Anything written on the process behind "multiplicative" production function? Intuitively, one might make a naive first guess that the production function of the economy, or of a firm, should be a "leontief" production function: "for example, you need both a factory and a worker to produce cars. A worker by himself, without the help of furnaces, and so forth, cannot construct a car, and the furnace by itself cannot do so either"

Obviously, this argument does not mean that the production function has to be leontief, but intuitively this might be what one expects.

I am looking for something written, that goes into great detail, on what the processes are behind the form of the production function (both firm-level and aggregate). Why would we expect a certain form of production function and not another? E.g. why would we expect a CES production function? why would the elasticity parameter be close to negative infinity, or to 0, or to 1? I hope that someone has written something that answers these questions on the basis of a micro level account (whether mathematical, or narrative).

As I understood from my lectures, a multiplicative function means that the marginal product of one factor increases when another factor increases, and decreases when another factor decreases. The extreme cases (leontieff or additive) don't have this property.

At the moment the teacher explained this, it made sense to me. If one factor increases, it expands the capacity of the other to produce more. I think it makes sense.


Benefits of a cartel among firms Suppose I have $n>2$ firms selling differentiated products. These firms form a cartel for the price. The cartel has size $n_c$. Let $\pi_{i,m}$ be the payoff of a firm $i$ outside the cartel and $\pi_{j,c}$ be the payoff of a firm $j$ inside the cartel.

I would like to know whether there exists a set of assumptions (a reference to a paper in the literature describing that set of assumptions and relative proofs is sufficient) under which

For any firm $j$ outside the cartel:

(i) entering the cartel is weakly convenient in terms of        profits for any $n_c$, i.e. $\pi_{j,m}(n_c-1)\leq \pi_{j,c}(n_c)$ $\forall n_c$

(ii) the higher is $n_c$ the higher is the profit increase from entering the cartel for any $n_c$, i.e. $\pi_{j,c}(n_c)-\pi_{j,m}(n_c-1)\leq \pi_{j,c}(n_c+1)-\pi_{j,m}(n_c)$ $\forall n_c$

For any firm $i$ inside the cartel:

(i) the profit is increasing in $n_c$, i.e. $\pi_{i,c}(n_c-1)\leq \pi_{i,c}(n_c)$ $\forall n_c$

(ii) the higher is $n_c$ the higher is the profit increase from letting someone else entering the cartel, i.e. $\pi_{i,c}(n_c)-\pi_{i,c}(n_c-1)\leq \pi_{i,c}(n_c+1)-\pi_{i,c}(n_c)$ $\forall n_c$

All inequalities could hold also strictly.

Cartel size and collusive stability with non-capitalistic players lists the reasons why it's highly unlikely that your question finds an answer for profit-seeking firms (see Friedman, 1971 for a threshold on cartel stability)

  It is widely accepted from both the theoretical IO literature (e.g., Tirole, 1988) and policy reports (e.g., Ivaldi et al., 2003) that high market concentration is a facilitating factor for (tacit as well as explicit) collusion. In addition to coordination being likely more difficult in larger groups, the intuition that the incentive to collusion shrinks with too many competitors is fairly simple: as the number of firms grows larger, the individual share of cartel profits shrinks monotonically and therefore implicit collusion becomes harder to sustain (cf. Tirole, 1988, ch. 6).

So you may find "toy" answers for $n=4$ or the like but probably not for reasonably big $n$.

However, the same paper also proves that

  An increase in cartel size makes implicit collusion among labour-managed firms easier to sustain.

which is exactly what you're stating in your question.

As the authors sum up,

  In words, the critical threshold for $LM$ firms is decreasing and convex in n and tends to zero as n becomes arbitrarily large. On the other hand, the critical threshold for profit-seeking firms is increasing and concave in n and tends to one as n becomes arbitrarily large. To complete the description of the critical thresholds w.r.t. n, we may also observe that

So according to this reference, an answer to the question is yes, on the condition that the firms studied are not profit-seeking but $LM$-firms.

Note: A $LM$-firms is an enterprise that operates under the ultimate control
of those who work in it, which as for consequences, among others, that the firm aims at maximising profit per worker rather than profit.


Many or few variables when testing for Granger causality? I am reading Levendis "Time Series Econometrics: Learning Through Replication" (2018) and there are two statements about Granger causality that kinda confuses me. The statements themselves are not confusing, but the implications.

"Granger causality is much harder to establish with more than 2 variables". So I guess few variables are better, and using just two variables are even more better.
"Tests of Granger causality are sensitive to omitted variables. Researchers should include all relevant variables in their analysis". So here, more relevant variables are better, I guess.

Can we add more relevant variables without jeopardizing Granger causality?

The implication is, the model should be adequately specified, without omitting relevant variables. Once the model is adequately specified, Granger causality will be easier to establish if the model has fewer variables than if it has more. (I am not taking a stance regarding how reasonable the quoted statements are but rather just rephrasing/interpreting them.)
This characterizes the systems you may be modelling (few or many variables) and the modelling choices (avoid omitting variables). In applications of time series econometrics (e.g. in macroeconomics or finance), usually you cannot change the underlying system (make it contain fewer variables). Then you do not have much choice over the number of variables in your model -- unless you are willing to violate the suggestion to avoid omitting relevant ones and risk working with an inadequate model and consequently obtaining invalid results.


What would happen to the economy if the Fed's discount window completely stopped? I'm curious what would happen the the US economy (and perhaps others) if the overnight lending capability of the Fed ceased operation for some reason (perhaps a cyber attack) for a non-trivial period of time (a week or more).  What are the possible implications of that?  Would there be panic, massive loan defaults, lack of operating capital or other nasty things?  Also, for the sake of argument, that we didn't know how long the overnight lending capability of the Fed would be down and only speculated at the reason.  Would banks just weather the storm for a week or so, or would thing get ugly?

First, one note on the premise. The Fed basically operates a giant ledger for financial institutions, each of which has a certain balance in its "master account". Over $3 trillion is moved between accounts each day via Fedwire, and these accounts are also used for settling most traditional checks and ACH transactions, which include many of the everyday transactions in the economy. Even alternative payment networks not provided by the Fed, like CHIPS, ultimately use the Fed's ledger to clear net payments.

When the Fed loans money to banks via the discount window, it simply adds to their account balance on this ledger; many "cyberattacks" that disabled this capability would probably also disable the ledger itself. This would certainly mean chaos, but the missing discount window wouldn't be the most important aspect of this chaos - the real problem would be the breakdown of the economy's payment system.

That said, now suppose that somehow the discount window vanished but the Fed's other services continued. There wouldn't necessarily be any immediate consequences: as of the end of 2014, the Fed was lending very little via its discount window. The H.4.1 "factors affecting reserve balances" release shows that the total of "primary", "secondary", and "seasonal" credit provided to banks was virtually zero relative to the size of the banking system as a whole, at $112 million. This is because the discount rate, currently at 0.75%, is well above other short-term interest rates and has additional strings attached; it only makes sense for banks to borrow from it if they don't have good other options.

The real purpose of the discount window, of course, is to serve as the lender of last resort. And it has been used substantially in that capacity during times of crisis: for instance, in October 2008 there was $100 billion in discount window lending, 1000 times the current level. (Other, newer forms of Fed assistance to the non-bank financial system made the total level of Fed intervention much higher still.) In fact, the acute phase of the 2008 financial crisis for Goldman Sachs and Morgan Stanley, two large investment banks, ended when they became bank holding companies with full access to the Fed's discount window.

In general, if a crisis was already underway, I'm sure that a missing discount window could lead to panic. But without an ongoing crisis, I doubt the ramifications of a temporary discount window shutdown would be too severe: the promise of a restored discount window in a week or two would be enough to stem any speculative run, and banks have many options to deal with short-term funding needs in the interim. They are required, after all, to hold certain levels of liquidity, meaning a combination of reserves and securities that can quickly be sold or lent out for reserves.

By the way, if not only the discount window but also all other interventions into overnight money markets stopped, then in normal times there would also be chaos. Banks' demand for reserves is inelastic in the short-run and subject to shocks; and if the New York Fed was not elastically supplying reserves to keep the federal funds rate at the target, there would be massive volatility in short-term interest rates. (Volatility in the early 80s, when the Fed partly targeted monetary aggregates rather than interest rates - but still engaged in plenty of discretionary interest rate smoothing - gives a small taste of what this volatility would look like. Or we can look at how irregular rates were before the establishment of the Fed.) This would not be true today, however, because the banking system is awash in excess reserves.


Has anyone studied how people's indifference curves can change? I'm wondering if anyone has looked at how people's indifference curves can change, whether systematically due to experimental manipulations, or if they just vary due to noise.

I thought about this because of a study I did in which I got violations of transitivity when we generate two options from one indifference curve. For example, let's assume we have these three choices

A[25,50]
B[50,25]
C[45,30]

and a participant is indifferent to the choice sets {A,B} and {B,C}. However, when we present the choices {A,C}, they end up preferring A over C. By indifference curves we mean the line in a 2-dimensional attribute space where any two options are equally preferable. Possibly any study that has looked at violations of transitivity from choices generated from a single indifference curve can address this, but I haven't found anything like that yet.

I think maybe the reason I haven't found anything is that I'm mostly only familiar with the literature in psychology, whereas this seems like an issue what would have been investigated in economics. That is why I am asking about it here.

One important thing to remember is that people don't necessarily "have indifference curves". More correctly, indifference curves are a tool used in economic literature to model human rationale and decision making.

Transitivity is one very common assumption regarding utility functions, and it lays on a  fairly reasonable explanation, which basically assumes people are "smart enough to do the math" and figure out that if they prefer A to B and B to C, then they should also prefer A to C.

So really what you're saying is that in your experiment, you found evidence that this doesn't model human behavior all that well. It's a perfectly reasonable claim, and if you think of it, such things make sense - since economic models are, almost by definition, a huge simplification of reality. Trying to adjust the models to better fit observed human behavior  is one of the things that drives the field forward.

It turns out that the issue you brought up - whether people actually display this "transitivity" quality -  is a pretty fundamental issue and has been studied quite intensively do date, in different scenarios.

