Is there a formal definition of opportunity costs, economic costs, and/or economic profits? [Edited to remove a mistake in a definition and some typos.]
According to various econ textbooks (e.g. this one), there is a fundamental distinction between economic profit and accounting profit:
(i) While accounting profit subtracts only explicit costs (out-of-pocket costs) from revenue,
(ii) economic profit subtracts opportunity costs, also known as economic costs, which consist of explicit and implicit costs. Here,
(iii) opportunity costs are generally defined as the "value of the best foregone alternative". In the context of firms, "value" of course means profits.
(iv) Furthermore, when economists talk about "costs" and "profits", they always mean economic costs and economic profits. For example, firms are assumed to maximize economic profits.
All the definitions I found were verbal and informal as above. Is there a formal definition of these concepts? Do they make sense at all? Since I didn't find anything in the literature (by a quick search, admittedly), I tried to formalize it myself for the firm context:
Let $X$ be a set of alternatives the firm can choose from, and let $z\in X$. Let's assume that alternative $z$ yields revenue $r(z)$ and generates explicit costs $c_e(z)$ for the firm. Accounting profit $\pi_a(z)$ is defined as revenue minus explicit costs, so $\pi_a(z)=r(z)-c_e(z)$. Economic profit $\pi_e(z)$ is then defined as accounting profit minus implicit costs $c_i(z)$, thus $\pi_e(z)=\pi_a(z)-c_i(z)=r(z)-(c_e(z)+c_i(z))=r(z)-c_o(z)$.
Opportunity costs of choosing $z$ are the value of the best foregone alternative, so $c_o(z)=\max_{k\in X,\,k\ne z}\pi(k)$.
Now, what is the "profit" $\pi(k)$ here? Economic profit or accounting profit? This might not be immediately obvious. Let's have a closer look.
Finite sets of alternatives
Assume for simplicity that there are only two alternatives, $X=\{x,y\}$, with $r(x)>r(y)$.
(i) Let's try economic profits, so $\pi(k):=\pi_e(k)$:
Then $c_o(x)=\pi_e(y)$ and $c_o(y)=\pi_e(x)$.
Therefore $\pi_e(x)=r(x)-c_o(x)=r(x)-\pi_e(y)$. Now, analogously, $\pi_e(y)=r(y)-c_o(y)=r(y)-\pi_e(x)$. Substituting, $\pi_e(x)=r(x)-r(y)+\pi_e(x)$, implying $r(x)=r(y)$. This is a contradiction, so this approach makes no sense.
(ii) Let's interpret "profit" as accounting profit, i.e. $\pi(k):=\pi_a(k)$.
Then $c_o(x)=\pi_a(y)$ and $c_o(y)=\pi_a(x)$, so $\pi_e(x)=r(x)-c_o(x)=r(x)-\pi_a(y)=r(x)-r(y)+c_e(y)$. Similarily, $\pi_e(y)=r(y)-c_o(y)=r(y)-\pi_a(x)=r(y)-r(x)+c_e(x)$. This is at least not contradictory.
Infinite sets of alternatives
But there are rarely only two alternatives. Consider instead a standard quantity-setting monopolist. The set of alternatives is the set of quantity choices, so $X=\mathbb R^+$. Let's denote by $q^*$ the firm's optimal choice. Then the firm accrues accounting profits denoted by $\pi_a(q^*)=r(q^*)-c_e(q^*)$, where both $r$ and $c_e$ (and therefore $\pi_a$) are assumed to be continuous. What is the firm's economic profit $\pi_e(q^*)$ then?
Well, the firm's "(accounting) profit from it's best foregone alternative" is the accounting profit resulting from the smallest strictly positive deviation from $q^*$, which, unfortunately, doesn't exist. To the rescue, let's interpret the "(accounting) profit from the best foregone alternative" as the supremum (instead of the maximum) of the foregone accounting profits: $c_o(q^*)=\sup_{k\in X,\,k\ne q^*}\pi_a(k)$. This, however, is just $\pi_a(q^*)$. Then $\pi_e(q^*)=r(q^*)-\pi_a(q^*)=c_e(q^*)$.
Economic profit of a profit-maximizing monopolist being equal to its out-of-pocket costs? This seems not to make sense.
So do the concepts of economic profit and opportunity costs as defined in (i)-(iv) make sense at all? Or which of (i)-(iv) above is wrong? Or is the "value" of the best foregone alternative in the context of firm decisions neither economic nor accounting profit of the best foregone alternative? What else?

Economic profit
I think there are some problems with the formulation in your question, first you heavily focus on opportunity cost but note accounting profit does not even properly capture all revenue firm gets.
I will first focus on economic profit more broadly and at the end go back to opportunity cost.
Following Varian Microeconomic Analysis pp 24 (emphasis mine),

Economic profit is defined to be the difference between the revenue a firm receives and the costs that it incurs. It is important to understand that all costs must be included in the calculation of profit. …
Both revenues and costs of a firm depend on the actions taken by the firm. These actions may take many forms: actual production activities, purchases of factors, and purchases of advertising are all examples of actions undertaken by a firm. At a rather abstract level, we can imagine that a firm can engage in a large variety of actions such as these. We can write revenue as a function of the level of operations of some $n$ actions, $R(a_1,...,a_n)$, and costs as a function of these same $n$ activity levels, $C(a_1,...,a_n)$.

The above is already rigorous definition for economic profit, economic revenue and economic cost.
Note accounting operates under its own sets of rules. Accounting, is not econometrics. Point of accounting is not to accurately estimate or measure economic relationships. So what you are doing above, defining economic profit at simply accounting profit minus opportunity cost is somewhat misguided (it would only hold in an unrealistic special case where we assume accounting only missed opportunity cost but accounting misses so much more).
First, following Varian we can start with a set of occurring actions $a$ that create revenue and costs. However, when it comes to accounting, not all of these will be reported. For example l, consider selling goods without issuing receipt to avoid paying taxes, which will not get reported as accounting profit. The same holds for many costs other than opportunity cost. For example, consider how depreciation costs are treated by accountants. From purely economic perspective most assets definitely do not depreciate in linear fashion yet accounting allows firms to use linear depreciation for most assets regarding what the true depreciation cost each period is. So the accounting depreciation costs will too be different from economic depreciation cost. Or consider the fact that many countries allow small business to just in their accounting declare portion of their profit as cost without actually even proving they actually incurred these costs (this is done in some countries to ease administrative burden for sole traders and similar one person businesses).
Consequently, it makes more sense to rather define accounting profit in terms of economic profit and then work backwards by inverting those functions if you would want to get back to economic profit from accounting one.
Call $A=(a_1,...,a_n)$.  set of all economic actions that actually occur, and $R(A)$ would be economic revenue from those activities. Now apply some function $\rho$ which tells you based on $R(A)$ what actually accounting revenue is.
So accounting revenue $R_{acc}$ would be:
$$R_{acc}= \rho(R(A))$$
Similarly accounting cost $C_{acc}$, we will have actual economic cost firm incurs $C$ based on set of actions it takes $A$ and then we will have some function gamma that tells us what enters into accounting and what not so we would have that
$$C_{acc} = \gamma (C(A))$$
Finally the accounting profit would be difference between the above so:
$$\Pi_{acc} = \rho(R(A)) -\gamma (C(A))$$
Note what $\rho(.)$ and $\gamma(.)$ are will depend on local accounting regulations and laws. in some country government could declare that any firm has to put  always just 1000€ as their cost (yes it is unrealistic example but I am just showing it to prove a point) and in such case $\gamma(C(A))=1000$ regardless of anything that happens.
Whereas the true economic profit would just difference between economic revenues and economic costs:
$$\pi=R(A)-C(A)$$.
If you would want work your way back from accounting definitions then you could use inverse functions and economic profit calculated from accounting one would be:
$$\pi= \rho^{-1}-\gamma^{-1}$$.
Note the above does not really require definition of opportunity cost since here simply the function $C(A)$ is just some function where we assume that $C(A)$ assigns true economic cost to every action $a_1,…,a_n$, for standard profit optimization it’s completely okay to treat $C(.)$ as a black box and thus you will not really require separate definition of opportunity cost. As a matter of fact note in situation where there are no alternatives like having mana (from the biblical story where it could only be immediately consumed not stored or used for anything else) opportunity cost would not even be part of $C$ but still there would be distinction and disconnect between accounting and economic profit.
For example if we have $C(A)=c_1 a_1+c_2 a_2… c_n a_n$ and if we define $C$ as a function that always assigns true economic cost then you definition $c_1$ includes all economic costs including opportunity cost, but the economic profit, economic revenue and economic costs are still rigorously defined (even if the constituents of costs such as opportunity costs aren’t).
opportunity cost
Next tackling the opportunity cost separately (which can be later used to build function $C$), good places to start are Buchanan (1987) or Alchian (1968). The authors do not necessarily derive rigorous opportunity cost functions but give rigorous verbal definitions on which we can build.
For example, according by to Buchanan (1987) :

Opportunity cost is the anticipated value of 'that which might be' if choice were made differently. Note that it is not the value of 'that which might have been' without the qualifying reference to choice. In the absence of choice, it may be sometimes meaningful to discuss values of events that might have occurred but did not. It is not meaningful to define these values as opportunity costs, since the alternative scenario does not represent a lost or sacrificed opportunity. Once this basic relationship between choice and opportunity cost is acknowledged, several implications follow.

First, if choice is made among separately valued options, someone must do the choosing. That is to say, a chooser is required, a person who decides. From this the second implication emerges. The value placed on the option that is not chosen, the opportunity cost, must be that value that exists in the mind of the individual who chooses. It can find no other location. Hence, cost must be borne exclusively by the chooser; it can be shifted to no one else. A third necessary consequence is that opportunity cost must be subjective. It is within the mind of the chooser, and it cannot be objectified or measured by anyone external to the chooser. It cannot be readily translated into a resource, commodity, or money dimension. Fourth, opportunity cost exists only at the moment of decision when choice is made. It vanishes immediately thereafter. From this it follows that cost can never be realized; that which is rejected can never be enjoyed.

since the opportunity cost is the value of the next best alternative you can rigorously define as follows.
Suppose that for each action that actually was taken in the set $A=a_1,…,a_n$, there are alternative sets of alternative actions (e.g. each $a_i$, has some alternative $b_i$, $z_i$ and so on, and let’s assume that all the other alternatives are mutually exclusive with $a$. Well then opportunity cost of each action $a$ is just value of the next best alternative so if we have that:
$a_i\succ b_i \succ z_i … $
Then opportunity cost will simply be $V(b_1)$ where $V$ is simply just some function that assigns monetary value (or in consumer problem utility to $b_i$).
If you want to then put this value into profit function explicitly then simply the cost function will be some composite function given by $C(a_i, V(b_i))$ (note this is ultimately just function of $a_i$ because the next best alternative necessarily depends on what you choose as $a_i$, so in the end it’s just more complex way of writing $C(a_1))$
I think the above is rigorous even though it’s very simple (of course perhaps the notation I use could be made more precise).


