've been deriving Bass diffusion model and keep consistently finding a different result than Bass' original answer. To make things worse, every single link in the Google results page just copies the Bass original solution, while I am finding the different one. You don't have to know the model, just let me show you the math part, so you can check my solution.

The premise:

We have two formulations of the hazard rate --- as Bayesian conditional probability and as a linear function:

\begin{equation}
 \frac{f(t)}{1-F(t)} = p + q F(t)
\end{equation}

where $f(t) = \frac{dF(t)}{dt}$. This gives the following differential equation:

\begin{equation}
 \frac{dF(t)}{dt} = (1 - F(t)) (p + qF(t))
\end{equation}

My solution

Using Chain Rule, we rewrite this as:

\begin{equation}
 \int \frac{dF(t)}{(1-F(t))(p+qF(t))} = \int dt = t
 \label{eq:diff}
\end{equation}

Notice that:

\begin{equation}
 \frac{1}{(1-F(t))(p+qF(t))} = \left( \frac{1}{p+q} \right) \left( \frac{q}{p+qF(t)} + \frac{1}{1-F(t)} \right),
\end{equation}

substituting this to the above equation, implies:

\begin{equation}
 \int \frac{q}{p+qF(t)} dF(t) - \int \frac{-1}{1-F(t)} dF(t) = (p + q) t
\end{equation}

integrating yields:

\begin{equation}
 \log (p + qF(t)) - \log (1 - F(t)) = (p + q) t
\end{equation}

using log properties:

\begin{equation}
 \log \left( \frac{p + qF(t)}{1 - F(t)} \right) = (p + q) t
\end{equation}

or:

\begin{equation}
 \frac{p + qF(t)}{1 - F(t)} = e^{(p+q)t}
\end{equation}

cross producting the fraction yields:

\begin{equation}
 p + qF(t) = e^{(p+q)t} - e^{(p+q)t} F(t)
\end{equation}

finally:

\begin{equation}
 (q + e^{(p+q)t}) F(t) = (e^{(p+q)t} - p)
\end{equation}

or:

\begin{equation}
 F(t) = \frac{e^{(p+q)t} - p}{e^{(p+q)t} + q}
\end{equation}

The problem:

But Bass, somehow found the following:

cancelling out my answer does not yield Bass' answer. The unnecessary $q$ is ruining everything.

Can you please help me with this inconsistency?

Thank you.

You are missing an integration constant

$$
\log\left(\frac{p + qF(t)}{1 - F(t)}\right) = (p + q)t + \color{red}{\tilde{C}}
$$

This constant you can name it whatever you want, I'm going to name it as

$$
\color{red}{\tilde{C}} = \color{blue}{C}(p + q) + \ln q
$$

where $C$ is just another constant. So I basically changed one constant for  another one (completely allowed). Now the problem becomes

\begin{eqnarray}
\ln\left(\frac{p + qF(t)}{1 - F(t)}\right) &=& (p + q)t + \color{blue}{C}(p + q) + \ln q = (p + q)(t + C) + \ln q\\
p + qF(t) &=& e^{(p + q)(t + C) + \ln q}(1 - F(t)) = qe^{(p + q)(t + C)}(1 - F(t)) \\
[q + qe^{(p + q)(t + C)}]F(t)&=& qe^{(p + q)(t + C)} - p \\
F(t) &=& \frac{1}{q} \frac{qe^{(p + q)(t + C)} - p}{1 + e^{(p + q)(t + C)}}
\end{eqnarray}

Rearranging a bit the terms

$$\bbox[5px,border:2px solid blue]
{
F(t) = \frac{1}{q}\frac{q - pe^{-(p + q)(t + C)}}{1 + e^{-(p + q)(t + C)}}
}
$$


statistics about loaning tradeoff It is very likely that Banks have more loans that have been repaid compared to loans that have not been repaid. Otherwise the bank would lose money instead of money. (otherwise the bank will go bankrupt)

Are there statistics (research papers with references) about this?
(Can be of any country or individual bank etc.)

Loans that have not been repaid are generally called "non-performing loans" or NPL. Each country's bank regulatory body should have statistics on this. Here's one from the World Bank.

Note that this is the ratio between outstanding NPL and total outstanding loans. The ratio could go down if the borrower agrees to continue paying back, or if the banks decide to "write off" the loans. It could also go down if there's a significant increase in loans (the denominator).

Since this statistic is a "stock" variable, the NPL to outstanding loans ratio could be huge, for example, after a financial crisis and stays high as NPLs got "stuck" in the system. It wouldn't be until these borrowers can pay back or banks write off that outstanding NPL could go down.

One way to rectify this is to look at the "vintage" of loans, essentially asking, of all loans originated in 2012, how much has turned into NPL after X months.


How would unlimited free energy affect the global market? What will the effect on today's global market if a new source of free unlimited energy was to be discovered?

How badly will it disrupt today's global market and how badly will it affect our currency?

Or it will do good to today's economy?

This would represent an extreme increase in long-run aggregate supply. In the AS/AD framework, this would result in a long-run increase in production growth and a decrease in the inflation rate.

How "badly" it will disrupt today's global market? You've built an assumption that it's bad into your question, but sure, it will be bad for anyone who has invested in current energy sources. It will be fantastic, however, for anyone involved in literally any other entrepreneurial activity.

The only disruption in such a sudden and unexpected technology improvement would be that some financial institutions would find themselves overinvested in the energy sector. Insofar as they cannot handle the financial capital losses, there may be a private debt crisis that pushes politicians to bail them out again (ideally using the increases in tax revenues caused by increased productivity), or to simply declare their debt null and void. This would cause some consternation, but given that people tolerated financial bailouts after the housing crisis (where financial assets were wasted without any obvious social benefits at all), it's unlikely that there would be overwhelming protest in such a scenario.

The negative impacts of such a productivity shock would only be temporary, however. Energy is one of the limiting factors of production, so free energy would cause production to grow as fast as entrepreneurs can find a use for it, which would be very quickly.


Securities traded in different currency Excuse me if this is not the site to ask this question but I read in meta that you have a accounting tag so here we go.

If I made a buy of an ETF in two different exchanges  with different currencies (same Isin, different currency see this question in personal money and finance exchange) and I'm valuing this securities at fair value. I have to take the ETF as the same or different security? (i.e. makes some difference the currency of the exchange)

I don't really see why you would price an ETF at fair value and not at last market price, given that those funds are very liquid. But in either cases you need to have two distinct securities in your portfolio, as the two classes of shares that you own in the ETF bear different risks, and will yield different performances, due to the xrate.


Unitary Elastic Demand My teacher defined Unitary elastic demand as demand which has $PED = (-)1$ . The formula I have been told for $PED$ is $\%\Delta Q_d /\% \Delta P$.  But how can total revenue $( = P\times Q)$  remain constant for such a demand? Suppose $P$ goes up $10\%$, so $P' = 1.1P$. For unit elasticity, $Q$ must go down $10\%$ so $Q' = 0.9Q$.  So $T' = Q' \times P' = 0.9Q \times 1.1P = 0.99 \times PQ = 99\%$ of $T$. So when we say $T$ stays constant, do we mean that as an approximation ?

The way to examine such issues is by general mathematical treatment, not arithmetic examples.

We have total revenue

$$TR = Q(P)\cdot P$$

When will Total Revenue remain constant as price changes?

We want

$$\frac{\partial TR}{\partial P} =0 \implies \frac{\partial Q(P)}{\partial P}\cdot P + Q(P) =0$$

$$\implies  \frac{\partial Q(P)}{\partial P} = -\frac {Q(P)}{P}$$

which is to say that the price elasticity of demand is equal to minus unity.

Is it possible for this to hold over the whole range of $P$ and not just momentarily, at a specific value of $P$?

This entails to find a solution to a simple differential equation (using generic notation)

$$y' + \frac{y}{x} = 0$$

which gives

$$Q(P) = \frac {A}{P},\;\;\; A>0$$

So if the demand function is as above, it has unitary price elasticity everywhere.


Quasiconvexity of the indirect utility function In Mas-Colell, Whinston, and Green's Microeconomics they define the indirect utility function, $v(p,w)$ as

$$ v(p,w) := u(x^*) $$

Where $x^* \in x(p,w)$ solves the utility maximization problem.

They state a property of $v(p,w)$ is quasiconvexity, i.e. the set

$$ \{(p,w): v(p,w) \leq \bar{v} \} $$

is convex for any $\bar{v}$.

Just the page before they said that convexity of preferences implies that $u(\bullet)$ is quasiconcave, so my question is why when we look at the max of $u$, it's quasiconcave property inflects (can't think of a better word) to quasiconvexity?

The functions and their variables are different, so there is no "inflection" or flipping.

The utility function $u$ which maps from the space of goods $X$ to $\mathbb{R}$ is convex and quasiconcave.

The indirect utility function $v$ which maps from the space of prices to $\mathbb{R}$ is quasiconvex.

Intuitively:
$u$: If you average two consumption bundles your utility is not lower than the average of the utility of the two bundles. Rather than eating just meat one day and just vegetables the other day you prefer to mix these everyday.