To read more about it  and get to know the work of people who previously challenged this assumption, try to look up "Transitivity of Preferences". This is one example of such paper which should get you into the subject:

  Any claim of empirical violations
  of transitivity by individual decision makers requires evidence beyond a reasonable doubt. We discuss
  why unambiguous evidence is currently lacking and how to clarify the issue

Good Luck!


Expected value of order statistics for uniform distribution I have $X$ ~ $U(0,1)$ interval.
Let n=2, i.e. $X_1 < X_2$
I have to calculate the expected value of ${X_2}^{m/(1-m)}$.
Where, $0≤m≤1$
I want to confirm if I have calculated it correctly?
$$\int_0^1 2x^{2m/(1-m)} \,dx = \frac{2(1-m)}{(1+m)}$$
Is the calculation correct?
Thanks!

I guess $m < 1$. Otherwise $x^{1/(m-1)} \to \infty$ as $x \to 0$.
There's a possibility that I made a mistake, so let me know if you spot one.
Let's first compute the cumulative distribution function of $X_2$:
$$
F_{X_2}(a) = \Pr(X_2 \le a) = \Pr(X_1 \le a \text{ and } X_2 \le a) = \Pr(X_1 \le a)\Pr(X_2 \le a) = a^2.
$$
This assumes that the two uniformly random variables are independent.
Then the density is given by:
$$
f_{X_2}(a) = \frac{\partial F_{X_2}(a)}{\partial a} = 2 a.
$$
The expected value of $X_2^{\frac{m}{1-m}}$ is then:
$$
\int_0^1 a^{\frac{m}{1-m}} f_{X_2}(a) da = \int_0^1 a^{\frac{m}{1-m}} 2 a\, da,\\
=\int_0^1 2 a^{\left(\frac{m}{1-m} + 1\right)} da = \int_0^1 2 a^{\frac{1}{1-m}} da = 2 \frac{1-m}{2-m}
$$


Consequences of hyperbolic discounting In reading the Wikipedia article about hyperbolic discounting, I read that it says that hyperbolic discounting created strange consequences:

  But note, the time inconsistency of this behavior has some quite perverse consequences.

Is it just that people make choices that their future selves would not make? The same article further says this:

  Individuals using hyperbolic discounting reveal a strong tendency to make choices that are inconsistent over time – they make choices today that their future self would prefer not to have made, despite using the same reasoning.

What are the consequences of hyperbolic discounting (HD)? (Although they seem to match some observed behavior, does HD produce predictions that are undesirable?)

Also, beside time inconsistency, what are the consequences of hyperbolic discounting, if any?

(Also, any references to good material are always welcome.)

As often with models embodying some form of "irrationality" (whatever that means), HD does a great job at matching a whole lot of behaviors, but leaves room for rather annoying Dutch Book situations (also know as "money pump" situations). These suggest that HD might generate some inaccurate predictions, and induce undesirable behaviors when included in models.

Here is an example. Suppose today is $t=0$ and I owe you a dollar one periods from now at $t=1$. I offer you the following sequence of deals:

In $t=0$, I offer to pay you some fee $f_0$ in $t=2$ in order to postpone my payment from $t=1$ to $t=2$.
In $t=1$, I give you the possibility to pay me some fee $f_1$ in $t=2$ in order to get the dollar back in period $t=1$ instead of $t=2$ (assuming you accepted the deal in $t=0$).

Case 1 : you have a classical exponential discount factor $\frac{1}{(1+\delta)^t}$.

Period $t=0$ : what is the minimal additional $f_0^*$ I can offer to pay in $t=2$ for you to let me postpone my payment to $t=2$?

$$ \begin{align} f_0^* & = (1+\delta)^2 \left[ \frac{1}{(1+\delta)} - \frac{1}{(1+\delta)^2} \right] \\
                       & = \delta \end{align} $$

Period $t=1$ : what is the maximal additional $f_1^*$ I can ask you to pay me in $t=2$ in order for you to get your one dollar in $t=1$ instead of $t=2$ ?

$$ \begin{align} f_1^* & = (1+\delta)  \left[ 1 - \frac{1}{(1+\delta)} \right] \\
                       & = \delta \end{align} $$

So summing up the two deals : in period $t=0$ I offer to pay you $\delta$ more in $t=2$ to postpone the payment, but then in $t=1$ you promise to pay me $\delta$ more in $t=2$ to get the money earlier. Overall the deals cancel out, I still give you the dollar in $t=1$ and no one owes the other anything in $t=2$.

Case 2 : you have HD with discount factor $\frac{1}{(1+\delta t)}$.

Period $t=0$ :

$$ \begin{align} f_0^*(HD) & = (1+ 2\delta) \left[ \frac{1}{(1+\delta)} - \frac{1}{(1+2\delta)} \right] \\
                       & = \frac{\delta}{1+\delta} \end{align} $$

Period $t=1$ :

$$ \begin{align} f_1^*(HD) & = (1+\delta)  \left[ 1 - \frac{1}{(1+\delta)} \right] \\
                       & = \delta \end{align} $$

Summing up the two deals, I still give you the dollar in $t=1$, but now you owe me an additional $\left[\delta - \frac{\delta}{1+\delta}\right]$ in $t=2$ which is strictly larger than zero for $\delta > 0$. Thus in a sense, I made money out of "nothing" (or some would say I made money out of your time-inconsistent preferences).

Whether this is bothersome for the HD model depends on whether you believe that these kinds of money pumps are likely or unlikely to occur.

==================

In the comments, the OP also asks whether HD would have any influence on risk behavior. I do not think it would. HD denotes a specific way to discount utility but does not impose restrictions on the form of the instantaneous utility function $u(\cdot)$ which determines risk aversion in uncertain environments.


Articles about the economics of non-compete contracts Today I read in a non-scientific article that Amazon requires some physical workers to sign non-compete agreements. I used to think that the idea behind allowing non-compete clauses in contracts is to protect a companies' intellectual property. The article mentions that non-competes may also serve to protect a company's investment in case it pays for the employee's education or training. Neither of these seems to fit this case.

What scientific articles (in fields of mathematical economics, such as Industrial Organization) describe models where allowing for non-compete clauses improves the situation of both the employer and the employee?

Ghosh and Shankar (2017) "Optimal Enforcement of Noncompete Covenants", Economic Inquiry

  Noncompete covenants or covenant not to compete (CNC) are clauses in employment contracts in which the employee agrees not to gain employment with a competitor firm. In this article, we study the efficiency aspects of such contracts by incorporating the effect of labor mobility restrictions on knowledge transfer across firms, investment decisions by firms, and investment by workers. Following research that shows state‐wise variations in the degree of CNC enforcement, we allow the strength of CNC enforcement to vary as a matter of regulatory policy and derive the optimal strength of enforcement. We also look at how regulations around CNCs should be optimally designed when employers can use collusive agreements, such as “no poaching” agreements, as an alternative to noncompete clauses. Given recent allegations of employer collusion among large Silicon Valley firms, we argue for a cautious approach in designing policies on CNC enforcement.

Garmaise (2011) "Ties that Truly Bind: Noncompetition Agreements, Executive Compensation, and Firm Investment", Journal of Law, Economics, & Organization

  We study the effects of non-competition agreements by analyzing time-series and cross-sectional
  variation in the enforceability of these contracts across U.S. states. We find that tougher noncompetition
  enforcement promotes executive stability. Increased enforceability also results in reduced
  executive compensation and shifts its form towards greater use of salary. We further show
  that stricter enforcement reduces research and development spending and capital expenditures per
  employee. These results are consistent with a model in which enforceable non-competition contracts
  encourage firms to invest in their managers’ human capital. On the other hand, our findings
  suggest that these contracts also discourage managers from investing in their own human capital
  and that this second effect is empirically dominant.

Two other recent empirical papers may also be of interest:

Jeffers (2018) "The Impact of Restricting Labor Mobility on Corporate Investment and Entrepreneurship"
Starr (2018) "Consider This: Training, Wages, and the Enforceability of Covenants Not to Compete"


Price of Anarchy when the cost is to society and not to the selfish agents Let's say there is some scarce resource and several agents compete to access this resource. Each agent is able to convert the resources into products that are beneficial to society, but each agent has a different efficiency with which it does so. Therefore, society would like to see the most efficient agent get the resource. However, the agent that pays more gets the resource.

Is it possible to model this scenario in a Price of Anarchy calculation? What would the model look like?

In the introductory examples of Price of Anarchy, I've come across Braess's Paradox and Pigou's example, but these are situations where the cost is incurred by the selfish agents themselves. In my example given above, the cost is incurred by society. That's why I'm not sure how to go about it.

If there is a free market for the product the agent who gets the resource becomes a monopolist. "Produce more efficiently"  is taken to mean "produce every quantity of output for lower cost". That is its usual meaning in economics. Thus if someone different from the most efficient producer by any means gets hold of the resource the best thing that someone could do for himself, is to sell this resource to the most efficient producer, who is going to make more profit than the initial owner could and hence is able to make the initial owner an offer he cannot reject. Hence in the end the product gets produced by the most efficient technology available and the prices for the product are the same in both worlds. The consumers are exactly as well off. There is only a shift of profits between the entrepreneurs.

If the resource is auctioned off to the highest bidder, the most efficient producer will win the auction, as he can outbid all others, because he is going to make the largest profits among all.


Is the value of a product measured in money a reliable measure of the economic value of this product? This could rather be a philosophical question but would be curious to know the economist's POV and how these two (value of the product, total economic value of the product) correlate.

No, the economic value and monetary value (price) are different concepts in economics.
Value of a good to an individual is usually defined as the utility derived from that good. Unlike prices, it is not necessarily same across individuals or even for the same individual with varying quantity of consumption. In fact, an important assumption on which many of the results of economics depend is that the value of good to an individual decreases with abundance.
The difference of utility derived and price paid is termed as consumer surplus. It is considered a measure of welfare because it measures the net gain from consuming that good.
On how the price amd value correlate: well price is just an outcome of the market forces. Valuation of the good by different economic agents in this market is the primary force here so naturally there is some correlation. However, some markets are controlled by the state (also an economic agent in such markets) to ensure such that it's price is actually much lower than it's value. For example, water, oxygen.
So value in terms of price is the outcome of many, many market forces. How you value it is one them.


What would happen if layoffs were made illegal? I was trying to explain to my friend why I don't think raising the minimum wage will benefit workers. He said "what if we just made layoffs illegal through legislation?". Is this even possible? If so, what would be the economic impact? Thanks.