Available code for computing solutions to matching algorithms? The question of designing matching procedure (between high-schools and students, med intern and hospitals, kidney donors and receivers,...) has been widely studied by economists and vastly contributed to Roth and Shapley receiving the Nobel memorial price in economics.

I was wondering if you knew about any freely available code out there (ideally in a relatively high-level language) able to compute solutions to the main kind matching problems for some of the most famous algorithms proposed in the literature. I am thinking of writing one, but I'd rather not it already exists.

I am chiefly interested in some piece of code to compute the solution to Deferred Acceptance algorithm in a school choice problem, but anything else would be appreciated.

While answering a comment, I realized I had a post-worth response. R has become the "default language" for a lot of computational research statistics (for a number of reasons; nice NYT article here). It's high level, free and open-source, and has a closely-related journal for publishing statistical algorithms. Citations and peer review are key for academia, so you get a lot of well-described code posted to the R archives (CRAN) with descriptions posted to JStat. This spills over into a lot of blogs and quick demonstration code posts.
That is to say, there's an enormous user-create code base for R. When I need to find an algorithm online, I'll often first look to the massive R codebase. A quick search for R code turned up the following:
From an R blogger, with code (see the gist link):

The Deferred Acceptance Algorithm (DAA) goes back to Gale and Shapley (1962). They introduce a rather simple algorithm that finds a stable matching for example for college admissions or in a marriage market. ... Variations of this algorithm are used in Hospital assignments in the USA, whereby recently graduated doctors submit preferences over hospitals, and hospitals submit preferences over graduates. ... Here I'm going to use R to make a little simulation of this

From an install-able github repository for matching markets:

R package matchingMarkets comes with two estimators:

stabit: Implements a Bayes estimator that estimates agents' preferences and corrects for sample selection in matching markets when the selection process is a one-sided matching game (i.e. group formation).

stabit2: Implements the Bayes estimator for a two-sided matching game (i.e. the college admissions and stable marriage problems).

and three algorithms that can be used to simulate matching data:

hri: Constraint model for the hospital/residents problem. Finds all stable matchings in two-sided matching markets. Implemented for both the stable marriage problem (one-to-one matching) and the hospital/residents problem, a.k.a. college admissions problem (many-to-one matching).

sri: Constraint model for the stable roommates problem. Finds all stable matchings in the roommates problem (one-sided matching market).

ttc: Top-Trading-Cycles Algorithm. Finds stable matchings in the housing market problem.

Functions hri and sri allow for incomplete preference lists (some agents find certain agents unacceptable) and unbalanced instances (unequal number of agents on both sides).

Hopefully one of these can help. The second one in particular looks extremely useful, particularly if it provides an empirical estimator.


Why do lenders dislike early loan repayments? I've frequently seen references in blogs and articles about how banks and other lending agencies like to refer to people who repay loans on an accelerated schedule as "deadbeats", because they get less interest out of that person.  Some institutions even implement early-repayment penalties in debt contracts, a practice that's been outlawed in some places.

But when I think about it, this doesn't make a lick of sense.  It seems to me that creditors should regard these "deadbeats" as their very best friends:

The lender gets their principal back ahead of schedule, improving their liquidity and making them able to loan it out again more quickly, should they wish to.
By reducing the principal outstanding, the amount at risk in the event of a default is reduced.
By demonstrating that the borrower has the ability to pay beyond the minimum, the risk of default is reduced.

What's not to like?

The reason that lenders dislike early repayments (known as "prepayments" or "voluntary prepayments") is that most lenders match their assets— the loans they've made to others— with liabilities of their own. This can lead to lenders facing significant interest rate risk. This is important to understand— while default risk is certainly significant, interest rate risk can be very large as well, sometimes greater than default risk.

Consider: a lender loans you money at 6.5% for 30 years to take out a mortgage, and funds this by issuing debt in the secondary market for 10 years at 4%. A recession comes along, the Fed drastically cuts interest rates, and the prevailing interest rate for mortgages drops to 3.5%. You repay your mortgage early by taking out a loan from another lender at 3.5%, and now the original lender has the principal back, but cannot reinvest it at a rate high enough to repay its own interest rate expense. If this happens on a broad enough scale, the lender is now bankrupt, with all that entails. That is why they don't like it.

With regard to prepayment penalties— the option to prepay debt is what is known as a call option, and it's often quite valuable. Prepayment penalties are simply a way for lenders to be compensated for the exercise of that option.

The specific case that you're talking about sounds an awful lot like the way that some credit card lenders feel about consumers who take out loans at low (often zero) "teaser" rates and refinance them before they ever have to pay anything to the lender, which bears its own interest expense in the meantime. That's probably best regarded as a strategy by consumers that takes advantage of lenders who are hoping that the consumers will not repay the debt in time. This hope on the part of lenders can sometimes cross the line into predatory behavior (see, for example, the discussion of teaser rates on mortgages in the Financial Crisis Inquiry Commission report), so the fact that the borrowers and lenders in such a situation aren't particularly fond of one another comes as little surprise.


Determining optimal consumption bundle The utility function of the consumer is $5x^{0.5}y^{0.5}$

The income of the consumer is $5000$

The price of good $x$ is $1,000$ and the price of good $y$ is $500$.

Determine the optimal consumption bundle.

Using the formula $\frac{MU_x}{P_x}=\frac{MU_y}{P_y}$ (1) I have derived the functions:

$MU_x = 2.5x^{-0.5}y^{0.5}$

$MU_y= 2.5x^{0.5}y^{-0.5}$

Substituting them into (1) gives:

$\frac{2.5x^{-0.5}y^{0.5}}{1000} = \frac{2.5x^{0.5}y^-{0.5}}{500}$

I'm not sure where to go from here?

Thank you in advance

I will only provide a general outline here since this is clearly a homework question.

You know that you should have, at an optimal point, that the marginal utility of each of your two goods is equal and so you can use:

$$MU_x=MU_y$$

You also have a budget constraint, yes? something like:

$$x+y=P_x(initial endowment of x) + P_y(initial endowment of y) + Income$$

Now you have enough equations to solve, I think. Isolate either x or y using your budget constraint. To be concrete here, I will assume you isolate x.

Take this representation of x and plug it in for x where you've equated your marginal utilities. This should allow you to solve for y in terms of exogenous factors. Take this representation of y and plug it back into $MU_x$. This gives both x and y in terms of exogenous factors.

So, all you are doing is equating marginal utilities and also using the budget constraint to express the optimal bundle (optimal amounts of goods x,y) in terms of exogenous factors.


Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve I am reading Modern Microeconomics by Koutsoyiannis. In a Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve.

Firm A produces half the total market demand to maximise revenue.

Further, Firm B takes A's output as given and operates on the left over demand curve eD' and produces 1/4th of output (AB).

Now Firm A in period 3 should respond by taking the leftover demand curve e'D' and produce $\frac{1}{2}$ of the leftover market that is $ (1 - \frac{1}{2} - \frac{1}{4})\frac{1}{2} = \frac{1}{8}th $ of total market output.

But it is mentioned

The temporal constraints (i.e. what happens in a period) are not very clear in this question. It is likely that the good sold is not a durable good and hence there is no "leftover demand" between periods, demand is simply 'reset'.

In period 2 leftover demand appears because firm B assumes firm A will not change its production from period 1.

Then in period 3 firm A will best respond to the unchanging production of firm B from period 2.


Job search theory in discrete time Let us assume that there is a labor who lives in discrete time universe and discounts future payoffs with the discount factor $b\in (0,1)$.

And we assume that this labor is at period $t=0$ at first.

Wages are assumed to have a discrete support defined as $W=\{4,16\}$. That’s, any wage offered by any company is either 4 or 16.

This labor has a job currently and the current wage is $w_t\in W$. If she wants to search for another job at period $t$, she has to incur a fixed search cost $k\in (0,4)$ per period.

If the labor wants to search for a job, either the labor takes the same wage as an offer from another company with prbability of $1/2$ or he takes the other wage level as an offer with probability of 1/2.

We Suppose that the labor consumes all of her wage income (I.e. net of the search cost) at any time $t$, and let the period utility from consumption is linear.

My question are

(1)Firstly, after defining the state, control variables and bellman equation, I would like to do an intuition that simply gives that the labor does not do job search
in period $t$ if $w_t = 16$ and then I want to calculate the value of this ”no search” policy.

(2) Secondly, I would like to show whether the following policy is optimal. “Search in period $t$ when $w_t=4$ and do not search in period $t$ when $w_t=16$. How can I explain why is this?

——

My solution attempt is

The labor wants to maximize $E_0\{ \sum_{t=0}^{\infty}b^t c_t\}$

And if the labor does not want to search for a job, then $c_t=w$ but if the labor want to search for a job, then $c_t=w-k$

Let $F(w)$ is i.i.d. distribution.

The bellman equation for searching for a job and don’t search for a job are given by

$W(w)=w+bW(w)$

$U= (w-k)+b\int_0^{\infty} \max \{U, W(w)\}dF(w)$

where $W(w)$ is payoff from accepting a wage $w$ and $U$ is payoff from searching a wage offer, earning $w-k$ and sampling again next period.

Then when I calculate the equations,I obtain that $W(w)=w/(1-b)$ which is strictly increasing in $w$. So, the reservation wage $w_R$ such that $W(w_R)=U=w_R/(1-b)$. Then the labor sohund accept if $w\ge w_R$ and doesn’t accept if $w<w_R$.

And I obtain that $w_R=(1-b)(w-k) b\int_0^{\infty} max\{w_R, w\}dF(w)$

I cannot proceed after that point. Please help me to do this question. Thanks a lot.

$W(4) = \max\left\{4+bW(4),\frac{1}{2}\left(4 - k + bW(4)\right) + \frac{1}{2}\left(16 - k + bW(16)\right)\right\}$

$W(16) = \max\left\{16+bW(16),\frac{1}{2}\left(4 - k + bW(4)\right) + \frac{1}{2}\left(16 - k + bW(16)\right)\right\} = 16+bW(16)$

First solve for $W(16)$ to get $W(16) = \frac{16}{1-b}$. Then substitute it in $W(4)$ to solve for $W(4)$ as a function of $k$ and $b$.


Are cryptocurrencies a ponzi scheme or a bubble? Several users in this forum have addressed bitcoin and other cryptocurrencies as ponzi schemes. Bitcoins have several uses which could legitimate its value as a currency, but also have received massive investments in the last months, making it considered a highly speculative asset. Are there signs and information that proves that cryptocurrencies are being used as a (intentionally fraudulent) scheme, or should we consider it a speculative asset similar to other assets in economic bubbles that happened before?