$v$: If the price vector is $p$ one day and $p'$ the other day you may be better off than if it was $\frac{p + p'}{2}$ every day. It is easy to check that anything you can buy under the second price regime you can also buy under the first. However there might be consumption bundles that you can only buy under the first price regime.


Compute variables in perfect competition, in monopoly and duopoly There are a given demand and MC value. How could I calculate quantity, price, and profit from these values in case of perfect competition, in monopoly and duopoly(Cournot and Stackelberg)?

Under perfect competition, $p=MC$. So you may substitute this price into the demand equation to obtain the quantity.

A monopolist chooses output in a way such that $MR=MC$. So you have $P‘(Q)*Q+P=MC(Q)$, where $P(Q)$ is the inverse demand  equation.

For Cournot, it is also simple. Note that the profit function of firm i is given by $$\pi(i)=P(q_{i}+q_{-i})*q_{i}-MC(q_{i})*q_{i}$$. You just use the first order condition to solve for the price and quantitiy respectively. $q_{-i}$ denotes the output of all players except for $i$.

Finally, for Stackelberg I would like to know how many players/firms you have. Then, I would be able to explain it to you in a suitable way. I hope this helps.


Economic implications of allowing competition with essential services i.e police, fire department, etc I'm wondering what are the implications of allowing competition between firms that deal with essential services in public welfare. I.e assuming there is no government regulation of such services, what would happen if there was competition between firms in the policing industry or if there was competition allowed among different fire departments?

What would the industry look like and what kind of methods would we use to analyse such a situation?

As already suggested in the comments of the OP, we find cases where the provision of essential services behave much like any other market when privatized.
As suggested by Henry it was found that in the case of fire fighters, they simply let the homes burn down. On the London Fire Brigade's Website they discuss the issue in question with great detail.

People paid a fee to an insurance company to insure their property against damage. The most common risk at this time was fire. The first insurance company was named Phoenix, after the Greek mythological bird that rose from the ashes, and was established by Nicolas Barbon.
Building insurance was very profitable and many more insurance companies were set up with the insurance companies establishing their own fire brigades. These brigades were sent to insured properties if a fire occurred to minimise damage and cost.
Firemarks were used to identify - and advertise - different insurance companies. They were placed on the outside of an insured building and brigades would use these firemarks to determine whether a building was insured by them. If a building was on fire, several brigades would attend; if they did not see their specific firemark attached to the building, they would leave the property to burn. You can still see some old firemarks on buildings today.

Similarly we in 2010 there was a case of Tennessee firefighters letting a home burn when the owner didn't pay fire-protection fee. Its clear that if an essential service is allowed to be privatized, they will function like any other business.


Monopoly equilibrium with a completely inelastic demand What is the impact of an inelastic demand function on a monopoly production and pricing strategy ?

Theory states, that a monopoly will strive to maximize its profits, by arriving to a point where the difference between the revenues and costs is at a maximum

The potential revenues derive from quantity of sales at a certain price, whixh by turn, are affected by demand

If the demand is inelastic, that means that quantity will remain fixed, no matter the price

Does that narrow or broaden the monopoly's options ?
What's the impact of that type of demand on the equilibrium price ?

Perfectly inelastic demand means quantity demanded is $q$ irrespective of the price. If producing quantity $q$ costs $c$ then the monopolist's problem is

$$\max_p \{pq-c\}.$$

This problem is not well-defined because the function $pq-c$ is increasing in $p$ and has no maximum. So there is no solution to the monopolist's problem. Intuitively, since the monopolist can sell $q$ units at any price, it would want to choose a price of $+\infty$.

You remark incredulously that we do not observe infinite oil prices. If the price of fuel increased to \$1000 per gallon then people would obviously drive their cars less and demand less fuel. So the demand for oil is not perfectly inelastic!

One way to make the problem more well behaved, which is quite common in the literature, is to assume a so-called "choke-price" (a price above which demand drops to zero). Demand is therefore
$$D(p)=\begin{cases}q\text{ if }p\leq\overline{p}\\[0.3em]0\text{ if }p>\overline{p}\end{cases}.$$

The monopolist's problem is then

$$\max_p \{pq-c\}\text{ s. th. }p\leq\overline{p}.$$

This is a well-defined maxmisation problem with a unique solition: $p=\overline{p}$ (assuming $\overline{p}q<c$, otherwise the firm would just shit down).


Proving there exists no arbitrage opportunities given 3 states and 2 assets Assume there are 3 states of the world: w1, w2, and w3. Assume there are two assets: a risk-free asset returning Rf in each state, and a risky asset with Return R1 in state w1, R2 in state w2, and R3 in state W3. Assume the probabilities are 1/4 for state w1, 1/2 for state w2, and 1/4 for state w3. Assume Rf=1.0 and R1= 1.1, R2=1.0 and R3= 0.9.

(a) Prove that there are no arbitrage opportunities.
(b) Describe the one-dimensional family of state price vectors (q1,q2,q3)>

For (a), I believe this is equivalent to showing there exists a state price vector.

I know p=Xq, but since we are only given two assets X doesn't have an inverse so I don't know how to compute q. Further, we are not given p. How do I show a state price vector exists?

First, you are in fact given $p$. You can think of return as a security that costs 1 in current period and pays off $R$ in the next period. The price vector and the payoff matrix are thus
$$
p = \begin{bmatrix} 1 \\ 1 \end{bmatrix}, \  X = \begin{bmatrix} 1.1 & 1.0 & 0.9 \\ 1.0 & 1.0 & 1.0 \end{bmatrix}
$$
and we need to find positive vector $q$ of state prices such that $p = Xq$. Because the system is undetermined, there can be many such vectors, but as long as some of them are positive, we can be sure there's no arbitrage. To actually do the computation, one way would be to treat $q_3$ as a parameter, solve for $q_1, q_2$ as functions of $q_3$, then try to find $q_3 > 0$ such that implied values of $q_1,q_2$ are positive. But in this case it's easy to see that $q = (\frac{1}{3}, \frac{1}{3}, \frac{1}{3})$ does the job.


Monetary policy and potential output growth Can monetary policy affect potential output growth? And if yes, how is this consistent with the neoclassical thesis's of money neutrality in the long run?

Can monetary policy affect potential output growth?

Yes. Otherwise, central banks would be indifferent to quantitative easing and other measures.

  how is this consistent with the neoclassical thesis's of money neutrality in the long run?

It is not. The premise that "new money neither creates nor destroys machines" sounds accurate only in isolation. But in the real world, companies bind themselves to financial (as well as fiscal) obligations which are in terms of nominal variables.

Certain monetary policies may render those companies cash-strapped, thereby triggering liquidity crises, bankruptcies, higher cost of financing, emigration of skilled workforce, and other effects. Altogether, this may result in structural changes in the economy.

Thus, while the thesis assumes that the aggregate supply curve is vertical, it misses the logical notion that this curve may shift to the left or to the right in the long run.


Soros shorting the pound How did Soros make money by shorting the pound? When he sold the pound and made its price to decrease, he had to buy it back again to return the amount he borrowed, but doesn't buying the pound raise its price, so that he should not make any profit?

How did Soros make money by shorting the pound?

As a preamble, it is important to keep in mind the context in which this occurred:

Two years earlier (in 1990), the UK government had made the controversial and largely political decision of becoming a member of the Exchange Rate Mechanism (ERM);
eventually, the macroeconomic reality presented a dilemma to UK
policymakers: (1) to devaluate the pound, or (2) to raise interest rates;
the UK government discarded devaluating the pound because the extent of an effective devaluation would discredit the UK government's ERM decision and be politically detrimental;
but UK policymakers also refused to raise interest rates, since that would strangle UK's already troubled economy and trigger another crisis (e.g., borrowers ending up with negative equity).

Soros was able to close his short position profitably because:

when the UK decided to enter ERM,
the UK unilaterally chose a sterling/DMark exchange rate which was recklessly high from the start (and impliedly, without anticipation or consideration of complications that could subsequent ensue in the economy);
the UK government stubbornly embraced the ERM as the magic solution
for its economy, and it ignored the macroeconomic growing disparities between German economy and that of the UK & members of the ERM;
the Deutsche Bundesbank decided to raise its interest rates so as to curb the inflation in Germany as well as the costly process of Germany's reunification;
the UK ministers' political stand was so arrogant that they naively presumed they could compel the Deutsche Bundesbank to tailor its policies so as to help the UK ministers avoid the discredit and embarrassment for having made the wrong decision as to joining the ERM;
after Italy devaluated its currency in 1992, there was mounting pressure or expectation that the UK would have to follow suit due to the systemic imbalances that were ensuing;
Soros (or his company) was not the only entity selling/shorting pounds in the critical days of September of 1992;
in the morning of September 16, the UK government raised rates from
10% to 12%, thereby fueling the selling of pounds because the markets
interpreted the abrupt raise of rates as a sign of weakness;
hours later, the UK government desperately raised the rates to 15%;
short time later that day, the UK government suddenly desisted from its attempt to keep the pound within the ERM range, at which point the pound went in free
fall (also the increase to 15% was withdrawn).

Buying pounds back so as to close Soros's short position simply could not reverse the free-fall of the pound that resulted from UK government's prolonged stubbornness/arrogance and its subsequent, sudden erraticism.