We can infer from what happens in countries where layoffs are difficult, e.g. France. There employees are (or at least were) harrassed to quit instead.

There's a practice in France called being sent to the closet — "le placard."
It's when your employer makes your work life so miserable that you are forced to quit. [...]
Being sent to the closet is a pretty awful practice, but it's something that a number of French employers resort to because it's so hard to fire people legally there.
Many workers in France have contracts called CDIs — contrat à durée indéterminée — or contracts of indeterminate length. Once you have one, you can lose your job only in very limited circumstances.

I think there is/was a similar practice in Japan with the so-called "boredom room" instituted for a similar reason.
As for broader economic effects, the IMF generally has working papers favoring labor market flexibility (which among other things entail easy layoffs) because it seems to lower overall unemployment, e.g.

The aim of this paper is to analyze the relationship between labor market flexibility and
unemployment outcomes. Using a panel of 97 countries from 1985 to 2008, the results
of the paper suggest that improvements in labor market flexibility have a statistically and
significant negative impact on unemployment outcomes (over unemployment, youth
unemployment and long-term unemployment). Among the different labor market flexibility
indicators analyzed, hiring and firing regulations and hiring costs are found to have the
strongest effect.


Demand function of a family Different family members have different utility functions, but
All family members consume the same bundle.

For example, consider a family $F$ that has to select a bundle of  funiture ($x$) and electronic equipment ($y$). Each member $i\in F$ has a different utility function $u_i(x,y)$. The family has a budget $I$. How can the demand of the family be calculated?

I thought of several options:

Calculate an aggregate utility function, e.g:

$$ u_F(x,y) = \min_{i\in F} u_i(x,y) $$

Then, calculate the demand in the usual way: select a bundle $(x_F,y_F)$ that maximizes the aggregate utility $u_F$ in the budget-set.

A problem with this method is that it requires to normalize the members' utility functions to the same scale.

Calculate the optimal bundle of each family member separately: each member selects a bundle $(x_i,y_i)$ that maximizes his utility function $u_i$ given the family's income $I$. Then, calculate the family bundle as an average of the members' bundles:

$$(x_F,y_F) = \frac{1}{|F|}\sum_{i\in F} (x_i,y_i)$$
If the budget-set is convex, then this bundle is also in the budget set.

Divide the family income $I$ among the family members, such that each member $i\in F$ receives an income $I/|F|$. Then, let each member select a bundle $(x_i',y_i')$ that maximizes his utility function $u_i$ in given his fraction of the income. Then, calculate the family bundle as a sum of the members' bundles:

$$(x_F,y_F) = \sum_{i\in F} (x_i',y_i')$$

Each definition probably has different implications on results such as competitive equilibrium, welfare theorem, etc.

What is a good reference on this problem?

I think any (and none) of your answers is correct. The market demand simply depends on how the family makes its purchasing decisions.

For example, suppose the matriarch $i$ decides on every purchase of the family and acts selfishly. Then obviously the utility function of the family is simply $u_i$.

Compare this with the case where the utility functions are cardinally comparable and the household is utilitarian. In this case, the family utility function is the sum of all utility functions.

More generally speaking, if purchase decisions are made via some game, then you have to solve the game first in order to obtain the demand functions. But whether a utility representation exists for the family utility and what it would look like crucially depends on the game structure.

One special case which has been discussed in the literature is the case where the household income is somehow distributed among family members and each family member spends separately. There then exists a class of utility functions for which the family expenditure will be independent of the distribution of income among the family members. For details, see https://en.wikipedia.org/wiki/Gorman_polar_form


Can there exist something that subsidises that is not a subsidy Is the set of subsidies exactly the same as the set of things that subsidise?

Put another way: can there exist something that subsidises that is not a subsidy?

Or are there two definitions of a subsidy: the narrow economic definition, and a wider definition that includes (for example) everything that has the effect of a subsidy.

My answer relies on two quotes. The first one:

  A rose by any other name would smell as sweet

And the second one is from the definition of State Aid by the European Union's competition authority:

  State aid is defined as an advantage in any form whatsoever conferred on a selective basis to undertakings by national public authorities.

There is a difference between illegal state aid and subsidies, but the difference is in the "selective basis". Aid in any form that confers an advantage is aid.


Is there a way to eliminate shilling, spiting, and overbidding in second price auctions? In a 2nd price option, if all the player choice their bids independently, the optimal strategy is to bid their valuation. However, in some situations, their decisions can effect each other.

For example, an over bidder could announce that they will bid \$1000000 for a painting worth \$1000. This would cause all the bidders to not bid (since now there is no point), and the over bidder pays $0 since there were no other bids.

A solution to the over bidder is a spiter, who predicts the bid of and underbids the highest bidder by 1 cent, forcing them to pay their bid. However, the spiter presents a new problem. If the players know their is a spiter, they will bid like they would in a first price auction, since they know they will end up paying whatever they bid. Even worse is a shill, someone who colludes with auctioneer to underbid the highest bidder by a cent. If they accidentally win (if they overestimated the highest bid), the auctioneer can secretly refund the purchase. If they succeed, however, they can share the extra revenue with the auctioneer, meaning that they have an incentive to succeed.

My question is, are there any modifications you can make to the auction to solve this? Of course, you could just say "no over bidders, spiters, or shills allowed", but I would prefer a mathematical solution.

Overbidding

The second price auction has an equilibrium in which player 1 bids a very large amount and all other players bid zero. None of the losing bidders have a profitable deviation because they would have to pay more than their value to win. People usually ignore this equilibrium because not bidding is weakly dominated. But we should acknowledge that it is indeed an equilibrium because it is relevant for some practical applications. A big challenge, for example, in spectrum auctions is convincing new entrants to show up to bid when everyone expects the big incumbents will win all of the licenses.

One way to eliminate this equilibrium is to make it strictly dominant for players to submit a bid. This can be done, for example, by modifying the auction in the following way:

  1) run a second price auction as normal.

  2) with probability $1-\epsilon$, determine the allocation and payments as usual. With probability $\epsilon$, ignore the bid of the highest bidder and give the item to the second highest bidder (who pays the third highest bid).

Even very small $\epsilon$ will suffice to make is strictly dominant for everyone to bid. Thus, the efficiency loss from this scheme can be kept relatively small.


If the Engel Curve of a Cobb-Douglas utility function is positive and linear, than does that mean it is neither a necessity nor a luxury good? Since the concavity of the Engel Curve determines whether it is a necessity or luxury (i.e. how fast quantity demand changes in relation to changes in income), and since the second derivative of a Cobb-Douglas Engel Curve is 0, does that mean it is neither category?

Edit:  In simple terms, if an Engel Curve is a straight positively-sloped line, it is obviously a normal good.  But if the curve is represented by a function like so:

$I = 10 * P_x * x.$

Then the curve is ambiguously sloped.  If the price of $x$ ($P_x$) happens to be greater than 1/10 then the good is a luxury, and vice versa for a good with $P_x < 1/10$.  But if it's ambiguous like this, then the second derivative (which indicates concavity and therefore what direction the curve is increasing/decreasing in) then is it impossible to tell?

For reference, this Engel Curve was derived from the Cobb-Douglas utility function:

$U(x,y) = x^{(1/10)}y^{(9/10)}.$

Recall the following equivalent definitions for luxury goods and necessities:

A good $x$ is considered a necessity if $e_{(x,I)}<1$.

A good $x$ is considered a luxury good if $e_{(x,I)}>1$.
As you can see, these definition do not encompass all possible scenarios, so any specific good does not have to be either a luxury or a necessity.

In the case of a Cobb-Douglas utility function $U(x,y)=x^\alpha \cdot y^\beta$ we get $x^* = \frac {\alpha I}{P_x}$. One can easily verify that $e_{(x,I)}=1$. In other words, the demand does for $x$ does not change with $I$. This means that in this case, $x$ is neither a luxury good nor a necessity.


Why is it assumed that covariance equal to $0$ or independence between $y$'s in the simple linear regression model? I have started a book of econometrics and in the first pages are stated the assumption used in the linear regression model, which are :

The third one is the one I don't understand, why it has to be assumed? how can be verified if this assumption is not met? My professor explained it with an example : "It is reasonable to say that the expenditure of a family with a certain income is independent of the one from another family with another income". What she says is okay to me, but it doesn't tell nothing about verifying the assumption when I have a set of datas, how can I have tuples of values in the case of the dependent variables $y_i$ and $y_j$ so that I can verify statistical independence or covariance equal $0$ ? Should I have the joint probability distribution of the variables? And why is it useful to assume one of these things, are not just the other assumptions sufficient? Any help is really appreciated.

The first assumption $E(y|x)=\beta_1+\beta_2 x$ identifies $\beta_2$. The roles of the rest are limited (if not nil) in terms of the identification of $\beta_2$ (identification = answer to the question 'what is $\beta_2$?').

Assumptions other than the first are all "if"s. They are useful for finding properties of OLS estimators, e.g., Gauss-Markov theorem, variance, efficiency, etc.

The third assumption should be written as $cov(y_i,y_j | x_1, \ldots, x_n)=0$ for $i\ne j$. Unconditionally, $cov(y_i,y_j)$ does not have to be zero. (If $x_i$ and $x_j$ are correlated, then $y_i$ and $y_j$ can be correlated.) But under the fourth assumption (nonrandomness), $cov(y_i,y_j)=0$ is equivalent to $cov(y_i,y_j | x_1, \ldots, x_n)=0$.

The fourth assumption is usually not well understood by beginners. It sometimes helps to state that $x_1$ is nonrandom, $x_2$ is nonrandom, and so on (instead of $x$ being nonrandom) in the context of repeated samples.

To the no autocorrelation assumption, it is usually regarded as sensible and acceptable to assume that individuals are independent each other. But it does not mean that it is true. Then what happens if it is violated? In fact, that's the question you want to ask, not why.

If you are doubt about the assumptions, the question goes this way: What happens to OLS and what should we do if the normality assumption is violated; what happens to OLS and what should we do if the heteroskedasticity assumption is violated; what happens to OLS and what should we do if the no autocorrelation assumption is violated; what happens to OLS and what should we do if $x_1, \ldots, x_n$ are random; what happens to OLS and what should we do if $E(u|x)\ne 0$?