In general, "Ponzi schemes" in the context of asset pricing refer to "rational bubbles", or a failure of the transversality condition you need when passing from a flow identity to a present value identity. They are not "fraudulent schemes". For instance, there can be a rational bubble on a "fundamentally" worthless asset in a perfect foresight world if its price grows at the real interest rate available in the broader economy. (This is actually what you're talking about, in case it's not clear to you - each investor assumes they can offload the asset at a higher price to another investor, and you push the problem of the "greatest fool" to infinity, which makes the assumption a rational one ex post.)

Is there any evidence for the existence of such rational bubbles? Cochrane (2002) points out that rational bubble theory does not account for the association of "bubbles" with high trading volume. In a rational bubble, it is rational to hold the asset in every period: there's no reason to observe high turnover along with high prices. They are also silent on the association of high prices with high volatility - in a rational bubble context, volatility (induced by shifting from one equilibrium to another) is always present, and the choice of equilibrium (the fact that we're on an explosive price path) does not produce more volatility than usual. Rational bubbles appear to be a poor explanation of events that people have historically described as "bubbles" (and of the price behavior of cryptocurrencies).

In contrast, the convenience yield theory outlined in Cochrane (2002) and also in this blog post seems to fit the data much better. If "overvaluation" is driven by a liquidity premium induced by shorting constraints and a short-term constraint on supply, then we would expect to see the standard prediction of monetary economics that high prices should be associated with high turnover. In that case, overvaluation relative to "fundamentals" should also require shorting constraints - in the case of dollars vs treasuries, for instance, it's illegal to print banknotes or close substitutes to money to finance a purchase of bonds, which is a kind of shorting constraint. Indeed, shorting constraints are what we see in the cryptocurrency market: BTC futures have only recently started trading on stock exchanges, and even then the "electronic paper" that you hold when you take the long side of a BTC futures contract is not the same thing as holding BTC directly, so what appears like a possibility to short BTC through these contracts is in fact not so. (It satisfies "speculative demand", so it's possible to "bet on cryptocurrencies" without having to hold any, but it's not possible to use these contracts in the place of cryptocurrencies in transactions.)

If you want to ask whether cryptocurrencies are a bubble, then you have to define what "bubble" means. If it is "overvaluation relative to fundamentals", then is USD a bubble? After all, it's trading at a premium relative to T-bills. If you include any convenience yield the asset may have in your definition of "bubble" so that USD is not one, then it's likely that cryptocurrencies are not "bubbles" either. It's very difficult to say anything about whether cryptocurrency valuations are "justified" or not by this explanation, since the convenience demand of cryptocurrencies, like of cash, has components which are not transparent. We're mostly in the dark, and I wouldn't try to outguess the market price of an asset in a circumstance where we know next to nothing about the factors which are driving the convenience demand for it.


Moderation effect of a variable Should we include some control variables in regressions when we test a moderation effect of a variable?

Without additional information, it is hard to answer your question but I would say that a moderation model is like any econometric model (and in fact, it is an econometric model).

Therefore, I would tend to agree with @Student, adding control variables is a good idea but it must represent your theoretical considerations (is there an omitted variable bias, a confounding variable, etc ?). So you should only add relevant variables to your model in order to increase its precision.

Just adding random/useless variables will unnecessarily increase the complexity of your model; and as my econometrics professor used to say: "why use a bazooka to kill a fly when you can use a fly swatter ?"

Edit: I (scholar) googled "moderation effect economics" and I randomly chose a paper published in a good journal, you can see that they also use relevant control variables (p. 512).


How does everyone not become poor over time? Look at the whole world --the union of all goods and services and workers and customers. Everyone who is a customer is a worker somewhere (they had to get the money to be a customer somehow). But not all revenue goes toward worker wages--some goes to cost of goods--production, not just labor. And considering the whole world--it's a closed system...so if everyone pays Z in as a customer--they lose X to cost of goods and are paid out up to Z-X as workers -- then, when they are next customers, next round of purchasing, Z-X goes back in as rev and Z-2X comes back to everyone... keeps going. You lose cost of goods each round of purchasing.  you need X more from customers to sustain this--which means you need  to keep injecting X from outside or have more customers than workers. But where do these injections come from if we are accounting for all goods and services? Or where is this larger set of customers who are not also workers? Where does their money come from if not from work? Elderly, children and those who do not work also derive their money from this cycle--they were workers, will be workers or live off a % of workers' wages from taxes or friends and family.
The answer is presumably wealth or value creation but how is this integrated into the cycle of workers and customers so that Z grows instead of shrinks?
Economic novice--thanks!

In short because economy is not a zero-sum game and because economic production does not need to decline but  can grow over time.
First of all, forget about money. Money in economics is just extra tool that solves issue of double coincidence of wants, allows you to store value over time and to do accounting. In fact, traditionally money consisted of commodities such as stone, or precious metals or even products, coffee, cigarettes or even alcohol etc at some point in time and place served as money.
As a non-economist this might come as a surprise to you but most microeconomic models do not even have money in them. Money can play an important role in macroeconomic perspective because in the short-run it can affect the real economy, but from micro perspective and even long-term macro perspective money is neutral and not important.
Next, as you pointed out a world's economy, taken as whole, is a closed system but that does not mean people should get poorer over time. This is not an equivalent of thermodynamically closed system where entropy has to dissipate energy overt time. A closed economy can be described as:
$$Y  = C + I + G$$
which says that output/income (they are economically equivalent) $Y$ has to be equal to consumption $C$, investment $I$ and government spending $G$. In turn, $Y$ is a result of production. A common specification for production process would be to use Cobb-Douglas production function, so I will do that here as well, although in principle there could be multiple functional forms that production process could have. Moreover, for simplicity I will restrict myself to two factors of production (labor and capital) even though in principle you could put into Cobb-Douglas also human capital (education), land and other factors, but I omit them for sake of brevity. Given these assumptions the production process would be given by:
$$Y = A K^{\alpha} L^{\beta}$$
where $A$ is the available technology (broadly defined - in economics better production strategies count as a technology as opposed to just 'gadgets' such as PC), $K$ is the stock of capital and $L$ is the stock of labor. Alpha and beta are parameters of the production function that determine other characteristics of production such as what sort of economies of scale production exhibits (e.g. increasing, decreasing or constant).
Thus, we can say that the consumption, investment and government spending is equal to this production process:
$$ A K^{\alpha} L^{\beta} = Y  = C + I + G$$
So as long as technology $A$ or capital $K$ or labor grows, output $Y$ will grow as well and even completely closed of economy can consume more, invest more or have more government spending.
Furthermore, what we really care about is usually output/income (in economics output and income are equivalent and interchangeable) per head. So if we for simplicity assume constant returns to scale ($\beta = 1-\alpha; 0 <  \alpha < 1$)  we can divide the last expression by $L$ to get whole expression per capita as:
$$A \left(\frac{K}{L}\right)^{\alpha} = \frac{Y}{L} = \frac{C}{L} + \frac{I}{L} + \frac{G}{L} $$
Here, if we keep the population growth constant then we can see that per capita incomes/output and consequently per capita consumption, investment and government spending will grow when our capital stock and technology stock grows. You get growth in capital stock from investment (investment is part of production that is not consumed but saved for future, possibly for further production), and growth in technology from human ingenuity or also depending on which economic growth theory you buy to also investment.
In addition, all the above is up till now just manipulation of definitional expressions. We could further continue by adding on some growth theory which could yield further insights. For example, the most popular growth model presently is the Solow-Swan growth model where it can be shown that what really matters is growth in $A$ because increase in investment and capital stock can only increase level of output not growth. If you buy into endogenous growth theories investment can even increase the growth rate further beyond that (you can read more on this in Barro & Sala-i-Martin: Economic Growth 2nd ed).
In order for people to get poorer over time (in per capita terms) an economy would have to experience either destruction of technology (for example ancient Romans, Greeks, Carthaginians etc had plumbing but this knowledge was lost in many parts of World - but not all - during dark ages, or another example would be concrete) or by destruction of capital (e.g. war, violence, natural disasters etc. but also just wear and tear i.e. depreciation). Empirically, and let me add thankfully, people historically turned out to be better at producing new technologies and adding new capital through investment, than at destroying either of them.
Consequently, to sum up people do not get poorer over time and in fact get richer because of growth in economic production (which in turn determines people's income), and economic growth occurs primarily thanks to growth in technology and investment. In fact note because the economic growth is to large extent driven by technology, it is possible for economic production to grow indefinitely (assuming technology has no limit - e.g. in real life it is possible you can't get at an end of technology tree like in some strategy game as it might have no end). In addition, more rich models would also include other important factors such as human capital (education) but the explanation above would not conceptually change (education macroeconomically functions in same way as capital - hence why economists call it human capital).


Discounting terminology confusion An example of the terminology that surrounds discounting that confuses me can be found in "Investment and Hysteresis" by Dixit:

Let future revenues be discounted at a positive rate $\rho > 0 \ldots$ Then, given a current level $R$ of revenues, the expected present value of the discounted future streams of revenues is $R / \rho$.

Hence, the net present value of the investment is quantified as $R/\rho - K$, where $K$ is the sunk cost.
What I would like to understand is what this formulation has to do with exponential discounting; in particular, where is the sum over the time periods (alluded to in the phrase "future revenue streams", but also made clear in the context of the paper)? Is this some kind of economist shorthand?
This matters because, as far as I can see, he uses the exact expression above for the NPV in the key derivation in the paper, which suggests to me that I've misunderstood his concept of "discounting".
(This notation is not unique to this paper: I've encountered this in several places; cf. Allcott and Greenstone "Is there an Energy Efficiency Gap".)

Well this is 'exponential discounting'. An infinite sum of geometric series:
$$\sum R+ R\delta + R\delta^2.... R\delta^t = \frac{R}{1-\delta}, \text{ if } |\delta|<1$$
Now lets call the denominator rho $1-\delta= \rho$.
The exponential discounting is there since its an infinite sum of geometric series.
Edit: In response to Giskard's +1 comment I tried to look deeper into the paper and while I think that the Dixit is actually implying the above and just not being clear on terminology it is also possible that he means simply net present value of infinite constant stream as:
$$\sum \frac{R}{(1+\rho)^t}= \frac{R}{\rho}$$
However, I think the former interpretation is the right one because its more closer to how discount rates are treated in some other papers I have seen and I think he was just sloppy with terminology.


Elasticity of Durable Goods vs Non-Durable Goods Does anyone know any seminal reference (either a paper in a top economics journal or a book) that compares own-price elasticities of demand for durable vs non-durable goods?