Pricing a negative externality under high uncertainty and severe non-linearity Take a negative externality such as excess greenhouse gas emissions.

We know some awkward things about the economic cost of this externality:

There is fairly large uncertainty about the timing of damage associated with a unit of emissions. And about the scale of economic consequences of that damage.

Furthermore, there are significant non-linearities: if the world were to emit just one more tonne of CO2, the unit cost of damage is tiny. If we hit a trillion tonnes total emitted, then we're looking at costs that start to hit percents of global GDP. If we burn most of our remaining fossil fuel resources, then we're looking at damage potentially of the order of tens of percent of global GDP, and potentially threatening the existence of human civilisation as we know it.

Normally, a pigouvian tax or similar would have a unit price that represented the cost of damage: here, the uncertainty means that there would need to be some sort of option pricing within that. But also, it is typically a fixed unit price, which cannot be efficient if the damage costs are highly non-linear. What sort of correction to market pricing could take account both of the uncertainties, and the non-linearities?

I've tagged with pigouvian-taxes, but that's just one possible instrument, so I'll add coasian-bargaining too (though my own hunch is that Pigou, rather than Coase, holds the answer here - YMMV)

This should probably be a comment, but it's too long so I am posting it as an answer.

I'm not sure I necessarily agree with "[A Pigouvian tax] is a fixed unit price, which cannot be efficient if the damage costs are highly non-linear." But I do definitely agree with the fact that non-linearity causes practical problems for a Pigovian implementation, as I note below.

Suppose that the private benefit from emissions is $\pi(e)$, and that emissions cause external damages of $d(e)$. Assume that more emissions lead to greater damage ($d'(e)>0$), that the marginal damages are increasing ($d''(e)>0$—so damages are non-linear), and that profits are concave ($\pi''(e)\leq0$).

The self-interested individual will maximise his payoff by solving $\pi'(e)=0$. In contrast, social welfare is maximised when $\pi'(e)-d'(e)=0$. As usual, there is an inefficiently high level of emissions.

Write $e^*$ for the level of emissions that is socially optimal, and suppose that we set a Pigouvian tax at $t=d'(e^*)$ per unit. This means that the individual's optimisation problem is now
$$\max_e \pi(e)-te=\max_e \pi(e)-d'(e^*)e.$$
The corresponding first-order condition is
$$\pi'(e)-d'(e^*)=0.$$
This is solved by $e=e^*$, so the private individual is therefore induced to choose the efficient level of emissions even though the external damages are non-linear. Intuitively, if decisions are made at the margin then all the Pigouvian tax needs to do is to ensure that the private marginal benefit is equal to zero exactly when the social marginal benefit it. That the tax does not equal the external cost for all of the infra-marginal units has no bearing on the marginal decision problem.

Although the Pigouvian tax implements the efficient level of emissions, its implementation has important normative consequences. In particular, the polluting individual is paying a tax of $d'(e^*)$ for every unit of emission, even though the marginal external cost of the first $e^*$ units is less than this (because $d$ is convex). This implies that the polluter is required to pay more than the cost that he imposes on society, which some might not consider equitable.

There is also an awkward inter-temporal dimension to this problem that is not considered in the above static "textbook" treatment. Because damages are non-linear, if I allow $e$ units of pollution "today" then the marginal cost (and hence the optimal level) of emissions "tomorrow" will be different to if I had allowed $e+1$ units today. This seems to suggest that what is really needed (if the solution is, indeed, to be Pigouvian) is a time-varying tax and the problem becomes one of optimal control. That is, rather than calculating a single tax rate, we need to find the time-path $\{e_t^*\}_{t=0}^{\infty}$ that characterises the optimal evolution of emissions and change the tax over time to implement this. This increases the burden on the central authority, which is now required to calculate not only the emissions it wants to allow today, but also the emissions that it anticipates allowing into the indefinite future. This makes the informational problems noted in the question significantly more acute.


Savings = investment with private money creation? I've been reading some introductory macroeconomics and I'm struggling to understand one of the basic accounting identities. In a closed economy with a fixed money supply it's clear that every dollar saved is a dollar invested. I'm happy with the standard story.

What I don't understand is how the identity works when money is created privately. I can go to a bank an ask for a million dollar business loan. The bank grants me the loan, and creates an asset (the loan) and a liability (the money in my account). I then invest the money. It seems from this example that I have created a million dollars of investment without creating any offsetting savings. Of course, I have to pay off the loan at some point, but then shouldn't the identity be something like investment = savings + debt?

What am I missing?

Say you take out a \$1m loan from ABC Bank - they create two entries on your books:

Assets: \$1m cash available funds.
Liablities: \$1m loan you owe the
bank.

Similarly on their books they create two entries:

Assets: \$1m owing from Simon Lyons
Liabilities: \$1m payment we must honor.

Now you buy a factory with the \$1m. You write a cheque to Bob who you're buying the factory from. He banks with XYZ bank.
Your books:

Assets: A factory worth \$1m.
Liabilities: \$1m loan you owe the bank.

The bank's books:

Assets: \$1m owing from Simon Lyons
Liabilties: We owe \$1m to XYZ bank.

In practise what happens is that the banks are exchanging money between each other all day (for example XYZ bank customers may have paid cheques to ABC bank customers), and at the end of the day they need to settle the difference by taking a loan from someone.
In New Zealand's system for example, that difference can be borrowed from the Reserve Bank (New Zealand's central bank) - paying interest at the Official Cash Rate (OCR). This rate is set by the Reserve Bank - and is the primary means that the Reserve Bank controls inflation.


What is the statistical program used in the Worldwide Governance Indicators? I am interested in understanding the algorithm/methodology of the WGI  (the most cited and popular corruption/governance) World Bank Methodology. They try to publish as detailed as possible to the public but I struggle to figure out how they manage to solve the maximisation at page 97-99 here Governance Matters VII: Aggregate and Individual Governance Indicators, 1996-2007

Basically, they end up with a maximum-likehood estimation with three unknown parameters and state that it is a standard estimation. I am not an expert in Stata/Mata/Mathlab but honestly I can't see the trivial point.

Can anyone help and refer me to some statistical packages?

This isn't a matter of statistical packages as much as it is a matter of how to write a program to maximize/minimize a function. You can do this readily in Stata, Matlab, R, Python, etc. No matter what language you use, though, the process is basically the same. You write a function that specifies the functional form your trying to, say, minimize, set the parameters you're optimizing over as the function arguments, then call some built-in minimization routine on that function. Here is a primer for doing this in Stata and here is an introduction for R. Matlab and Python will both be very similar to R, with the primary exception being that you will have to declare the function in a different .m file for Matlab.


Negative neutral real interest rate What is the intuition behind having a negative neutral real interest rate?

The intuition is simply that there is an excess of savings on the market and consequently the market gives people a signal to save less. You can see the situation visualized below in a tikz picture of IS-LM model I drew shown below.
The $y$ axis measures interest rates both real and nominal and $x$ axis output. The IS curve gives all the combinations of interest rates and output at which investment equals to savings. Whereas the LM curve gives you all combinations of interest rates and output at which money supply equals money demand  (see Blanchard et al. Macroeconomics an European perspective for more detail behind IS-LM). Furthermore, the LM curve becomes flat at zero lower bound as, if nominal interest rates become negative, peoples preference for holding money as cash becomes infinite.  Furthermore, the $Y^*$ line here would represent the natural level of output economy can attain.
If there is too much savings in the market but too little worthwhile investment opportunities (i.e. there are excess savings) the IS curve will shift to the left. The intuition for that is that if there is low demand for saving and huge amount of saving then any equilibrium interest rate (which can be viewed as the price for saving) at which $I=S$ will be lower for a given level of output (where $S$ is saving and $I$ investment).  Since nominal interest rate cannot be negative it will stay at zero but the real interest rate will be given by the intersection of the IS curve with the natural level of output which will be below zero.
So the intuition is really just that people want to save too much while at the same time they do not want to invest enough so the market tells them to reduce their savings rate with negative interest rate.
The intuition is similar to why oil futures price became negative recently - too many people wanting to sell the oil while too little people being interested to buy it. With the oil price, there was also an additional problem that people did not have any space to store the oil and so they were willing to pay people to take it off them. Here the problem is not so much with storage space but the fact that people simply often have to save - for example, due to precautionary savings or other reasons and even though they could hold cash at nominal 0 rate the problem is that it will be eaten by inflation as from Fisher equation we know that nominal interest rate $i$ is approximately equal to the real interest rate $r$ plus inflation $\pi$ - which in turn implies that if the nominal interest rate is above real we get inflation $i \approx r+\pi \implies \pi \approx i-r$. So people might desperately supply savings even when the real interest rate is negative because they have no other choice (except for stopping to save altogether- which again might not be reasonable for many people who might need to save due to various reasons such as to form precautionary savings).


Bandwidth, latency and price Can a market be seen as a set of nodes (market actors) connected by edges with bandwidth and latency characteristics?

Are these terms used in economics?

If so would an import tariff affect bandwidth and/or latency?

There is an active body of research on network economics. See, for example,

Social and Economic Networks by Jackson
Connections by Goyal

for an introduction to the topic.