So my answer to "why no autocorrelation" is: because it is a leading case and it is believed to be empirically relevant. And its violation does not necessarily mean the model is wrong. It only means that the unobserved determinants are correlated among individuals. The $\beta_2$ is  still the causal effect of $x$ on $y$. The identification of $\beta_2$ is the very starting point. Don't let the tail wag the dog. (That said, someone might want to identify $\beta_2$ by the no autocorrelation condition. This is rather unusual. $\beta_2$ is usually identified by $E(y|x)=\beta_1+\beta_2 x$.)

Related is, I don't think it is possible in general to completely account for autocorrelation by adding more $x$ variables. (For example, family members sharing the same experience but can this factor be sufficiently well observed?) More importantly, adding more variables to the right-hand side changes your model, by which you change the definition of your $\beta_2$. Sometimes you can do it (e.g., randomized experiments) but in most cases your definition of $\beta_2$ changes by changing your model.

My answer pertains to econometrics that tries to find causal effects. There can be other areas of statistics that have different approaches.


Has this differential calculus inequality approach to optimizing the production possibility curve exist? I just started micro-economics at my community college and my teacher mentioned the derivative of the PPF for two output resources. I thought about it a while and came up with this approach. Some of the notation may be incorrect as the highest math course I completed was college algebra (I tested out of it but still have todo trigonometry).

Does this approach I came up with already exist?

Here is the equations:

I don't really understand your optimization problem as it stands. Just as a few examples, when you write out

$$\min \sum_m \sum_v \left( \frac{\partial \vec f_v (\vec Q_v)}{\partial \vec f_m (\vec Q_m)} - \frac{\partial \vec f_m (\vec Q_m)}{\partial \vec f_m (\vec Q_m)} \right)$$

I have questions about why you are minimizing the difference between optimal conditions for output that has all equal opportunity costs. The justification is unclear to me. The function $\vec f_v(\vec Q_v)$ also leaves me confused looking at your work. Why is $f$ taking a vector of $n$ aggregate outputs as its argument? $f(q)$ is defined as the adjusted cost of purchasing $q \cdot n$ resources, so how does $f$ transform a vector as opposed to a scalar and what interpretation are you trying to give it?

Or in your optimization problem when you write out

$$\frac{dy}{d\sqrt{r^2 - x^2}} \rightarrow - \frac{x}{\sqrt{r^2 - x^2}} = y$$

I have no idea what you are differentiating with respect to and how you arrived at the equality on the right. In step c.) later on you substitute $x = 0$ which doesn't have a justification either. (If it does, I think you should try to be more explicit about what is happening.)

I think as is, the method of finding an optimal point on the production possibilities frontier is cumbersome, and I don't think the optimization problem is well defined.

If you wanted to refine your method, you'd have to give

conditions under where an optimum exists (the conditions you state are not sufficient)
identification strategies for an optimum
a situation where this method is more practical than the industry standard

So for that last point, why can't someone just have a production function (where they can derive the PPF) and a budget constraint from prices, regularity conditions and then solve? Since you seem to have some familiarity with higher level math, you may find Chapter 5 and 15 of Mas-Colell, Whinston, and Greene a good resources for seeing the foundation of how production problems are approached. Chapter 15 in particular more explicitly talks about production possibility sets.


Does people paying back their debts cause deflation? The majority of the monetary supply results from credit, with every loan creating pairs of assets and liabilities representing the same underlying value. Considering that every time someone pays back a loan, the asset and liability collapse back into a single copy of the money, intuitively it feels like people paying back loans causes a reduction in the monetary supply, which should cause deflation. Forgiveness or "writing off" of loans would seem to have the same effect, removing the value of an asset being used as the basis of additional monetary supply, so in theory reducing the monetary supply and causing deflation.
Is this the case? If not, why?

It is true that paying back loans causes contraction of money supply (if not offset by faster creation of new loans). However, it is not correct to say that this generally happen when debt is forgiven and it does not need to lead to deflation.
First, debt forgiveness can actually be thought of as a permanent expansion of money supply not contraction. An example: central bank buys $\\\$100$ of government bonds that government then gets to spend. Afterwards, central bank decides that the bond will be destroyed without asking for government to pay back the $\\\$100$. The $\\\$100$ still exists and still can be used to purchase goods and services and circulate in the economy. Moreover, since the debt which originally created it was scrapped that $\\\$100$ can continue to exist forever leading to permanent expansion in money supply.
Second, for money supply to contract it is not enough that one loan gets repaid if new loans are issued at the same time - money supply is aggregate quantity. Furthermore, money supply can be expanded even by different ways than just by loans (see this past question on Economics.SE), so also in principle if central bank intervened money supply could expand or stay constant even when borrowing drops. However, lets assume that that there will be on net less loans in economy and central banks will just do nothing and so money supply actually indeed contracts. That is still in itself not necessary enough to cause deflation.
For deflation to happen the price level has to drop, and the price level $P$ is by standard textbook monetary equation given as $P = MV/Y$. Where $M$ is the money supply, $V$ velocity of money, $Y$ real output. Thus for decrease in $M$ to cause deflation we also have to additionally assume that such decrease won't be offset by changes in velocity or real output. That is not always realistic. Usually, credit drops during recessions for various reasons (for example as argued by Bernanke in his research during recessions it might be hard to distinguish good and bad borrowers which would lead to credit rationing and consequently drop in borrowing). More generally, the amount of credit in economy is very pro-cyclical (see for example Gaiotti (2013) and sources cited therein). Hence, often when $M$ contracts due to lower amount of loans $Y$ contracts at the same time and the two can in principle cancel each other. $V$ also does not stay constant across business cycle generally decreasing during the recessions (see for example Anderson, Bordo & Duca (2017)). Thus while ceteris paribus decrease in credit and contraction of money supply would lead to deflation in real world you might not observe deflation whenever credit drops due to effects of other factors that are changing at the same time.


Interpreting the ratio of two variances in a Bayesian decision problem Given a normal prior with mean $\mu_0$ and variance $\sigma_0^2$, and a normal likelihood with known variance $\sigma^2$, the Bayesian posterior, after observing $n$ iid signals $x_1,\dots,x_n$, is also a normal distribution with mean
$$
\left(\frac{\mu_0}{\sigma_0^2}+\frac{\sum_{i=1}^nx_i}{\sigma^2}\right)
\left(\frac{1}{\sigma_0^2}+\frac{n}{\sigma^2}\right)^{-1}
$$
and variance
$$\left(\frac{1}{\sigma_0^2}+\frac{n}{\sigma^2}\right)^{-1}.$$
See https://en.wikipedia.org/wiki/Conjugate_prior#Continuous_distributions.

Pratt, Raiffa, and Schlaifer (2008) suggest that we could define
$$n'=\frac{\sigma^2}{\sigma_0^2}$$
so that the posterior mean and variance can be written as
$$
\frac{n'\mu_0+\sum_{i=1}^nx_i}{n'+n}\quad\text{and}\quad\frac{\sigma^2}{n'+n}.
$$

They say that

  The parameter $n'$ can be interpreted therefore as the "fictitious sample size" or equivalent number of sample observations that describes the amount of information implicit in the prior distribution.

I'm having difficulty understanding the interpretation of $n'$, especially the part after "or". Could anyone help me understand it, by perhaps putting it in a different way, or elaborate it a little?

Excuse the word-play, but the interpretation of $n'$ is a... posterior one. Meaning, the important thing is not how $n'$ is defined (ratio of variances, although this will prove consistent with the interpretation), but how it functions in the posterior mean and variance.

What does it do? For the posterior variance, it is easiest: firstly, it appears as an addition to the expression's denominator, an addition comparable to the actual sample size. This permits the authors to talk about "equivalent number of sample observations". Secondly, its effect is to lower the variance, which is a metric of dispersion but also of uncertainty. This effect now permits the authors to talk about "the amount of information implicit in the prior distribution": more information in the prior - lower uncertainty in the prior - lower uncertainty in the posterior - and indeed, $\sigma^2_0 \downarrow \implies n' \uparrow \implies \text{Posterior Variance} \downarrow$.

For the posterior mean we have (setting $N \equiv  n' + n$)

$$\text {Posterior Mean} = \frac{n'\mu_0 +\sum_{i=1}^nx_i}{n'+n} =
\frac{n'}{N}\mu_0 + \frac{n}{N}\bar x$$

i.e. a convex combination of the prior mean and the sample mean - so the magnitude $n'$ weighs the prior information against the sample information, as though you had two separate samples from the same population of sizes $n'$ and $n$, and considered their pooled average. Again, this can be interpreted as "information implicit in the prior distribution expressed in terms of virtual/fictitious sample size".


Total cost function and (dis)economies of scale I'm really confused about how I'd tackle this.

I have an equation, $TC(Q) = 100Q + 20Q^2 + 3Q^3$.

And I'm trying to find where the economies of scale, diseconomies of scale and constant return to scale occurs.

My instinct would be to take the derivative of that function, and then set it to 0, and then see what the values to the left and right of 0 are which would be the slope and allow me to see depending on whether or not they're positive or negative whether it's an economy or diseconomy of scale.

Is this along the right road?

First of all, knowing the cost function is not enough to know whether we have decreasing, increasing or constant returns to scale. Returns to scale are a property of the firm's production function -- and the relationship of the production function to the cost function is not as straightforward as you might think. However, if we assume that the firm takes factor prices as given, then we can apply a (rather intuitive) result from Sandmo (1970):

  Average cost is decreasing, constant or increasing according as returns to scale are increasing, constant or decreasing.

In light of this, we simply need to consider the average cost curve:

$$ AC(Q) =100+20Q+3Q^2 $$

Clearly, this is strictly increasing in $Q$. Therefore, if we are willing to assume price taking in the factor markets, we know that the firm's underlying production function exhibits decreasing returns to scale.


Why inflation is still reported low? Recently I heard from Richard Koo's video, that central banks have injected so much money to the banking system. There is enough reserves in the U.S. banking system to increase money supply 16 times. In other words, according to Richard Koo, the inflation should have been around 1600% over the last 10 years. However, as per the inflation reported by the federal reserve, it is still under 2%.

I understand that the asset prices have gone up in the last 10 years in terms of stock prices and housing prices. But why is inflation still low?

