Short-run and Long-run cost against the price of the variable input This is an image of page 133 of Microeconomics; Gravell and Rees.In the fourth line there is a statement about the slope of those curves. Can anyone please explain me the reason??

Everything comes from the constraint

$$
C(p, \gamma^0) \leq S(p, \gamma^0, z^0_k) \tag{C.17}
$$

By construction at $p_0$ these two things are equal:

$$
C(p^0, \gamma^0) = S(p^0, \gamma^0, z^0_k) \tag{1}
$$

Consider a very small positive number $\delta p_i$, and note that (I dropped the other components of $p$ since they remain constant)

\begin{align}
C(p_i^0 - \delta p_i^0, \gamma^0) &<  S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) \\
C(p_i^0 - \delta p_i^0, \gamma^0) - C(p_i^0, \gamma^0) &<  S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) - C(p_i^0, \gamma^0)\\
C(p_i^0 - \delta p_i^0, \gamma^0) - C(p_i^0, \gamma^0) &<  S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) - S(p_i^0, \gamma^0, z_k^0) \\
\frac{C(p_i^0 - \delta p_i^0, \gamma^0) - C(p_i^0, \gamma^0)}{\delta p_i^0} &<  \frac{S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) - S(p_i^0, \gamma^0, z_k^0)}{\delta p_i^0}\\
\lim_{\delta p_i^0\to 0^+}\frac{C(p_i^0 - \delta p_i^0, \gamma^0) - C(p_i^0, \gamma^0)}{\delta p_i^0} &<  \lim_{\delta p_i^0\to 0^+} \frac{S(p^0_i - \delta p_i^0, \gamma^0, z^0_k) - S(p_i^0, \gamma^0, z_k^0)}{\delta p_i^0} \\
-\frac{\partial C}{\partial p_i} &< -\frac{\partial S}{\partial p_i}
\end{align}

or in other words,

$$
\frac{\partial C}{\partial p_i} > \frac{\partial S}{\partial p_i} ~~\mbox{for}~~ p_i < p_i^0 \tag{2}
$$

or in plain English: $S$ is flatter than $C$ for $p_i < p_i^0$. You can repeat the same argument for $p_i > p_i^0$


heteroskedasticity variance estimator bias direction If I have a model with heteroskedasticity issue, can I tell the bias direction of the coefficents variance estimator?

I would think that because I would correct it with WLS then I get BLUE (Best Linear, Unbiased Estimator) which means the variance estimator is the smallest for unbiased coefficient but i am wrong.

Can someone please explain to me if I can know the direction of the bias and how?

I think the problem is that you are mixing up terminology. The statment about an estimator being BLUE states given the Gauss-Markov assumption, OLS is the best linear unbiased estimator. But as your model is heteroskedastic the Gauss-Markov assumptions no longer hold and the proof of OLS being BLUE is no longer true.

Unfortunalty there is no general result that shows whether a estimater is the "best" in the case of hetroskedacity. In theory if you know the exact functional form of the heteroskedascity you can perfectly correct for the hetroskadicity and you WLS is just as effective as OLS when the Gauss-Markov assumptions hold. But in reality this is never the case, and unless you have a small sample or a very strong argument of why you know the functional form of the hetroskedacity then you are better of using Whites robust standart errors.


Why can utility functions be continuous, and what does this imply for marginal utility? I am studying microeconomics at the introductory undergraduate level and two related but distinct questions are puzzling me.

First, my textbooks express utility functions as continuous functions by default, but this is puzzling. If the consumer can only consumer in whole number quantities (indeed from what I've seen so far, the solutions for the optimal basket all involve whole number quantities), then surely the utility function should be a discrete function, not continuous? A continuous utility function implies that an optimal basket could be say, x=8.232324232342, y=3.23942, for instance.

Secondly, even we if we accept as fact that a utility function can be continuous, how exactly do we interpret the concept of marginal utility at a point? So for instance, given the utility function (single good) $U(X)=X^2+6X+7$, the marginal utility of consuming the 6th good should be $U(6)-U(5)$, because marginal utility is the increase in utility as a result of consuming an additional unit of the good. Instead, marginal utility is, in fact just, $U'(6)$ which is usually not equivalent to $U(6)-U(5)$ (it's not in this case, too). So what's going on here? Am I missing something? I know the former way is called the "arc" measure, and the latter the "point" measure - I understand the arc measure, but I cannot understand the point measure. Doesn't marginal utility always measure the increase in utility arising from consuming one additional unit of the good? The point measure seems to imply $U'(6) = U(6)-U(5.999999999...)$.

Utility functions can be continuous because quantitites can be continuous. (Think liters instead of bottles of wine or kilos instead of loafs of bread.) But even if quantities are discrete; whenever a unit is reasonably small (grains of salt: yes; cars: no) it is just way more convenient to work with smooth functions than with discrete ones, since the former allow you to calculate derivatives.

Introductory textbooks often use discrete quantities ("additional utility of consuming the next unit") to define marginal utility, since this is more intuitive. However, as soon as you have smooth utility functions, you better use the derivative of utility instead. Think of the point measure as the limit of the arc measure as the increase in quantity goes to zero. (That's more or less how the derivative is defined.) If quantities are discrete but very small and your utility function is reasonable, then the two measures are almost identical anyway. As an example, if your utility function is defined over $x$ = the number of grains of salt on your chips, then, using e.g. $u(x)=1-(x/100-1)^2$, your $MU$ at $x=100$ is $0$ if you use the derivative and $-0.0001$ if you just calculate $u(101)-u(100)$. To find the optimal quantity, setting $MU=0$ is of course easier than listing 200 discrete values and searching for the maximum.