My intuition tells me that durable goods should be more elastic ... but not sure how to defend that statement without a reference.

Edit:

As requested I added some more content to the question. However, the question trying to find an answer to is merely an empirical question and therefore I do not have a specific model in mind. To be slightly more precise:

Consider a demand function for good $i$: $P_i = f(Q_i, X_i)$ where $P_i$ is the price of good $i$, $Q_i$ is the quantity and $X_i$ are other factors that influence demand. What I am looking are empirical estimates for $\frac{\partial Q_i}{\partial P_i} \frac{P_i}{Q_i}$ for two sectors: durable goods and non-durable goods. Now usually there is a problem in estimating this elasticity given the standard endogeneity problems. However, there are methods that have been used to disentangle such quantities. Two examples are: Berry,Levinson and Pakes (1995) and Broda and Weinstein (2004).
There are few anecdotal evidence of differences in elasticities for durable and non durable goods. One example taken from here is:

Duration of price change: For non-durable goods, elasticity tends to be greater over the long-run than the short-run. In the short-term it may be difficult for consumers to find substitutes in response to a price change, but, over a longer time period, consumers can adjust their behavior. For example, if there is a sudden increase in gasoline prices, consumers may continue to fuel their cars with gas in the short-run, but may lower their demand for gas by switching to public transportation, carpooling, or buying more fuel-efficient vehicles over a longer period of time. However, this tendency does not hold for consumer durables. The demand for durables (cars, for example) tends to be less elastic, as it becomes necessary for consumers to replace them with time.

But this is not an sufficient academic reference which is what I am looking for.

For the theory, House (JME several years ago), Barsky, House and Kimball (AER, circa 2006) Barsky, Boehm, House, and Kimball (working paper on SED website).  Johannes Wieland has a new paper on this, maybe not yet available.

The key theoretical point (put somewhat loosely) is that purchases of an "idealized durable", one with a very low depreciation rate, should have a near-infinite intertemporal elasticity of substitution.


Why is collective bargaining by a group of employees not the same thing as price-fixing? Employees sell their labor for wages. If a critical mass of employees get together and demand higher wages, how is this not the same thing as a critical mass of merchants illegally fixing the price of some commodity?

Can't a strong union be considered to have an illegal monopoly on labor?

This is more of an elaboration of The Almighty Bob's answer:

It is true that if we start from a competitive market (i.e. large numbers of buyers and sellers), then granting market power to sellers (e.g. workers) by allowing the formation of a monopolistic cartel is bad for efficiency. Those sellers will use their market power to increase the price (and reduce the quantity traded), resulting in a deadweight loss. Thus, we tend to look suspiciously upon practices that create market power. Note that here, the policy intervention we have in mind is to break up the cartel and return us to a competitive world.

Why should the labour market be viewed differently? Part of the answer is that the relevant counterfactual has changed. Begin with a world without labour unions. The market will then typically not be competitive because there are often a small number of employers who themselves enjoy market power. Just as a monopolist seller can drive up the price, these monopsonistic (or oligopsonistic) buyers of labour can use their power to drive down the price.

Now we are faced with the following policy problem:

  How can we correct for employers' market power and restore wages toward the (higher) efficient level?

Two simple solutions come immediately to mind:

Reduce employer's market power by stimulating competition between employers. This is achieved, to some extent, by antitrust policy. But it's hard to do much more here short of forcing more businesses to hire more workers.
Allow workers to form unions so that both workers and employers have market power. If the firms try to use their power to drive wages down and the workers use it to drive them up then there is a sense in which the two will 'cancel out' and the result can be closer to the efficient wage than a market in which only employers have market power.

Whether the second solution indeed works or not depends upon a whole range of factors. Here are a few:

If the employer side of the market is, in fact, quite competitive then the correction will likely be too big and we will end up with wages that are inefficiently high.
If bargaining is very costly then it might be more efficient to have one side (e.g. the employers) unilaterally set the wage.
If there is uncertainty about the wage that firms are willing to pay/workers are willing to accept then bargaining may inefficiently break down (see the Myerson-Satterthwaite Theorem).


What's the difference of economic capital and liquidity buffer? Economic capital is what for example a bank has and uses in order to stay solvent. Isn't this in a way a liquidity buffer? or what would be the difference between them?

Different sides of the balance sheet.

Capital represents long-dated instruments (infinite lifetime in the case of common equity) issued by a bank that are subordinated in a way to make them comparable to equity. (Can include instruments that are technically liabilities.) The existence of capital means that assets are greater than non-capital liabilities, i.e., the bank remains solvent.
A liquidity buffer are assets that are deemed liquid, which means that they can be readily sold at prices near carrying value to meet payment requirements. Note that a solvent entity that only holds hard-to-liquidate assets may be unable to meet a sudden payment obligation. That is, it is solvent, but illiquid.


What are the economic justifications of the size premium? What are the economic justifications of the size premium?

In factor pricing models like the intertemportal capital asset pricing model (I-CAPM) or arbitrage pricing theory (APT), it is assumed that exposure to one of these factors represent exposure to some sort of undesirable risk. In this question, I'm trying to understand how to interpret exposure to size (measured by market capitalization) as exposure to some form of common risk.

This question is related to this question about momentum: "How is momentum justified as a common risk factor?"

The following are NOT my words. Found this online. Please check full article here:

http://www.multifactorworld.com/Lists/Posts/Post.aspx?List=3b285530-ccfa-416a-ba3b-de55213abe17&ID=59

Hope this helps...

Size Premium: Why Does it Exist?
There seems to be general agreement that the size premium is a reward for bearing the risk that small companies may do poorly in bad economic environments. For example, compared to larger companies smaller companies may not be able to easily obtain credit in such environments. Bankruptcy risk is also typically a bigger risk for smaller companies in tough economic environments and in general. It could also be that some portion of the size premium is a reward for bearing the liquidity risk of small stocks compared to large stocks.


Is there any academic paper documented about firms' trade credit collection approach? I am looking for some papers that documented some trade credit collection approaches, especially when the market becomes more competitive. In another word, what should the managers do to improve the efficiency in collecting the account receivable?

My hit from Google Scholar (had to go to the bottom of page 1 for this one!) is
Macro-Economic Growth,Enterprise Competitive Status and Trade Credit Policy
Abstract:

This paper investigates the effect of macro- economic growth and enterprise competitive status on trade credit policy from suppliers with trade credit's perspective,and the moderate effect of industry characteristics. The study indicates that: The higher the competitive status,the shorter the trade credit collection period to downstream enterprises,while this relation is not obvious among enterprises in less concentrated industry; When macro- economic grows fast,regardless howconcentrated industries that enterprises are located in,enterprises with higher competitive status are more prone to reduce the account receivable collective period; With further considering industry characteristic,the effect of macro- economic growth and competitive status of enterprises on trade credit policy shows significant difference in the quadrant formed by different industry prosperity and concentration.


Credit risk of interest rate on excess reserves vs fed funds rate? I noticed that the interest rate on excess reserves and the fed funds rate are almost exactly the same at all times. Why is this the case? Shouldn't the credit risk of a bank be higher than the Federal reserve and shouldn't this premium be reflected in the Fed Funds rate?

Actually the IOER has slightly exceeded the Fed Funds rate in recent years.  Currently IOER is 10bp and FF last set at 8bp for example.  During the period 2009 to 2015, IOER was set at  25bp and FF averaged about 13bp.  So what is going on? The FOMC sets IOER as a matter of policy , but FF is set by supply and demand for overnight loans between financial institutions in the Fed system.  In this era of excess reserves , many financial institutions have excess cash, so the problem is to lend it at the best rate.  The problem is that not all institutions can access IOER, because it is for depository banks only , so there is additional cash to invest held by others, such as the Federal agencies (home loan banks) for example.  They invest in overnight Fed funds, driving the rate down below IOER.  A bank could (and some do) borrow at these lower rates to invest in IOER, locking in a few bp.
Thus, the spread is driven by considerations of supply and demand rather than credit risk.


marginal utility of consuming vs marginal rate of substitution good day all

I am taking second year economics, but my textbook is not very clear on this topic

A quoted from

  Intermediate Microeconomics and Its Application. Nicholson, Snyder. 11th Edition.

Used in question: 2 Extracts from textbook, 1 text and 1 graph:

  Indifference Curve Used as reference:

  Text Extract

Tutorial Question given by university:

My question:

From the extract, I understand that the MRS is determined by the change in hamburgers / change in softdrinks which gives MRS = |2|.

From my tutorial question, slightly different terminology was used ("consumption"), which resulted the answer shown.

I do not understand why the answer for the tutorial question is 1/5 and not 5 (based on the example from the book).

Help would be very much appreciated!

This is because the question is asking the MRS of soda for hotdogs not the MRS of hotdogs for soda.

i.e

$MRS(MU(soda),MU(hotdogs))=MU(soda)/MU(hamburgers)= 2/10=1/5$ To get 5 you need to solve the MRS of hotdogs to soda $MRS(MU(hotdogs),MU(soda))=MU(hamburgers)/MU(Soda)=10/2=5$

Hope this helps.


Controlling for interaction effects In a recent paper, Edelman et al. examine (amongst other things) how discrimination on AirBnB varies with the characteristics of hosts. First, they conduct a field experiment which involves sending a large number of fictitious applications, some of which are associated with African-American names and some of which are not. Then, they regress whether an applicant is accepted on the guest race, a host characteristic and the interaction. For example, they regress acceptance on guest race, host race and the interaction of the two. The idea is that if African-American hosts (for instance) are less likely to discriminate, then the coefficient on the interaction term should be non-zero since the effect of receiving an application from an African-American should depend on whether the host is African-American.

So far, so good. However, given that host characteristics are not randomly assigned, we should control for them. Otherwise, we might find that African-Americans are less likely to discriminate even though the real explanation is that they tend to offer expensive properties, and people who offer expensive properties are less likely to discriminate (made up example to illustrate the point). They seem aware of this, since they throw in various host and location characteristics as controls. But wouldn't it have been better to use the interactions of these covariates with applicant ethnicity as the controls? After all, we want to control for the fact that people with certain characteristics might respond to African-American applicants differently, and this means controlling for interaction effects.

I leave for another thread the issue "What is the justification of using the arithmetic operation of multiplication and so the product of two variables in order to model the concept of interaction?"

Practically, product-terms come from the tradition of the Translog regression specification, which is a second-order approximation to any actual specification, and produces such products.
They are therefore considered "second-order" effects, meaning that they are included in a specification alongside the stand-alone variables. This means that their importance is judged after the effect of the stand-alone variables has been taken into account.

I have not seen in the literature a situation where "interaction terms" are included alone, without the stand-alone presence of the two variables forming the product.

So for the specific study mentioned by the OP, conventional practice would ask "why not include also interaction terms?"