There's a pretty simple answer to that.  The money injected into the banking system does not acquire any velocity- it just gets redeposited at the Fed.  If they had spent the same amount of money into the general economy in the form of goods and services, then you would have seen higher inflation.


What exactly is the difference between the PPP ("purchasing power parity") and LOOP ("law of one price")? For PPP & LOOP: e = EP/P* = 1
So both are valid if goods in the US and EU cost the same in $ for example.
But then, what exactly is the difference between both?

PPP uses the price level, the price of the consumer basket. The price level can be identical without all prices being identical. An example:

Consider a consumer basket with just two goods and assume the weight of both goods in the basket is one half. If $p_1 = p_2 = 4$ then the price of the consumer basket is
$$
P = \frac{1}{2} \cdot p_1 + \frac{1}{2} \cdot p_2 = 4.
$$
However you get the same price level if you have $p_1 = 3,  p_2 = 5$.

So you can have two countries with identical price levels but differing prices. The converse of course is not possible. Thus LOOP implies PPP but PPP does not imply LOOP.


Does a trade union of YouTubers exist? Would YouTubers see a sense in having a trade union?

For example, to establish policies how much the value of their contribution is.

The controversy here is, professional YouTubers make a bet for their income on the platform and have to accept its conditions, on the other hand YT has enough dominance and yet dependant on YouTubers making the bet their content will get them enough ad turnover.

Yes. In 2018, the German YouTuber Jörg Sprave established YouTubers Union (see also FairTube).

In 2019, it entered into a partnership with IG Metall: IG Metall press release, news stories by Observer, Bloomberg, CNBC.


The law of supply and demand - How does it work? I've learned what the principle of supply and demand says, and would paraphrase it like this:

The price of a good is at equilibrium when supply and demand are
equal.

Or with other words:

The price of a good is dictated by the principle of supply and
demand when supply and demand are equal.

My question is:

How does the principle (or even law) of supply and demand work in practice? Which
forces force the price to be at equilibrium?

That's what I came up with (a very raw model):

The producer or seller of a product notices that the product sells better than before.
From this he draws the conclusion that there is a bigger need for the product: consumers want to have it more urgently than before.
That means, consumers will probably be willing to pay a higher price for it than the current one.

Now there are different cases:

The producer can produce as much of the good as he could sell. He does so and sells it for the old price (making people happy). Or he takes a higher price (because he can, but not too high).

The producer can not produce as much of the good as he could sell. a) He doesn't want to grow, so he produces as much as he can and
sells it for the old price ("first come first serve"). Or he takes a higher price (but not too high).
b) He grows (taking credits) and raises the price to compensate the interests to be paid. Or he raises the price even more (because he can, but not too high).

Which of these scenarios is mainly responsible for rising prices
in case a good is demanded more strongly?
And what is responsible for rising prices of goods with no rise of demand? (Is this only a collateral effect?)

You need to take into account the cost of producing a good as well. In most cases, the marginal cost of producing something is increasing. A profit-maximizing producer would want to produce until price is equal to marginal cost. That means that scenario 2 is responsible.

For the case of rising prices with no increase in demand, just think about the basic demand and supply model. What could cause an increase in equilibrium price without the demand's changing? (Hint: a shift in ____). What could cause that shift?


Are there Nash Equilibria that aren't mixed strategies? We can consider only finite games if it makes a difference, but are there nash equilibria that can't be characterized as mixed equilibria?

Nope, every pure strategy equilibrium can be characterized as a degenerate mixed strategy equilibrium.

That is, it is a mixed strategy in which a pure strategy is played with probability $1$.


The Shapiro-Stiglitz model. Why under full employment do unemployed workers find jobs instantly? Under the Shapiro-Stiglitz model the No-Shirking Condition is:
$$w=\bar{e}+\left( \rho +\frac{\bar{L}}{\bar{L}-NL}b \right)\frac{\bar{e}}{q}$$
Where:
$\bar{e}=$ exerted effort by employees
$\rho=$ discount rate
$\bar{L}=$ total number of workers
$N\bar{L}=$ number of employed workers
$b=$ job separation rate
$q=$ shirking detection rate
(From Romer's Advanced Macroeconomics 3rd edition, pg. 453)

[The no-shirking condition shows] the wage that firms must pay to induce workers to exert effort. When more workers are employed there are fewer unemployed workers and and more workers leaving their jobs; it is easier for unemployed workers to find employment. [...] At full employment, unemployed workers find work instantly, and so there is no cost to being fired and thus no wage can deter shirking

My Question
The definition of full employment is:
(Source from Investopeida)

Full employment is an economic situation in which all available labor resources are being used in the most efficient way possible. Full employment embodies the highest amount of skilled and unskilled labor that can be employed within an economy at any given time. Any remaining unemployment is considered to be frictional, structural or voluntary

Based on this definition is appears that even under full employment workers do not find work instantly under the Shapiro Stiglitz model. What exactly am I missing?

I think that the confusion is caused by the different meaning of "full employment" in both contexts.

In the Shapiro-Stiglitz model, full employment in the sense that $\bar{L}\rightarrow LN$ implies that the job finding rate $a\rightarrow \infty$, which means no frictional unemployment.

In the other definition, full employment is merely defined by any remaining unemployment being only frictional (or structural/voluntary, not important here). Situations of no full employment could exist, for example, due to minimum wages, according to this definition. This view considers the unemployment arising from workers being laid off and waiting some time to find a new job (frictional unemployment) as a technological necessity that cannot be avoided so as to further increase efficiency.

Last but not least, please note that your quote from Romer concerns the labor supply curve only, while the employment rate will be determined in equilibrium.


Find Variable Cost per Unit I am trying to do this problem, and I am  not getting the answer.
I need to find the fixed cost of system 1, and system 2.
I know that the fixed cost will be the y-intercept of the equation.
Fixed cost for system 1 is 1000, and fixed cost for system 2 is $5000.
When I tried to find the variable cost per map dispensed, I am not getting the answer.
I know that the variable cost changes with the output. Therefore, it is the slope of the equation. In this case, the variable cost for system 1 is supposed to be 0.90, and the variable cost per map dispensed for system 2 is 0.1. However, the solutions manual shows that the variable cost per map dispensed for system 1 is 0.8, and variable cost per map dispensed for system 2 is 0.16.
Did I do something wrong?

Based on the information you have given, both the solution manual and your solution are wrong. You are correct that the fixed cost for system I is 1. Variable cost is given by $$VC(x)=TC(x)-FC.$$ The variable cost for system I is therefore equal to $0.9x$. Note that the variable cost depends on $x$! For system II the variable cost is $0.1x$.

You appear to have confused variable cost with marginal cost. Variable cost is the part of the total cost that changes with quantity; marginal cost is, roughly, the cost of producing one more unit (and is given by the slope of the total cost curve). Thus, the marginal cost of system I is $0.9$ and the marginal cost of system II is $0.1$.


What is the difference between HM Treasury and HM Exchequer? Both terms refer to collecting tax revenue, right? What's the difference then? I hoped the relevant Wiki pages would help but they didn't.

Collection of tax revenue in the UK is the responsibility of neither of those but of HM Revenue & Customs which has the status of a non-ministerial department.

HM Treasury is the UK's economic and finance ministry. Its responsibilities include advice to ministers on taxation policy and government expenditure. Confusingly, perhaps, the most senior minister at HM Treasury is known as the Chancellor of the Exchequer.

HM Exchequer is not a UK government department but a rather old-fashioned name for the Government's account into which is paid money from taxation and other sources and from which government expenditure is paid. The account is more commonly known as the Consolidated Fund.


Fundamental question on marginal utility I was just thinking back to some introductory economics courses, but now I'm extremely confused on a fundamental concept. How is marginal utility interpreted as the additional "happiness" gained from consuming one more unit of some good? If marginal utility is the derivative of utility, then isn't it only measuring how the gains from an incredibly small consumption of some good? And then I started thinking about indifference curves and the MRS. I'm not sure how the MRS tells you the slope at which you are willing to exchange 1 unit of good x for however many units of good y? Take this simple indifference for instance where y = 100/x:

The MRS at (20,5) is -1/4 which should mean that at (20,5) this person will be ok with trading in 4 units of good x for 1 unit of good y correct? But this agent is only indifferent at (16,6.25) so I'm not really sure what the interpretation of the slope MRS here could be and how that differs from the indifference curve.

How is marginal utility interpreted as the additional "happiness" gained from consuming one more unit of some good?

Not sure what you mean. Utility is not interpreted as some biological measure of happiness. A bundle of goods with high utility is prefered by the consumer to bundles with lower utilities. This is all that utility describes; it is a modelling/storytelling tool.

If marginal utility is the derivative of utility, then isn't it only measuring how the gains from an incredibly small consumption of some good?

Yes, it is.
On your graph: kudos for using Desmos!

The MRS at (20,5) is -1/4 which should mean that at (20,5) this person will be ok with trading in 4 units of good x for 1 unit of good y correct?

Strictly speeking this is only true for marginal quantities (infinitesimally small quantities). Basically you are approximating the indifference curve with a linear curve (a line) at the (20,5) point. This line only coincides with the indifference curve at (20,5), and as you move farther away from this point, the line becomes a more and more imprecise approximation of the curve. (Note that 6.25 instead of 6 is not too bad as an approximation.)
The line about MRS representing the ratio at which a consumer is willing to trade is just to get the intuition across, it is not an exact definition.


Why do some perfectly competitive, loss-making firms shutdown and others don't? Question:

Why do perfectly competitive, loss-making firms that have (AC>AVC>AR) shutdown but

Firms that have (AC>AR>AVC) not shutdown?

-Both of these types of firms are making a loss. How is it significant that the latter type's AVC is less than AR ? How does that affect whether it shuts down ?**

These two graphs are for the two types of firms in perfectly competitive markets:

Loss-making firms where their AC > AR & AVC > AR that shutdown

Loss-making firms where their AC > AR & AVC < AR that don't shutdown.

$AVC<AR$ means, without considering fixed cost, the firm is making a profit of $AR-AVC>0$ per unit of output. Compare the two options: keep producing vs  shutdown:

Keep producing: $\text{Avg Profit}=\underbrace{AR-AVC}_{>0}-AFC$
Shutdown: $\text{Avg Profit}=0-AFC$

Since $AVC<AR$, staying in production is better since the revenues can be used to offset part of the fixed costs already incurred.

