Existence of market sharing equilibrium in hotelling model I'm reading a paper on Competition in Two-Sided Markets. The model is a Hotelling-type model, with consumers on some interval, choosing their preferred firm based on price and 'distance' to the different firms (see below). In it, there's an assumption made that guarantees that there's no single monopoly that serves all consumers, which amounts to the condition:

$$4t_1t_2>(\alpha_1\alpha_2)^2$$

But I'm not sure how this is derived. Annoyingly, the paper says: "it turns out that the necessary and sufficient condition for a market sharing equilibrium is $4t_1t_2>(\alpha_1\alpha_2)^2$", without providing the derivation. I'd appreciate a hint on how to derive this, or an actual derivation of this condition.

These screenshots are from page 8 from Competition in Two-Sided Markets.

Market sharing simply means that both platforms have some market share. So the condition can probably be obtained by finding the closed-form solution for market shares (not only implicitly as in (7)) and imposing the condition that all market shares are positive. This is akin to each platform having an interior solution.

I am not sure which Hessian you are referring to, but my guess is that you mean the hessian of a firm's optimization problem (choosing both of their prices) taking the prices of the other platform as given. In that case, if the Hessian is negative definite, regardless of the other firm's prices, an interior solution exists.


Aggregating CRS Production Functions If thera are two firms and both of them have constant returns to scale production function. Will the aggregate/industry production function still be the sum of individual production functions. How does CRS effect the aggregate production function of industry?

Consider two firms with production functions $A_1 F(k,l)$ and $A_2 F(k,l)$. Both have the same curvature (and are CRS), but one is more productive. Here we can solve the social planner's problem (why?) instead of looking at a competitive equilibrium. He will want to equalize marginal returns across the firms. As one is more efficient, it will get more inputs.

And what is the maximum? Give all of the inputs to the more productive firm. This is because of CRS (which indeed means that as you scale up one production function, it's marginal product will always be larger than the other one's).

That is, define $G(l, k)$ as the aggregate production function. It is given by

$$ G(l,k) = \max_{(l_i, k_i)_{i=1,2}} A_1F(k_1,l_1) + A_2F(k_2,l_2) \text{ s.t. resource constraint}$$

The solution here is $G(l,k) = A_1F(k, l) $ if $A_1 > A_2$, and vice-versa.

Adding Up Makes No Sense

If you think that adding them up makes sense, you're not thinking things through:

If one cook can bake one cake with each egg, and the other cook can also bake one cake with each egg, then the two cooks together can bake two cakes with each egg?

Decreasing returns to scale

Now, it won't be the case that one firm is more productive than the other one always. Consider $F_1(k_1) = A_1 k_1^\alpha$ and $F_2(k_2) = A_2 k_2^\alpha$. You will want to split up capital between the two firms such that marginal returns equalize: $k_1, k_2 : F_1'(k_1) = F_2'(k_2)$. Due to DRS, this necessarily means that both $k_1, k_2 > 0$. I leave the actual derivation of the aggregate production function as an exercise.


Negative Externality with Tax and Free TRade I am unsure of how to think about this negative externality question when there is both tax and free trade.

A country is producing plastic, but it has a negative externality cost of 4 dollars/bottle. The demand is $Q_D=12-P$ and the supply is $Q_S=P$. If a 4 dollars/bottle tax is enacted and the country is opened up to free trade with a world price of 4 dollars, what would the total social surplus be? Based on my calculations, it would be 24 dollars, just the same as when the country has no tax and is open to free trade. Is this correct thinking? Or am I not thinking about the tax and free trade correctly? Thanks.

Rearranging your demand and supply equations gives us:
$$P=Q_s\quad and\quad P=12-Q_D$$

Adding the tax on the supply side gives us:
$$P=Q_s+4$$

Solving for equilibrium, we get $P=8$ and $Q=4$

However, we did not necessarily need to solve for this equilibrium because the Supply curve shifted left, and the new intercept is at $P=4$. This implies that no plastic will be produced domestically because the world price will be lower at any positive level of production.

To solve for total surplus, we need only solve for consumer surplus because no production will occur domestically. We need to solve for $Q_D$ when $P=4$.
$$4=12-Q_D\implies Q_D=8$$
$$\implies TS=CS=\bigg(\frac{1}{2}\bigg)*8*8=32$$

Is this the same as when there is no trade and no tax?

$$P=Q_s\qquad P=12-Q_D$$

Equilibrium yields $P=Q=6$
$$TS=CS+PS-DWL$$
$$TS=CS=\bigg(\frac{1}{2}\bigg)*6*6$$

To calculate $DWL$, we split the cost into private cost and social cost. When we do this
$$PC=Q\qquad SC=Q+4$$

The values we need to calculate the $DWL$ triangle end up being $Q=4$, $P_{PC}=4$ and $P_{SC}=8$

$$DWL=\bigg(\frac{1}{2}\bigg)*4*4=8$$

$$\implies TS=18+18-8=32$$

Your intuition was correct that the total surplus is the same in both cases.


Does every allocation have a maximal Pareto-improvement? Consider an economy with a finite number of goods and a finite quantity of each good. Each agent $i$ has a preference-relation $\succeq_i$ which is a total, reflexive and transitive relation over the set of bundles. Given an allocation $x$ of the goods among the agents, say that $x^*$ is a maximal Pareto-improvement of $x$ if:

$x^*$ is Pareto-optimal,
Every agent weakly prefers the allocation $x^*$ over the allocation $x$.

What is the weakest condition on the preference-relations $\succeq_i$ that guarantees that every allocation has a maximal Pareto-improvement?

I would guess that it is somehow related to compactness, however, I do not see how to define this condition on preference-relations.

I think there is a short proof if you also assume that the number of agents $n$ is finite and that the preferences are continuous.

Given the second assumption Debreu's theorem (1954, "Representation of a preference ordering by a numerical function") states that a continuous utility function exists which represents the preferences. I will denote the utility function representing the preference of agent $i$ by $U_i$.

Though this is somewhat uncommon, I will denote the utility agent $i$ gets from an allocation $x$ by $U_i(x)$.

An algorithm resulting in a maximum Pareto-improvement of $x$:
Step 1. Initially set $i=1$ and set $y = x$.
Step 2. Maximize the utility of agent $i$ over the set of allocation where all other agents $j$ have at least utility $U_j(y)$. As all functions $U_j$ are continuous, there is a finite number of goods and a finite quantity of each good, for all $j$ the upper set of $U_j$ is a closed set. A finite intersection of closed sets is also a closed set. As $U_i$ is also continuous, it will have a maximum over this set. Select an allocation $y'$ which maximizes $U_i$ and let this be the our allocation $y$ from now on, so set $y = y'$.
Step 3. If $i = n$, stop. Otherwise set $i = i+1$ and proceed to step 2.

Notice the following:

Any move from $y$ to $y'$ in Step 2. is a Pareto-improvement.
Pareto-improvements are transitive, therefore the set of Pareto-improvements is narrowing, i.e. if $y'$ is a Pareto-improvement to $y$ then the set of Pareto-improvements to $y'$ is included in the set of Pareto-improvements to $y$.
As the utility of agent $i$ is maximized in Step 2. over the set of Pareto-improvements to $y$, it is impossible that his utility can be further increased by a Pareto-improvement. Therefore once we reach Step 3. for $i = n$ we have a Pareto-optimal allocation $y$, that is either a Pareto-improvement of $x$ or where $\forall i$: $x\sim_i y$. Hence $y$ is a maximal Pareto-improvement of $x$.

A comment: It seems to me you could replace continuity with monotonicity, but that would require another proof. Hopefully someone else is up to it!


Additive multiattribute nonlinear utility functions I am interested in the cases where a decision maker possesses a multiattribute utility function ($u$) of the form:

$u(x) = \sum\limits_{i=1}^{n} u_i(x)$, with $x=(x_1, \ldots, x_m)$, and where $u_{i \in [1, n]}$ is a multiattribute nonlinear utility function.

In particular, what is their relevance in microeconomics, utility theory, and decision-making in general? Are there any examples or references?

Thanks.

These are sometimes known as "quasi-separable utility functions".  A recent paper that describes the theory is Quasi-Separable Utility by Qin and Rommeswinkel.

Utility of this form arises fairly naturally in macro and finance.  If your current utility depends on lagged consumption as well as current, then you get utility of this form,
$$
\sum_{t=1}^\infty u(C_{t-1}, C_t),
$$
where $C_t$ is time $t$ consumption.  One particularly common form is
$$
\sum_{t=1}^\infty u(C_{t} - h C_{t-1}),
$$
which is known as habit utility, since it captures (for $h > 0$) the idea that get used to a certain level of consumption, so if it drops you are very unhappy.


Dominated Strategies in an Infinitely vs Finitely Repeated Game How does the concept of weak dominance work with infinite games? The abundance of concepts seems to muddy things.

In particular, suppose two players play the following game an infinite number of times.

$$\begin{array}{l*{2}{c}r}
             & A & B  \\
\hline
A & 1,1 & 0,0 \\
B & 0,0 & 0,0
\end{array}$$

In the one shot game, it is clear that playing $A$ weakly dominates the action $B$.

However, what if we consider a bizarre kind of grim trigger:

In the first period, a player plays $B$.
If the other played $A$ in the first period, play $B$ forever.
Otherwise, play $A$ forever.

For a patient enough player, it is weakly best to respond to this strategy with the same one. Any strategy that begins with $B$ and then $A$ afterwards is a best response (the off-path details can be different, so that a best response may not stipulate $B$ forever if the other chooses $A$ at the beginning).

The pareto efficient equilibria involve always playing $A$ on the equilibrium path, and it's tempting to say that playing $A$ no matter what should be weakly dominant, but that doesn't seem to be the case. Has much been written on this kind of thing? What kind of ideas exist to rule out the kind of strategy described above?

Is the strategy in question itself weakly dominated? I would guess that we could concoct an equally sinister trigger strategy $s'$ so that the strategy in question is not dominated by any other $s''$.

A usual refinement concept used to deal with weakly dominated strategies is the trembling hand perfect equilibrium. (I do not know others but this one works quite well.

The strategy in question is indeed weakly dominated by the following strategy

In the first period, player plays $B$.
In all other periods, player plays $A$.


Is Myerson's Lemma valid for piecewise linear allocation functions? In Tim Roughgarden's fantastic course on Algorithmic Game Theory, he begins the course by introducing basic mechanism design, and Myerson's Lemma. He then proves that Myerson's Lemma is valid for piecewise constant allocation functions. I would like to know if a proof also exists for piecewise linear allocation functions.