Why not talk about utility functions on the surreal line when preferences are lexicographic, etc? I've been reading about the surreal numbers out of curiosity. Though I don't totally understand them, I wonder why I don't see them used more often. Surreal numbers extend the real line to also include infinitesimal and infinite numbers (transfinite ordinals like $\omega$ which is identified with the cardinal number $\aleph_0$, itself the cardinality of $\mathbb{N}$).

Often, there are interesting preferences which can't be represented by a real-valued utility function. The obvious example is for lexicographic preferences. But why not have $u:\mathbb{R}^n\rightarrow S^*$, like $u(a,b)=a+\frac{b}{\omega}$?

Lexicographic probability spaces are another place where these numbers could have application. If we want to differentiate between two probability zero events, let one have probability $\frac{1}{\omega}$ and the other $\frac{2}{\omega}$.

One might ask, sure you can use them, but what's the point? What do we gain? Fair question. I just kind of think the use would make things cleaner--making lexicographic prob spaces less of a tortured construction perhaps.

The first thing that comes to mind is that some economic models have more than one agent.

If one agent has a utility function with values in ${\mathbb R}$, then two agents have a pair of utility functions with joint values in ${\mathbb R}^2$.  If one agent has a utility function with values in $S^*$, then two agents have a pair of utility functions with joint values in ...what?  We can't just form a product of $S^*$ with itself, because $S^*$ is not a set.

There are probably ways around these difficulties, but they're going to be clumsy and they're going to require lots of mucking around with foundations that are almost surely not interesting to most economists.

Set theory lets us form unions, products, coproducts and power sets.  It lets us talk about subsets and supersets without having to worry about whether they exist.  Economists use these constructions all the time without stopping to think about them.  I doubt that we want to switch to a new foundation that forces us to think about them constantly.


Buy a company with credit or bonds. Does this happen? I have a question. A company is worth 1 million dollars, in terms of present value of revenues, discounted at rate R. Can I borrow 1 million dollars from a bank and buy the company? If the bank charges me R, I am indifferent?

Or, can I issue a bond for 1 million, with coupon R? Am I indifferent too?

Do these things happen? Do businesses ask for credit or issue bonds in order to buy companies?

I have a question. A company is worth 1 million dollars, in terms of present value of revenues, discounted at rate R. Can I borrow 1 million dollars from a bank and buy the company?

Yes.  It is done all of the time.

  Can I borrow 1 million dollars from a bank and buy the company? If the bank charges me R, I am indifferent?

No, you are not indifferent unless there is a mandatory repayment schedule.  This is a riskless contract to you otherwise.  If there is no better rate of return for you, then you begin to repay the loan, but if a new opportunity develops at $R'>R$ then you stop repaying the loan.  If there is no mandatory repayment schedule then you would always opt for the loan as you can require the bank to keep a bad opportunity and you can keep any good opportunity.

In periods where $R$ is the superior opportunity, you repay the loan until it is fully repaid.  In periods where $R'$ dominates the original opportunity, you send the cash flow into the new opportunity.  The loan is acting as if it were a free option contract.

There is an implicit cost to not taking the loan.

None of this necessarily holds if there is a repayment schedule or if there is a loan rate of return which does not equal $R$.

As to bonds, again it is the terms and conditions that matter.  In the real world bonds are costly to issue.  It appears here that bonds and bank loans are identical so you would be indifferent to using a bond or a loan, but not indifferent to buying the firm on credit since the bank or bondholders will accept taking all of the risk for the return $R$.

If the return $R$ were risky and there were cash repayment obligations, then it is difficult to determine if you would be indifferent or prefer to borrow because the option requires exercise making it a forward contract and not an options contract unless there is also the capacity to prepay.  You would be strictly indifferent if and only if there existed a mandatory principal repayment scheme.  Otherwise, assuming that at the moment, no opportunity $R'>R$ existed, then you would take the loan and buy the firm.

This entirely depends upon the bank accepting the profit of the firm as the interest payment.  This would never happen in the real world.


Incomplete and Intransitive Preferences: Reference Request I've had the opportunity to read this blog post on incomplete and intransitive preferences and would like to cite it in a informal presentation. However I cant seem to find the author.

The main site seems extremely old, though I find this essay extremely insightful for someone at my level any guidance for who the author is appreciated.

The site link: https://cruel.org/econthought/essays/get/intransitive.html

Based on the contact page my guess would be Gonçalo Fonseca, whose research focuses on the intersection of the history of economic thought and economic theory, or/and Leanne Ussher. You can probably drop them an email (there is an email contact).


What makes a shareholder a "shareholder of record"? In public companies filling some reports with the SEC (10K for example), there is a mention of the number of shareholders of record.
Example:
"As of April 20, 2021, we had approximately 40 shareholders of record of our common stock."
Source: DTST 10K filling
A. What makes me legally titled the shareholder of record?
B. Is there a minimum equity to be owned to be recognized as a shareholder of record?
For example, if I bought 1 stock, am I included?
C. Can I view the list of shareholders, or get any information about them, or is it censored?