$AVC>AR$ means, without considering fixed costs, the firm is making a loss of $AR-AVC<0$ per unit of output. Compare the two options: keep producing vs shutdown:

Keep producing: $\text{Avg Profit}=\underbrace{AR-AVC}_{<0}-AFC$
Shutdown: $\text{Avg Profit}=0-AFC$

Since $AVC>AR$, shutting down leads to a smaller loss than staying in production.


Is charging of interest inherently rent seeking? Is the real interest rate component of interest (excluding default risk premium, etc) inherently rent seeking?

The real interest rate is typically considered to repay the opportunity cost of lending money, however, note that there is some degree of circularity in this definition: if charging of interest were prohibited on grounds of being rent-seeking, then the opportunity cost of lending would be less. So the question remains.

rent is about uncompetitive markets. In very competitive banking sector, interest will still exist. So it's not rent seeking. If laws forbide charging real interests, no private bank would be on business.

If you look at Investopedia for "Economic rent", you find:

  "Economic rent" is a term that defines an amount of money earned that exceeds that which is economically or socially necessary. This can occur, for example, when a buyer working to attain a good or service that is considered exclusive makes an offer prior to hearing what a seller considers an acceptable price. Market imperfections thus lead to the rise of economic rents; it would not exist if markets were perfect since competitive pressures would drive down prices. Economic rents should not be confused with normal profits or surpluses that arise in the course of competitive capitalist production. This term also differs from the traditional use of the word "rent," which applies to payments received in exchange for temporary use of a particular good or property, such as land or housing.

Notice: "Market imperfections thus lead to the rise of economic rents; it would not exist if markets were perfect since competitive pressures would drive down prices. "

Bill's definition is the "old version", which is not what you mean by "rent".

https://www.investopedia.com/terms/e/economicrent.asp


What is the interpretation of the output matrix of pivoting? I have the following matrix:
$$A=  \begin{bmatrix}
    1 & 2 & 3 \\
    2 & 3 & 4
  \end{bmatrix}$$

After pivoting, I got this matrix:
$$B=  \begin{bmatrix}
    1 & 2 & 3 \\
    0 & -1 & -2
  \end{bmatrix}$$

It's very embarrassing, but I know how to pivot, but I don't understand the interpretation of this matrix operation. What is pivoting and why is it important for linear optimization in economics? I only found resources on the mathematical intuition of pivot operation.

In the meantime, thank you so much for your attention and participation.

Pivoting helps solving linear system of equations. Imagine you want to solve for X that satisfies :

\begin{equation}A\cdot X = Y\end{equation}

where
\begin{equation}X = \begin{bmatrix}x_1\\x_2\end{bmatrix}\end{equation} and \begin{equation}Y = \begin{bmatrix}y_1\\y_2\end{bmatrix}=\begin{bmatrix}3\\4\end{bmatrix}\end{equation} and \begin{equation}A = \begin{bmatrix}1&2\\2&3\end{bmatrix}\end{equation}

Then if applying Gauss' Pivot to A' (concatenation of A and Y) with
\begin{equation}A' = \begin{bmatrix}1&2&3\\2&3&4\end{bmatrix}\end{equation}

yields
\begin{equation}B' = \begin{bmatrix}1&2&3\\0&1&2\end{bmatrix}\end{equation}

you instantly have that $x_2=2$ and $x_1=3-2x_2=-1$. On large linear system it is very fast to solve them that way.


Finding an economic policy that worked in a developed country but failed in a developing one As the term paper of development economics in BSc, I am assigned this topic but I have no idea where to begin with. Of course I can’t look up every economic policy that was ever made then check whether it failed in a developing country but succeeded in a developed one. Can anyone suggest me a book or any article which might be of any use to me?

Thanks!

In his book The Elusive Quest for Growth: Economists' Adventures and Misadventures in the Tropics, William Easterly discusses the failed efforts of states to use education, family planning, and debt forgiveness as means to grow out of poverty. You may find one policy that worked in developed countries.


Applications to Green's Theorem in Economics? I was wondering about possible of application of integration to economics (other than welfare), more specifically, how might Green's theorem be useful for an economist?

Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C . If G and H are functions of (x,y) defined on an open region containing D and have continuous partial derivatives there, then

$$\oint_C{(G\ dx + H\ dy) = \int\!\!\!\int_D {\left({{\partial H} \over {\partial x}} - {{\partial G} \over {\partial y}}\right)\ dx\ dy} } $$

where the path integral is traversed counterclockwise.

The idea behind this theorem is that if you have a line integral in two dimensions, then Green's theorem can be used to compute the integral:
 Green's theorem transforms the line integral around a simple closed curve $C$ into a double integral over the plane region $D$ bounded by $C$.

Here and here are two application of the theorem to finance.

Here is an application to game theory.

This is an application of the theorem to complex Bayesian stuff (potentially useful in econometrics).

Also, the Green's theorem is used in this proof, which relates to dynamics system, and therefore could be related to economic models (source of this here)

Last but surely not least, this book might have relevant stuff. At least Chapter 12 does use it.


When and why women left the labour market? It is well documented that women in now developed countries entered the labour market all thoughout the 20th century. As such, female labour participation have consistently increased. For example, this is a table from Godin (1977):

Here is a graph from a more  recent report:

However, I have the impression that the feudal, or pre-capitalist societies, which were mainly agrarian and textile based, relied heavily on female labour. We can probably all picture housewives working in the field or sawing textiles.

So, the question is, when and why women left the labour market? Is this because of a transition from feudalism toward a capitalistic mode of production? Or the shift from agriculture to industry?

They worked at home. Like "Household Engineers" do today, doing everything working from down to dusk like their husbands, and like their husband they shared in the earnings of the household.
Until the industrial revolution came each household operated like a mini business.

It was the Industrial revolution that divided "work"(e.g. business) from home.

They never left the workforce, They just stopped being called the workforce.

Ironically with people working from home more and more we are returning to such a system.


Is economics Turing Complete? I am interested in economics from the perspective of mathematical physics and complexity theory. An important set of systems in complex systems are systems that are Turing Complete and are cases of universal computation.

This raises the issue of whether a virtual Turing Computer can be constructed in economics. Can accounting be considered a case of a universal computer? I find it interesting that the Ethereum cryptocurrency's support for smart contracts is Turing Complete.

I am not a CS guy so this answe may be flawed in many ways. Take it more as a long comment and please give some feedback.

Economists view Ethereum as a pure Arrow-Debreu market economy. In an AD economy you can write fully contingent contracts specifying commodity trades conditional on any future event at any particular date. Therefore, an AD economy is, by definition Turing complete. In that sense, for economists Ethereum is a cool implementation of an ideal but nothing new.

The problem is that, as Arrow himself recognized (but not Debreu!), this model of the economy is not realistic in any way because there are frictions to contracting, undescribable events, unawareness, asymmetric information, uninsurable risks, etc.

At a more fundamental level, economics has another problem that seems to me to relate to the halting problem. if an economic system was decidable, then the agents in the economic model would have to either know the answer or not know the answer. In the former case, there would often be an eternal loop, since the answer to the problem would be part of the problem itself (this is the essence of the Lucas critique). If you assume they do not know the answer then you are imposing a certain rule on their actions that will not be universal and therefore would not allow for Turing completeness on the whole economy.


A few clarifications on Utility equations and indifference curves? I have the utility equation $U(a,b) = a^{2}b^{3}$

How can I tell if the indifference curves are convex?
I was under the impression that if:

$U_{a} > 0$  and $U_{b} < 0$

then the curve would be convex. In this case, those conditions don't hold, but when I try graphing the equation, the curve appears convex. What am I missing?

Also are these conditions true:

if $U_{a} > 0$ , there is not diminishing marginal utility.
if < 0 , there is diminishing marginal utility,
and if = 0 , constant.

Are these conditions the same for good $b$ ?

I've been given lots of conflicting info and am now just confused.

From a mathematical point of view, the indifference curve is an equation

$$I_{\bar u}:a^{2}b^{3} = \bar u$$

for every fixed $\bar u$. Put $b$ on the vertical axis and $a$ on the horizontal axis and write this as a function of $a$:

$$b^3 = \bar ua^{-2} \implies b = (\bar u)^{1/3} a^{-2/3}$$

This fully characterizes the indifference curve for $\bar u$. Now you have a one-dimensional function, and for it to be convex, its second derivative with respect to $a$ must be non-negative. In fact it is strictly positive (we assume goods are measured in positive quantities, and we ignore the uninteresting corner solution for $\bar u=0$ which is a single point).


Has any country attempted to inflation adjust capital gains before taxation? Inspired by the answer to a different question I wondered:

Can anyone think of a case study example, past or present, when capital gains are inflating adjusted before being taxed. I could imagine this making a lot of sense in high inflation currencies.

If there is an example, what prompted the introduction and was it considered a success?

Mexico has a 3% per annum adjustment to basis on real property when calculating capital gains, though they still have a 5% floor on capital gains tax.

I cannot weigh in on the "success" of the program given everything else they're juggling.

Source


How to choose between fixed and random effects using economic intuition? In class, our professor said that when it comes to deciding between estimating panel regression with fixed and random effects we should not just blindly follow the Hausman test, but also think about how we expect the omitted variables to behave based on economic intuition.
But I don't understand how we are supposed to this. Are there any examples of situations where just from an economic perspective fixed effects are better than random effects or the other way around?

Here is an example where just from an economic perspective fixed effects are better than random effects.
Suppose you have panel data and you want to regress earnings $y$ on some observable characteristics $X$ of an individual like education, tenure, experience, age, birthplace, etc. The regression you would estimate is
$$y_{it} = \alpha + X'_{it} \beta + \epsilon_{it}$$
where the error term $\epsilon_{it} = \alpha_i + \eta_{it}$, is a function of individual heterogeneity $\alpha_i$, which is not varying over time and some random shock $\eta_{it}$.
Pooled ordinary least squares and random effects assume that the observable characteristics and the individual heterogeneity component are uncorrelated, $Cov(\alpha_i,X_{it})=0$. As you know this does not hold when there is a correlation between your controls $X$ and the error term, which will bias your estimates - that's the standard omitted variables bias.
Does the assumption $Cov(\alpha_i,X_{it})=0$ hold in the earnings context?
In this context, your economic intuition will be useful. You may think of $\alpha_i$ as individual ability, which is unobserved by the econometrician but potentially correlated with some of the observed individual characteristics $X$, such as education or tenure. So, the $\alpha_i$ correlate with the regressors $X_{it}$, and the assumption $Cov(\alpha_i,X_{it})=0$, is violated. Then, a fixed effect approach, which effectively fits such intercepts will be more convincing.