Milgrom's excellent Putting Auction Theory to Work is a reference for what you're looking for. If I'm not mistaken, Myerson's lemma works for quasi-linear payoffs.


Auction Theory: Proving that the found equilibrium is indeed optimal I have been looking at auction theory and in the book Auction Theory by Krishna, there is one (seemingly simple) inequality that I just cannot follow.
Context: given a private valuation $x$, the optimal bidding strategy has been found $\beta(x)$. Now, the author wants to show that behaving and bidding as if you were of type $z$, $\beta(z)$ does not increase profits.
Then, calculating the difference between the profit in the optimum and the profit if you would behave as if you were of type $z$ leads to the following inequality.
$G(x)$ being a probability distriubtion:
$$\pi(\beta(x),x) - \pi( \beta(z),x) = G(z)(z-x) - \int_x^zG(y)dy \geq 0$$
The profit functions were calculated from a first-price auction in case it helps anyone.
My question is why the inequality holds. Why is $G(z)(z-x) - \int_x^zG(y)dy$ larger than 0?
I hope you can help me :)

$$
G(z) (z-x) =
\int_x^z G(z) dy
$$
and since $G$ is increasing on $[x,z]$, the right hand side is larger than
$\int_x^z G(y) dy$.


Prove if $\succsim$ is rational then: if $x \succ y \succsim z$, then $x \succ z$ Prove if $\succsim$ is rational then: if $x \succ y \succsim z$, then $x \succ z$

By definition of $\succ$,

\begin{equation} \tag{1}
x \succ y \iff x \succsim y, \; \neg \; y \succsim x
\end{equation}

Where $\neg$ is the negation symbol.

So we want to show both

$$ x \succsim z \; and \; \neg z \succsim x $$

We are given

\begin{equation} \tag{2}
y \succsim z
\end{equation}

By $(1)$ and $(2)$ and transitivity of $\succsim$ (since $\succsim$ is rational),

\begin{equation} \tag{3}
x \succsim y \succsim z \Rightarrow x \succsim z
\end{equation}

We also need $\neg \; z \succsim x$

Suppose the contrary that $z \succsim x$, but then

$$ z \succsim x \succ y \succsim z $$

Such that

\begin{equation} \tag{4}
z \succ z
\end{equation}

is a contradiction  (as $\succ$ is irreflexive) so it must be that

\begin{equation} \tag{5}
\neg \; z \succsim x
\end{equation}

Applying $(3)$ and $(5)$ we have the desired property

$$ x \succsim z, \; \neg \; z \succsim x \Rightarrow x \succ z $$

My question is if I am allowed to arrive at the statement $(4)$ from the line above it?

By contradiction, assume $z \succsim x$. However, we already know that $y \succsim z$, which is a contradiction (after a couple more steps). Can you now see this?


Is information technology going to turn most "common goods" into private goods? Common goods, (not public) are so because they are non-excludable and rival.  Often this reflects the impracticality of excluding some users, rather than an absolute impossibility. For example, a park is public because it's impractical to be charging everybody that derives a benefit from using it. However, if it becomes easy to track who uses the park,  for how long,  who looks at the parks,  etc. then the park could be financed privately!

Gadgets that track people's use of different goods could change which ones we deem to be excludable and which ones non-excludable....

A basic example is toll roads. If we mount GPS's on all cars and figure out how much tim they spend on the road, we could charge people for their use of streets directly. No more publicly financed road construction!

Many obstacles to converting common goods into private goods are legal or normative rather than technological. For example, the technology necessary for congestion pricing of traffic is long established and indeed in use since the 1970's in Singapore. The existence of electronic transmitters or plate readers (London) may make for finer gradations of pricing and simpler administration but haven't made for widespread adoption. In fact, many notably congested larger cities like New York and Hong Kong have had failed congestion charge proposals. Or take a crowded national park. If ticket prices at Yellowstone were \$115 per person like Disney World instead of the nominal \$30 per car they actually charge it wouldn't be nearly as crowded. Prices are well below the market clearing rate as a matter of public policy, not because there is a technological obstacle to charging more.


What would make a restaurant offer all-day breakfast? Some restaurants particularly fast food ones offer breakfast food only during, well, breakfast hours. Other restaurants however offer breakfast food throughout their opening hours. Some restaurants are specifically breakfast only so of course they do.

What's up with that? What would make a restaurant offer some food only sometime while others (besides breakfast restaurants) offer said food throughout opening hours?

I was thinking that this might have something to do with low demand or something, but then why do all-day breakfast restaurants, like, not go out of business?

This question makes a hidden assumption:  that all diners are on the same circadian rhythm.  A significant portion of the US population works nights, spans time zones, etc. For example, truckers.

That's one answer, that addresses the market.  There's also the question of inventory logistics for the restaurant.  Most eateries have to do extensive prep for a meal shift, and that includes thawing proteins, advance-cooking certain items, chopping, etc.

Imagining an ideal world for the restaurant, they would prep exactly as much food, in various menu-item-proportion, as was ordered in a meal shift, and end up with none left over.  Meal prep left over would represent wasted inputs, and very often it is not able (or allowed) to be kept for the next meal shift.

Menu prep is "expensive" whether you end up selling one meal or a dozen.

Also, often "lunch cooks" have a different set of training/skill sets than "dinner cooks" than "breakfast cooks."


Economic Profit and the Return on Invested Capital In my finance classes, I always learned that the a firm earning an "economic profit" is one for which its return on invested capital (ROIC) is greater than it's opportunity cost of capital (usually calculated using the Weighted Average Cost of Capital). But, in my economics classes, I learned that economic profit accrues to a firm that has the ability to price above marginal cost (the demand curve for its product is not infinitely elastic).

Are these two definitions compatible? Is there a way to connect the two? The reason for my question is that I have noticed situations in which the two don't concur. For example, oil companies have negligible market share (when considered globally; e.g. Exxon, the largest U.S. oil major, has about 3% market share - will try to find the reference for this, can't currently remember) and sell a commodity product, and so that's pretty close to the "competitive ideal" as depicted in any Intermediate Micro class. However, if you look at Exxon's ROIC, it has at times been in the 30% range, much higher than any reasonable estimate of WACC (usually around 7-12%). So there appears to be a discrepancy between two different measures of "economic profit".

Both of them are consistent. The economic profit is the total revenue $TR$ minus total cost $TC$ but in economics costs must include also opportunity costs not just accounting ones.

However, for all standard market structures  $TR>TC$ happens only if the marginal revenue or price  $P$ is above marginal costs $MC$.

Also if there is positive economic profit then also return on the capital will be higher than opportunity cost of that capital, because by definition such profit must be higher than the minimum necessary to compensate for the opportunity cost.

So it’s not that the definitions are inconsistent they are just different results based on the same principle. However, if you would try to calculate the true economic profit by different estimation methods you could get different answers because some opportunity cost might be not easy to observe. For example, weighted average costs of capital (WACC) is a crude way how to estimate opportunity cost it’s not the definition of it. Also many inputs in WACC are only proxies not actually directly observable variables.

Now turning attention to your example it’s simply not true the demand for oil is elastic or that oil market is perfectly competitive market. Due to organizations as OPEC oil market was for long time almost monopolized and even though the strength of OPEC decreased in recent years I would still put it somewhere more close to oligopoly. It’s definitely not even close to perfectly competitive market which requires many sellers not just few key players. Also perfect competition requires (virtually) no barriers to entry and in oil industry the entry barriers can be high.

Moreover, demand for oil is also very inelastic. Unfortunately even now in 21st century our civilization crucially depends on fossil fuels to run. Oil is still virtually a necessity and demand for it is highly inelastic. In fact if you try to survey the literature on google scholar by checking for elasticity of oil demand you find that most mean estimates report elasticity less than 1 and many close to 0.1 which is very small. In such setting in most market structures you get a room for significant economic profit as market power varies inversely with elasticity of demand.


Calculating present value using Euler's number So I was reading here where they calculate the expected value of an option at present given the expected value of the option in a year by calculating

$$C_0 = C_1 e^{(-r)}$$

where r is the interest rate. But where does e come from here? Shouldn't present value just be calculated using

$$C_0 = C_1 / (1 + r)$$

What am I missing?

$e^{-rt}$ is the continuous discounting factor while $(1 + r)^{-t}$ is its discrete counterpart.

Identically/equivalently, there is the continuous manner of computing factors of variation, e.g. $1 + \ln \frac{x_{0+t}}{x_0}$, and its discrete counterpart $\frac{x_{0+t}}{x_0}$.

It all depends on whether you think you are dealing with a continuous quantity or not.

In asset pricing (or finance in general) the underlying notion is that of continuous (interest) compounding.


Kuhn Tucker Conditions with fewer non-negativity constraints than number of variables I have a following type of problem:

$Maximize\,\, F(s,x,y,z)$
$s,x,y,z$

s.t. (i) $g(x,y,z) \le I$
(ii) $x \ge 0$
(iii) $y \ge 0$
(iv) $s > 0$

That is there is no non negativity constraint on variable $z$. I have read about the Kuhn-Tucker method in the books but in all those cases the problem is fourmulated such that the non-negativity constraints apply to all the choice variables. How would my K-T optimality conditions change if I have no non-negativity constraint on $z$?

My sense is that other than the regular K-T conditions for $x$ and $y$ and Lagrange multiplier, $\lambda$, we would have (a) $\frac{\partial \Large{L}}{\partial z} = 0$ (i.e. no inequality here) and NO such condition as (b) $z\,.\frac{\partial \Large{L}}{\partial z} = 0$ (which is obviously true given (a)). My entire confusion is because I have not seen such a formulation in books where K-T conditions are discussed and just want to be sure about my steps.

What would the conditions be in case of $s$, where the inequality is strict?

Here I would think that with strict inequality the problem is not well defined. The constraint set is not compact (not closed).

Thanks a lot in advance.

Non-negativity constraints have nothing special and are not critical for the general validity of the Karush-Kuhn-Tucker approach. First, realize that we could have $x \geq a >0$ and then we could write $x-a \geq 0$ and view this "non-negativity" constraint as just one more inequality constraint on the solution.

When a decision variable is weakly bounded, the new phenomenon that emerges is that we may have the partial derivative non-zero (strictly negative, for the maximization case), if at the solution this decision variable lies on the boundary.

If it is unbounded, than we must have the first-order derivative equal to zero. As another question pointed out, this may create issues in certain contexts, but it does not invalidate the approach.