I typed "shareholders of record" into Google, and I got

Stockholder of Record
Also known as shareholder of record, record holder or owner, or registered holder, or owner. The stockholder whose name is listed on the company's books and records as the owner of shares as of a particular date (the record date). A stockholder of record holds stock in a direct relationship with the company and has direct title to the shares, as opposed to a beneficial owner that owns stock indirectly through a broker, dealer, bank or other entity. Beneficial owners holding through a broker, dealer or bank are also said to hold their shares in street name.

Source

A. You have to have a direct relationship with the company.
B. Seems like the one share you can buy through a brokerage won't cut it. If somehow, before the company went public you made an agreement with them to get a share and hold it in your name - I guess?
C. You can if you are a shareholder:

Shareholders [...] are entitled to review only basic documents, such as the charter, bylaws, minutes of board meetings, and the list of shareholders of record.

Source: Page 14 of Velasco: The Fundamental Rights of the
Shareholder


How does the Greenspan/Bernanke Put semantically relate to put options? If rational investors reckon that "the Fed, under Alan Greenspan, its longtime chairman, would always bail stock investors out of their losing positions", then rational investors would buy call options or sell put options, not buy puts. So how can a Greenspan or Bernanke Put be sensibly analogised to a Put Option?
Greenspan and Bernanke Put and Other Central Bank Tools

The term Bernanke put has become almost as ubiquitous as the Greenspan put was during the late-1980s and 1990s. Derived from the concept of a put option, these terms refer to central bank policies that effectively set a floor for equity valuations. For instance, Alan Greenspan was known for lowering the Fed Funds rate whenever the stock market dropped below a certain value, which resulted in a negative yield and encouraged movement into equities.
In these situations, investors have been given a put option of sorts by central banks, since they have a price floor in place. For example, an investor holding shares of a broad market index may have a sort of guarantee from the central bank that the stock won’t drop below 20% since if it did, the central bank would intervene with low-interest rates to boost equity valuations. There was no actual guarantee by the central bank, but the precedent was enough for many investors.

Economist's View: The "Greenspan Put" and Excessive Risk Taking

This article argues that many people view the Fed as an insurance policy against financial market risk and believe that the Fed would not allow substantial asset devaluation.  My own view is that people ascribe all sorts of motives to the Fed that aren’t there.  The Fed is trying to tell us that it’s really simple (as are Kash at Angry Bear and Tim Duy in a Fed Watch).  Watch output and inflation relative to target and adjust accordingly.  We can argue about how to measure output, the target, and how to parameterize “accordingly” in the Taylor rule, but those are details, the essence is simple.  The Fed’s behavior is explained very well with a Taylor rule and reinterpreting it as an insurance program or something else is an entertaining exercise, but we probably shouldn’t take it much beyond there.

Understanding the Greenspan, Bernanke, Now Trump "Put" - Halbert Wealth Management - Commentaries - Advisor Perspectives

The term Greenspan Put was coined in the late 1980s as a result of certain policies implemented by then Federal Reserve Chairman Alan Greenspan. He was Fed Chairman from 1987 to 2006, followed by Ben Bernanke from 2006 to 2014 when the term changed to the Bernanke Put.
Throughout both men’s terms as Fed Chair, they routinely lowered the Fed Funds rate to help support the economy, which in turn helped the stock markets. As this practice went on, investors came to view the Fed’s policy of lowering interest rates to shore up the economy and risk assets as something akin to a “put” option.

then rational investors would buy call options or sell put options, not buy puts. So how can a Greenspan or Bernanke Put be sensibly analogised to a Put Option?

Investors do not need to buy or sell anything, the story is that the Greenspan Fed was giving out free puts to investors.
It doesn’t literally work that way, but it is directionally close  to making sense.


Short cuts to solve Cobb Douglas Utility function (minimization) Say a Cobb Douglas like:

$$\max_{X,Y\: s.t. X \cdot P_x+ Y \cdot P_y=I} U=X^\alpha Y^\beta$$

When it comes to maximization I would do the following way (for the fastest result):

x: $\alpha/(\alpha + \beta) = r; r*income = r_2$; $r_2$/price good = x$

Is there a similar (or really fast) method to solve for minimization problems?

A shortcut to solve $$\min_{x,y} x^{\alpha} y^{\beta}$$ s.t. $$xp_x + yp_x \leq m$$ and $$0 \leq x,y$$ is to set $x = 0$ and/or $y = 0$, as this results in $U(x,y) = 0$, and the function does not map to negative values.


How to read PPP$ aloud? How to read PPP$ aloud?

That is in a paper that I should read loud in a presentation, but I don't know the most

Is it "purchasing power parity in US Dollar,"

or "purchasing power parity in terms of US Dollar,"

or ... ?

It isn't necessary to stress that these figures are pegged to the US dollar. A PPP dollar is a dollar in its own right. Thus, simply saying "The budget is three billion purchasing power parity dollars" is good. Mentioning PPP in the context of a US project is unnecessary.

The World Bank uses the phrase "international dollars" on its data portal, so you can say "international dollars" if you are willing to explain what that means to anyone unfamiliar with that phrase. That phrase has the advantage that it is shorter, so it is less cumbersome to say out loud.