Fannie Mae and Freddie Mac as substitute benchmark bonds "The reduction seen in US government debt in the late 1990s has led to a redution in the supply of intermediate and long-term government bonds, and some concern has arisen over this fact. In the United States, some efforts have been made to promote the long-term debt of Fannie Mae and Freddie Mac as substitute benchmark bonds."

This comes from a passage connected to US treasury bond futures.

I cannot understand why Freddie Mac and Fannie Mae have been chosen as closest to government debt? Didnt one of them go bust in the recession making them not quite default free (as one usually assumes in US debt)?

Fannie Mae and Freddie Mac bonds have long been viewed as having an implicit government guarantee, and though they received government support during the crisis, they never missed a payment to bondholders. This implicit guarantee was strengthened in July 2008 when Congress passed the Housing and Economic Recovery Act of 2008, which created a channel through which the Director of the Federal Housing Finance Agency could place them in conservatorship, which was done in September 2008. The GSEs remain in conservatorship today, and have access to lines of credit with the US Treasury. So while it's true that they still do not have an explicit guarantee today, it's easy to see why they're viewed as having a guarantee, at least implicitly.


Asymmetric information assumption This question isn't about asymmetric information per se but rather one of the assumptions. Consider a market for second hand cars; there are lemons (low-quality cars) and plums (high-quality cars).

For lemons, the valuations are: $V_{b} = 1500 $ and  $V_{s} = 1000$. The subscripts denote buyer (b) and seller (s).

For plums: $V_{b} = 4000$ and $V_{s} = 3000$

The buyer knows that there is an equal amount of each car (i.e., the probability of the car being high or low quality is 50%) but she doesn't observe the quality. This results in market failure because the buyer is willing to pay

$\frac{1}{2}(1500 + 4000) = 2750$

Therefore the sellers of plums leave the market because $2750 < 3000$ and only sellers of lemons remain. And now the buyer is only willing to pay 1500, therefore only lemons will be traded.

What is confusing me is that it seems like we are assuming that the buyer knows the sellers valuations. I.e., the buyer knows that because the seller values plums at 3000, and the buyers expected valuation is below this, those sellers will leave the market. Am I misunderstanding something or is this the actual assumption in this case?

In this setting, both buyers and sellers are usually assumed to be risk neutral. So adding an additional layer of uncertainty over seller's valuation is not really going to change the model's prediction in any "qualitative" way, in the sense that market unraveling (perhaps only partial in this case) is still an inevitable outcome, even though the exact equilibrium may be different.

Suppose the buyer is unsure of the seller's valuation, but the buyer believes that the seller's valuation follows a distribution with a mean of $3000$. Further, let's assume that under this distribution, a fraction $p\in[0,1)$ of the plum seller's value is below $2750$, the buyer's average value of the two types.

So, by offering to buy a car of unknown quality at $2750$, the buyer gets an expected payoff of
\begin{equation}
\frac{p}{2}(4000-2750)+\frac12(1500-2750)=1250\left(\frac{p}2-\frac12\right)<0.
\end{equation}
This is worse than the zero payoff the buyer gets by offering $1500$ for a lemon.

Since the mean of seller's valuation is $3000$, there is always a positive fraction of the sellers with values greater than $2750$, i.e. $1-p>0$. These sellers will leave the market as they don't anticipate fetching a price higher than their own values for the car. The exit will then trigger the usual cycle of downward revision of buyer's conditional expected value and more exits. Depending on the distribution of seller value, full market unraveling may or may not occur.

Nevertheless, what underpins the unraveling of (necessarily a fraction of) the plum market is still the same: the buyer's anticipation of a positive fraction $(1-p)$ of the plum sellers not willing to sell at $2750$.


How to get details on all the models used for evaluating ACA? I am trying to track down the models and the underpinnings/details for them for models that may have been used to evaluate the ACA/Obamacare.  I am aware of Gruber's (proprietary) model, and am thinking that the Urban Institute's HIPSM model may have been used, but not sure if there are others.  Even for those two, it seems I'll need to do a good bit of research to figure out what's in them and how they work.

In terms of actually getting it passed as legislation, the only evaluation that has any real significance is the one done by the CBO, as that's the official scorecard for Congress and debates that come up on the floor. I have no idea what the specific models they use are called, but I do know they are very linear and simplistic (by design) compared to other mainstream models. It's definitely bound to be a fruitful search if you look there.


Monthly price elasticity and possibility of using daily values I am calculating the price elasticity as a starting point to find a theoretical optimal price that would maximize our revenue.
I am looking at 2 years data and to use the price elasticity formula, I am considering monthly values separately (this also because given the strong seasonality we have, i would expect different elasticity per month and I would like to suggest different prices every month).

To get the monthly Price Elasticity, I calculate for each month Prices and Quantities of the respective year:

$$
\frac{(Q^{2018} - Q^{2017})/Q^{2017}}{(P^{2018} - P^{2017})/P^{2017}}
$$

Question 1: Is this correct? Using aggregated monthly data is enough? What if I had also 2016 data? How could I put this extra information in the formula?

Question 2: Could I use daily data to calculate the price elasticity? Could I plot 2 years data and use the linear trend line for the elasticity calculation?

Thanks in advance, any help is highly appreciated!

What you're trying to approximate is the quantity

$$
\gamma(t) = \frac{{\rm d}\ln Q(t)}{{\rm d}\ln P(t)}
$$

$\gamma = \gamma(t)$ is a function of time, the better sampling you have of $P$ and $Q$ the better estimation of $\gamma$ you are going to get. Imagine you have one sample every $h$ units of time. From what I can read $h  = 1 ~{\rm month}$, what you can do to measure $\gamma$ at time $t_k$ is calculate

$$
\frac{{\rm d}\ln P(t_k)}{{\rm d}t} \approx \frac{\ln P(t_k) - \ln P(t_k - h)}{h} \tag{1}
$$

with a similar expression for $Q$. But this is really bad in general, here's a better approach

$$
\frac{{\rm d}\ln P(t_k)}{{\rm d}t} \approx \frac{-2\ln P(t_k + 2h) + 8\ln P(t_k + h) - 8\ln P(t_k - h) + \ln P(t_k - 2h)}{12h} \tag{2}
$$

So to give you an idea, if you are measuring the elasticity on ($t_k$ = November 2018) with data measured each month, you will need to know the prices and quantities for ($t_k - 2h = $ September 2018), ($t_k - h = $ October 2018), ($t_k + h = $ December 2018) and ($t_k + 2h = $ January 2019).


Relation between marginal cost and output elasticities Does anyone know of any results that show the link between marginal cost and the output elasticities analytically? I am looking at production and cost theory books but can't find any results that posit a direct dependence.

I figured it out:
The first-order condition of the cost minimization problem for, say, material inputs $m_{it}$ gives:
$ \lambda \frac{\partial F}{\partial M} = P_M $
Where F is the production function, $P_M$ the material input prices. Multiply by $\frac{M}{F}$ and rearrange,
$ \lambda = \frac{P_M M}{\beta_M F}  $,
where $\beta_M$ is the output elasticity with respect to material inputs. Similar results obtain for other inputs. Summing them all gives the relation to the short-run returns to scale.


Wage regressions: Nominal versus real wage I'm wondering do I need to convert nominal wages to real wages when running wage equations using panel data sets? My dependent variable is log of wage and I'm looking at returns to education across countries over time. Does the decision to use nominal versus real wage depend on what model I'm using- namely random, fixed effects or pooled OLS?

Because you want to measure the real impact of education.

If there is inflation, the nominal wages most likely will go up over time, but you don't want to think that your return to education does that, it's just inflation.

If, on the other hand, you're comparing wage differentials, say $\log w_s - \log w_u$, where $s$ indicates skill and $u$ indicates unskilled, you do not need to correct for the price level.

To see, note that

$$
\log w^s_t - \log w^u_t = \log \frac{w^s_t}{w^u_t} \\
\frac{w^s_t}{w^u_t} = \frac{\frac{w^s_t}{p_t}}{\frac{w^s_t}{p_t}}
$$


I don't understand how a graph would look like for this situation If there is a negative production externality of agriculture which is water wastage, and the government provides a 100% subsidy to the farmers so they can buy irrigation gadgets to reduce water wastage, thus eliminating the negative externality of production and increasing and improving their yield, will the graph look like what I attached as if MSC curve does shift to overlap with MPC (sorry for typo on graph) then they won't be intersecting at the optimal price and optimal quantity.

I suggest that the graph could be improved in two ways (apart from the point, which you seem to recognise, that the upward-sloping line labelled MSB should be labelled MPC (marginal private cost)).
Firstly, the inclusion of the vertical arrow labelled subsidy rather suggests that the vertical distance between the two marginal cost curves equals the amount of the subsidy (per unit of output).  This is unlikely to be the case: there is no particular reason why the cost of the gadgets should equal the social value of their effect in reducing wastage of water.  Instead you might add an explanation that the result of the subsidy, via its effect in reducing wastage, is to reduce the MSC of the agricultural production, shifting the MSC line down and to the right.
Secondly, there is nothing in the graph to represent the effect of the gadgets in improving yield.  It might be assumed that an improved yield implies a reduction in marginal private costs (although that is not necessarily the case, eg the harvesting of the extra output might disproportionately raise labour costs).  If that is a reasonable assumption in the context, you might draw a second MPC line below and to the right of the first (which would also represent MSC) which might be labelled (MPC with gadgets = MSC).


The assumptions of Rational Expectations Models What are the assumptions between rational expectations models and how restricted are there for the following results of economic theory? Where can I find them all gathered in some textbook or in the internet and what is the objection against REE models?

The assumptions are that the agents understand the situation, model or game they are in, that they are rational - in economic sense of the word and try to maximize their utility.