As for your second question, indeed strict inequalities may create problems, but don't jump immediately to a "not well-defined" heavy statement. The problem will arise only if (stars denote the optimal solution)

$$\frac {\partial F(s^*,x^*,y^*,z^*)}{\partial s^*} <0$$

which would "push" the solution vector towards the unreachable zero-lower boundary for $s$. To avoid that, we require that at the solution the first-order derivative w.r.t to $s$ equals zero, and see whether we can indeed obtain a solution vector. If we can, it means that the $s>0$ constraint does not even "tend to" be binding, so you can ignore it.


Risk Premia in Continuous Time Take some state variable $X(t)$, which follows the law of motion

$$ \dot X(t) = f(t)X(t) $$

where $f(t)$ is a policy function, and determines the growth rate of $X(t)$. As a second shock, we have $\psi$, which is iid. The agent defaults whenever

$$ g(X(t), \psi) \leq 0$$

Allow the agent to borrow some money that he will have to repay continuously. Let's compute the risk premium. The probability of default at $t+\epsilon$ is

$$Prob(g(X(t+\epsilon), \psi) \leq 0) $$

As the lending has to be repaid continuously, the interest rate, given some risk-free interest rate $r^*$ and risk-neutral lenders, is given by

$$ r^* = r \cdot \lim_{\epsilon\to 0} \left(1 - Prob(g(X(t+\epsilon), \psi) \leq 0)\right)$$

However, as the law of motion for $X(t)$ is continuous, in the limit, this becomes

$$ r^* = r \cdot \left(1-Prob(g(X(t), \psi) \leq 0) \right)$$

This would mean that the agent's risk premium is independent of what he is doing: his policy $f(t)$ does not appear anymore.

But since $f(t)$ affects the state $X(t)$ and the latter the default probability, I feel it should. What's my mistake here?

References are fine. Most of continuous time finance references I know are much too deep for this rather simple question.

The easiest way to model short-term but risky debt in continuous time is to have your $\psi$ be the increment of a compound Poisson process.

Jumps in this process correspond to events that might or might not cause default; the size of the jump can enter together with the state $X(t)$ into a function like your $g(X(t),\psi)$ to determine whether or not default actually occurs. Using this formulation, one can circumvent your concern in the comment that "debt is risk-less, if it is almost immediately paid back".

If, for instance (in a simple case), default occurs whenever there is a nonzero increment in the compound Poisson, regardless of the size of this increment, then if the arrival rate of these jumps is $\mu$, the interest rate will be $r=r^*+\mu$, the risk-free rate plus the flow default rate. If (in a more complicated case) default only occurs for some increment sizes, according to a threshold that depends on $X(t)$, then we can get $r$ varying with $X$.

In this environment, your observation that $f(t)$ does not affect $r(t)$ is completely correct. But this is because $f(t)$ does not contemporaneously affect $X(t)$ and hence does not affect whether or not there will be a default if the Poisson shock occurs at time $t$. $f$ does affect future $X$, and thus will potentially affect future default probabilities and interest rates.

The property we see here - where your policy today doesn't affect your interest cost today, because short-term creditors only care about the current probability of default and your policy can't affect that right away - is generically a strange feature of short-term debt models, and is brought into starkest relief in the continuous-time environment. This is why models of long-term debt are often more realistic, because the price of long-term debt incorporates future default decisions and therefore the effects of policy on future values of the state variable.


Does the US stock market tend to rise after natural disasters? It seems counter intuitive that markets would rise after a huge disaster that probably affects multiple industries like oil or produce.

For example, can someone explain why the US markets actually rose in the days following hurricane Harvey?

Edit: changed title to include natural disasters as a whole.

This news article with some statements from financial workers makes a case that usually big storms don't impact the national economy that much, even despite the large localized damages. While insurance companies will suffer in the stock market because of all those payouts they'll have to give, oil prices as you mentioned will be impacted, but in this case, gas prices will rise because of the change in the supply curve, so they will actually benefit in the stock market. The various effects combined end up with the stock market not really going up or down. It's more or less a wash.

To think of it another way, a shock in the short term capital in the economy won't particularly change the steady state level of capital. If markets know this, there isn't a need for huge changes in prices. In the case of the insurance companies, their money isn't so much based on capital as it is based on states of the world, so they will end up needing to adjust prices.

There are other reasons why the stock market may not have moved up or down in particular, but for the most part it is speculation, and even my answer is just intuitive exposition.


Why can anyone buy insurance of an, without owning the, underlying asset? A Random Walk Down Wall Street (2015 11 ed, but an 2019 ed. is upcoming). p. 100 Top.

    To make matters even more complicated, there was not just one bond issued against a package of mortgages. The mortgage-backed securities were sliced into different “tranches,” each tranche with different claim priority against payments from the underlying mortgages and each with a different bond rating. It was called “financial engineering.” Even if the underlying mortgage loans were of low quality, the bond-rating agencies were happy to bestow an AAA rating on the bond tranches with the first claims on the payments of interest and principal from the underlying mortgages. The system should more accurately be called “financial alchemy,” and the alchemy was employed not only with mortgages but with all sorts of underlying instruments, such as credit card loans and automobile loans. These derivative securities were in turn sold all over the world.
    It gets even murkier. Second-order derivatives were sold on the derivative mortgage-backed bonds. Credit-default swaps were issued as insurance policies on the mortgage-backed bonds. Briefly, the swap market allowed two parties—called counterparties—to bet for or against the performance of the mortgage bonds, or the bonds of any other issuer. For example, suppose I hold bonds issued by General Electric and I begin to worry about GE’s creditworthiness. I could buy and hold an insurance policy from a company like AIG (the biggest issuer of credit default swaps) that would pay me if GE defaulted. The problems with this market lay in the fact that the issuers of the insurance such as AIG had inadequate reserves to pay the claims if trouble occurred. And anyone from any country could buy the insurance, even without owning the underlying bonds. [I bolded.] Eventually, the credit-default swaps trading in the market grew to as much as ten times the value of the underlying bonds, pushed by demand from institutions around the world. This change, where the derivative markets grew to a large multiple of the underlying markets, was a crucial feature of the new finance system. It made the world’s financial system very much riskier and much more interconnected.

Please see the bolded sentence and the titled question. I believe that personal life insurance requires the beneficiary to be related to the insured. Why not for credit-default swaps?

In a free market, two parties should be free to contract/trade whatever they like, under whatever conditions they like, unless the state has good reasons -- be it economic, moral, religious, or otherwise -- for intervening.

So I would instead rephrase your question as the following two questions:

Question 1. Why is it that in life insurance, the state intervenes by imposing the requirement known as insurable interest?

Question 2. Are there good reasons for the state to likewise impose a similar requirement on credit default swaps (CDS)?

Question 1. Actually, during the early (modern) history of insurance (which involved primarily life and marine insurance), you could buy insurance even without having an underlying stake in the insured object or what we now call an insurable interest.

As you can imagine, this led to a number of abuses, including murders and ships getting lost or destroyed. The term moral hazard actually originated in this context (and has since been appropriated by economists to mean something slightly different).

One result of such abuses was that in 1746, the Marine Insurance Act came into effect in Great Britain and introduced the doctrine of insurable interest:

  WHEREAS it hath been found by Experience, that the making Assurances, Interest or no Interest, or without further Proof of Interest than the Policy, hath been productive of many pernicious Practices, whereby great Numbers of Ships, with their Cargoes, have either been fraudulently lost and destroyed ... no Assurance or Assurances shall be made ... without further Proof or Interest than the Policy, or by way of Gaming or Wagering, or without Benefit of Salvage to the Assurer ...

Question 2. With CDS, the arguments in favor of imposing the insurable interest doctrine are weaker. For example, the risk of moral hazard is lower, because it is harder to cause a firm or sovereign state to default than to murder someone or burn a ship.

So by and large, CDS are treated by most governments as being just like any speculative asset that anyone is free to trade in at one's own risk.

Nonetheless, Germany (2010) and the EU (2012) have imposed this doctrine on CDS, though only for debt issued by European governments and not by firms  -- see e.g. Aldasoro and Ehlers (2018).

Some of the blame for the Global Financial Crisis has been rightly ascribed to CDS. However, I think the two big problems with CDS were the lack of transparency and the systemic risk (or "domino effect"), rather than the lack of an insurable interest requirement.

Imposing the insurable interest requirement would not have much mitigated these two problems, except perhaps by increasing the transaction costs associated with CDS and thus decreasing their use.


Auction theory reference request I am interested in finding the literature or at least some references (books, journal papers etc.) for the following problem:

  Suppose there is an auction with one seller and one buyer. The seller has two distinct and indivisible goods to sell and the buyer wants to buy at most one good.

Also, has the community of mechanism design dealt with this problem?

The reason I'm asking is because I want to design an auction for an engineering problem. But first I need to understand the theory behind auctions.

I'd appreciate any help. Thank you.

Mechanism design with multi-dimensional types (here: the willingness-to-pay for each object) is a notoriously difficult problem. Even when you abstract from bundling as you do by assuming that the seller only wants to buy one of the goods.
Your problem is studied by John Thanassoulis in "Haggling over substitutes", JET 2004. Unfortunately, there is no "nice" solution. While it is always optimal to post a fixed price in the single-good case, fixed prices are not optimal with two distinct good and randomization is part of the optimal seller strategy:

Using a model of substitutable goods I determine generic conditions on tastes which guarantee that fixed prices are not optimal: the fully optimal tariff includes lotteries. That is, a profit maximising seller would employ a haggling strategy. We show that the fully optimal selling strategy in a class of cases requires a seller to not allow themselves to focus on one good but to remain haggling over more than one good. This throws new light on the selling strategies used in diverse industries. These insights are used to provide a counter-example to the no lotteries result of McAfee and McMillan (J. Econ. Theory 46 (1988) 335).

Gabriel Carroll looks at a simpler problem in "Robustness and Separation in Multidimensional Screening", Econometrica 2017, where the seller does not know the joint distribution of the willingness-to-pay and considers "worst-case" profits.

A principal wishes to screen an agent along several dimensions of private information simultaneously. The agent has quasilinear preferences that are additively separable across the various components. We consider a robust version of the principal's problem, in which she knows the marginal distribution of each component of the agent's type, but does not know the joint distribution. Any mechanism is evaluated by its worst‐case expected profit, over all joint distributions consistent with the known marginals. We show that the optimum for the principal is simply to screen along each component separately. This result does not require any assumptions (such as single crossing) on the structure of preferences within each component. The proof technique involves a generalization of the concept of virtual values to arbitrary screening problems. Sample applications include monopoly pricing and a stylized dynamic taxation model.