Optimal choice for a weird leontief function Compute the optimal choice for a consumer with the following utility function:

$$u(x_1, x_2) =\max \{\min(2x_1, x_2), \min(x_1, 2x_2)\}$$

I'm familiar with computing optimal choice for perfect complements but this has 2 expressions and I'm stumped with how to go about doing this. I'd also appreciate if anyone could explain what exactly is happening in a function like this.

One needs to go case-by-case and arrive at a utility function with branches. To get you started, if $x_1 < x_2/2 \implies \min(2x_1,x_2) = 2x_1$, but then also $\min(x_1,2x_2) = x_1$. Therefore in this case, $u(x_1,x_2) = 2x_1$. etc

There are two other intervals to consider as regards the relation between $x_1$ and $x_2$, so in all you will obtain a utility function with three branches. The middle one will be a $\max$ operator, and it can usefully be split in two, resulting in four branches.


Linking top-down and bottom-up models for analyzing electricity price-based demand response: Expenditure constraint is violated? I have a question about the contents of this paper*, which links a building energy model and a utility-maximization component. In it, the author tests several electricity prices using a Cobb-Douglas utility function. As I understand, the C-D function ($U=X^\alpha*Y^\beta$) stipulates that $X=\frac{\alpha}{\alpha+\beta}*\frac{Income}{P_x}$ at optimality. If Income and share parameters are fixed, that would mean $(X)(P_x)$ is always constant; if $P_x$ doubles, $X$ is halved, etc..

That is not what the paper finds in the linkage of the two components. P_electricity*ElectricityUse is not always constant. The expenditure equation implied by the C-D function is violated, but the paper applies an expenditure equation from the building energy model instead of it. They just maximize the utility function as the objective, subject to the budget constraint, and given the electricity use and expenditures from the building model, but do not factor in the implied relations.

Is this a violation that would nullify such linkage?

*Sorry if it is blocked behind a paywall, there isn't an alternate free copy.

Citation: Matar, W. "Households' response to changes in electricity pricing schemes: Bridging microeconomic and engineering principles." Energy Economics 75.

Constant expenditure in monetary terms requires constant Income indeed. Does the paper you site adjusts its equations and the data to account for possible changes in income present in the data?

What the CD utility function $U = X^aY^b$ does impose, is constant expenditure shares,

$$\frac{X^*p_x}{I} = \frac {a}{a+b}$$

So the question would be for the appropriateness of the utility function specification whether the data support $X^*p_x/I = const.$

On the methodological front the OP writes

  ...the paper applies an expenditure equation from the building energy
  model instead of it. They just maximize the utility function as the
  objective, subject to the budget constraint, and given the electricity
  use and expenditures from the building model,...

This begs the question: if consumer demand / consumer expenditure is postulated from outside the model, exactly what is the purpose of solving the utility maximization problem? The main purpose of utility maximization is to provide the demand functions, namely to show how utility considerations determine choice and consumer decisions.

Are we sure about what the authors are doing exactly?


It's unclear how market equilibrium is reached in case of overproduction Let's assume that there is disequilibrium, namely that $P=P_2$, thus $Q_s > Q_d$. In other words, there is overproduction. This is perfectly competitive market, so competition between producers will make them lower prices in order to get rid of excessive production, thus allowing the market equilibrium (in the point $E$) to be reached. But wait a second! When we said that producers will change price we said nothing about quantity of production. But you can clearly see that in point $L$ (before producers lowered prices) the quantity was equal to $Q_2$, while in point $E$ it's equal to $Q'$, and $Q' < Q_2$.

What happened with all these ${\bf Q}_2$ minus ${\bf Q}'$ goods? It looks like producers collectively decided to destroy part of their excessive goods in order to reach the point of equilibrium. Because if producers will change only price of their goods (i.e. $Q_s$ is constant) there is NO way they can reach equilibrium without moving their supply curve (or alternatively - without moving the demand curve).

You are basically asking a dynamic question on the basis of a static model, although this often done for convenience. In a real static model, over production is impossible.

You answered the first part of your question yourself: In the short run the Q2-Q'goods got sold off at a lower price. For the long run: recall that the supply curve is also the industry's marginal cost curve. If producers lower their prices below P2, some of them will start to operate at less than max profit and either go out of business or reduce production, to operate at max profit level again. In the long run we thus move along the supply curve, downwards to point E.


What is 2nd round of rationalizability for a 1st price auction? Consider a first-price auction.
Suppose that we have $N$ bidders, and they believe that their opponents' values is drawn from a uniform distribution on interval $[0,1]$.
Let us eliminate weakly dominated strategies.
The 1st round will clearly eliminate all bids higher than the private value $x$. But what range of prices will be eliminated in a 2nd round?
My conjecture: after elimination of bids higher than private values, bidder $i$'s objective function in a 2-bidder situation will be $(v_i-b_i)\Pr(b_{-i}\leq b_i)$. The probability $\Pr(b_{-i}\leq b_i)$ is maximized when $b_{-i}$ is approaching $v_{-i}$. So maximized form of objective functions of bidder $i$ is $(v_i-b_i)\Pr(v_{-i}\leq b_i)$, which is $(v_i-b_i)b_{i}$. (Since we assume uniform distribution on values) So after 1st round of rationalizability, a bidder's maximized payoff will be $\frac{v^2_i}{4}$. This means that in 2nd round of rationalizability, any bidder will not be bidding higher than $v_i-\frac{v^2_i}{4}$.