These models occasionally use weighted edges ("bandwidth") to model economic phenomena.

I'm not aware of work making use of the concept of latency, except when literally modelling latency (as in models of network congestion). An example of such a paper (though without the notion of nodes or edges) is Net neutrality and investment incentives by Choi and Kim.


market equilibrium quantity $\ne$ firm profit maximising quantity? Consider a perfectly competitive market with equilibrium price $P_{eq}$ and quantity $Q_{eq}$ and firm with profit maximising quantity $Q_f$ as illustrated below:

I guess any firm in the market would have the same demand, marginal revenue and average revenue (or am I wrong?), but what about profit maximising quantity $Q_f$? It seems to depend on $MC$. Is $MC$ different for each firm?

If so, then $Q_f$ is not necessarily the same for each firm?
If not, why?

In intro micro you usually assume that every firm in a perfectly competetive market has the same costs and production function etc. Hence, the MCs are the same for every firm. Under this assumptions, every firm will produce the same quantity in equilibrium.


Why does the price and wealth derivatives, weighted by the price and wealth, sum to 0? From Mas-Colell, Whinston and Green (Microeconomic Theory), we have this proposition on page 27. If homogeneity holds,

$$ \Sigma_{k=1}^{L} \frac{\partial x_l (p,w)}{\partial p_k} p_k + \frac{\partial x_l (p,w)}{\partial w} w = 0 $$

That is, the price and wealth derivatives, when weighted by the price, $ p_k$ and wealth $w$, equate to 0. What is the economic logic behind this? Homogeneity implies this -- but for this to hold, we don't require that prices and wealth increase proportionally (am I right?)

From this, we can also derive that the sum of price elasticities (own and cross price elasticities) equate to 0. I understand we can derive this mathematically-- but again, why'd these elasticities equate to 0, economically?

(Also, if these results are held only when prices and wealth increase proportionally, I completely understand -- but the book doesn't make that distinction).

As mentioned by Mas-Colell, Whinston and Green, the equality is true "for all $p$ and $w$". It is a consequence of the budget constraint, which is satisfied for any prices and income values:
$$
\Sigma_{k=1}^{L} p_k x_k (p,w) = w.
$$
As you mention, the equality
$$ \Sigma_{k=1}^{L} \frac{\partial x_l (p,w)}{\partial p_k} p_k + \frac{\partial x_l (p,w)}{\partial w} w = 0 $$
arises when applying the Euler-theorem to the budget constrained demand functions. As demand functions are homogeneous of degree zero in $(p,w)$, they are left unchanged when prices and income are up- or downscaled by any number $\kappa>0$:
$$
x_l (\kappa p,\kappa w) = x_l ( p, w) ,
$$
and this equality holds for any value of $p$ and $w$. This implies the former equality and also explains why it is not only true for the upscaled new prices and income $(p,w)=(\kappa p_0,\kappa w_0)$ but actually for any prices and income because both $\kappa$ and $(p_0,w_0)$ can be arbitrary.

What about the economic interpretation? Hmm... I would say that any simultaneous (marginal and arbitrary) change in $p$ and $w$ triggers changes in the values of demands such that the (own- and cross-) price reactions and the income response compensate. It is equivalent saying that all price elasticities and income elasticity add to zero for any demand function $x_l$.


Does it make economic sense for only some universities in a certain area to pay their sports scholars? Apparently

  ‘Athletic scholarships are common in the United States, but in many countries they are rare or non-existent.’

But are there countries where there are some universities that offer sports scholarships while other universities in the same country don't? We can shrink country to city, town, district, etc if you like (Note 2). I'll just say 'area'.

I have this relative: My relative and I are expats living in a certain area but permanent residents of the area. My relative recently got accepted into a first world university for an undergraduate degree in engineering and was accepted as a sports scholar...sort of.

None of the tuition is waived. The only thing my relative gets is a reduced fee to be on the team: Yeah, the university charges its students a fee to be on the team. My relative also gets lower grade requirements in admissions or retention, but my relative does not need that due to having outstanding grades in secondary. I figured this was a practice in this area where we both live and where we are both expats (see quote above).

However, I found out that several universities in this area apparently do offer sports scholarships ranging from 50-100% off tuition. One of the universities that offer is even of a lower QS ranking than the university that my relative is attending (Note 1). This to me seems like a big misunderstanding on my part, so I've emailed the university, although my relative has already asked, just to get first hand confirmation.

In the mean time: Why would anyone play sports for a university against other universities but not get paid or get tuition waived for the playing?

Some guesses:

Lower admission grade requirement
Lower retention grade requirement
Admission or retention for dormitory requirement
Possibility of future scholarships
Prospects of a sports-related careers after graduation that include but are not limited to professional sports

The thing is none of my guesses explain why those universities apparently have sports scholarships that waive tuition at least partly while this university doesn’t. Why wouldn’t sports scholars from a university that doesn't pay their sports scholars just transfer to another university in the next year thus causing the university to lose in inter-school competitions?

(Note 1): My relative applied to all universities in our area for sports scholarships and was rejected for all but this university. Also, our area has less than 10 universities, and they're all in the QS... Wait, lemme check...Yeah, ACTUALLY, my relative's university has the highest world QS ranking in our area. Meanwhile, the university with the lowest world QS ranking in our area has sports scholarships. Also, all universities in question are in the top 100 in our continent's world QS ranking, our continent is not Africa, and my relative's university is not the highest in our area for our continent's world QS ranking.

(Note 2): I'm thinking perhaps of a possibility where, say, in North America or Europe this might be the case but is not the case for a specific state or city or something like Massachusetts, Boston, UK or London. You can shrink as much as you want on the condition that universities in your shrunken area compete with each other in sports.

I mean, even in the US, the ability of a school to offer sports scholarships is determined by what athletic conference(/division) they belong to: Division III schools are forbidden from offering athletic scholarships. (So in that regard- it can vary even at the city level. Boston has some schools that give athletic scholarships, and some that don't). In fact, in that example, Northeastern University provides athletic scholarships, but three blocks away is Wentworth Institute of Technology that doesn't.

As far as why would someone play a sport without the possibility of scholarship? For some, I'm sure it's the potential for a future athletic scholarship (for example, many US football players will play their first couple of seasons for a community college in the hopes of attracting attention from NCAA Division I programs). For others, I'd guess the potential of going pro- if you didn't get offered a spot on a team that provides athletic scholarships, this might be your only chance to improve and try out for a pro team later.

But for most, I'd guess it's probably because they enjoy it. Many US schools have club teams in many sports, which compete against local schools and offer no real chance for financial returns. Moreover, why do so many students participate in other competitive extra curricular activities? I'd guess the same reason.


Implications of the concepts of combination/expansion of an information structure I would like your help to understand the concept of combination/expansion of an information structure in the incomplete information game at p.6-9 this paper.

Let me summarise the game as described in the paper.

There are $N\in \mathbb{N}$ players, with $i$ denoting a generic player.

There is a finite set of states $\Theta$, with $\theta$ denoting a generic state.

A basic game $G$ consists of

for each player $i$, a finite set of actions $A_i$, where we write $A\equiv A_1\times A_2\times ... \times A_N$, and a utility function $u_i: A\times \Theta \rightarrow \mathbb{R}$.
a full support prior $\psi\in \Delta(\Theta)$.

An information structure $S$ consists of

for each player $i$, a finite set of signals $T_i$, where we write $T\equiv T_1\times T_2\times ... \times T_N$.
a signal distribution $\pi: \Theta \rightarrow \Delta(T)$.

A decision rule of the incomplete information game $(G,S)$ is a mapping
$$
\sigma: T\times \Theta\rightarrow \Delta(A)
$$

Combination/Expansion:

Consider two information structures, $S^1\equiv (T^1, \pi^1)$ and $S^2\equiv (T^2, \pi^2)$. We say that $S^*\equiv (T^*, \pi^*)$ is a combination of $S^1$ and $S^2$ if

$T_i^*=T_i^1\times T_i^2$ $\forall i$.
$\pi^*:\Theta \rightarrow \Delta(T^1\times T^2)$ has $\pi^1$ and $\pi^2$ as marginals.

An information structure $S^*$ is an expansion of an information structure $S^1$ if there exists an information structure $S^2$ such that $S^*$ is a combination of $S^1$ and $S^2$.

Question 1:  Is it correct to say that $S^*$ is at least as informative as $S^1$?

Question 2:

The game described above assumes that, before privately receiving the signal, each player $i$ knows nothing about what will be the realisation of the state. I call this "baseline level of information".

Let $\underline{S}$ denote an information structure that is totally uninformative, i.e., it does not add anything to the baseline level of information assumed (also called DEGENERATE at p.26 of the linked paper). In other words, $\underline{S}$ consists of

(a) for each player $i$, a finite set of signals $\underline{T}_i$, where we write
  $\underline{T}\equiv \underline{T}_1\times \underline{T}_2\times ... \times \underline{T}_N$.

(b) a signal distribution $\underline{\pi}: \Theta \rightarrow \Delta(\underline{T})$ such that $\underline{\pi}(\cdot|\theta)=\tilde{\pi}$ $\forall \theta \in \Theta$ for some $\tilde{\pi}\in \Delta(\underline{T})$. In other words, the conditional probability is equal to the unconditional one and players' belief about the probability distribution of the state is not updated.