If you punch the title into youtube you will find two of his talks about the paper. His introduction may give you an idea on how other researchers have failed to find a cute solution.


Trade in services between the US and China International trade consists of both goods and services, yet in the case of US-China trade for some reason both the media and official government releases only seem to quote the goods component.

So for example for 2017 imports were $\$505.6$ bn, exports $\$130.4$bn giving a trade deficit in goods of $\$375.2$bn with China.

I cannot for the life of me find import and export figures for services to and from China.

Can anyone please point me in the right direction? Thanks.

Table 2.2 of https://www.bea.gov/scb/pdf/2017/10-October/1017-international-services-tables.pdf suggests

US exports of services to China in 2016 worth $\$54$bn and
US imports of services from China in 2016 worth $\$16$bn

Later parts of table 2.2 give a breakdown of types of services.  Travel (for all purposes including education) - which should not include transport - seems to be a large part of US exports of services to China


Comparative data on agricultural subsidies Where can I find data on the agricultural subsidies of each country, ideally in a comparable fashion? I've googled without success. I hope there are some experts on this forum that can direct me to specialized data sources, or perhaps books.

It seems this is all surrounded with secrecy, so no much is available online.

World bank website doesn't have this information.

Which countries are you looking at? This paper seems to suggest there's data from OECD countries.

You might also take a look here and here. I downloaded zip files and, if I understand correctly, there seem to be data of subsidies by country, product, and year.


Do open market operations permanently increase the money supply? Suppose the Fed buys 1000 dollars worth of T-Bills in the open market to try decrease interest rates and increase the money supply. It does this by printing money and electronically increasing the sellers (a private bank) reserves by 1000 in exchange for the T-Bill thus boosting the private banks reserves and in this way the newly printed money has entered into the economy. Once the banks reserves have increased, the money multiplier process begins and the ultimate increase in the money supply is equal to 1000 dollars times the money multiplier. Depending on the money multiplier (that is, how willing banks are to lend that new money), the increase to the money supply could be only $1000 (in the case of no lending) or potentially a lot more. This much I understand as most textbooks describe the process fully.
But now what does the Fed end up doing with these T-Bills? Since they are T-Bills, they must mature within a year, so when they mature surely the government has to pay the Fed the face value of the T-Bill? The money the government uses to pay the Fed will then leave the economy and the money supply will not have changed ultimately. Even if the initial Fed purchase of the T-Bill had a high money multiplier and thus caused an increase in the money supply much larger than 1000, the government must pay the Fed with real currency or reserves at maturity. Thus, through open market operations, I can only reason that the money supply can increase at best only in the short term (maximum of 1 year when the last purchased T-Bills mature) and hence it does not constitute a permanent increase in the money supply. Also, when the government pays the Fed at maturity, this decrease in the money supply should lead to some deflation counteracting the initial boost that the open market operations were intended to do. So am I missing something or can open market operations only increase the money supply in the short term (being max 1 year assuming the Fed is purchasing T-Bills)? This reasoning would lead me to believe that quantitative easing can also only increase the money supply until the maturity date of the purchased government bonds (around 20 years) at which point the money supply must decrease to where it was before the quantitative easing began?
Any help on this would be most appreciated as all my textbooks describe how the Fed buys T-Bills and how this increases the money but not what the Fed ultimately does with these T-Bills and how that may or may not decrease the money supply.

If these T-bills mature and are repaid then you are correct money supply will decrease. In fact that might be desirable. Just because central bank wants to increase money supply in one year that does not mean they will not want to decrease it at some further period.
When the T-bill matures central bank also have option to then buy new T-bill to replace the old one if they want to keep money supply constant.
Lastly, central banks could also retire the T-bill meaning government never needs to repay it and the increase in money supply is now permanent (or more precisely there might be some other ways how it can be decreased but not anymore through the same instrument so if we are talking only about OMO's it would be permanent).   This is possible but given that it is permanent and central banks might want to not just increase money supply but also decrease it in the future they might prefer just buy new bonds as old ones expire until they decide that they want to decrease money supply.


Black-Scholes Model question Suppose a company has a zero coupon bond with face value of 200 million which matures in a year.  Its assets has a market value of 300 million. The standard deviation is 30%  and the risk free rate is 5%. It does not pay any dividends. Based on the Black-Scholes model, what is the value of debt and equity? How can we replicate this option?

I'm new to finance, but don't we need to know whether this is a call or a put option to replicate it? Also how do we go about solving for the value of debt and equity using the B-S model? Wouldn't the value of debt just 200M/(1+5%)? What does it have to do with the model?

For simplicity, numbers are in millions.

We assume that markets are efficient, and that the value of equity and liabilities equals that of assets. So debt + equity = 300. We want to solve for the value of the debt, and get equity as the residual.

The valuation debt $=\frac{200}{1.05}$ assumes no default. We model default by the probability of the value of the assets dropping below 200 (redemption value of debt) after one year.

We can value the default risk by nothing that it could be cancelled out by buying a put on the asset values, with a strike at 200. I leave to the reader the determination of this value. Buying the bond and the put creates a default risk free bond, which has the discounted value above.

The value of bond with default is therefore the value of the default free bond less the value of the put.


Deriving optimality conditions in the New Keynesian model framework with an undefined consumption function I am trying to solve the household's optimization problem in the New Keynesian model framework, where utility is given by
$$
E_0\sum_{t=0}^\infty \beta^t \mathcal{U}(C_t,L_t,N_t;Z_t)
$$
and period utility is defined as $\mathcal{U}(C,L,N;Z)=(U(C,L)-V(N))Z$.
$U(\cdot)$ is increasing and concave, $V(\cdot)$ is increasing and convex and $h(L/C)\equiv U_l/U_c$ is a continuous and decreasing function that satisfies $h(\bar{\varkappa})=0$ for some $0<\bar{\varkappa}<\infty$.
$L_t\equiv M_t/P_t$ and it is assumed that $C_t,N_t,L_t\geq 0$ for all t.
The household's budget constraint sequence is given by
$$
P_t C_t+B_t+M_t=B_{t-1}(1+i_{t-1})+M_{t-1}+W_t N_t+D_t-P_t T_t
$$
for $t=0,1,2,...$ and we rule out Ponzi schemes by imposing
$$
\lim_{T\to\infty}\Lambda_{0,T}\mathcal{A}_T\geq0
$$
with $\mathcal{A}_T\equiv [B_{t-1}(1+i_{t-1})+M_{t-1}]/P_t$ as the household's real financial wage at the beginning of period t. $W_t$ are nominal wages and $D_t$ are dividends paid by firms.
I am supposed to arrive at the optimality conditions below

Euler equation: $U_{c,t}=\beta(1+i_t)(P_t/P_{t+1})U_{c,t+1}$

Intratemporal labor supply: $W_t/P_t=V_{n,t}/U_{c,t}$

Money demand schedule: $h(L_t/C_t)=i_t/(1+i_t)$

In combination with the transversality condition: $\lim_{T\to\infty}\Lambda_{0,T}\mathcal{A}_T=0$
How do I set up the Lagrangian?

I'm not quite sure what $Z$ stands for in this model (looks like some kind of multiplier over the standard utility) but I can generally guess the rest. $C$ stands for consumption, $L$ for real money holding, $N$ for hours worked, $B$ is one-period bond, $M$ is nominal money, $W$ is wage, $D$ is dividend, and $T$ is tax.
$U(C,L)$ denotes the utility derived from consumption and real money holding while $V(N)$ is disutility from working. Rewriting the problem as follows,
$$\underset{C_t,N_t, L_t, B_t}{\max} E_0\sum^{\infty}_{t=0}\beta^t\mathcal U(C_t,L_t,N_t;Z_t) \\ \text{subject to} \\
P_tC_t+M_t+B_t\leq B_{t-1}(1+i_{t-1})+M_{t-1}+W_tN_t+D_t-P_tT_t
$$
You can now set up the Lagrangian
$$\mathcal L= E_0\sum^{\infty}_{t=0}\beta^t\mathcal U(C_t,L_t,N_t;Z_t) + \lambda_t [B_{t-1}(1+i_{t-1})+M_{t-1}+W_tN_t+D_t-P_tT_t-P_tC_t-M_t-B_t]$$
Taking the partial derivative with respect to the choice variables,
$${\partial \mathcal L\over \partial C_t}=\beta^tZU_{C,t}-\lambda_tP_t \tag{1}
$$
$${\partial \mathcal L\over \partial N_t}= -\beta^tZV_{N,t}+W_t \tag{2}$$
$${\partial \mathcal L\over \partial L_t}=\beta^tZU_{L,t}-\lambda_t P_t+\lambda_{t-1}P_{t-1} \tag{3}$$
$${\partial \mathcal L\over \partial B_t}= \lambda_{t+1}(1+i_t)-\lambda_t \tag{4}$$
Solving with equality (I'll leave the steps for you to complete the exercise), you can derive the Euler equation from (1) & (4). The intratemporal labor supply can be derived from (1) & (2). Lastly, the money demand schedule can be derived from (1), (3) and (4).


Monopsonistic & competitive labour market, which one is better for the labour buyers? Since the marginal cost of hiring workers will rise when the producers hire more and more workers, what is the advantage of having monopsony power (while in a competitive market, labour buyers can hire workers at a fixed wage rate)?

Furthermore, what are the disadvantages to have monopsony power?

Having monopsony power means that all suppliers of labour have to come to you to sell their labour. This gives the monopolist the possibility to extract more surplus from the market than in the case of was a competitive labour market.

More rigourously, in a competitive market, labour supply for the individual firm is perfectly wage elastic. The height of this wage (w*, the fixed wage you refer to) is determined at the labour market, where aggregated labour supply meets labour demand, and will equal the value of its marginal product (vmpl, represented by the demand curve).
When the firm has monopsony power in the labour market, it can pay wages lower than the vmpl. That's the benefit of the monopsonist. To the monopsonist, having monopsony power is never disadvantageous.

A graph or some algebra will certainly prove this point.
http://econpage.com/301/handouts/labormkts/monopsony.GIF


Objections to total surplus as tool for welfare measurement I think people would agree that the most common tool for welfare measurements in economics is the notion of total surplus.

Throughout it's history, total surplus has been criticized several times and on different grounds. This post aims at being a repository of all those critiques.

Which are the critiques of total surplus which seem the most relevant to you?

Note : this is not meant to be a "total surplus bashing" repository. I believe some of the best critique of a concept like total surplus are rarely the one attempting to destroy the concept, and more often those which help us understand when it is best to use it, and when it might be better not to use it.