Elimination of (weakly) dominated actions will not get you far. In fact, all bids strictly between 0 and the value are undominated. Hence, a buyer's optimal bid in a first-price auction can't be determined without knowing the bidder's belief (unless the buyer's value is 0).
Claim: For any type $x>0$, all bids $c \in (0,x)$ are undominated.

$c$ is not dominated by any bid $b>c$: $b$ yields a strictly smaller
than $c$ if all other bidders bid $b_j<c$.
$c$ is not dominated by any bid $b<c$: $b$ yields a strictly smaller utility than $c$ if all other bidders bid $b_j=c$.

You can show that, for all types $x>0$, bidding zero is dominated by any $b\in (0,\frac{N-1}{N} x)$, though.
Suppose $p$ is the probability that all other $(N-1)$ bidders bid zero. Then, bidding zero yields utility $\frac{p}{N}x$: winning by a randomization because everyone bids the same and then winning the lottery and paying nothing.
However, when bidding $b$ from the interval above, your exepected payoff is at least
$$\geq p(x-b) > p (x - \frac{N-1}{N} x) > \frac{p}{N}x.$$


Negative Marginal Returns In my economics class, we learned that in the short run, there are three stages of marginal returns: increasing, decreasing, and negative.

As a firm adds the first few units of labor, specialization allows for increasing marginal returns (Stage 1).  This makes sense to me.

As one adds more units of labor, marginal returns decrease due to limited capital (Stage 2).  This also makes sense to me.

However, in Stage 3, there are negative marginal returns (total product decreases).  How is this possible?  In practice, the firm would lay off the final worker(s), and the firm would never reach Stage 3 unless management was totally incompetent.  However, by the theory of specialization that causes Stage 1, if, say, a factory could produce 30 items with 6 workers but could only produce 27 items with 7 workers, it seems as though the factory, assuming it kept 7 workers on its payroll, would simply have one worker "specialize" in sitting outside, letting the other 6 workers operate independently of the one sitting outside and thus produce 30 items.  By that argument, if the firm kept hiring more workers, it could have those newly hired workers sit outside, so that total product would remain constant and marginal product would never be negative.  Where am I going wrong?

Thanks!

I don't understand your problem: negative marginals returns are a feasible situation. The fact that a rational optimizing firm won't let itself reach such a stage is another matter.


Slutsky Decomposition of Given Labor Supply Model Let utility curve an individual given as $U(C,R) = C^aR^{1-a}$ where $(0\lt a  \lt 1)$ and $C$ denotes consumption commodity and $R$ denotes its leisure, and price of $C$ is given as $P$, and the nominal wage for a unit of labor given as $W$. Total amount time available for the individual is $T$.

Now I would like to derive the change of labor supply when nominal wage get increased with two different effect decomposed - income effect/substitution effect.

What I have got is $L^s$ only, which is equal to $T-R$, following below process:

first, $P\cdot C = L^s\cdot W $

second, $T-R = L^s$

by, first and second, $P\cdot C= (T-R)\cdot W$ (*)

and the from the utility function we can derive the condition of maxmizing its utility, $MU_C = MU_R$, which is eqaul to $\frac{a}{1-a}=\frac{C}{R}$(**)

Now, since the (*), (**) must hold at the same time, we can derive equation between $W$ and $R$ without $C$ as below:

$P\cdot \frac{a}{1-a}\cdot R = (T-R)\cdot W$

Then we get $R = \frac{TW}{P(\frac{a}{1-a})+W}$ and $L^s =T\frac{P(\frac{a}{1-a})}{P(\frac{a}{1-a})+W}$

but my derivation of $L^s$ looks only decreasing while W is increasing.

Any points did I do wrong? I want to did some decomposition of Slutsky, but lack of skills to deal with partial derivatives, it makes me hard to do also.

In this static model with no savings/intertemporal aspect, labor supply does not depend on the wage. Using the equality relations, we can maximize over $L^s$ without constraints

$$\max_{L^s} U = \left(\frac{L^s\cdot W}{P}\right)^a\cdot (T-L^s)^{1-a}$$

$$\frac {\partial U}{\partial L^s} = \frac a{L^s}\cdot U - \frac {1-a}{T-L^s}\cdot U$$

and setting this equal to zero we get the optimal $L^s$

$$\frac a{L^s}= \frac {1-a}{T-L^s} \implies L^s = aT$$

One can verify that, at the optimum, the second derivative of the Utility function is negative so we do have a maximum.


Anscombe-Aumann Acts and Lotteries Notation: Throughout I will let $\Delta X$ denote the set of probability distributions over the set $X$.

I have been studying expected utility theory, and especially Savage Acts and Anscombe-Aumann Acts. However I am new to it and am not sure if I have the terminology correct.

Let $S$ be the finite set of possible states, let $Z$ be the set of possible outcomes. An Anscombe-Aumann act is defined as a function $f:S \to \Delta Z$. Let the space of acts be denoted $X$. Preferences are defined over acts.

If preferences have a state independent expected utility representation (SIEU) we have that there is a function $u: Z \to \mathbb{R}$ and a distribution over states $p \in \Delta S$ such that for any two acts $f,g \in X$,  $$f \precsim g \iff  \sum_{s \in S} p(s) \sum_{z \in Z} u(z) f(s,z) \leq \sum_{s \in S} p(s) \sum_{z \in Z} u(z) g(s,z)$$

Suppose I want to define a lottery $L \in \Delta Z$ in this situation. For simplicity, suppose $L$ is the lottery that assigns probability $1$ to outcome $z^{*}$ and probability $0$ to all other outcomes.