Let $\mathcal{S}$ denote the collection of all possible information structures. More precisely,

$$
\mathcal{S}\equiv \{S| T \text{ is a separable metric space}, \text{ $\pi:\Theta \rightarrow \Delta(T)$ is a probability measure on $(T,\mathcal{B}(T))$}\}
$$
where $\mathcal{B}(\cdot)$ denotes Borel sigma algebra.

Note that $\underline{S}\in \mathcal{S}$.

Is it correct to say that: $\forall S \in \mathcal{S}$ where $S\equiv ((T_i)_{i=1}^N, \pi)$, there exists a combination $S^*\in \mathcal{S}$ of $\underline{S}$ and $S$ such that $S^*$ and $S$ are informationally equivalent. In particular, one can set $S^*\equiv ((\underline{T}_i\times T_i)_{i=1}^N, \underline{\pi}\times \pi)$. Therefore, every $S\in \mathcal{S}$ is at least as informative as $\underline{S}$.

Answer to Question 1: Yes. To see this, note that for every combination of elements of $T^1\times T^2$ in the support of $\pi^*$ you get a, possibly different, posterior. To show $\pi^*$ is at least as informative as $\pi^1$ you need these posteriors to be a mean-preserving spread the posteriors induced by $\pi^1$ (there are actually several characterizations of Blackwell's partial order, I'm thinking there is a more elegant proof, but this is the one I can think of right now). You can easily show this is the case if you average up the posteriors induced by $S^*$, over the realizations of $T^2$.

Answer to Question 2: Yes. For any signal $S$, you can find a "trivial" expansion by combining it with $\underline \pi$, so the resulting signal $S^*$ (which is informationally equivalent to $S$) is at least as informative than $\underline S$.

In that sense, Bayesian decision makers can never have less information than their prior.


Why is economic growth correlated with long-term interest rates? Historically, growth rate is not always equal to long-term interest rate, but there does seem to be some relationship between the two. Is it that rates influence growth, growth influences rates, or something else entirely? In a nutshell, how are long-term rates and economic growth related, and why?

Very simply, economic growth is correlated with long term interest rates in the sense that interest rates are set according to the growth of the overall economy and GDP. If economic growth is weak, interest rates are set very low as a means of economic stimulus. If economic growth is too strong due to demand and the economy is overheating, interest rates are slashed.

The Federal Reserve alone determines interest rates, as well as the federal funds rate and the discount rate, through the Federal Open Market Commitee. Visit Federal Reserve System


When a support function is found to be more profitable than the primary business Sometimes in the course of pursuing its primary business, a company discovers an unexpected source of revenue.  It is particularly interesting in cases when a humble support function is found to be more profitable than the final product or service.

For example, I was reading about a company which set up an aluminum smelter in a developing country.  Aluminum smelters require a lot of electricity, and since the power supply in this country was unreliable, they also had to build their own mini power station.

They soon realized that the power they could generate from their power station was more valuable than the aluminum they could produce, so they shut down their aluminum smelter and made money from selling power!

Are there other examples of this?  Is there a name for this, other than listening to the market and being responsive?  (I don't like the word "pivot" because that has the connotation of what entrepreneurs and startups do when their effort has failed and they're trying to put a brave face on it.)

I am looking for more examples of joyful serendipity in business.

The Aerobie Sports company mostly makes odd-ball equipment for having a catch. But they made a coffee maker called the Aeropress as a side project and now it makes up more than half of their sales.

The Woolworth Company (of five and dime fame) founded the Foot Locker shoe store as a side business and now it is the core-surviving brand of that corporation when the main Woolworth business was closed.

Post it notes were a side business for 3M but now amount to \$1 billion in sales a year. But that's only about 3 percent of revenue.

The Michelin Guide books were developed to help promote the sale of tires through encouraging road touring. It survives today and though the business might be a small fraction of the revenue produced by the tire business it has significant cultural influence and an independent life.


Prices on year by year basis I want to know the cost of milk on a year by year basis, say for the last 10 or 20 years. similarly I may want to know price of other items also (petrol, rice, biryani, etc). I just need the average values. What is the best source of knowing these things. I'm particular about India. Please give me any website name or so that provides such statistical data.

You might want to try the Indian Government's open data website https://data.gov.in/

I am not sure if all your requirement will be met, but this is a good place to begin your research.

To find the data you require, you might want to use the "search box" on the header.When I searched for "retail milk price" (keywords), I could find several datasets for different timeframes.


What happens when government bonds purchased as part of central bank quantitative easing (QE) reach maturity? Does the central bank ask the government to pay or are they rolled over?

The bonds mature and pay the principal.
However, central banks tend to reinvest the principal, keeping their holding amounts relatively stable over time. This can be validated by looking at central bank balance sheet statistics.


Why is a solution concept of Bayesian Persuasion a subgame perfect equilibrium? Many papers on Bayesian persuasion adopt SPE as a solution, by arguing that the sender has no private information.
This does not make sense to me: Regardless of whether the sender has private information, we need to restrict the belief of the receiver about the state of the world after the receive observes an off-path disclosure policy, which SPE has no bite. Should we understand SPE in Bayesian persuasion literature as something that does not really mean subgame perfect equilibrium?

Here are my thoughts. Because the sender commits to a disclosure policy, how you stipulate off-path beliefs doesn't matter (phrased loosely). That is, the modification to PBE is trivial: any optimal persuasion policy corresponds to a class of optimal persuasion policies in which any belief is assigned to each off-path message.
Moreover, you could also resolve your off-path message beliefs issue by assuming that the cardinality of the message set is so small that no off-path messages are sent. This would correspond to, e.g., there only being two messages available in the canonical prosecutor-judge example from KG.


Stock Valuation - Interest rates, Dividends, and Shares Repurchases I'm reading a macro book (Blanchard's) and the way he values shares is by calculating the net present value of all dividends we expect to receive by owning some stock, discounted by the interest rates (assuming investors are risk-neutral and only care about expected return). Well, by reading some newspapers and some chapters of a book on corporate finance, I've noticed that not many firms' shares pay dividends, being the paid dividends concentrated in a few firms only. In fact, in corporate finance, it seems managers are taught that with the existence of taxes on personal income(dividends apply), it's preferable to repurchase shares which increase the earnings per share ratio (EPS), which in turn multiplied by the price-per-earnings of the industry the firm is in, gives an expected price for the stock. My question is why should we value stock if no dividend is paid? Aren't selling stock and receiving dividend the only two sources of current income that owning shares give?

Any help would be appreciated

We value stock if no dividends are paid, exactly for the reason you mention, we can sell them at a higher value later on. The value added to the stock if we invest the profits (would be dividends) into the company should be around the same value the dividends would pay off. However instead of paying taxes each time we get a dividend we can pay them just once when the stock is sold potentially saving on taxes.

P.s. Blanchard is a great book and how I first started learning macro :).


What impact does the paid vacation leave have on labor productivity? I'm asking just one question (it's in bold). If you treat any sentence with a question mark as another question and thus violating the policy on "focusedness", please steer clear of the text below the sentence in bold.
What impact does the paid vacation leave have on labor productivity? Do employees get re-energized and work better, or is there no such effect (or is it outweighed by 160 or whatever lost working hours)? Are there any studies on that, what are their conclusions? Are American employers stupid or, on the contrary, prudent when they show reluctance to grant such leaves to their employees in the absence of employee-oriented labor laws in the US? Note, I'm not asking whether there is any positive effect of paid vacation leaves generally (on mental health, reported happiness, etc.).

What impact does the paid vacation leave have on labor productivity? Do employees get re-energized and work better...

There are not many studies that examine this question directly, but it is argued in the literature that based on the indirect evidence that shows that vacation does have health and happiness benefits on the employees that it increases productivity (Strauss-Blasche et al. 2005; Bellet et al. 2020).  Studies that examined directly various paid leaves from work generally find positive but not always significant effect of provision of paid leave/vacation on productivity (e.g. Bassanini & Venn; 2008). Moreover, Zenger and Folkman (2015) provide some tentative evidence for increase in productivity from paid vacation that is also based on international comparison. However, the effect will also likely be heterogeneous across individuals, industries, time and place. One should not just assume just because the average treatment effect is positive the policy has the same effect everywhere every time.

Are American employers stupid or, on the contrary, prudent when they show reluctance to grant such leaves to their employees in the absence of employee-oriented labor laws in the US?

This question makes no sense. It is simply not possible to judge employers 'prudency' or 'stupidity' from their decisions to provide or not provide paid vacations and stupidity and prudence are not even opposites.

Prudence is defined as individuals proclivity to save more when faced with increased risk (Sandmo, 1970). Consequently, to the degree that there is any uncertainty about productivity gains from paid vacation a prudent employer would spend less on paid vacations not more.

Stupidity is not rigorously defined. If by stupid behavior you mean irrational behavior then game theory clearly shows that rational (and thus not stupid) behavior can often lead to failure of getting maximum possible payoff or profit in a strategic interaction like in a classic prisoner dilemma where fully rational actors typically end up play strategies offering much lower payoff than possible (See Tadelis Game Theory: An Introduction pp 48).