This is an answer to the closely related question of "why don't competition/antitrust authorities aim to maximise total welfare rather than consumer surplus?" There are a number of reasons for this:

If there are a small number of firms participating in a market then they have a very concentrated interest in that market and therefore have a large incentive to lobby for favourable treatment by a regulator. By contrast, it is likely that only a relatively small fraction of a consumer's income is spent in any one given industry and, therefore, each individual consumer has less interest in lobbying for consumers' interests in any antitrust proceeding. This leads to producers having a louder voice (a problem known as regulatory capture).
The total welfare and consumer surplus effects of a behaviour often point in the same direction (e.g. lower prices and higher quantities typically correspond to both higher consumer surplus and higher total welfare). If measuring both consumer and producer surplus is costly then measuring only consumer surplus will often be a sufficient heuristic.
There are information asymmetry problems insofar as firms have better information about their expected profit gains from a practice than do regulators. Producers are likely to overstate the private benefits of anti-competitive practices and the regulator would need to find a mechanism to induce truthful reveltation.

However, these points must be weighed against

Ignoring producer surplus understates the benefits of a practice and will lead to the  prohibition of some practices that increase total welfare.
Firms are owned by people (i.e. consumers) so that the distinction between consumer surplus and producer surplus is, in some sense, a false dichotomy.
We should give firms enough profit to (a) cover the fixed costs of operating in an industry and (b) ensure that they have an incentive to innovate and be successful. If we insist on maximising consumer surplus by driving price to marginal cost then neither (a) nor (b) will be satisfied.


Derivation of Equilibrium Strategy in 1st-price Auction? Hey, everyone. I desperately need help understanding some math in auction theory.  I have been writing a paper as an undergrad for auction theory, and after all of my research I just cannot understand one step the author of a book uses to derive the equilibrium strategy for first-price auctions under independent private value conditions.
The steps in the derivation process essentially follow this:
Let x = the chosen player's personal valuation, G(x) = the probability that the highest opposing bid, an order statistic, Y_1, is < x.
\begin{equation}
\beta(x) = x - \int_0^x\frac{G(y)}{G(x)} \, dy \\
\end{equation}
Then without much explanation, other than "values are uniformly distributed on [0,1]" he just converts this equation to
\begin{equation}
\beta(x) = \frac{N-1}{N},
\end{equation}
Which makes sense and is usable.

The book I am using is Vijay Krishna's Auction Theory, and I would extremely appreciate someone helping me understand this last step.

I think you have a typo -- the equilibrium bidding strategy in the first-price auction you specify should be $$ \beta(x) = \frac{N-1}{N}x $$

Here's a hint that might help. The CDF of the order statistic, $Y_1$, is $$G(x) = x^{N-1}$$

To see why this is the case, notice that this is exactly the probability that some given quantity $x$ is greater than or equal to $N-1$ independently drawn random variables that are uniformly distributed on $[0,1]$.

I'll write something in more detail when I have more time tomorrow, but I think this should tide you over for now. (At the very least, it'll help you evaluate the integral.)


Stock market in india While economy in india is experiencing a slowdown, the stock markets are having record highs.
can someone explain this dichotomy in simple language ?

Two possible explanations I have:

The stock market capitalization to GDP in India, although high, is at around 70–80 percent, compared to 100+ percent for countries with more developed capital market. This means that any gains or losses in the stock market would have an average 70% impact on the economy.
Being one of the fastest growing markets in the world (due to its population size, urbanization, and the rise of middle income families), the market has huge potential in the years to come, and the stock market takes that into account.


Why is the Supply of Labour More Elastic in a Single Province/State then it is in the Country as a Whole? Apparently, the federal government has a greater ability than provincial government to increase tax revenues by raising tax rates because the supply of labour is more elastic in a single province than it is in Canada as a whole.

However, why would supply of labour be more elastic in a single province than in the country as a whole?

Because there is freedom of movement between provinces; and the language barrier is low. When international borders are involved, there is much less freedom of movement, and much greater potential for language barriers.

So it's easier for labour to move between provinces if incentivised to do so by a change in relative taxation rates; than it is to move between countries.


Price elasticity and optimal pricing in a monopoly with zero marginal cost I am having trouble understanding how to calculate the optimal price P for a good and understand the optimal price elasticity of demand in the following condition:

The firm is a monopoly seeking to maximise profit.
It also has a zero marginal cost (MR = 0).
The firm can only produce/sell an upper limit/number of the good (I am not sure if this changes anything in the analysis)

I found a lot of documentation on the web regarding price elasticity, but I did not find (enough) details about the conditions described above. My understanding is that, even in the above conditions, the optimal price elasticity of demand is at unit elastic (E= -1) [is this correct?], but I have no clue how to calculate the optimal price of the good [is there any formula for it?].
Apologies if my questions is a bit broad, I am very new to this area of study and any help (or reference to a worked solution) is appreciated.

Hint

You are probably working with (or given) a linear demand function of the form $Q=\frac{a}{b}-\frac1bP$, or its equivalent inverse form $P=a-bQ$, where $a$ and $b$ are positive numbers.

Given that price elasticity of demand at the optimum is $-1$, which you were right to point out (assuming linear demand), you can use the elasticity formula
\begin{equation}
-1=\frac{\mathrm dQ}{\mathrm dP}\cdot\frac{P}{Q}=-\frac1b\cdot\frac{P}{Q}
\end{equation}
and the demand equation to solve for the two unknowns $P$ and $Q$.


Why loans/debt can cause inflation? I learned that inflation can be a result of more loans or debt. When there are too much borrowers in the country, people will have more money to spend and the amount of products is the same so prices will increase.

This does not make sense to me because for each new borrower, there is a new lender. Number of borrowers equals the number of lenders. So, when someone has more money to spend, the lender has less to spend. What can cause inflation?

Imagine an economy with only one good, tomatoes, and three people, Lender, Borrower, and Owner. Owner owns all tomatoes. Lender owns all the money. And Borrower owns nothing. If Lender doesn't lend any money to Borrower and Lender doesn't purchase any tomatoes, the price of tomatoes is 0 as there is no demand. When Lender loans Borrower some money and Borrower uses that to purchase tomatoes, the price of tomatoes will rise - inflation.

So how is this situation different than if Lender just bought the tomatoes themselves instead of loaning money to Borrower? First, the Lender is often not in the same position as the Borrower: money owned by the Lender is less likely to be immediately spent than if the Borrower held it and thus the velocity of that money will differ - after all, the Borrower is probably borrowing for a reason. Second, often times because of fractional reserve banking, the amount loaned to Borrower is more than what Lender has in reserve: in other words, more credit is created and if there is more credit chasing a fixed number of goods, price increases will follow.


Does anyone know of any resources that discuss the differences between Hicksian and Marshallian remanding in depth and in an organized way? I don't understand why the Marshallian and Hicksian demand have such different properties.
Both are functions from $$\Bbb{R}^n_+ \times \Bbb{R}_+ \rightarrow \Bbb{R}_+^n$$both are solved using the method of Lagrangian multipliers. Yet the properties of the two are very different.

Does anyone know of any resources that discuss these differences in depth and in an organized way? My professor has us using his lecture notes. These are a good introduction but just don't rigorously discuss the differences.

Technically they are related but are not the same Marshallian (or Walrasian henceforth) demand is the result of $x(p,w)\in argmax_{y\in\mathbb{R}^{L}_{+}}u(y)$ subject to $p'y(p,w)\leq w$. The Hicksian demand is the result of the dual problem $h(p,u)\in argmin_{y\in\mathbb{R}^{L}_{+}}p'y$ subject to $u(y)\geq u$.
The formal relationship is established trough the value functions of both problems, for the walrasian demand we have the value function or indirect utility $v(p,w)=u(x(p,w))$ and the value function of the second problem (hicksian demand) is the expenditure function $e(p,u)=p'h(p,u)$.
Now, the indirect utility and the expenditure are inverses of each other in the following sense:

$e(p,v(p,w))=w$
$v(p,e(p,u))=u$

And to answer your question $x(p,e(p,u))=h(p,u)$ and $h(p,v(p,w))=x(p,w).$
This means that this demands have different properties but can be made equal by adjusting the wealth in the case of the walrasian demand such that I maintain the consumer in a fixed utility level u, thus obtaining the hickisan demand and vice-verse changing the utility level with changes in wealth using to go from the hicksian to the the walrasian.
The properties of each demand comes from the properties of the value functions and are a consequence of the theorem of the maximum. Like continuity of the objective.
A good source is Nolan Miller notes http://business.illinois.edu/nmiller/documents/notes/notes4.pdf.
But every micro theory books covers this material.


Why would regression coefficients be different on a subsample? If I'm running a linear regression for example, and I take out some points, wouldn't the same line/plane still fit the data? If not, wouldn't that show that the data doesn't have a linear relationship?
Example: https://ocw.mit.edu/courses/economics/14-382-econometrics-spring-2017/lecture-notes/MIT14_382S17_lec1.pdf. On page 10, in the gender wage gap example, it finds a predictive effect of ~20% in the full sample and ~7% in the never married sample. But then if dWage/dGender depends on Marital Status, how can the functional form be right?

If I'm running a linear regression for example, and I take out some points, wouldn't the same line/plane still fit the data?

Aside from special cases no, OLS fits a line that is created based on minimization of sum of squared errors:
$$\min \sum e_i^2 = \min \sum (y_i-\hat{y_i})=\min \sum (y_i - \mathbf{x}_i^{\prime}  \beta)^2 .$$
If you remove some observations then you will likely change the objective function above leading to some other line having the best fit through data (save for special cases like when all observations are on a single line).

If not, wouldn't that show that the data doesn't have a linear relationship?

Not necessarily, the linear relationship is assumed to exist between the variables in the 'background', but since we cannot directly observe the data generating process and there will always be some disturbance term even if we are sure there should be a linear relationship between the two variables the observations will not necessarily all fall on a single line.
Non-linearity cannot be detected just from the fact that line you fit changes when you remove some data (although that is an indicator of robustness of a result - robust results should not change too much when sample is expanded/cut slightly). However, you can detect non-linearity in other ways. For example, you can look for patterns in residual plot. If residual plot shows some curved pattern then that is an indicator of potential non-linearity. There are also rigorous tests for non-linearity (like Ramsey test etc) but to go over all of such ways would be beyond the scope of an SE answer - you can read more about them in econometrics textbooks such as Wooldridge Introductory Econometrics: A Modern Approach.


Is there a name for this family of games (Binomial games?)? I'm wondering if there's a name for a $n$-player symmetric game, such that the payoff for player $i$ playing strategy $j$ only depends on the number of other players which played $j$.