Nevertheless, it appears intriguing to argue convincingly that in a certain case, we should only include the "interaction term" of two variables.


What is an example of a choice which is not necessitated by scarcity? I am first year economics student and for the past month we have had it constantly drilled into us that all choices have an opportunity cost and thus they are all necessitated by scarcity. Thus when I saw this quesiton in my homework I was baffled.

I don't need an exact answer to this, but a hint would be great. My current line of thinking is leaning towards infinite resources like the sun, but I simply can't work it out. Thanks.

The basic idea behind scarcity and opportunity cost is fundamental to economics. Basically, if resources are infinite, you have everything.

In my opinion, there are no infinite resources because a lifetime is finite. In one way or another, it can be argued all choices are necessitated by scarcity.

Eating chips means at that time, you cant be eating a burger. That is your opportunity cost.

This may be the point of your homework question, to make you realise that scarcity is a key driving force behind decision making.


What is supply-side of economics? I've got a question for economics that I need help with, here is the question:

"What is meant by the supply side of economics? Define the term ‘supply’ in the context of economics and explain the factors from which it is derived."

I have answered it though but I don't understand this part in the question "Define the term 'supply' in the context of economics and explain the factors from which it is derived."

If you could help me with that, I would appreciate it.

Here is what I have answered already:
"Supply-side of economics is a theory that is built upon the concept that an increase in goods and services will increase output while also lowering prices and lead to economic growth. When companies overproduce goods, they create excess inventory which results in the prices falling and consumers buying more to offset the excess supply.
It is called “supply-side economics” because it focuses on how and what the government is able to do to increase the overall supply of goods and services created in the economy."

The principle supply-side policies that are currently advocated are reductions in tax rates on labor and capital income.  Its claimed that lower tax rates on wages, interest, dividends and corporate income will increase output by increasing the incentives to work, increasing in the supply of labor.

https://www.philadelphiafed.org/-/media/research-and-data/publications/business-review/1981/br81mjap.pdf?la=en

While supply-side economists expect a little government regulation of the free market, demand-side economists expect a more active government.

Supply-side works by giving incentives to businesses to expand. Deregulation removes restrictions on their growth.

A corporate tax cut gives businesses more money to hire workers, invest in capital equipment, and produce more goods and services.

An income tax cut increases the dollars per hour worked. It boosts workers' incentive to remain employed and creates more labor.

the supply-side premise is that an increase in supply (i.e. production of goods and services) will increase output and lower prices.


What exactly is L in a Cobb-Douglas production function? Cobb-Douglas is $Y = AK^{1-\alpha}L^{\alpha}$.
What exactly is $L$ in Cobb-Douglas? Is $L$ the number of workers available in a single year? Working hours?

It can be both. The number of working hours are of course easier to interpret. You can also make the assumption that every employee works some fixed number of hours, say 8 per day (or 220 per month, or 38 a week, etc). In this case if you denote by $n$ the number of workers and $L$ the number of hours worked you have of course
$$
n \cdot 8 = L
$$
and then
$$
A \cdot K^{1-\alpha} \cdot L^{\alpha} = A \cdot K^{1-\alpha}  \cdot ( n \cdot 8 ) ^{\alpha} = 8^{\alpha} \cdot A \cdot K^{1-\alpha}  \cdot n ^{\alpha} = \left(8^{\alpha} \cdot A\right) \cdot K^{1-\alpha}  \cdot n ^{\alpha}.
$$
So you can choose $L$ to represent either quantity as long as you take it into consideration when choosing/calibrating $A$.  (Provided that some conditions like $n \cdot 8 = L$ hold or are a reasonable approximation of reality.)


Why is the price of books set by the manufacturer rather than the distributor? For almost all manufactured goods which the manufacturer doesn't sell directly to the end consumer, the manufacturer sells to a distributor, and the distributor is then free to resell the good to the consumer at whatever price she wants (although of course if the distributor wants to stay in business, then the final price will be primarily set by market forces).

But the market for books is an exception: the manufacturer (i.e. the publisher) physically inscribes the sale price directly onto the manufactured good. The distributor (i.e. the physical or online bookstore) can offer a "discount" and sell it at a lower price than the prescribed one, but can't reasonably sell for a higher price for reasons of consumer psychology. I can't think of any other good which uses this strange business model. It seems to deprive the market of pricing flexibility to adapt to e.g. regional variations in demand, transportation costs, etc.

Of course, the market for books is very distinct from a standard market described in microeconomics textbooks, because so much of the value of the book comes from intellectual property rights rather than from physical resource and manufacturing labor costs, which makes it more like a monopoly than a competitive market. (Moreover, depending on how the author's compensation is structured, the publisher may face very high fixed costs.) But on the other hand, other markets like video rentals seem similar in that respect, but the movie studio doesn't set the sales price - the video distributor does, as in a standard market.

Why is the market for books so weird?

It’s the manufacturer’s suggested retail price (MSRP); manufacturers cannot dictate the final retail price. Any manufacturer that has a catalogue or a website has a suggested retail price.

If retailers want to sell at a higher price, they just slap a price sticker over the MSRP. From what I recall, this was standard practice back in the 1970s-1980s, when inflation was more of an issue.

The point of negotiation between publishers and distributors is the discount from the MSRP the distributor gets the books at. This discount is normally fixed for the entire line of books; they are not going to negotiate prices on a per-title basis. (Some best sellers might have special negotiations.) The retailer will then set prices relative to the discount received. Since the default is to sell at the MSRP, it can save booksellers the expense of putting on their own price stickers.

Why are books different? Well, go into a bookstore and count the number of unique products on 10 feet of floor space.

Other differences include:

Unsold books can be returned, which is unusual. This was a desperation measure that publishers resorted to in the Great Depression, which they never managed to undo. This means that most books have a limited shelf life, so inflation affecting the MSRP is less of an issue.
Books can be special ordered at book stores. The order price is going to have to be the MSRP.


What caused "excess liquidity" in equity market, when CPI was deflationary at the same time period, which caused 'market crash in 1929' in USA? To begin with, my question is NOT about the reasons of "the great depression" or "market crash" which led to the great depression.

Rather, my question is about the reasons for the 'excessive cash liquidity' which resulted in 'market crash in 1929'.
Traditional patterns tends to reflect cash liquidity distribution somewhat even across different sectors. How liquidity during 1920's in USA stands different was that, the sectors like Consumer Price Index is constantly DEFLATIONARY in the same decade when share market(and only share market) was extremely inflationary.

1970's : CPI inflationary : Other sectors inflationary(caused bubble burst)

1990's : CPI inflationary : Tech market inflationary(caused bubble burst)

2000's : CPI inflationary : Housing market inflationary(caused bubble burst)

1920's : CPI DEFLATIONARY : Equity market inflationary(caused bubble burst)

To simplify, my question is, what caused 1920's stock market inflation(presumably due to excessive liquidity) at the same time period when CPI was DEFLATIONARY(enough money was not present/spend in sector).

I am not educated in economics. I follow the subject only because it interests me. I work in a totally different field of study and thereby please excuse my ignorance about the subject for where ever I went wrong :).

thanks in advance.

The inflation data provided are not useful in this context. The average inflation shown is a mixture of the outcome of a post-WWI deflation, recovery, and price stability. One would need to look at more specific periods. FRED CPI data

Equity prices are supposed to equal the discounted value of future earnings/dividends (the dividend discount model). This means that fair value is highly sensitive to expectations about the future. The 1920s was a period of economic dynamism, where many large firms using new technologies became dominant. It is completely unsurprising that stock prices rose during the expansion.

The linkage between monetary tightening and stock prices is a standard feature of Austrian economics and/or financial market commentary, but it is not widely respected among other economic theories.


Do capital goods have to be valued so that (discounted) real expected return on capital goods equal current present value of capital goods? Let $P_k$ be the value of 1 quantity of a capital good. If one does not sell the capital good and keep it, the good provides interests.

In such a case, does standard macro say that all expected discounted real expected returns (or net present value of all future and present returns) be equal to $P_k$?

Here is a somewhat standard presentation that might be taught in intermediate macroeconomics at US universities.

Let $p_t$ be the price of a unit of capital at the end of period $t$. Suppose that production takes place at the start of each period. After production takes place, depreciation occurs. Let us say that the depreciation rate is constant at $\delta$. Let us also say that the real interest rate across any two consecutive periods is $r$. Assume also that the price of each unit of output is equal to $1.

If so, we would expect that

$p_1=\frac{1}{1+r}[MP^k_2+(1-\delta)p_2]$.

This has a nice interpretation. The price of capital at the end of period 1 equals: The present discounted value of the additional output it can give us at the start of period 2, plus the after-depreciation resale value of that unit of capital at the end of period 2.

We can write down an analogous expression for $p_2$:

$p_2=\frac{1}{1+r}[MP^k_3+(1-\delta)p_3]$

Now substitute this latter expression for $p_2$ into our first equation above, to get:

$p_1=\frac{1}{1+r} \left\{ [MP^k_2+(1-\delta)\frac{1}{1+r}[MP^k_3+(1-\delta)p_3] \right\}=\frac{1}{1+r}[MP^k_2+\frac{1-\delta}{1+r}MP^k_3+\frac{(1-\delta)^2}{1+r}p_3]$

This last expression has again a nice interpretation. The price of capital at the end of period 1 equals: The present discounted value of the additional output it can give us at the start of period 2, plus the additional output it can give us at the start of period 3, plus the resale value of that unit of capital at the end of period 3.

If we keep going, plugging in expressions for $p_3$, $p_4$, ..., eventually we'll find that

$p_1=\frac{1}{1+r}[MP^k_2+\frac{1-\delta}{1+r}MP^k_3+(\frac{1-\delta}{1+r})^2MP^k_4+(\frac{1-\delta}{1+r})^3MP^k_5+\dots]$

This has the desired result: The price of a unit of capital today is simply equal to the present value of the future stream of income that this unit of capital will generate, appropriately taking into account depreciation.

This generalizes to a broader principle employed not just in standard macroeconomics but in the real world too: The price of any asset should be equal simply to the present value of the future stream of income that the asset will generate.


Moral Hazard with risk neutral agent We have a principal-agent model with hidden actions in which the principal is risk averse and the agent is risk neutral; Assume also there are two levels of output, $x$ and $x'$ (with $x'>x$) and two actions $a,a'$. Define $p(a),p(a')$ the probabilities of $x'$ under actions $a,a'$ respectively. Also, the agent disutility from action $a'$ is $-1$. The wages associated to $x,x'$ are $w,w'$ respectively.

My problem is that I am not sure how to show that the optimal contract requires $x'-w' =x-w$, i.e. that the agent, being risk neutral, takes on all the variability associated with the project.