My Question is: Is this lottery (or any lottery for that matter) a compound lottery first over states ($p$) and then over anscombe -aumann acts ($f$)? Or how is a lottery defined in this situation?

Let me know if any clarification is required.

You are right, but to make sure that the odds are really exogenous ("objective") you need to make sure that the subjective uncertainty has no bite here. In other words, you need to assume that the objective lottery played after the horse race is independent of the result of the horse race (in Anscombe-Aumann's terminology).

Let's assume that $Z$ is finite, $Z=\{z_1,\cdots,z_n\}$ and that $L$ is the objective lottery that puts weight $l_i$ on the prize $z_i$, with $l_i \geq 0$ and $\sum_{i=1}^{n}{l_i}=1$.

You can identify the lottery $L$ with the act $f:s \rightarrow \Delta Z$ such that $f(s)=L$ for any $s \in S$. That is, for any $s \in S$, $f(s)$ is the objective lottery that puts weight $l_i$ on the prize $z_i$, exactly as $L$ does.


Whatever happened to Henry George's ideas? I have heard that Henry George wrote one of the biggest selling economics books in history (Progress and Poverty) and was so famous that 100,000 people attended his funeral, and yet his ideas about land are nowhere to be seen in most economics textbooks. Why is this? Were his ideas thoroughly rebutted?

If you're referring to a land-value tax, I'll just quote The Economist:

Other economists like it too. Adam Smith said “nothing could be more reasonable”; Milton Friedman termed it “the least bad tax”. Winston Churchill said scornfully that a landlord “contributes nothing to the process from which his own enrichment is derived”. The Organisation for Economic Cooperation and Development, a Paris-based thinktank for industrialised countries, supports the idea. So too did a recent working paper by the International Monetary Fund and the Mirrlees Review of British taxation by the Institute of Fiscal Studies. The mayor of New York City, Bill de Blasio, hopes that taxing vacant lots by value will help deal with urban blight in the Bronx and elsewhere.
[...]
The idea has wide-ranging support among modern economists, and more than 30 countries have some form of land-value taxation, usually in harness with other property taxes, on buildings.

While the idea of a land-value tax certainly has its drawbacks, it's far from being discredited.


Initial creation of reserves I am currently reading the book "Where does money come from?" which is co-authored by Richard Werner after I took the "Money and Banking"-class in coursera by Perry Mehrling.

There are certain questions which always pop up in my mind and which I find them either to remain unanswered or I simply don't understand the procedures.

Assumption:
I assume that Banks do not function as financial intermediaries as in neoclassical economics, which has been proven wrong by Richard Werner in his 2014 empirical study at the latest (but was well known to specialized economists, central bankers and bankers whose daily business are money market operations). Instead, I assume that money is created at the push of a button by a bank deciding to grant a loan to a customer. From this follows, that money in the form of cash/reserves is equally accepted by other agents as deposit accounts, which is why they are exchanged at par (i.e. at face value).

Now, as long as customers make electronic transactions within their bank or to other banks, the reserves of the respective bank remain unchanged. It is only when the customer withdraws cash that the reserves of the bank have to be converted to cash for the case that the bank doesn't hold enough.

There exists basically two ways of a bank accessing reserves (at least in the Euro-area, the UK and the US):
1) Borrowing reserves in the interbanking market at the Fed Funds Rate (US), the LIBOR rate (UK), the EURIBOR rate (Euro-zone)
2) By selling government securities to the central bank (or doing repos)

So far, I get the part with the interbanking market and why it works. What I don't understand is the following:

1) If a bank is selling government securities to the central bank in order to get reserves (or making a repo), where does this government security come from?
It is obvious that the security is issued by the government, but the government issues the security against receiving liquidity from the bank that buys the security. However, at the initial stage the bank doesn't have other liquidity than being able to open a deposit for the government to the amount of bought securities that the government in turn can access. Let's assume the government would like to access instantly the account of, say, 1 bn Euros and to withdraw the money in cash - will the central bank provide this 1 bn Euros without any discount?

2) As a follow up question: How could money be created if a government does not issue securities?

Thanks in adanvace.
BR

The current international monetary system based on pure fiat currency is a post-1970s system. For a long time before that most of the international monetary system was based on the gold standard. With the gold standard, governments issued currency relative to the amount of gold they held or they pegged their currency to another currency that was backed by gold. Hence, the bootstrapping issue you point out wasn't an issue. Note while current central banks often use government securities and bonds as assets to back the issuance of their currency, there is no rule that the asset needs to be a security (it could be gold like before) or that there even needs to be an backing asset at all (at risk of inflation).


Market Clearing with Dividend and Investment In pure exchange GE models, a typical goods market clearing condition for good $n$ looks like:

$$\sum\limits_{i=1}^Ic_n^i=\sum\limits_{i=1}^Ie_n^i.$$

Consider a model with production where firms can pay dividends and invest in new capital. New capital can be produced from output goods using a linear technology.

My Question: Taking the existence of dividends and investment into account, how does the goods market clearing condition look like in this case?