Such family of games would capture many real-life games, such as career choosing (where the profit of becoming, say, a programmer, depends on the number of people studying programming, and it is not effected by the ratio of, e.g., agronomists to athletes).

There seems to be quite a lot shared properties for such games, especially if the profit $U_i(j)$ is decreasing as the number of players that chose $j$ increases, so I was wondering if such family was researched before and if it has a name.

OK,  Erel Segal Halevi's comments have placed me on the right track for finding what I was looking for;

This family of games is called "Resource Selection Games", and it has quite a few papers written on it (such as this one).


What are the effects of the increase/decrease in stock options after an IPO? Research :

As far as I can understand :

Stock options are used to increase the capital of companies to realize some projects
Shares are divided into two categories :

o    Free float (which is the part of shares important for my next question)
o    Locked-in stock

For the free float, it’s easy to understand. Public investors can earn money by playing with stock prices.
For the company it’s harder for me to understand.
    When a company wants capital to run projects, she can do an IPO. The initial price depending on the financial situation.

Question :  What are the effects of the increase/decrease of stock prices after that IPO ?

For exemple : Initial stock price was 20 dollars and public investors paid 20 dollars which got into the capital of the companies. If stock price is now 25dollars, company won’t earn 5dollars more. So what’s the point for the company to be devalued after an IPO if she got the amount of capital she wanted ?

Attempt :

I saw only 2 easy solutions :
-   If company wants to increase capital a second time, she needs to have a big value on the market to reduce the dilution of control.
-   If company is too much devalued, she can be acquired by concurrents.
If company doesnt decrease too much and doesnt want to increase capital again, she has no point regarding the increase/decrease of her stock prices, right ?

Exactly.  The main issue is if they want to raise capital a second time. The secondary market does not affect the company itself, but it affects its investors. And as investors are important, they need to be treated well.  Another problem related to this is that several employees in the company have stock options, so it really affects them.

What companies can do also is buy their own stocks if the price dropped considerably. This is not something that happens right after the IPO because it would make no sense to return the money to the markets right after you received it.

So, to sum up, the direct effects for the company are on the primary market (when the company makes the IPO), the secondary market is between public investors that have little to do with the company.


How purchasing power reduces when currency is commodity money(say gold) First of all I am new to Economics. I'm a B.Sc.(Mathematics) final year student. I was curious to learn Economics so I started with "Economics in one lesson" by Henry Hazlitt.

In this book I encountered few phrases like 'inflation' and 'purchasing power'. On Wikipedia I started reading about purchasing power. I was even unable to understand its first paragraph. The first para goes like:

  Purchasing power (sometimes retroactively called adjusted for inflation) is the number and quality or value of goods and services that can be purchased with a unit of currency. For example, if one had taken one unit of currency to a store in the 1950s, it is probable that it would have been possible to buy a greater number of items than would be the case today, indicating that one would have had a greater purchasing power in the 1950s. Currency can be either a commodity money, like gold, silver and bitcoin, or fiat money emitted by government sanctioned agencies.

Suppose I have  10,000 in the year 2000 and at the same time my friend also have  10,000. We both wanted to save this money for future. I decided to put this cash in my lock whereas my friend decided to buy gold of it. For simplicity say my friend bought 1 kg of gold.

Now in year 2010, after 10 years, due to inflation, our purchasing power is reduced. Now my question is that in this 10 year period due to inflation the price of gold is also high, so for the same amount of 10,000 my purchasing power is reduced much more than my friend's. Why or how?

As I said I'm new to Economics so please be simple while explaining.

Any suggestions for further reading will also be appreciated.

Here is a chart from The Economist in July 2010 showing the nominal and real (i.e. inflation adjusted) price of gold in US dollars back to 1970.  The nominal price later continued to rise until 2012 and then fell, and it is currently at about its 2010 level; the real price also rose and then fell and is currently below its 2010 level.  The lines would look different in other currencies

So while the purchasing power of most currencies including the US dollar tends to fall over ten-year periods due to inflation, the purchasing power of gold (shown by the real line) may rise or fall depending on precisely which ten-year period you choose.  For example it rose from 2000 to 2010 and from 1970 to 1980 but fell from 1980 to 1990 and from 1990 to 2000; indeed from 1980 to 2000 the purchasing power of gold fell faster than the purchasing power of the dollar

An additional consideration is that you can store your currency in a bank by depositing it, and you can then receive interest on it, which may offset the decline in the purchasing power. If you store gold in a bank, the bank is likely to charge you a storage fee and you will not receive interest


Request of references regarding Friedman's Nobel Prize I've been trying to find the work for which Friedman was awarded the Nobel prize in economics. Does anybody know what was he awarded the prize for and where can you read the original paper?

The Royal Swedish Academy of Sciences has decided to award the 1976 Prize in Economic Sciences in Memory of Alfred Nobel to Professor Milton Friedman, University of Chicago, Illinois, USA, for his achievements in the fields of consumption analysis, monetary history and theory, and for his demonstration of the complexity of stabilization policy. [...]
  His major work, A Monetary History of the United States,1867 - 1960, is regarded as one of Friedman's most profound and also most distinguished achievements. Most outstanding is, perhaps, his original and energetically pursued study of the strategic role played by the policy of the Federal Reserve System in sparking off the 1929 crisis, and in deepening and prolonging the depression that followed. The critics agree that this is a monumental scientific work which will long stimulate the re-examination of the course of events during this epoch.

http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1976/press.html


Is the mid-market currency exchange rate something real? Or are bid and ask rates the real rates? Reading from this and other sources, it appears to me that there are three different ratios between any two currencies, namely

the bid rate
the ask rate
the real rate

My understaning is that the two primal ratios are 1 and 2, while 3 is just a derived quantity, specifically the mid-point between the former two. In other word, I understand that 1 and 2 are the two real, market-driven numbers, and that 3 is just a convenience to know where 1 and 2 roam in that specific historical moment.

Is my understanding correct?

In the following I just report my line of reasoning.

For instance, if I have an amount $A_1$ in one currency and I want to exchange it with another currency, I would receive the amount $A_2$ in this other currency, defined as

$ A_2 = E_{1 \rightarrow 2} A_1$

where $E_{1 \rightarrow 2}$ is the exchange rate.

If I change my mind and decide to convert $A_2$ back to the previous currency, then I will be given the amount $\overline{A_1}$,

$ \overline{A_1} = E_{2 \rightarrow 1} A_2 = E_{2 \rightarrow 1} E_{1 \rightarrow 2} A_1$

I've understood that, if we leave the time elapsed between the two operations aside (or if we do the two exchanges at exactly the same moment), we are sure that $\overline{A_1} < A_1$, because we are sure that in any given moment in time the following holds:

$E_{2 \rightarrow 1} < \displaystyle\frac{1}{E_{1 \rightarrow 2}} \tag{1}$

Is this true?

To me it seems obvious, since if $(1)$ had an equal sign, that would mean that I can freely exchange between currencies at zero cost (hence I could lose or earn money only as a consequence of the change of that unique rate over time due to other factors).

Indeed the bid and ask spread is very real. The liquidity taker cannot buy and sell at the same price. The market maker extracts a "liquidity premium" for providing liquidity.

When you buy with a market order, you pay the ask price. When you sell with a market order, you get the offer price.

(OTOH, what you mean by "real rate" is not at all clear.)

So, in your hypothetical example, assuming all else constant---yes, after making the round trip trade, you will end up with less than you started. This already happens at, for example, the currency exchange booths at an airport. The booth is acting as the market maker.

Now you can also buy with a limit order. That is, post a offer price and wait. If your order gets hit by someone's sell market order, then you get to buy cheap. Downside is execution risk---you may have to wait a while, possibly a very long while.

Some further comments:

The mid-quote between the best bid and ask could be a vacuous quantity when the spread is equal to the minimal price increment.
The spread is the difference between the best bid and best ask. If an market order size is larger than number of limit orders at those best prices, it will deplete those orders at the best prices and hit orders at the second best price and so on. So if an order size is large or market is thin at the best prices, the spread is a conservative indication of transaction cost. Professional investors split their large orders into smaller ones in order to minimize price impact.
How much the spread matters depends on the type of trader. For a retail trader who occasionally transacts small orders, the cost is probably negligible. On the other hand, slippage is an important issue for institutional investors. Also, on inter-dealer platforms where orders are placed in units of million, spread is closely watched.


Proving the De Finetti Theorem Let us have a finite state space, $\Omega = {\omega_1,\cdots,\omega_s}$, where $2 \leq s < \infty$. Define a bet as a function $x:\Omega \rightarrow X$, where $X \subseteq \mathbb{R}^s$ is the set of monetary outcomes. Assume that the agent only cares about expected payoffs. Let $\succcurlyeq$ be a rational, continuous preference relation on $X$.

Additivity:
$$\forall x, y, z \in X, \text{then} \ x \succcurlyeq y \iff x+z \succcurlyeq y+z$$

Monotonicity
$$\forall x, y \in X, \text{then} \ x \geq y \iff x \succcurlyeq y$$

Non-Triviality
$$\exists x, y \in X, \text{s.t.} \ x \succcurlyeq y$$

De Finetti Theorem

$\succcurlyeq$ on $X$ is rational, continuous, additive, monotonic, and nontrivial if and only if

$$\exists p \in \mathbb{R}^s \setminus {0} = \{p \in \mathbb{R}^s \mid \sum^s_{i=1} p_i = 1, \ p_i \in [0,1] \ \forall \ i \}$$

s.t. $\forall x,y \in X$, we have $x \succcurlyeq y \iff p \cdot x \geq p \cdot y$

Moreover, p is unique.

So my professor has asked us to prove the De Finetti Theorem, in which she told us that:

First, prove that $\succcurlyeq$ is rational, continuous, additive, monotone, and nontrivial.

$$( \exists \ p \quad \text{s.t.} \ \forall x,y \ \text{and} \ x \succ y \Leftrightarrow px \geq py )$$

Use the uniqueness of p with a proof of contradiction using:

Assume $\succcurlyeq$, then suppose $x \succcurlyeq y$ but $px < py \ \forall \ p$. Then suppose $px \geq py, \ y$  but $y \succ x \ \forall \ p$.

Second, let $U(\lambda) = px$, then show the property holds.

Then with the uniqueness of $p$, let $s = 2 \rightarrow ( p , 1- p)$

Consider $x \sim y$, and then suppose $p$ is not unique $\rightarrow$ $( p + \epsilon , 1 - p - \epsilon )$.