I think that one reason why you might have trouble finding a list of assumptions behind rational expectations is that rational expectations don’t really rely on their own assumptions rather they are application of rationality (with its set of assumptions) and utility maximization to uncertainty. Rationality and utility maximization under uncertainty simply give you rational expectations as rational expectations are just the mathematical/statistical expectations of any uncertain situation.

To illustrate this if you have a gamble $G$ where you toss a fair coin with payoffs $T=100$ and $H=-200$ the statistical expectations are given by:

$$E[G]=0.5(100)+0.5(-200)=-50$$

Now rational expectations are also -50 as if you understand the game, and want to maximize your utility the best possible expectation of the outcome of gamble is just to calculate it statistically.

You can find assumptions behind utility maximization and rationality in almost any economic textbook, but the most detailed explanations is in game theory textbooks. For example, Tadelis game theory: an introduction has clear treatment of the assumptions behind rationality.

It’s not really possible to say how restrictive rational expectations are without comparing them to some other model of expectations and considering the specifics model you want to apply them.

The critique of rational expectations is that the predictions of rational expectations don’t always hold in empirical testing. However, they are still being widely used even though we know they are not completely correct as there is no other consistent general theory of expectation formation that would provide better predictions than rational expectations even though in some isolated individual instances different expectation theories may actually provide better predictions.


Have there been any attempts to turn free-trade agreements into Pareto improvements? The textbook economic case for free trade agreements is that they constitute a Kaldor-Hicks improvement, which that in any given country the winners win more than the losers lose, when the benefits and losses are measured in dollars.  (See this blog post by Steve Landsburg for a proof.)  The reason that it matters that something is a Kaldor-Hicks improvement is that any Kaldor-Hicks improvement can be turned into a Pareto improvement, i.e. a policy that benefits some people and hurts no one, by having the winners pay the losers to compensate for the losses.
But the thing is, even though free-trade agreements are often argued for on the basis of this textbook case, once the agreement is passed the Kaldor-Hicks agreement is not actually turned into a Pareto improvement.  This is illustrated well in this dialogue by Gene Callahan:

Joe: An unemployed steel worker.
Thaddeus: An economist holding a chair at Free Market U.
Joe: Boy, free trade sure hasn't worked out as promised. Just look at the devastation it has created in the Rust Belt.
Thaddeus: I can't imagine what you are talking about: why, I have a very sophisticated model in which it is clear there are always net gains from free trade.
Joe: What you mean by "model"?
Thaddeus: It is a mathematical abstraction, that leaves out large parts of the real world in order to reach a determinate result.
Joe: So if your model leaves out large parts of the real world, how do we know its results apply to the real world?
Thaddeus: I did mention that it is a very sophisticated model, didn't I?
Joe: OK, let's say I grant that the results of your model do apply to the real world. You said it shows that there are always "net gains" from free trade. That implies that some people gain while others lose. How do you decide that the gains of the gainers are greater the losses of the losers?
Thaddeus: We use a compensation principle: if those who gained from some free trade agreement could, in principle, compensate those who lost, so that both sides would now prefer the free trade outcome, then we can conclude that free trade creates net gains.
Joe: Can you give me a concrete example of how this works in practice, for instance, in terms of the steel industry?
Thaddeus: I am glad you asked, because of course I can! Free trade allowed the steel company you used to work for to shut the plant at which you worked and move that production to China. Certainly, this move devastated the lives of workers in your town, and essentially left the town for dead. But other people benefited, for instance the consumers of goods that contain steel, but especially people like the upper management of the steel company that endows my chair at Free Market University. Let me tell you, those executives are doing really, really well as a result of that plant moving! I've been to a party at the CEO's house, and the upgrades he's been able to commission are just fantastic. I've never seen an infinite pool so sweet. Plus, they have been able to double my speaking fees at their summer seminar series.
Joe: I see. So, per your compensation principle, you will be recommending that those executives give up a portion of their gains to help out the town they left in ruins?
Thaddeus: I'm sorry, did you miss the part about "the company that endows my chair"? Jeez, do we really have to wonder why low-IQ workers like you are suffering in the great, global economy?

So my question is, have there been any attempts to turn a free-trade agreement from a Kaldor-Hicks improvement to a Pareto improvement? That is, a policy that taxes the winners in order to compensate the losers.

The US has a  "Trade Adjustment Assistance" for (almost) this exact purpose.

  Trade Adjustment Assistance (TAA) is a federal program of the United
  States government to act as a way to reduce the damaging impact of
  imports felt by certain sectors of the U.S. economy. The current
  structure features four components of Trade Adjustment Assistance: for
  workers, firms, farmers, and communities. ...it was proposed by President John F. Kennedy as part of the total package to open up free trade. President Kennedy said: "When considerations of national policy make it desirable to avoid higher tariffs, those injured by that competition should not be required to bear the full brunt of the impact. Rather, the burden of economic adjustment should be borne in part by the Federal Government."...As a 2012 Report by the Joint Economic Committee states: "TAA needs to remain an integral part of trade policy because it compensates those harmed by import competition without sacrificing the larger demonstrable benefits of trade

Trade Adjustment Assistance at Wikipedia

Canada had a program like this into the 1980's. The comparable EU program is called The European Globalisation Adjustment Fund.


When can one safely talk about decreasing marginal utility? One thing I hear a lot is talk of decreasing marginal utility—the idea being that additional units of a good become progressively less attractive the more units of that good one has already.

However, this always made me a little uncomfortable because of the ordinality of utility. If we take the trivial case of a world in which there is only one good with utility $u(x)$ satisfying $u'(x),\ u''(x)<0$ (decreasing marginal utility) then it is clearly possible to construct an increasing function $f$ such that $(f\circ u)$ is linear in $x$. Moreover, since utility functions are invariant to monotone-increasing transformations, $(f\circ u)$ is a utility function that represents the same preferences as $u$ (but now has constant marginal utility). Thus, in a world with a single good it seems that it never makes sense to talk about diminishing marginal utility.

My question is this: consider a market with $L>1$ goods. Is there a formal condition under which we can safely talk about decreasing marginal utility? That is to say, is there a class of preferences such that every valid utility representation, $u(\mathbf{x})$, has $u_{ii}(\mathbf{x})<0$ for some $i$?

Alternatively, is there some simple proof that, for $L>1$, the existence of a utility representation with $u_{ii}(\mathbf{x})<0$ for some $i$ necessarily implies that all utility representations have $u_{ii}(\mathbf{x})<0$?

The concept of "marginal utility" (and therefore of decreasing such) has meaning only in the context of cardinal utility.

Assume we have an ordinal utility index $u()$, on a single good, and three quantities of this good, $q_1<q_2<q_3$, with $q_2-q_1 = q_3-q_2$.
Preferences are well behaved and satisfy the benchmark regularity conditions, so

$$u(q_1)< u(q_2) < u(q_3)$$

This is ordinal utility. Only the ranking is meaningful, not the distances. So the distances $u(q_2) - u(q_1)$ and $u(q_3) - u(q_2)$ have no behavioral/economic interpretation. If they don't, neither do the ratios

$$\frac {u(q_2) - u(q_1)}{q_2-q_1},\;\; \frac {u(q_3) - u(q_2)}{q_3-q_2}$$

But the limits of these ratios as the denominator goes to zero would be the definition of the derivative of the function $u()$. So the derivative is devoid of economic/behavioral interpretation, and so comparing two instances of the derivative function would not produce any meaningful content.

Of course this does not mean that the derivatives of $u()$ do not exist as mathematical concepts. They can exist, if $u()$ satisfies the conditions needed for differentiability. So one can ask the purely mathematical question "under which condition the  function representing ordinal utility has strictly negative second derivative" (or negative definite Hessian for the multivariate case), trying not to interpret it as "decreasing marginal utility" with economic/behavioral content, but as just a mathematical property that may play some role in the model he examines.

In such a case, we know that:
1) If preferences are convex, the utility index is a quasi-concave function
2) If preferences are strictly convex, the utility index is strictly quasi-concave

But quasi-concavity is a different kind of property than concavity: quasi-concavity is an "ordinal" property in the sense that it is preserved under an increasing transformation of the function.

On the other hand, concavity is a "cardinal" property, in the sense that it won't necessarily be preserved under an increasing transformation.
Consider what this implies: assume that we find a characterization of preferences such that they can be represented by a utility index which is concave as a function. Then we can find and implement some increasing transformation of this utility index, that will eliminate the concavity property.


Why charge higher interest rates to poorer customers? Consumer loans/credit charge different rates depending on the individual's risk.  In particular, it charges more to poorer individuals. Whilst this seems to make sense from a risk perspective, there is some circularity involved. This is, "the more an individual has to pay, the more risk there is s/he doesn't pay".

In other words, higher interest rates increases the risk of the loan, which means higher interest rates are charged, which increases the risk of the loan, which... etc.

is this studied by economic/finance theory? Can someone explain me the circularity and provide some intuition? It's like if standard theory looks at a linear demand and supply curve, but it seems the supply curve is exponential (more cost increases the risk which increases the cost which increases the risk...).

First I would not call this problem a circular problem as that term has specific meaning in modeling and it does not really apply here.

Rather you can think about this as a version of a multiplier. For example, consider standard concept of money multiplier. In fractional reserve system if a central bank issues 100€ and reserve ratio is 10% then the original 100€ gets deposited 10€ is kept and 90€ lent which is then again deposited ad infinitum. So you might get puzzled here and think that the original 100€ creates infinite money but that would be incorrect as sum of infinite addition can be still finite. In this case even with infinite banks the original 100€ would crate only max $100(1/0.10)=1000€$.

How this applies here? Well here again even though higher interest rate makes person poorer and hence riskier leading to even higher interest rate it does not necessary make the person twice as riskier. Assuming for simplicity proportional relationship between riskiness and interest rate (relaxing this would not change the intuition) as long as the total effect of this increase measured as a fraction is less then 1 then the problem will converge to some final interest rate $r$ at which it would be possible to lend money to the poor person. If the fraction would be above 1 the series would be divergent meaning the optimum interest rate would be infinity and in that case bank would simply not lend money to this poor person.

More nuanced and complex versions of this kind of questions are studied by development economics. You may want to look into literature discussing borrowing constraints, micro-finance etc. I think good place to start would be: Poor Economics from Banerjee and Duflo