Increase labor productivity does not automatically means there is increase profitability. Labor productivity is defined as value of output over labor inputs. This does not take into account the costs that employer has to undertake to achieve this increased productivity. However, even if paid vacation would be directly and unambiguously linked to increased profitability, it is not possible to make any conclusions on whether employer is 'stupid' or 'prudent' for above mentioned reasons.

Amount of paid vacation days is part of total compensation. As such it is negotiated over by both employee and employers. A poll among American workers showed that significant amount of them do not fully use all their paid vacation days. Consequently, this provides at least some evidence that in the US workers are not interested in paid vacations. Hence, a rational employer would minimize provision of benefit that their employees do not want, and maximize provision of work benefits they do want, because benefits (provided they are wanted) are substitutes for higher wages. It would be irrational to provide benefit a worker does not want since then employer has to still pay for high wage in addition to unwanted benefit (see Borjas Labor Economics 223-224).


Saudi Arabia motivations for OPEC production cut I'm wondering whether one of Saudi Arabia's principle motivations for supporting OPEC production cuts is so that the price of crude oil will increase and so Saudi Aramco, Saudi's state-owned oil company, will be valued higher prior to its upcoming IPO?

I would appreciate any help understanding whether this is the case.

You could think this in terms of an oligopoly. As an imperfect market, firms get more profits than possible in a competitive market because decisions around levels of production influence prices. All members of the OPEC have an incentive to reduce production as a whole (to raise prices), and an incentive to increase production individually (to earn more profits at those higher prices).

You can also consider political issues like production outside the cartel: they don't hold a monopoly and the higher the OPEC raises prices, firms with costlier ways of extracting oil (like fracking in the US) can turn a profit and compete with them, which naturally reduces profits (and value).

While the IPO may be a possible explanation, you can think of it in terms of oligopolies and still get a reasonable answer.


Where to find information to establish causation between economic policies and economic data? I've merely taken a few economic courses in college -not an economics major-, so my knowledge regarding the field is limited. Lately I've been interested in learning about the economic impact of government policies, particularly in the USA and as easy as it is to find data on median household income, gdp per capita, poverty rates, dow jones index and so on, I'm unable to find much information on how the government policies have affected those metrics (beyond simple correlations).
I'm simply wondering how one could investigate causation regarding these metrics.

You might be inspired by Joshua Angrist (MIT) who talks in this podcast about the craft of econometrics--how to use economic thinking and statistical methods to make sense of data and uncover causation.
Using natural experiments is a good way to establish causation. A natural experiment is an empirical setting in which individuals are exposed to the experimental and control conditions that are determined by nature or by other factors outside the control of the investigators. A growing literature relies on natural experiments to establish causal effects in macroeconomics (see Nicola Fuchs-Schuendeln and Hassan, 2016).
For those trying to find such natural experiments as a basis for their own research, Angrist says:

One thing I learned is that empiricists should work on stuff that's
nearby. Then you can have some visibility into what's unique and try
to get on to projects that other people can't do. This is particularly
true for empiricists who are working outside the United States.
There's a temptation to just mimic whatever the Americans and British
are doing. I think a better strategy is to say, "Well, what's special
and interesting about where I am?"

Angrist has also written accessible and relevant papers on data and causation:

Angrist, Joshua D., and Jörn-Steffen Pischke. 2010. "The Credibility
Revolution in Empirical Economics: How Better Research Design Is
Taking the Con out of Econometrics." Journal of Economic
Perspectives, 24 (2): 3-30.
Angrist, Joshua, D., and Alan B. Krueger. 2001. "Instrumental
Variables and the Search for Identification: From Supply and Demand
to Natural Experiments." Journal of Economic Perspectives, 15 (4):
69-85.


What is Islamic Banking? What is "Islamic banking," and how is it similar to and different from banking as it occurs in the U.S.?

I have heard Shariah Law prohibits usury, the taking of interest on loans. How do Muslim bankers justify the prohibition of interest? Are there any prominent Muslim economists, contemporary or older, who justify their prohibition of interest not only from a religious perspective?

Both another answer and the OP have linked to the wikipedia article on the matter. I think the following passage from the article sums adequately the situation (bold mine):

  "The term “Islamic banking” refers to a system of banking or banking activity that is consistent with Islamic law (Shariah) principles and
  guided by Islamic economics. The contemporary movement of Islamic
  finance is based on the belief that "all forms of interest are riba
  and hence prohibited".[48] In addition, Islamic law prohibits
  investing in businesses that are considered unlawful, or haraam
  (such as businesses that sell alcohol or pork, or businesses that
  produce media such as gossip columns or pornography, which are
  contrary to Islamic values). Furthermore, the Shariah prohibits
  what is called "Maysir" and "Gharar". Maysir is involved in
  contracts where the ownership of a good depends on the occurrence of a predetermined, uncertain event in the future whereas Gharar
  describes speculative transactions. Both concepts involve
  excessive risk and are supposed to foster uncertainty and fraudulent
  behaviour. Therefore, the use of all conventional derivative
  instruments is impossible in Islamic banking. In the late 20th
  century, a number of Islamic banks were created to cater to this
  particular banking market."

  "Islamic banking has the same purpose as conventional banking: to make money for the banking institute by lending out capital while
  adhering to Islamic law. Because Islam forbids simply lending out
  money at interest, Islamic rules on transactions (known as Fiqh
  al-Muamalat) have been created to prevent it. The basic principle of
  Islamic banking is based on risk-sharing which is a component of trade
  rather than risk-transfer which is seen in conventional banking.
  Islamic banking introduces concepts such as profit sharing (Mudharabah), safekeeping (Wadiah), joint venture
  (Musharakah), cost plus (Murabahah), and leasing (Ijar)."

I can also offer my professional experience on the matter, which says that some times these are used as merely veils for what is essentially a conventional loan earning interest.

As a side remark, Christian institutions like the Catholic Church never officially lifted their condemnation of "usury"/charging interest -they just don't actively enforce the doctrine. (As far as I could find, the most recent papal discussion of usury occurred in Pope Benedict XIV’s encyclical of 1745, Vix pervenit.)


The $\sqrt{N}$ convergence of semiparametric estimators of Newey 94, why does it converges to a normal distribution? The famous Newey 94 paper on the asymptotic convergence of semiparametric estimators with a first non parametric step and a second parametric one, http://www.jstor.org/stable/2951752, establishes that it does not matter the rate of convergence of the particular non parametric estimator, as long a a number of regularity assumptions are fulfilled then the estimator of the second step is $\sqrt{N}$ convergent to a normal distribution. Here I am asking for intuition why does this a complicated stochastic process, say Naradaya-Watson asymptotic distribution converges to this nice distribution.

The usual proof of the classical Central Limit Theorem (CLT), I believe provides the most intuition there is about this phenomenon. And it is not much of an intuition anyway.

This "usual" proof is through characteristic functions.

Consider a random variable $X$ with characteristic function

$$\phi_X(t) = E(e^{i tX}), \;\;\;i^2 = -1$$

Now consider its centered and scaled version

$$Y = \frac {X-\mu}{\sigma} = \frac 1{\sigma}X - \frac {\mu}{\sigma}$$.

with $E(Y) = 0 , {\rm Var}(Y) E(Y^2)= 1$. Moreover, $Y$ is the sum of two independent random variables, the second degenerate (being a constant, and so also independent of everything). So, by the properties of the characteristic function for the sum of two independent random variables

$$\phi_Y(t) = \phi_Y\left(\frac 1{\sigma}t\right)\cdot e^{-i\frac {\mu}{\sigma}t} = E\left[\exp{\left\{it\frac 1{\sigma}X - i\frac {\mu}{\sigma}t\right\}}\right] = E(e^{i tY})$$

Now take the second-order Taylor expansion of $\phi_Y(t)$, with respect to $Y$ and with center of expansion $E(Y) =0$:
$$\phi_Y(t) = E\left[e^{it\frac 1{\sigma}\cdot 0} + ite^{it\cdot 0}Y + \frac 12 i^2t^2e^{it\cdot 0}Y^2 + o(t^2)= \right]$$

The first term is zero, the second term vanishes because $E(Y) =0$, and for the third term we use $i^2=-1, E(Y^2) =1$ to arrive at

$$\phi_Y(t) = 1  - \frac {t^2}2 + o(t^2)$$

The "phenomenon" is already here because

$$ \frac {t^2}2 = \ln MGF_{Z}(t),\;\; Z\sim {\rm N}(0,1)$$

In words: The characteristic function of any random variable with finite mean and variance that is centered and scaled accordingly, has a strong connection with the moment generating function of the Standard Normal distribution ($\ln MGF_{Z}(t)$ is actually the cumulant generating function).

How can this happen? Have we uncovered a "law of nature" here, this fundamental connection of different "types of uncertain behavior" to the specific type labelled "standard normal distribution",  or it is just our mathematical system, through which we have modeled this thing called "uncertainty", producing some artificial connection that perhaps reveals some aspect of its own internal structure, but it has nothing to do with the real world?