$\epsilon \in \mathbb{R}$

So the question is: how do I construct $\epsilon$ for it to be consistent with the model? Any help would be appreciated in applying the outline of this proof.

Here was my attempt at a proof:

First let us look at the "if" case.

Assume $\succcurlyeq$ on $X$ is rational, continuous, additive, monotonic, and non-trivial.

BUT

Case 1: $x \succcurlyeq y$ and $p \cdot x < p \cdot y \ \forall p$

Suppose $p = \{\frac{1}{s} \cdots \frac{1}{s}\}$

$$p \cdot x < p \cdot y \implies \frac{1}{s} \sum^s_{i=1} x_i < \frac{1}{s} \sum^s_{i=1} y_i \implies \sum^s_{i=1} x_i < \sum^s_{i=1} y_i$$

So $x \succcurlyeq y \iff x \geq y$ by monotonicity

$x \geq y \iff x_i \geq y_i \ \forall i$ by definition

but then $\sum^s_{i=1} x_i \geq \sum^s_{i=1} y_i$ which is a contradiction.

Case 2: $p \cdot x \geq p \cdot y$ and $y \succ x \ \forall p$

Similarly, pick the same $p$.

$$p \cdot x \geq p \cdot y \implies \sum^s_{i=1} x_i \geq \sum^s_{i=1} y_i$$

$y \succ x \iff y > x$ by monotonicity

but then $\sum^s_{i=1} x_i < \sum^s_{i=1} y_i$ which is a contradiction.

Now, let us look at the "only if" case.

Let $u(x) = p \cdot x$ and $\exists \ p$ s.t. $\forall x,y$ then $x \succcurlyeq y \iff p \cdot x \geq p \cdot y$

Now we wish to show our five properties hold and the uniqueness of $p$.

The above implies that

$\exists \ p$ s.t. $\forall x,y$, then $x \succcurlyeq y \iff U(x) \geq U(y)$

This we have utility function representation, by definition. It is a basic proof from the beginning of your class probably that representation implies rationality.

We can also say if $U(x)$ is continuous in $X$ and $U(x)$ represents $\succcurlyeq$ on $X$, this implies the preferences are continuous.

$x \succcurlyeq y \iff p \cdot x \geq p \cdot y \iff p \cdot (x + z) \geq p \cdot (y + z) \iff x + z \succcurlyeq y + z \quad \forall x,y,z \in X$

So that shows additivity.

Now suppose monotonicity does not hold. Suppose $x \succcurlyeq y \implies p \cdot x \geq p \cdot y$

but additionally, $x < y$
$\implies p \cdot x < p \cdot y$ which is a contradiction.

Suppose non-triviality does not hold. Suppose $x \sim y \ \forall \ x, y$, where $x \neq y$, so $x$ and $y$ are unique. But we have monotonicity now.

but $x > y \iff x \succ y$
and $y > x \iff y \succ x$

For the uniqueness of $p$, building off of the outline you gave pick $x, y \in X$ where $x \sim y$ for both $p$ and $p' = (p + \epsilon, 1-p- \epsilon)$

This can only be true if $\epsilon = 0$ or if $x$ and $y$ are not unique, that is, $x_i = y_i \ \forall i$. We will rule out the trivial case where $x$ and $y$ are not unique and show $\epsilon = 0$ (and thus $p = p'$)

$$px_1 + (1-p)x_2 = py_1 + (1-p)y_2$$
and
$$(p+\epsilon)x_1 + (1-p-\epsilon)x_2 = (p+\epsilon)y_1 + (1-p-\epsilon)y_2$$
The second equation implies
$$px_1 + \epsilon x_1 + (1-p)x_2 - \epsilon x_2 = py_1 + \epsilon y_1 + (1-p)y_2 - \epsilon y_2$$

Subtract the first equation from this equation.

$$\epsilon x_1 - \epsilon x_2 = \epsilon y_1 - \epsilon y_2$$
$$\epsilon (x_1 - x_2) = \epsilon (y_1 - y_2)$$

Consider if $x_1 + \delta = y_1$ and $x_2 + \delta = y_2$ for any $\delta > 0$.

Then the differences $x_1 - x_2$ and $y_1 - y_2$ are equal, but bundle x will have higher monetary outcomes in whichever state occurs, so $x \succ y$. Contradiction.

Similarly, if $x_1 = y_1 + \delta$ and $x_2 = y_2 + \delta$, then $y \succ x$, which is again a contradiction with $x \sim y$

Thus $\epsilon = 0$.

$\square$


Is the use/consumption of natural resources considered an externality per se? On a finite planet natural resources are rival goods by definition, i.e. if one agent uses/consumes a natural resource it becomes unavailable for other agents.

Mankiw defines an externality as "the uncompensated impact of one person’s actions on the well-being of a bystander".

--
EDIT:

To illustrate my question imagine an isolated island that hosts two agents: Alice and Bob. Every year the agents are replaced with new agents Alice1 and Bob1, Alice2 and Bob2, etc. The only natural resource on the island is a tree that yields three fruits per year. The agents need two fruits as sustenance and plant the third one to grow a tree for Alice1 and Bob1 to enjoy the following year.

A third agent, Chris, visits the island and offers a massage. Alice values the massage at \$50 and Bob at \$40. The market clears at \$40.01 and Alice receives the massage. Even though the massage is a rival good, Bob can hardly argue that the massage given by Chris to Alice causes a negative externality since it does not affect him other than that he would have liked to have a massage at a lower price point.

However, during his visit Chris also needs to eat.

Case 1: Alice who is harvesting the fruits sells Chris the fruit that Bob would have eaten.
Does the sale of the second fruit by Alice to Chris cause a negative externality for Bob?

Case 2: Alice sells Chris the third fruit available that year and shares the proceeds with Bob. Consequently Alice and Bob cannot plant it and when Alice1 and Bob1 arrive at the island the following year there is no fruit tree and they perish.
Does the sale of the third fruit by Alice and Bob to Chris cause a negative externality for Alice1 and Bob1?

Use or consumption of natural resources is not in mainstream economics considered as an externality per se.

First of all the quote from Mankiw is probably from undergraduate textbook and taken out of context as it is incomplete.

For example according to Economics by Mankiw and Taylor (2014) 3rd ed the externality is defined as:

  the cost or benefit of one person's decision on the well-being of a bystander (a third party) which the decision maker does not take into account in making the decision.

Moreover, if you consider the above definition somehow 'tainted' because it is not just Mankiw but Mankiw and Taylor then consider the following quote from Mankiw (2018) Principles of Microeconomics 8th edition:

  An externality arises when a person engages in an activity
  that influences the well-being of a bystander but neither pays nor receives
  compensation for that effect. If the impact on the bystander is adverse, it is called
  a negative externality. If it is beneficial, it is called a positive externality. In the
  presence of externalities, society’s interest in a market outcome extends beyond
  the well-being of buyers and sellers who participate in the market to include the
  well-being of bystanders who are affected indirectly. Because buyers and sellers
  neglect the external effects of their actions when deciding how much to demand
  or supply, the market equilibrium is not efficient when there are externalities. That
  is, the equilibrium fails to maximize the total benefit to society as a whole.

These more complete quotes bring necessary context into the discussion. First as is clear from the both first and second quote, not any decision that has effect on third party causes externality. As both of the quotes above clearly state for the third party effect to qualify as an externality the third party's well being and cost for the third party must not be taken into an account.

However, assuming perfect market the cost that is created by the fact that if rivalrous good is consumed other person cannot enjoy it is taken into account through supply and demand interactions. Consider the following simplistic model:

We have single buyer offering some commodity, lets use an egg sandwich as example - clearly rivalrous good - also if we would replace the egg sandwich by wood or stone or iron the result would not change. Now lets assume there are two people Aria and Ceresi. Aria values sandwich at \$50 and Ceresi at \$40. Also for the sake of simplicity lets assume that the sandwitch was produced at no cost to seller (its purely simplification assumption to make the problem easier to solve) - it was just an endowment. Also I will assume for simplification total informational symmetry so we dont need to go through some game theory to solve the problem. In such situation there will be a bidding war between Aria and Ceresi, and since Ceresi values the sandwich at \$40 but Aria which values the sandwich more will bid \$40.01 and gets the sandwich. Now it is true that this can be considered as a negative effect to Ceresi as now she missed opportunity to consume sandwich that would give her utility equal to \$40 dollars, but is this an externality? No! Why? Because the fact that Ceresi is not going to enjoy the sandwich is already captured in the market price that Aria payed for the sandwich! Hence here we cannot say that the condition that the effect on the third party was not taken into account applies.

In order to create negative externality in this case, the egg sandwich would have to make Aria fart which would create additional disutility to Ceresi which was not captured in the market transaction because if Ceresi would knew that the sandwich would create fart she might be willing to bid the price more in order to avoid that disutility but this was not captured by market.

Now replace egg sandwich with a natural resource - oil - and you get the same effect. If the oil is bought just to be consumed as a part of some art installation there would be no externality, the fact that the oil is consumed and so other people cant enjoy it is already reflected in the market through supply and demand interaction. However, if the oil is burned which creates pollution which then harms people, and this harm is no longer captured by the market interactions we get the negative externality.

This is also clearly expressed by Mankiw in his principles of economics where he says:

  In the
  presence of externalities, society’s interest in a market outcome extends beyond
  the well-being of buyers and sellers who participate in the market

However, the condition for an externality is even stricter because to truly satisfy the condition that the well-being of the bystander is not taken into account there cannot be any other market effect that would result in internalizing the effect on a bystander.

For example, consider a factory that processes oil and during the production process spills some oil waste on a nearby ground where some rancher herds his cattle. If the rancher has no property rights over the land this would create externality as the well being of the rancher would not be taken into an account. However, if the rancher owns the land and the oil refinery creates a damage to it through the oil waste he can sue for the damages which forces the factory to internalize the externality and making it disappear.

Consequently, the rivalrous property does not cause in itself externality. In fact most often the externalities have nothing to do with whether the good is rivalrous or non-rivalrous but with whether the good is excludable or non-excludable. Most often externalities arise due to the fact that some good is non-excludable.

Furthermore, Mankiw is an excellent economist but he writes textbooks for undergraduates. Any undergraduate text will have to sacrifice some precision in order to make the text more accessible. According to the more advance texts, like for example MWG - the bible of microeconomics, the externality is defined as a situation where as a result of makret failure the joint surplus of actors is not maximized. For example in our Aria - Ceresi example I gave above the joint surplus is maximized even though Ceresi did not received anything as Ceresi's surplus was zero while Arias's surplus was \$9.99, the 'producer surplus is \$40,01 and hence total surplus is \$50. Moreover, it is easy to see that given that no other allocation of sandwich would increase the total surplus, if the sandwich is not sold everyone gets zero, if Ceresi gets sandwich maximum total surplus would be \$40 in this situation.