I formalize the problem (assume the principal wants to induce $a'$, otherwise my question is trivial)

$\max\limits_{\{w,w'\}} u(x'-w')p(a') + u(x-w)(1-p(a'))$

st

$w'p(a') + w(1-p(a')) - 1 \geq 0 $

$w'p(a') + w(1-p(a')) - 1 \geq w'p(a) + w(1-p(a))$

In particular, when I try to solve the problem by maximizing the principal expected payoff subject to the "standard" Individual rationality (with $\lambda$ multiplier) and incentive compatibility (with $\mu$ multiplier) constraints (I assume the principal is interested in the more costly action $a'$) I end up with two equations which are not consistent with the aforementioned result. In particular:

$ u'(x-w) = \lambda + \mu [1- \frac{(1-p(a))}{(1-p(a'))}]$

$ u'(x'-w') = \lambda + \mu [1- \frac{p(a)}{p(a')}]$

It is evident that $x-w = x'-w'$ holds iff $p(a) =p(a')$ which is not the case in this problem (here we have that $p(a') >p(a)$). Another possibility would be to assume that the Incentive compatibility constraint is slack (hence $\mu = 0$); however I cannot understand why that should hold, when the principal wants to induce the most costly action $a'$ (help here)

I have read online that another approach would be to assume that the principal "sells" the project to the agent and the agent, after having chosen which level of effort maximizes its expected utility, pays back a fixed amount to the principal (call it $\beta_{a}, \beta_{a'}$)

So we would have something like:

$w'p(a') + w(1-p(a')) - 1 -\beta_{a'} \geq 0 $
if the agent chose to undertake high effort and
$w'p(a) + w(1-p(a)) -\beta_a \geq 0 $ otherwise.

But then how to go from there? How to insure that the agent is going to choose the action $a'$? How are the fixed amounts determined? Why are they optimal?

A thing that bothers me here is the following: the Incentive Compatibility constraint is

$$IC: w'p(a') + w(1-p(a')) - 1 \geq w'p(a) + w(1-p(a))$$

$$\implies w'-w \geq \frac {1}{p(a')-p(a)}  \tag{1}$$

...since by assumption $p(a')-p(a) >0$. We are told that we should find that at the optimum,
$$x'-w' = x-w \implies x'-x = w'-w \tag{2}$$

Combining $(1)$ and $(2)$, if indeed this is the optimum under the given constraints, we must also have

$$x'-x \geq \frac {1}{p(a')-p(a)} \tag{3}$$

But this is an additional, necessary constraint on a priori magnitudes, that must hold if the postulated optimal solution is to be admissible. Even if indeed such a constraint is assumed, in any case, it visibly reduces the generality of the problem (which purports to show something general, i.e. how the risk-neutrality of the agent affects the solution).

Nevertheless, let's work this a bit more formally. I will assume that $w, w'$ can be zero, but not negative. This is a maximization problem in normal form with inequality constraints, non-negative decision variables and non-negative multipliers. The full Lagrangean of the problem therefore is (I will compact notation in an obvious way),

$$\Lambda =  u(x'-w')p' + u(x-w)(1-p') + \lambda\cdot [w'p' + w(1-p') - 1 ]\\ + \mu \cdot [ w'p' + w(1-p') - 1 - w'p - w(1-p)] + \xi w + \xi' w'$$

The essential first order conditions are

$$\frac {\partial \Lambda}{\partial w} \leq 0, \;\;\frac {\partial \Lambda}{\partial w} \cdot w = 0$$

and analogously for $w'$. These result in

$$\frac {\partial \Lambda}{\partial w} = -u'(x-w)(1-p') +\lambda (1-p') - \mu (p'-p) + \xi \leq 0$$

$$\implies u'(x-w)(1-p') \geq \lambda (1-p') - \mu (p'-p) + \xi $$

$$\implies u'(x-w) \geq \lambda - \mu \frac {p'-p}{1-p'} + \frac {\xi}{1-p'} \tag{4}$$

$$\frac {\partial \Lambda}{\partial w'} = -u'(x'-w')p' +\lambda p' + \mu (p'-p) + \xi' \leq 0$$

$$\implies u'(x'-w') \geq \lambda + \mu\frac {p'-p}{1-p'} + \frac {\xi'}{p'} \tag{5}$$

First note that not both wages can be zero, because the constraints would be violated. Given this, consider the possibility that the $IR$ is binding (so $\lambda >0$). If it is binding, then with not both wages zero, the $IC$ constraint will necessarily be violated. So we conclude that

$$\lambda_* = 0$$

and the first-order conditions now become

$$u'(x-w) \geq  - \mu \frac {p'-p}{1-p'} + \frac {\xi}{1-p'} \tag {4a}$$

$$ u'(x'-w') \geq  \mu \frac{p'-p}{1-p'} + \frac {\xi'}{p'} \tag{5a}$$

Now note that if $\xi =0$ (i.e. $w >0$) then $(4a)$ should hold as an equality and with the last term on the right equal to zero. But this would require negative marginal utility which is inadmissible. We also know that not both wages can be zero. So we conclude that we must have

$$\xi_* > 0 , w_*=0,\;\;\; \xi'_* = 0,\; w'_* >0$$

and the conditions now become

$$u'(x) \geq  - \mu \frac {p'-p}{1-p'} + \frac {\xi_*}{1-p'} \tag {4b}$$

$$ u'(x'-w') =  \mu \frac{p'-p}{1-p'}  \tag{5b}$$

Eq. $(5b)$ implies that $\mu_*>0$ , under a usual utility function specification, which does not give zero marginal utility except at infinity. This in turn means that the $IC$ constraint should hold as an equality. Given that $w_*=0$ this gives

$$IC:  w'p'  - 1 - w'p =0 \implies = w'_* = \frac 1{p'-p} \tag{6}$$

This should ring a bell, because the right-hand-side of $(6)$ is the same as the right-hand-sides of $(1)$ and $(3)$.

Namely, if we are assuming a priori that $x'-x = \frac 1{p'-p}$, then the solution we have arrived at validates the claim $x'-w'_* = x-w_*$

Under this additional assumption, we also obtain

$$u'(x) \geq  - \mu_* \frac {p'-p}{1-p'} + \frac {\xi_*}{1-p'} \tag {4c}$$

$$ u'(x) =  \mu_* \frac{p'-p}{1-p'}  \tag{5c}$$

Combining, we obtain

$$ \mu \frac{p'-p}{1-p'} \geq - \mu \frac {p'-p}{1-p'} + \frac {\xi_*}{1-p'}$$

$$\implies \mu_* \geq \frac {\xi_*}{2(p'-p)} \tag{7}$$

This is admissible. So under $x'-x = \frac 1{p'-p}$, we obtain the solution

$$\left \{w'_* = x'-x = 1/(p'-p), w_* =0, \lambda_*=0, \mu_* \geq \frac {\xi_*}{2(p'-p)}, \xi_* >0, \xi'_* =0\right\}$$


What conditions must we demand for the economy to be always on the saddle path? Is it enough to assume that agents have perfect foresight, or have 'rational' expectations for the economy to always - except in few cases - be in the stable saddle path?

With rational expectations, I think with shocks, there can be a temporary dislocation from the stable path, but then the agents will reoptimize, shifting the economy back to the stable path.

Are there more situations where this may happen?

Edit: Looking for conditions in the deterministic and stochastic case.

To stick to the simpler deterministic case, it is perfect foresight and the Transvarsality condition (TVC)that guarantees that an optimizing agent will stay on the saddle-path, because all other paths lead to the violation of TVC (corner solutions violate the TVC).  In a deterministic environment and with perfect foresight the agent knows this and so he sticks to the saddle path. The chapter on the basic Ramsey model in Barrow and Sala-i-Martin's Growth  book has a good discussion on the matter.


Why is the derivative of a monotonic transformation of a utility function assumed to always be greater than 0? I'm looking into utility functions and their relation to indifference curves.
Now, I understand a positive monotonic transformation does not change the order (it's a rank-preserving transformation).
I thought the same is true for a negative monotonic transformation (I'm reading H. Varian, he distinguishes between negative and positive monotonic transformations) except it reverses the order.
However in a paper I've read just recently: https://ocw.mit.edu/courses/economics/14-03-microeconomic-theory-and-public-policy-fall-2016/lecture-notes/MIT14_03F16_lec3.pdf
It says:

Definition: Monotonic Transformation
Let I be an interval on the real line ($R1$) then: $g : I → R1$ is a monotonic transformation if
g is a strictly increasing function on I.
If $g(x)$ is differentiable then $g'(x) \gt 0\ \forall x$
Informally: A monotone transformation of a variable is a rank-preserving transformation. [Note: not all rank-preserving transformations are differentiable.]

But how is that true for a negative monotonic transformation such as $g(x) = -x$ where $g'(x)=-1$?
I don't understand. Does the paper not take into account that there are negative monotonic transformations?

Let's look at the use of monotonic transformations of utility functions (which I guess is the most frequent occurrence of this concept in econ).
Let $u: \mathbb{R}^n_+ \to \mathbb{R}$ be a utility function. We say that $g: \mathbb{R}^n_+ \to \mathbb{R}$ is a monotonic transformation of $u$ if for all $x, y \in \mathbb{R}^n_+$:
$$
u(x) \ge u(y) \iff g(x) \ge g(y).
$$
Let $D \subseteq \mathbb{R}$. Then $h: D \to \mathbb{R}$ is called strictly increasing if for all $x, y \in D$:
$$
x \ge y \iff h(x) \ge h(y).
$$
There's the following result:
Th Let $D$ be the range of $u$, i.e. $D = u(\mathbb{R}^n_+)$. Then $g$ is a monotonic  transformation of $u$ iff there exists a strictly increasing function $h: D \to \mathbb{R}$ such that $g(x) = h(u(x))$.
proof: ($\leftarrow$) If $g(x) = h(u(x))$ and $u(x) \ge (>) u(y)$ then $h(u(x)) \ge (>) h(u(y))$ so $g$ is indeed a monotone transformation of $u$.
($\rightarrow$) For the reverse, define
$$
h(z) = g(x) \text{ whenever } u(x) = z.
$$
First we need to check that $h$ is indeed a function. As such, let $x, y$ be such that $u(x) = u(y) = z$. We need to show that $g(x) = g(y)$. Indeed as $g$ is a monotone transformation, we have that $g(x) \ge g(y)$ and $g(y) \ge g(x)$ so $g(x) = g(y)$. To see that $h$ is strictly increasing, let $z \ge (>) w$ and let $x$ and $y$ be such that $u(x) = z \ge (>) w = u(y)$. Then as $g$ is a monotone transformation $h(z) = g(x) \ge (>) g(y) = h(w)$. $\blacksquare$
To see the connection with the derivatives we have the following:
Th if $g: D \to \mathbb{R}$ is differentiable, $D$ is convex and if $g'(x) > 0$ for all $x$ in $D$, then $g$ is strictly monotone.
proof: Let $x \ge (>) y$ then by the mean value theorem there is a $c \in [x,y]$ such that:
$$
g(y) - g(x) = g'(c)(y - x) \ge (>) 0.
$$
Remark: as @Michael Greinecker said, the reverse is not true, there are strictly increasing functions whose derivative is zero at some points, like $g(x) = x^3$.