Let's first complete the proof of the CLT: consider the random variable
$$Z_n = \frac 1{\sqrt{n}}\sum_{i=1}^nY_i$$

where the $Y_i$'s are independently and identically distributed. Again by the properties of the characteristic function we have

$$\phi_{Z_n}(t) = \prod_{i=1}^n\phi_{Y}(t\sqrt{n}) = \Big[1  - \frac {t^2}{2n} + o(\frac {t^2}{n})\Big]^n \xrightarrow{n\rightarrow \infty} e^{-t^2/2} = \phi_{Z}(t),\;\; Z\sim {\rm N}(0,1)$$

and so

$$Z_n \xrightarrow{d} {\rm N}(0,1)$$

...and now we have arrived at the Standard Normal distribution proper. And this is a law of nature: mathematics aside, computer simulations aside, real world data consistently validate this result. So there is no further "why?" here -as it cannot be with any law of nature. We just discover them -and we feel like gaining added intuition when we discover the interconnections between these laws (but this is not really insightful, it is just more discoveries).

Of course this is the first and most simple case, in a long line of Central Limit Theorems that increasingly deal with more complicated, interdependent, functions of random variables, stochastic processes etc as the one mentioned in the OP. And there are also the generalizations of CLT to stable distributions and not just the normal, and there is extreme value theory... all these are different aspects of the same conclusion: that collective behavior (even in the simple sense of pooled behavior) is much more homogeneous than individual behaviors, even though it is just the pool of the latter -and this should be one of the most counter-intuitive results ever encountered.

P.S. An inspired attempt at bottom-up intuition is provided by @whuber in this Cross Validated thread: https://stats.stackexchange.com/questions/3734/what-intuitive-explanation-is-there-for-the-central-limit-theorem


In a social accounting matrix, what does Capital refer to? In the process of building a social accounting matrix for Panama, I am trying to understand what capital refers to. The Panamanian National Accounts have tables on capital, but they describe gross capital formation. In a social accounting matrix, gross capital formation represents investment and not capital. So what does capital mean?

I was also wondering if capital was included as part of Gross Value Added (GVA) and, if so, could it be calculated using GVA data?

Thank you!

You need to take care here as capital appears twice in your table; once as a factor of production, and once as an "institution" (although it's really better thought of as a capital account).

"Profit" in the first column basically refers to Gross Operating Surplus in national accounts, and it's paid by industries (activities) to the capital factor - GOS can be considered the earnings of the capital factor of production (analagous to wages being the earnings of the labour factor).  Looking at the capital factor column, you can see that these earnings are in turn "paid" to the household sector.

The capital account, on the other hand, "receives" savings from government and households, and "spends" on Investment/Gross Fixed Capital Formation (and possibly valuables and inventories too depending on how your SAM is set up). The row=column balance on this account is just the typical Savings = Net Investment accounting identity.


What would be the economic impact of the "fair tax" plan? So I read about an interesting proposal about completely replacing income tax with a heavy national sales tax of about 30% (23% inclusive to compare to income tax).

I was thinking about what the impact of this would be. On one end, income goes up both because people would want to work more and they get to keep everything they earn.

On the other end, prices go up because of the sales tax. I was also learning that spending is crucial for short term economic growth, so that may hurt. But does the laffer curve apply to sales tax as well? People may buy more frequently if it went down, increasing tax revenue. I know the laffer curve is unreliable, but it was just a thought.

Is this thinking process correct, or would the fair tax be a complete disaster? I apologize I just got interested in economics so I don't know much.

Well, one advantage to a sales tax is that it affects everyone (even those who don't pay income taxes). However, some people may see that same fact as a problem. This problem lies in analysis of the equity of the tax. When we consider every single person being taxed 30% on everything they buy, we need to think about how that affects different income groups. Lower income groups spend a much larger portion of their income on consumption, which means that they will be taxed relatively much more heavily than high income groups. This fact alone is enough to discourage this sort of action because the government tries to encourage saving in the lower income groups (so they can move up to higher income levels). This is one large reason why a tax like this may not be as fair as the name makes it seem.

Another piece of information that must be considered is the incidence of the tax. As we know, the incidence of a sales tax depends upon the relative own-price elasticities of supply and demand. This means that in a market with very inelastic demand (such as cigarettes or oil), the buyer is paying most of the tax whereas in a market with elastic demand the sellers would pay most of the tax. This fact would make it so that different industries would end up paying a different amount of the sales tax compared to one-another. For example, an oil company would end up paying much less of the percentage of the tax than a company making a selfie stick. This, again, seems to be unfair.


How is it traditionally defined the minimum wage legislation in economics? How is it traditionally defined the minimum wage legislation in economics? And which countries does not have a minimum wage legislation as defined in these terms?

It depends. Some countries use hourly wage (Australia, Morocco, UK, US), other use daily (Mexico), other monthly (Argentina, Brazil, Chile, Colombia, France, Peru, Spain), others annually (Bolivia). (this is not an exhaustive list)

Countries without a minimum wage established by law are: Denmark, Iceland, Italy, Norway, Sweden, Switzerland. They do however have minimum wages negotiated at the trade union level, even at industry level.

Given this information, the "traditionally" adjective you are using is not very helpful.


Why is fuel more expensive on the high way in Europe? In Europe it's usual, that fuel prices are 10-20% higher on the highway, than in the city. This is not only my personal observation, but also mentioned on travel sites (eg here and here). I don't have much expertise in economics, but as I understand this should not be possible in a competitive market, since what would stop a petrol station to lower their prices to the same level as the ones in the city, and get all the customers?

One solution could be, that they are different companies, but even the big ones like Shell and OMV have higher prices on the highway.

My question is: what is the reason for this situation, and what stops petrol stations from lowering their prices?

Because there is no indication in your question that you are a student or practitioner of economics, I am writing an answer for a lay audience. Let me know if you would like more technical detail.

A fairly general prediction from economic models of competition between firms is that the price that maximises their profit is higher the less sensitive is demand to that price (this sensitivity is measured by the "price-elasticity of demand"). Intuitively:

if demand is very sensitive to price then a cut in price will cause demand to increase a lot. The firm receives less for each unit it sells, but sells very many more units and is better-off overall.
if demand is not sensitive to price then the firm can increase price without causing its sales to fall very much and will therefore wish to do so.

There are lots of things that affect the sensitivity of demand. One example, as DornerA mentioned in a comment, is geographic location. If the nearest competing seller is very far away or inconveniently located then buyers will be reluctant to shop elsewhere, meaning their demand is likely to be less sensitive to price increases at locations that are geographically isolated in some way. This seems like a reasonable way to think of highway fuel stations.

A little thought should convince you that the same principle (that prices are higher when demand is less sensitive) holds for other cases where demand is price-insensitive too. For example:

why is food so expensive on trains/airplanes?
why are branded goods more expensive than generic ones?
why are the photographs from theme park rides so expensive?
etc.

Edit: A comment by AndrejaKo reminds me to add that the other very common reason why firms might increase their price is that they have higher costs. However, economics theory predicts that only unit costs (i.e. those that increase when you sell more units) matter for optimal pricing. Thus, for example, the fact that land near a highway is expensive would not seem like a very convincing explanation for high fuel prices (because the land costs the same regardless of how many units of fuel are supplied). But if, for some reason, supplying each litre of fuel was more expensive at highway fuel stations (because, for example, transporting the fuel there is more expensive) then we would indeed have an explanation for higher highway fuel prices.


Utility functions of countries In international relationships, often the interacting agents are countries. For example, countries negotiate, sign agreements, give loans to each other, trade, etc. Thus it is interesting whether these interactions are analyzed analogously to economic interactions between individuals, starting with the assumption that each country has a utility function.

Utility functions of countries are mentioned the context of a fair division procedure called adjusted winner. This procedure has been applied (hypothetically) to some international agreements, such as the Israeli-Egypt peace treaty, the Spratley islands disputes,  and the Panama Canal treaty. In each of these cases, the authors assume that each of the two involved countries has a cardinal utility function over the debated issues, and apply the procedure to find a fair and efficient agreement.

My question is: are there other papers in international economics that assume such 'utility function' of countries?

Caveat: my familiarity with the international agreement literature is limited to that of environmental and resource economics problems.

For those cases instead of a utility function the usual approach is to formulate the problem in terms of costs and benefits for countries' economies as a whole.

When it comes to environmental problems this usually boils down to individual benefits of pollution versus collective damages, or its inverse individual abatement costs versus collective benefits. For resource problems it is individual profits (or consumption) from harvest versus the collective diminishing returns in terms of stock growth or increasing harvest costs.

Active authors in this field are a.o. Scott Barrett, Carlo Carraro, Michael Finus in terms of environment and Marco Lindroos and Pedro Pintassilgo for fisheries.