Look at textbook definitions of equilibrium in macro models of General Equilibrium with production and investment. Basically, the Equation $Y_t=C_t+I_t$ that says that the amount produced at a certain period must equal the consumption plus investment in that period is the relevant market-clearing condition in the market for goods.


GDP (Is this a part of GDP Calculation)? The GDP Calculation is for US.
If a Canadian company decides to change from a US supplier to a Canadian supplier, will that change the GDP?

I thought it would - as that it would reduce exports - but the answer given is "no change"

GDP is a measure of the value of final goods produced in a country over a period of time. Final goods are those that are sold to consumers. Therefore, the intermediate step of a supplier selling to another company would not be counted in the GDP calculation. Since it wouldn't have been counted in US GDP when the US supplier was selling to the Canadian company, there is no change in US GDP when the Canadian company changes to a Canadian supplier.

Consider car production across many companies in the US (some make tires, some make engine parts, etc.) that then sell these parts to the final manufacturer. We wouldn't count the production of each part separately, we just count the final value when the car is sold to a consumer.

EDIT: Apparently, I was mistaken. What I said regarding intermediate/final goods is generally true. However, after doing a little more research on this, it turns out exported intermediate goods are an exception to this rule. The value of these exports IS included in the calculation of GDP. For more details on this, see https://research.stlouisfed.org/publications/page1-econ/2018/09/04/how-do-imports-affect-gdp. I apologize for the confusion.

Given this revelation, I am somewhat stumped by your original question. Are there any other details provided in the statement of the question?


How does a reduction in consumer spending in favour of consumer saving, affect economic activity? Let's say our government runs an advertising campaign, encouraging its citizens to reduce spending money on consumer items, and instead save more money.

Let's say the campaign is successful, and that happens.

How does this affect economic activity?

On one hand the factory and shop owners appear to produce less, and thus hire less people, but on the otherhand, there is more money available to build new factories etc.

Such a "planned" and sought-after re-allocation of given income from consumption to saving, is justified only if the savings in an economy are sub-optimal (or we think so), in the sense of hurting the investment rate, which in turns hurts the (human and physical) capital infrastructure.

Think about the extremes: consume all that you produce, save nothing (as a society). Your capital base will erode, leaving in the end only the other factor of production, labor, an orphan, without the necessary capital to produce, leaving perhaps only land for the society to return to a non-industrial agricultural state.

So it is a matter of intertemporal (re)allocation of resources in order to guarantee that the economy survives, and then that it does a bit better than just surviving.

The conundrum: if businesses see consumption declining, why would they rush to make new investments even though now the "price" of these investments is lower, due to increased savings and so to increased availability of funds?

I would invoke here "Say's Law": Supply finds its own demand. (see the controversies over it).
For me, this law is better interpreted in the context of heterogeneity: no matter what overall consumer spending does, there is always some fields where consumer desire goes unfulfilled. Entrepreneurs try to identify these fields, and invest there (this has a Schumpeterian flavor).

The above discussion does not mean that we will not observe phenomena like increased unemployment. After all, investing in new fields requires re-allocation of productive resources, and this is not easily nor quickly done. And there is always the case that the "savings drive" may overshoot, and the economy will be led to a lengthy recession, Japan some 20 years ago being the classic modern example (in fact in Japan, the government tried actively to persuade the citizens to raise their consumption, but it failed).


Is there a solution to the Joker's game in The Dark Knight? In the final battle in the movie, the Dark Knight (2008), the Joker has rigged two ferries carrying people out of Manhattan Gotham to explode. One ferry carries mostly civilians with a substantial National Guard presence. The other ferry contains large numbers of prison inmates and some guards. The Joker has rigged both to explode, and he has given the crew on each boat the detonators — only they have the detonator for the other boat. He announces the rules of the game to the crew and passengers of each vessel.

  Each of them have the power to blow up the other boat and then their boat will live.
  If they get to midnight with know no exploded boats, the Joker will detonate both.
  Any attempt to leave or defuse the bombs will result in the destruction of both boats.

Is this a known variant of the prisoner's dilemma? How to model this game and what is the actual solution? Why is the equilibrium as shown in the game attained?

Suppose first that the groups are not altruistic and care only about their own survival. It is not exactly a prisoner's dilemma since the outcome obtained by mutual cooperation (if both groups wait) is not Pareto-improving: everyone dies in that case. The only equilibrium is that one of the groups destroys the other boat as soon as possible; and any action played initially by the other group is possible in equilibrium, since this team is indifferent between waiting and triggering other the bomb (they will die one second later anyway).

As @Alecos_Papadopoulos wrote, the game becomes more interesting if the groups have pro-social preferences. For instance, they might be reluctant to sacrifice the other group and prefer that everyone dies (including themselves). If there is no uncertainty, the outcome is trivial: the only equilibrium is that both groups wait until the Joker triggers the bombs.

The most interesting scenario is the one in which the types of the groups are uncertain: each boat can be either selfish or altruistic. In that case, it seems reasonable (but other specifications are possible) to assume that cooperation is desirable only if the other group is also altruistic, but if the other group is selfish the individuals prefer to kill them first and survive. The equilibrium strategies are the following:

If the group is selfish, it triggers the bomb of the other group as soon as possible (it is a dominant strategy).
If the group is altruistic, its initial action depends on its beliefs about the other boat. If it is sufficiently optimistic (i.e it believes that its opponent is altruistic with a sufficiently high prior), the group waits. If it has not exploded one second later, the group understands that it faces an altruistic opponent and therefore waits until the Joker kills everyone. Notice that the explosions happen either at $t=0$ (as soon as the game starts) or at midnight (when the game ends) but never in between.