But how is that true for a negative monotonic transformation such as g(x)=−x where g′(x)=−1?

In principle we could define the reverse notions. Say that $\tilde g$ is a "negative" monotonic transformation of $u$ if for all $x, y \in \mathbb{R}^n_+$:
$$
u(x) \ge u(y) \iff \tilde g(x) \le \tilde g(y).
$$
Notice that $\tilde g$ reverses the ranking given by $u$.
Next, we can look at functions $\tilde h: D \to \mathbb{R}$ that are strictly decreasing:
$$
x \ge y \iff \tilde h(x) \le \tilde h(y).
$$
We have the following:
Th The function $\tilde g$ is a negative monotone transformation of $u$ iff there exists a strictly decreasing function $\tilde h: D \to \mathbb{R}$ such that $\tilde g(x) = \tilde h(u(x))$.
The proof is similar to the proof for the monotone/strictly increasing case.
Remark: In economics, "negative" monotonic transformations are not really used. We would like the functions $u$ and $g$ to give the same ranking over all bundles $x \in \mathbb{R}^n_+$ then they should be monotone transformations of each other. If you use a negative monotonic transformation, you are reversing the order.


Robust Standard Errors in Fixed Effects Model (using Stata) I'm trying to figure out the commands necessary to replicate the following table in Stata. This table is taken from Chapter 11, p. 357 of Econometric Analysis of Cross Section and Panel Data, Second Edition by Jeffrey M Wooldridge. Here I'm specifically trying to figure out how to obtain the robust standard errors (shown in square brackets) in column (2). I'm trying to do this in Stata. I was able to to get the conventional standard errors using the command

xtreg lpassen lfare ldist ldistsq y98 y99 y00, i(id) fe

. I was able to get column (1) with

xtreg lpassen lfare ldist ldistsq y98 y99 y00, i(id)

and the corresponding standard errors with

xtreg lpassen lfare ldist ldistsq y98 y99 y00, i(id) vce(robust)

. However, the command

xtreg lpassen lfare ldist ldistsq y98 y99 y00, i(id) fe vce(robust)

does not work for column (2). It gives results that are different from the book. Could someone explain how to obtain these standard
errors in Stata?

Note that the data to go along with this question can be found here: https://mitpress.mit.edu/books/econometric-analysis-cross-section-and-panel-data
Alternatively, you can load it directly into Stata using

use http://www.stata.com/data/jwooldridge/eacsap/airfare, clear

Use -areg- in Stata, and the standard errors will come out as in the textbook. Specifically, the command

areg lpassen lfare ldist ldistsq y98 y99 y00, absorb(id) vce(robust)

will produce the desired result.

-xtreg- with fixed effects and the -vce(robust)- option will automatically give standard errors clustered at the id level, whereas -areg- with -vce(robust)- gives the non-clustered robust standard errors. The latter seems to be what Wooldridge estimated.

Moreover, -xtreg- assumes that the number of -xtset- groups (id in your example) grows when more data is added to the sample. -areg-, however, assumes that the number of groups is fixed. I.e., the two estimators have different asymptotic properties. The point estimates will be identical, but standard errors will be different, sometimes substantially so.

Old versions of Stata (e.g. Stata 9) did not make the appropriate degrees of freedom adjustment when -xtreg, vce(robust)- was called, which is why you get a bigger standard error when specifying -version 9-. In fact, those standard errors are identical to -areg, absorb(id) vce(cluster id)- in newer versions of Stata.

As a side note, it is puzzling that Wooldridge got non-clustered robust standard errors when calling -xtreg, vce(robust)- in version 9, but perhaps I have a flawed understanding of what the call -version 9- does.

For more information on -xtreg- vs -areg-, see the blogpost and comments here.

(I recognize that this is a year-old thread, and that the question might have been answered on the Statalist. Consider my answer as "for future reference".)


Risk Premium in the Expected Utility Theory Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have

$$ Eu(w+x) = u(w+E(x)-R). $$

The classical derivation of the risk premium is as follows:

A Taylor series expansion of order 2 in the neighborhood of $(\omega + E(x))$ of the left-hand side (LHS) gives

$$u(\omega+x) \approx u[\omega+E(x)] + u'[x-E(x)] + \frac{1}{2} u''[x-E(x)]^2,$$

A Taylor series expansion of order 1 in the neighborhood of  $(\omega + E(x) - R)$ of the right hand side (RHS) gives

$$u(\omega + E(x)-R)  \approx  u(\omega+E(x)) - u'R.$$

Taking expectation of the first series expansion and combining the results of the two series with the definition of the risk premium yields

$$u(\omega + E(x)) + u'E[x-E(x)] + \frac{1}{2} u''E[x-E(x)]^2  \approx   u(\omega+E(x)) - u'R.$$

This implies

$$R \approx - \frac{1}{2} \frac{u''}{u'} E[x-E(x)]^2.$$

My understanding of this derivation is that we can take a 2- or higher-order expansion of the LHS if we want the risk premium to be related not only to the variance of $R$ but also to higher moments of $R$.

However, is there any (economic) rational for the first-order expansion of the RHS? And for its different neighborhood evaluation?

Is there any (economic) rational for the first-order expansion of the RHS? And for its different neighborhood evaluation?

As for your first question:
This is a purely mathematical tactic in order to obtain an (approximate) equation for $R$. The expansion of first order on the RHS is motivated by this fact, i.e. to bring $R$ alone "in the surface".  The reason why the LHS is subjected to a second-order expansion is in order for something to be left (the variance term). Higher-order expansions of the LHS can certainly be applied.

As for your second question, you are making a mistake. The center of expansion for the RHS expansion is the same as that for the LHS expansion, namely $w-E(x)$ (or equivalently, around $R=0$). It is meaningless (and it fails) to expand a function around its exact argument. Specifically we have

$$u\left(w+E(x)-R\right) \approx u\left(w+E(x)\right) + u'\cdot [(w+E(x)-R)-(w+E(x))] = u\left(w+E(x)\right) - u'\cdot R$$

Finally, why not consider a second-order expansion on the RHS? We would then get

$$u\left(w+E(x)-R\right) \approx u\left(w+E(x)\right) + u'\cdot [(w+E(x)-R)-(w+E(x))] \\+\frac 12 u''\cdot [(w+E(x)-R)-(w+E(x))]^2 $$

$$= u\left(w+E(x)\right) - u'\cdot R + \frac 12 u''\cdot R^2$$

Then we would obtain a quadratic polynomial in $R$,

$$\frac 12 u''\cdot R^2 - u'\cdot R - \frac 12 u''\sigma^2_x = 0$$

$$\ R^2 - \frac {2u'}{u''}\cdot R - \sigma^2_x = 0$$

This has roots

$$R_1,R_2 = \frac {(2u'/u'') \pm \sqrt{(2u'/u'')^2+4\sigma^2_x}}{2}$$

$$\implies R = \frac{u'}{u''} + \sqrt{\left( \frac{u'}{u''}\right)^2+\sigma^2_x}$$

You can totally validly use this expression for $R$, but I guess you understand why the simpler one is used instead.


Are sales (discounts) an investment or a loss? Are sales (discounts) during a promotional period considered an investment by the company/manufacturer to drag in more customers? Or a loss that wouldn't be paid back anytime in the future, but also drags in customers? If its the former (i.e investment) how do they pay back the money that's being discounted?

e.g A product officially costs 100USD. There's a sale for that product for 50% off (so that product is now 50USD), how do they make profit or get back that other 50USD?

Suppose that the wholesale cost of the product is 40USD, and the maximum price that most customers are prepared to pay for the product is 50USD, but a few customers are prepared to pay 100USD for the product. Suppose also that the few customers who are prepared to pay more for the product will put less effort into waiting for discounts. Suppose also that some customers are more likely to buy a 50USD product if it previously costed 100USD than if it had always costed 50USD.

What would be the optimal pricing strategy in this circumstance?


I do not quite get a phrase that I read in the Financial Times today. "a share that has fallen by 95 per cent has fallen by half since it has fallen by 90 per cent"

Can you explain the logic behind that?

When the share price has fallen 90% from some price P, the current price is P $\cdot$ 10%.

When it has fallen 95% from some price P, the current price is P $\cdot$ 5%..

P $\cdot$ 5% is half of P $\cdot$ 10%.

As the share price falls from P, it will first pass through P $\cdot$ 10% before reaching P $\cdot$ 5%. So if we obsere the time period from when the price was P until it was P $\cdot$ 5%, it has hallen 95%. But if we observe the time period from when the price was P $\cdot$ 10% until it was P $\cdot$ 5% the share price has fallen by half.


Estimating causal effect for educated people on wages I have a problem regarding causation and effect. I have a linear model
$ wage=\beta_0+\beta_1educ+\beta_2female+\beta_3hourseworked+errorterm$
When I need to estimate the causal effect for educated people on wages, I have chosen a subpopulation educ==1 (educated people) and made a regression in stata.
The used commands are
reg wages educ female hourseworked

From this regression I obtain 0 for the educated people, and it says that it is omitted. How can I find the causal effect of educated people on wages, when I have this problem?

I have tried to remove the intercept, from which I get an estimate causal effect of education, but is it correct just to remove the intercept?

Do I have to think about endogeneity - omitted variables - instruments?

Yes, you have to worry about the difference between correlation and causality. In these situations, it helps to try to force a case of ommited variable  bias.

In this case "talent" or "effort" is unobserved. Both this might make people more likely to pick up additional education, and also be more successful at their jobs.

Or family background: If your parents are high achievers, they might induce you to take more education, and they also are well-linked to ensure you get a well-paid job.


Duopoly vs Collusion (quadratic costs) Suppose there are 2 firms; Demand curve is given by $P=1400 - 5(q_1+q_2)$ and cost function is given by $C_i = 5q_i^2$.

For cournot, the best response function comes out to be $q_i=70 - 0.25q_j$ giving $q_1=q_2=56$ and $P=840$. Thus $\pi_1=\pi_2$= $840 * 56 - 5*(56)^2 =31360$.

For collusion $MC=MC_1+MC_2=10q_1+10q_2=10Q$. Thus $MR=MC$ gives $1400-10Q=10Q$ which in turn gives $Q=70$ and $q_1=q_2=35$. And $P= 1400 - 5(70) = 1050$. Thus $\pi_1=\pi_2=1050.35 - 5(35)^2 = 36750-6125=30625$.