Internalising an externality for a free merit good I am researching vaccinations as a merit good and I am focusing on an article which discusses how some people are rejecting one of the COVID vaccines because of misinformation about how it may be less effective than the other vaccine. Can this externality be internalised since the vaccine is free to those receiving it because for example, with the flu vaccine the externality can be internalised by providing people with a voucher to receive a free vaccine however the COVID vaccines are already free. If not, is there any other way in which I can discuss how this can be done?
Article Link - https://www.theguardian.com/world/2021/feb/25/acceptance-problem-as-most-oxford-covid-jabs-delivered-to-eu-not-yet-used
Thanks

Even if the vaccine is free it is possible to additionally internalize the externality with subsidy. That is government can just pay people to take the vaccine.  Note, that even with a flu vaccine just providing voucher for a free vaccine might not be enough to fully internalize the positive externality (or it could be too much this is always case dependent).
For covid-19 specifically, there is an interesting recent paper on optimal covid-19 vaccine subsidies (among other things) by Goodkin-Gold et. al. (2020).  Their model shows that optimal subsidy will depend on the reproduction rate of the disease. Higher reproduction rate makes stronger case for subsidies, while if the reproduction rate it sufficiently low there might be no need for the subsidies at all. Moreover, the authors show that optimal level of subsidies also depends on competition in the industry. Specifically, they show that generally the more competitive industry is the greater case there will be for per unit subsidy.


Who first used the term "externality" in economics? Who first used the term externality in economics, as the term is currently used in its modern sense?

(I believe it was already used in philosophy to mean something else and the economics version of this term came into use later.)

The earliest instance I've found so far is Bator (1958). However, he uses it without any introduction and as if it's already a well-known term so I suspect someone else may have used it before.

I suspect you have found the author responsible for the original coinage of the word "externality" within economics, with this meaning.

In the 1950s (and earlier), the discussion of externalities was typically done using the phrase "external economies", as Francis M. Bator frequently did too. Bator built on Scitovsky (1954) and Meade (1952), both of whom used "external economies", as did JK Galbraith and others around that time (as well as several others before them).

Boudreaux and Meiners wrote the paper: "Externality: Origins and Classifications", 2019, within which they say:

  Bator's article likely forms the basis for the now-common notion of
  externality

which is probably as close as we can get to confirmation that the word is Bator's original coinage for this particular meaning, together with Fizz's Medema reference. There's a long footnote in the reference that Fizz found - Medema 2019 (p20) (my emphasis):

  Bator first used the term in his 1956 MIT Ph.D. thesis, from which his 1957 and 1958 articles were derived (Bator 1956). Whether it was Bator who coined the term is hard to say. Paul Samuelson, Bator’s MIT colleague, used it at nearly the same time in an article on the subject of intertemporal price equilibrium that appeared in Weltwirtschaftliches Archiv(Samuelson 1957). Samuelson noted simply that “knowledge is a resource loaded with externality” (1957, 210). Bator’s article seems to have appeared first and was certainly more widely read, being cited nearly fifty times over the next dozen years as against eighteen cites to Samuelson’s piece. (Source: Google Scholar, accessed August 22, 2017). Moreover, none of the citations to Samuelson’s article were in the welfare economics/externalities context. There is no input from Samuelson acknowledged in Bator’s opening footnote, nor is mention of Bator made in Samuelson’s article. The term was picked up relatively quickly though, being used another half-dozen times before 1960. It was also Bator who introduced the term “market failure” into the literature, this in his 1958 article, “The Anatomy of Market Failure.

Bator's 1956 PhD thesis for MIT (pdf) uses the term 78 times, with no earlier citations or quotes of its use.

So, with both Samuelson (1957) and Bator writing around that time about externalities, using that specific word, and both at MIT, there's a fair chance that the word was coined there within that MIT department by one of them, or a colleague of theirs (with Robert Solow being the most likely candidate, as Bator's PhD supervisor), and entered the writings of both of them organically at around the same time, through the usual social and professional interactions that go on in an academic department.

And Medema's footnote quoted above makes a persuasive case that it is Bator's 1957 & 1958 papers that established the term in the literature, from where it became widely disseminated.

Robert Solow is, at time of writing, still with us. I wonder if a direct enquiry to him might shed any light on this?


Refinements of Walrasian equilibrium In Walrasian equilibrium there is a market clearing price, that is
$$
D(p) = S(p)
$$
or the supply is worthless, so you can have
$$
D(p) < S(p) \mbox{ if } p = 0.
$$
This can be summarized as
$$
p \cdot D(p) = p \cdot S(p)
$$
If the demand function is not always downward sloping (e.g. Giffen goods, markets with asymmetric information) or the supply function is not always upward sloping (e.g. economies of scope) multiple Walrasian equilibria may exist. If this is the case, are these all considered equally 'valid' equilibria or are there some established refinements to the equilibrium concept?

An illustrative example:

Are $A$, $B$, and $C$ all equilibria?

(Personally I dislike $B$. You may well have no problems with the bugger.)

Forgive me in advance if this is already familiar. I'll be talking about stability of equilibrium the way I (briefly) learned it.

Let $\xi^j(p)$ denote the excess demand for good $j$ given price $p$.

$$\xi^j(p) = \sum^m_{h=1}\left( x^j_h(p) - e^j_h \right) = x^j(p) - r^j$$

For $m$ households/consumers, $e$ being an endowment to a household, and $r^j$ being the total resource available of good $j$. We say the rate of price adjustment over time $\left(\frac{\partial p^j}{\partial t}\right)$ is proportional to excess demand.

For either of your market clearing prices $p^*$, we then know that $x^j(p^*) = r^j \ \forall j \implies \xi^j(p) = 0$
Otherwise,

$\xi^j(p)> 0 \implies \text{excess demand} \implies \frac{\partial p^j}{\partial t} > 0$

$\xi^j(p)< 0 \implies \text{excess supply} \implies \frac{\partial p^j}{\partial t} < 0$

Out of the three equilibrium you have up there, we'd probably want to find one that was locally stable and say that's where the market is more likely to realistically go.

Steady state $p^*$ is locally stable if $\exists \epsilon > 0 \ \text{s.t.} \ \forall \ p(0) \in B_\epsilon (p^*)$, an open neighborhood with radius $\epsilon$ around $p^*$, then we have $p(t, p(0)) \rightarrow p^*$

I don't want to fuddle this too much with math (particularly when you linearize the system and have to deal with eigenvalues/eigenvectors), so let's just take a look at your supply and demand curves above.  We can peruse the math on our own time.

Case A: Let's say you are at point A, your nice equilibrium. Suddenly there is a downwards quantity shock and you are now to the left of $q_A$. Since there is excess demand, the change in price over time should be positive, so the price will rise, and you will arrive back at point A.

What if you are shocked to the right of $q_A$ in the short run? Now there is excess supply and price over time should fall. If you were still above $p^*_A$ at this point, you will arrive back at point A. Otherwise price will fall all the way until you reach point B.

Case B: We know what happens with a shock to the left of point B now. What about to the right? If point C looks like a global minimum of the supply curve from what it looks like, then any shock that gets you before point C gets you excess demand, which means the price will rise and you will arrive back at point B.

Case C: To the right of point C, there is excess supply, and prices will fall back down until you reach C again.

None of these equilibria seem globally stable. It seems C is not locally stable on the left, so I wouldn't say the market would hang out there for very long. Points A and B are locally stable, but it seems B has greater room to get shocked and still move back towards B.

So for this scenario, I personally like B as your long run equilibrium.

If you had extra information about how shocks in the market happen (how often, variance, etc.), it may allow you to describe what percentage of the time you stick around at each equilibria, and you could describe an aggregate equilibrium like that as well.


Should central bank raise interest rates during a condition of liquidity trap? I was studying about liquidity traps and understood it fairly well that according to widespread beliefs the monetary policy turns out to be ineffective as nominal interest rates are close to zero and the public has deflationary expectations. Since nominal rates are close to zero nobody wants to hold financial assets and prefer cash instead.
My question here is that in such a condition when nobody is investing in bonds, should not the central bank raise interest rates to give higher incentive to bond holders. I know I am missing some point but can someone please explain this relationship between interest rates, inflation and bonds in the context of liquidity trap.

In rough terms the central bank wants the nominal interest rates low so as a) to incentivize people to consume their income rather than save it and b) to make loans more attractive as they are linked with lower interest, thus bolstering consumption (again). During a crisis however, consumption remains low as expectations of economic growth deteriorate. Moreover, as interest rates are low, there is no point in saving money into the banks. Thus, people choose to hoard money, essentially removing it from the economy. With less money in the banking system and a generally pessimistic economic environment, banks become more skeptical towards providing loans as they doubt that they will get their investment back. All these processes empower the endurance of the vicious circle of the liquidity trap.

In theory, such prolonged periods of near zero interest rates would mean higher inflation. However, the recent crisis has proven that zero interest rates and stable inflation can co-exist. Therefore, the central bank has, up until now, been reluctant towards increasing the interest rates and in the past years it has made sure to inform the public that it is going to keep them quite low for some time (forward guidance). There is a whole debate of whether low interest rates are or should be linked with high inflation during financial crises and recently we see a drift, especially in the US, towards an interest rate increase even though it has not yet materialized.

Bonds are not considered a "go to" solution under a liquidity trap as their demand is really low. This stems from the fact that when a government faces a recession, its bonds are not considered a safe investment as they are paired with a high interest rate. Thus, the public awaits that they are unlikely to be honoured in the future. And if the recent financial crisis has taught us anything is that even bond holders are not safe.