Hence even though I personally consider Mankiw's textbook superb and I use them when I teach microeconomics to undergraduates as a TA, you have to keep in mind that undergraduate books always have to sacrifice some accuracy for the sake of accessibility. Even I had to do that here, the full formal mathematical description of externality in MWG is more nuanced still but I hope that all of the above already provided enough clarity that I don't need to present it here.

In response to @KennyLJ,  it is true that in the past the definition of externality was quite vague. Moreover, it is also true that there might not be consensus on what externality is between different schools of economic though. However, I dont know of any textbook or mainstream paper that works on externalities that would define externality in a broad term as any rivalous good as @KennyLJ using the definition:

"A decision's effects are called external if they fall on someone other than the decision-maker(s). A positive (negative) external effect is called an external benefit (cost)."

Here is the list of different definitions given in different widely used textbooks:

Mankiw and Taylor (2014) Economics 3rd ed:

the cost or benefit of one person's decision on the well-being of a bystander (a third party) which the decision maker does not take into account in making the decision.

concept more narrow then what @KennyLJ claims

Mankiw (2018) Principles of economics. 8ed.

  An externality arises when a person engages in an activity that influences the well-being of a bystander but neither pays nor receives compensation for that effect. If the impact on the bystander is adverse, it is called a negative externality. If it is beneficial, it is called a positive externality. In the presence of externalities, society’s interest in a market outcome extends beyond the well-being of buyers and sellers who participate in the market to include the well-being of bystanders who are affected indirectly.

which is again much more narrow than what KennyJL claims and also it disproves the claim of KennyJL that "My guess is that Mankiw would agree that his quoted definition is the same as the above." - Clearly Mankiw does not agree with KennyJL definition - to the extend that his own textbook shows.

Mas-Colell Whinston Green (1995) Microeconomic theory states:

  "Definition "11.B.1 An externality is present whenever the well-being of a consumer or the production possibilities of a firm are directly affected by the actions of another agent in the economy." .... "When we say 'directly,' we mean to exclude any effects that are mediated by prices.

Again inconsistent with what KennyJL claims to be the "standard" definition.

Varian Microeconomic Analysis 3rd edition:

  When the actions of one agent directly affect the enviroment of another agent, we will sa that there is an externality.  ... the first theorem of welfare economics does not hold in the presence of externalities. The reason is that there are things that people care about that are not priced.

Hence again even Varain's definition which is arguably less precise is clarified by Varian's statement that the reason why externalities exist is that "The reason is that there are things that peoole care about that are not priced."

Moreover, all examples given in Varian on chapter on externalities indicate that his definition is basically consistent with previous sources.

Varian distinguishes between consumption externalities and production externalities and gives examples such as smoking tobacco or having loud music or smoke affecting a production of clean laundry. None of the examples he gives an no fair reading of the chapter suggest he means that any external effect qualifies.

Cowen \& Tabarok Modern Principles of Economics 3rd ed:

  Externalities: external costs or external benefits. External cost: a cost borne by people other than the consumers or the producers trading in the market. External benefit: a benefit recieved by the people other than the consumers or producer trading in the market.

Hence yet again this definition is more narrow as it specifically mentions it has to occur outside the market.

Hence, I cant understand how @KennyJL can claim his interpretation is standard. Of course nobody can prove negative, but all this points to the fact that such interpretation is not standard.

Moreover, I think that @KennyJL grossly misrepresented his quotes that I would like to point out:

  Scitovsky (1954):

The concept of external economies is one of the most elusive in economic literature. … full clarity has never been achieved. Definitions of external economies are few and unsatisfactory.

yes but the same source also says this:

  It is
  agreed that they mean services (and disservices) rendered free (without compensation) by one producer to another;
  but there is no agreement on the nature
  and form of these services or on the
  reasons for their being free. It is also
  agreed that external economies are a
  cause for divergence between private
  profit and social benefit and thus for the
  failure of perfect competition to lead to
  an optimum situation

It is true that Buchanan and Stubblebine (1962) say:

  Externality has been, and is, central to the neo-classical critique of market organisation. … Despite this importance and emphasis, rigorous definitions of the concept itself are not readily available in the literature.

but the same paper also says:

  "Pigovian discussion concerning the divergence between marginal social cost (product) and marginal private cost (product). By saying that such a divergence exists, we are, in the terms of this paper, saying that a marginal externality exists

Hence again the authors here do not even claim that anything goes or that the broad definition of KennyJL would be valid. In fact the paper itself suggests that externality is something that happens outside price system.

I did not double checked books as due to current coronavirus with my university proxy I can only check papers and not books but the two above sources are clearly misrepresented.


Prove that the profits of the firm weakly decreases with input prices Prove that the profits of the firm weakly decreases with input prices. More formally, suppose that
the firm has a production function f, so that its profit function is
π(p, w) = max(x≥0) $pf(x) − w · x$,
where p denotes the output price and w denotes the input price vector. Then show that if $w$ and $w'$ are two input price vectors such that $w'_j$ = $w_j$ for all $j \neq i$ and $w'_i$ > $w_i$
, then $π(p, w') ≤ π(p, w)$
I know that as input prices decrease, the toal costs for the firm decrease as well. Due to the decrease in TC, the firm then produces more output at the same cost. However, due to the increase in supply, the price of the output falls to a new equilibrium, causing profits to fall as well unless the increase in q is proportionate to the decrease in price that would prevent profits from dropping.
However, I am unsure on how to start the proof using $\pi (p, w)$. Since it is $w$ that is changing, would I hold price of output fixed at $p$?
Then I would assume that $x'$ is profit maximizing at:
$$pf(x) − w'· x ≤ pf(x') − w'· x'$$
and $x$ is profit maximizing at:
$$pf(x) − w · x \geq pf(x') − w· x'$$
Then I would multiply the second equation by -1, getting
$$-pf(x) + w · x \leq -pf(x') + w· x'$$
I would then add that to the first equation getting:
$$ (− w'· x) + (w \cdot x) ≤ (− w'· x') + (w \cdot x')$$
which simplifies to:
$$ (w - w') (x - x') \leq 0 $$
Since all components of $w'− w$ are 0 except the ith
$$ (w_i - w_i') (x_i - x_i') \leq 0 $$
We are left with:
$$(x_i - x_i') \leq 0 $$
$$ x_i \leq x_i' $$
Leaving us with the fact that factor input demands at $x' \geq x$ therefore we assume that the demand for output is greater, causing prices to fall.
However, I have no idea how to prove that $π(p, w') ≤ π(p, w)$ if $w'_j$ = $w_j$ for all $j \neq i$ and $w'_i$ > $w_i$.
I understand that the idea is based on the fact that $w'_j$ = $w_j$ and $w'_i$ > $w_i$, $w' > w $, that means that the $w' \cdot x$ in the profit function is greater than $w \cdot x$. Since the cost is greater in $\pi (p, w')$, that means that $π(p, w') ≤ π(p, w)$. However, I am confused as to how I can approach this proposition using the given profit function.

From FOC, we know that:
\begin{align}
\nabla_x\pi(\mathbf{x},\mathbf{w})=p\nabla f(\mathbf{x})-\mathbf{w}=\mathbf{0} \tag{1}
\end{align}
This will be true at equilibrium, i.e. for any given $\mathbf{w}$, the input vector $\mathbf{x}$ will adjust so that the above holds.
Now consider $d\pi(\mathbf{x},\mathbf{w})/d w_i$ (and using $(1)$):
\begin{align}
\frac{d\pi(\mathbf{x},\mathbf{w})}{d w_i} &=\nabla_x\pi\cdot\nabla_{w_i} \mathbf{x} \, + \nabla_w\pi\cdot\nabla_{w_i} \mathbf{w} \\
&=0 +\nabla_w\pi\cdot\nabla_{w_i} \mathbf{w} \tag{*}\\
&=\nabla_w(pf(\mathbf{x})-\mathbf{w}\cdot \mathbf{x)} \cdot \nabla_{w_i} \mathbf{w} \\
&= \Big(p\nabla_wf(\mathbf{x})-\nabla_w(\mathbf{w}\cdot \mathbf{x)}\Big)\cdot \nabla_{w_i} \mathbf{w} \\
&= \Big(p \frac{\partial\mathbf{x}}{\partial\mathbf{w}}\nabla f(\mathbf{x})-\frac{\partial\mathbf{x}}{\partial\mathbf{w}}\mathbf{w} - \mathbf{x}\Big)\cdot \nabla_{w_i} \mathbf{w}\\
&= \mathbf{J}(p\nabla f(\mathbf{x})-\mathbf{w})\cdot \nabla_{w_i} \mathbf{w}  -\mathbf{x} \cdot \nabla_{w_i} \mathbf{w} \\
&= \mathbf{J} \nabla_x\pi(\mathbf{x},\mathbf{w})\cdot \nabla_{w_i} \mathbf{w}-\mathbf{x} \cdot \nabla_{w_i} \mathbf{w} \tag{**}\\
&= -\mathbf{x} \cdot \nabla_{w_i} \mathbf{w} \\
&= -x_i
\end{align}
where, in steps $(*), (**)$, FOC is used and $\mathbf{J}$ is the Jacobian matrix.
Since, $x_i \geq0$, we have:
$$\frac{d\pi(\mathbf{x},\mathbf{w})}{d w_i} \leq0$$


Currency Devaluation and the causes of the Tequila Crisis I was reading about some of the famous crisis that happened in the past and i came across "the tequila crisis" in mexico during 1994-96.

As a background, The Tequila crisis (also known as the Mexican Peso Crisis or December mistake crisis) was a currency crisis sparked by the Mexican government's sudden devaluation of the peso against the U.S. dollar in December 1994, which became one of the first international financial crises ignited by "capital flight", as investors pulled out of Mexico.

The extended issuance of Tesbonos, a mexican bond also contributed to the crisis

What are the mechanisms for a currency devaluation in a case like this?

The Mexican government has a complicated history of currency intervention, which can be read about in a detailed timeline here.

However, in 1994 the devaluation was caused by the end of government intervention. Up until that date the Mexican government had a set range of USD values that the peso could float within, so a sort of flexible peg to the USD. In December of 1994 the government decided to allow the peso to float freely and the peso was devalued naturally through market forces.