What I don't understand is, how is profit greater in Cournot duopoly as compared to a collusion. Is it possible? Or did I make a mistake somewhere during the calculation of $MC$ for collusion?

Your computations are OK, but this is a trick question

The total quantity set by the colluding firms and the quantity chosen by  a monopolist are not the same in this question. By setting $MR = MC$ you are solving the profit maximization problem a monopolist instead of the profit maximization problem of the colluding firms.

The reason for the difference is that the marginal cost is increasing over the entire domain of the production function. Suppose the monopolist wanted to produce $Q=10$. The cost would be $5 \times 10^2 = 500$. If each of the colluding firms produced 5 the total cost of producing 10 units would be $5 \times 5^2 + 5 \times 5^2 =250$. I.e. the two colluding firms have smaller diseconomies of scale than the monopolist.

The most efficient way to produce any quantity for the cartel is to split production between the colluding firms equally. In this case the marginal costs of the cartel members are equal. Shifting a unit of production from firm 1 to firm 2 will make producing that unit more expensive, as the marginal cost increases in $Q$.

Viewed through the  $MR = MC$ argument that you used, the cartel of two colluding firms has access to a lower cost function unavailable to the monopolist: $C(Q) = 5\big[\big(\frac{Q}{2}\big)^2 + \big(\frac{Q}{2}\big)^2\big] = 5\frac{Q^2}{2}$.

Thus the cartel's profit function  is $\pi (Q) = (1400 - 5Q)Q - 5\frac{Q^2}{2}$. $MR(Q) = 1400 - 5Q - 5Q = 1400 - 10Q$, $MC(Q) = 5Q$
and $MR(Q) \overset{!}{=} MC(Q) \Rightarrow 1400 = 15Q \Leftrightarrow Q^* = 93\frac{1}{3}$. The total profit of the cartel is $\pi(Q) = 65333\frac{1}{3}$. The profit of the individual cartel member is $\frac{\pi(Q)}{2} = 32666\frac{2}{3},$ which is larger than the Cournot equilibrium you correctly obtained.

The monopolist, as described in your solution has a profit function of
$\pi(Q) = (1400 - 5Q)Q - 5Q^2$ For him $MR(Q) = 1400 - 5Q - 5Q = 1400 - 10Q$, $MC(Q) = 10Q$. And $MR(Q) \overset{!}{=} MC(Q) \Rightarrow 1400 = 20Q \Leftrightarrow Q^* = 70$. I.e. the monopolist stops producing earlier, as its higher $MC$ prevent it from making profits at larger quantities.


Extension on the suspension of national debt ceiling So I just want to make sure i got this right,

The national debt ceiling was suspended, i.e. the government can now freely spend until Dec.8, which they "say" was for providing $15bn in hurricane relief.

But lets face it, the treasury was running out of "extraordinary measures" to keep the debt below the ceiling, thus the extension. Source -> http://www.businessinsider.sg/us-debt-20-trillion-how-much-2017-9/?r=US&IR=T

The debt increased by 317 billion. But that aside, I want to get into the economics fundamentals. What does this mean for the dollar?

So foreign debt is increased, I am assuming the USD is going to plummet if expectations of quantitative easing to pay off the debt increases?

Debt is between US govt and The Fed.

If the Fed reset the debt back to 0 and bail out the govt, nothing changes. The next debt epoch starts.

Viscious if my understanding is correct. No other govt in the world has this freewheeling !!


Why do developing countries adopt 21st century technology, but stay behind in output per capita? The economic growth rate of Latin America has been about 3% per year for decades; but if you have ever visited, many of the natives have: internet, smartphones, tomography, hybrid cars, etc.
Why don't they catch up when they adopt cutting edge technology?

Probably if you go to almost any country in the world, however poor, you will find considerable use of relatively cheap cutting-edge consumer technology such as smartphones and some more expensive cutting-edge technologies used in manufacturing or service industries.  However, there is a big gap between 'adopting' cutting-edge technology at that level and the much more comprehensive adoption of such technology by developed countries.  The benefits of technology in developing countries may be limited by any of the following:

Lack of adequate supporting infrastructure, eg electricity supply
unreliable or subject to regular power cuts, unreliable internet service.
Lack of adequate skills to maintain and make best use of technology.
Limited adoption, eg of smartphones, so that network benefits are
not fully realized.
Lack of capital equipment, knowledge and skills to produce
cutting-edge technology equipment, so that all such technology has to be
imported using scarce foreign exchange; or, for slightly more
developed countries, production of high-technology goods is limited
to low-level assembly work within an international supply chain
where most of the value is added elsewhere.

Suppose, then, that (recognizing the above problems), a developing country tries to adopt cutting-edge technology in a comprehensive way, so as to quickly catch up with developed countries.  Such an approach is heavily criticized in Justin Yifu Lin's book The Quest for Prosperity, which argues, in outline, that developing countries should target industries in which they have a comparative advantage (or can achieve one via improved infrastructure) and which offer an opportunity for gradual upgrading of technology.  While countries differ, this will often mean labour-intensive manufacturing, and it is suggested that industries to be targeted should be those currently dominated by countries whose GNP per capita is about twice theirs.  By contrast, attempting to compete immediately with countries with the most advanced technology is likely to lead to a continuing need for subsidy, distortion of resource allocation, financial repression to channel scarce capital to the subsidised sector, and political problems in handling those profiting from or dependent for employment on subsidies.


Economics of Homelessness: Are housing prices to blame? Lots has been written in terms of the social context of homelessness. Often attributing the causes due to mental illness, previous criminal activity and addiction.

I've been wondering, how much of a role (if any) does home price or rent play into the phenomenon of homelessness?

Im guessing estimates will be different depending region, but I'd like to know if the relationship is consistent across the board.

This paper is close to what you want.

  It is generally believed that the increased incidence of homelessness
  in the United States has arisen from broad societal factors, such as
  changes in the institutionalization of the mentally ill, increases in
  drug addiction and alcohol usage, and so forth. This paper presents a
  comprehensive test of the alternate hypothesis that variations in
  homelessness arise from changed circumstances in the housing market
  and in the income distribution. We assemble essentially all the
  systematic information available on homelessness in U.S. urban areas:
  census counts, shelter bed counts, records of transfer payments, and
  administrative agency estimates. We estimate similar statistical
  models using four different samples of data on the incidence of
  homelessness, defined according to very different criteria. Our
  results suggest that simple economic principles governing the
  availability and pricing of housing and the growth in demand for the
  lowest-quality housing explain a large portion of the variation in
  homelessness among U.S. metropolitan housing markets. Furthermore,
  rather modest improvements in the affordability of rental housing or
  its availability can substantially reduce the incidence of
  homelessness in the United States.

Quigley, John M., Steven Raphael, and Eugene Smolensky. "Homeless in America, homeless in California." Review of Economics and Statistics 83.1 (2001): 37-51.

  The results in table 5 provide the strongest evidence that housing
  market tightness is an  important determinant of homeless. For
  permanent caseloads, vacancy rates have a strong negative and
  statistically significant  effect (at the 1% level) on the incidence
  of homelessness. Moreover, these elasticity estimates are quite
  similar across specifications. In the two specifications including
  fair market rents (specifications (1) and (3)), rents exhibit a
  significant  positive effect on the incidence of homelessness as
  predicted by theory. In addition, the specification including the
  ratio of rents to income indicates a strong positive effect. Hence,
  for homelessness, as measured by the incidence of  homeless
  house-holds seeking permanent assistance, measures of housing market
  tightness consistently exhibit strong and statistically significant
  effects, which is consistent with the predictions of theory. We also
  find a negative and significant effect of per capita income. There are
  no important effects of county unemployment rate  s and no consistent
  and significant effect  of the SSI populations across specifications.
  Similar to the results from the S-night and continuum-of-care data
  sets, the results in table 5 also indicate that warmer weather is
  positively associated with homelessness

The key results table:

Open access version?


How are economic principles applied to non-financial models, such as a democratic election? Economic agents make decisions in particular models. These models do not need to be related to financial contexts, and economics can be used to describe how agents will act in any other field in which humans act.

As an example, how would economic principles be applied to the process of a democratic election?

Long story short: Preferences orderings are over more abstract outcomes instead of money. It's still a story of maximizing expected utility.

Agents are usually assumed to have preferences over outcomes. This is assuming something like consequentialism. In financial models, the outcomes are dollar amounts and so there is a natural preference ordering. In something like a political model, outcomes are policies. So, people have indirect preferences over political candidates based on beliefs and seek to influence the outcome by voting. This is probably a bad model of voting, as most people don't honestly believe their vote matters I'm guessing.

Beyond voting to influence current decision-making, here is a good paper about voting as communicating: Piketty (2000)


What is a super deduction? This is a term often encountered in documents published by the Big Four (Deloitte, Ernst & Young, Price Waterhouse Coopers, KPMG), for instance in the E&Y 2018 Worldwide R&D Incentives Reference Guide.

However, I've been unable to find a definition, formal or other, anywhere on the web for this term. I would associate it with superannuations (sometimes called super), but this doesn't seem to make a lot of sense here. Another possibility would be that it is some sort of tax deduction, reducing your taxable income, and this seems more likely, but I still don't understand the super part then.

Would anyone be so kind as to explain the meaning of this term in the context in which it is used by the Big Four?

Deloitte managed a semi-intelligible explanation. It's called "super" when an income tax deduction is applied twice for the same item (e.g. for R&D)...

  In early 2015, Slovakia introduced a new type of tax incentive aimed at supporting companies conducting corporate R&D (most common is development of new or substantially improved products, services, technologies and processes). [...] Similar regimes have been in use for years in the world's most advanced economies.

  In practice, eligible expenses can be deducted from the tax base twice. First as a normal tax-deductible expense and second as an additional super-deduction. [...]

  Super-deductions can be utilized by any company, which in the relevant tax period incurs expenses directly related to R&D projects. In case of tax losses, the super-deduction may be transferred to the next tax period (up to maximum of four subsequent years).

KPMG has a more concise definition and some examples/figures:

  Income tax is reduced by deducting
  R&D expenses from the tax assessment basis by
  more than 100% (“super deduction”) or from the
  tax liability (“tax credit”). [...]

  Tax-free amounts are applied to obtain a discount
  of more than 100% of the qualifying R&D costs.
  From a practical perspective, this is usually
  achieved by deducting these costs against tax
  more than once. The majority of multipliers in
  other jurisdictions are between 130% and 210%.
  This leads to the fact that these increased R&D
  expenses can be also claimed as expenses
  for tax purposes and reduce the taxable profit
  accordingly.