IS-LM , Eurozone and Interest Rate Parity In the IS-LM framework, when the CB expands Money supply, interest rates are driven down, investment is boosted, and aggregate output increases (shift of LM curve, movement along IS curve). In the case of the Eurozone, given that member countries are not able to unilaterally expand money supply- this is the mandate of the ECB- it is often said that there is no monetary independence. However, interest rates in different European countries are different. I have two questions:

i) Even though the currency is the same, the interest rates are different. Would a risk premium be the only explanation for the interest parity condition not holding here (there is no risk of devaluation for the same currency)?

2) The Central bank of each country has no power over the money supply. However, the yields are still different. Is this purely a result of market forces (again determined by differences in risk?)?

In a broader sense, what is the role of the European network of central banks when they can't control the Money supply ? (the main purpose of existing for most central banks).

It’s the same currency and interest rate structure for all countries. The only difference is that there is a default premium for some countries. You see the exact same thing in Canada, with the Canadian provinces trading at different yields.
The ECB is literally the union of all the national central banks. When the ECB makes a decision, it is implemented at the national central bank level.

The IS/LM model has severe limitations. The ECB sets interest rates; it’s ability to control “the money supply” (which aggregate?) is debatable. (It can increase the size of the monetary base, but that does not imply that bank deposits etc. will grow.)


Quality of French wine in the US vs French wine in France I remember reading a study/paper saying that the AVERAGE bottle of french wine drunk in the US is better than the average bottle of french wine drunk in France, due to the fact that nobody bothers to ship the crappy stuff. Anyone got a link?

This is called the Alchian–Allen effect.

  The Alchian–Allen effect was described in 1964 by Armen Alchian and
  William R Allen in the book University Economics (now called Exchange
  and Production). It states that when the prices of two substitute
   goods, such as high and low grades of the same product, are both
   increased by a fixed per-unit amount such as a transportation cost or
   a lump-sum tax, consumption will shift toward the higher-grade
   product. This is true because the added per-unit amount decreases the
  relative price of the higher-grade product.

  Suppose, for example, that high-grade coffee beans are \$3/pound and
  low-grade beans \$1.50/pound; in this example, high-grade beans cost
  twice as much as low-grade beans. Now add a per-pound international
  shipping cost of \$1. The effective prices are now \$4 and \$2.50;
  high-grade beans now cost only 1.6 times as much as low-grade beans.
  This reduced ratio of difference will induce distant coffee-buyers to
  now choose a higher ratio of high-to-low grade beans than local
  coffee-buyers. (Prices are illustrative only).

  The effect has been studied as it applies to illegal drugs and it has
  been shown that the potency of marijuana increased in response to
  higher enforcement budgets, and there was a similar effect for alcohol
  in the U.S. during Prohibition.

  Another example is that Australians drink higher-quality Californian wine than Californians, and vice versa, because it is only worth the  transportation costs for the most expensive wine.

From the Alchian–Allen Wikipedia page, emphasis mine.

I learned about this paradox in the context of Why the Best Washington Apples are Shipped out of State, discussed in a chapter of a fun popular economics book Puzzles and Paradoxes in Economics which also happens to be a great source of undergraduate economics exam questions.


Monopoly with price discrimination A city has a single electricity supplier. Electricity production cost is $c$ per unit. Utility function $U(q,t)=a\ln(1+q) - t$, where $q$ is electricity consumption and $t$ is electricity tariff. What is the profit maximizing tariff?

I have figured out $\text{MC}=c$ and the supplier is monopolist so $\text{MR}=\text{MC}$ condition have to be used but I can't figure out how to get MR from the utility function.

I assume $t=pq$ is meant. $p$ is the price per unit.

We want to know when

$$U(q,p)=a \ln(1+q) - pq$$

is maximal, given $a>0$ and $p>0$, since this is the utility function and the quantity $q$ the customer buys is the quantity where the utility function is maximal.

The derivative with respect to $q$ is

$$\frac{d}{dq} U(q,p) = \frac{a}{1+q} - p$$

Set derivative to zero gives $q =\frac{a-p}{p}$.

Now we want to know when $(p-c)q$ is maximal, since that gives maximal profit.

Insert $q =\frac{a-p}{p}$ to get $\frac{(a-p)(p-c)}{p}$ is maximal. Rewrite this to $-p+a+c-\frac{ac}{p}$. Take the derivative with respect to $p$ and set to zero to get

$$-1+\frac{ac}{p^2}=0$$

$$-p^2+ac=0$$

$$p^2=ac$$

$$p=\sqrt{ac}$$

Thus we get $t=pq=a-p=a-\sqrt{ac}$.


Why utility should be bounded (or unbounded)? For Expected Utility and SEU, people make axioms to ensure that the utility is bounded. However, I personally believe that the utility function must be unbounded, especially if we are considering cardinal utility. I'll explain my point in a though experiment.
Even if I have a diminishing marginal utility, there will be always some increase in money that will improve my utility by one unit. For example, it is possible that doubling money means one unit of utility for me, or it is possible that tripling money means one unit of utility for me. Either way, the range of my utility function must be unbounded. In a more rigorous language, if a utility function of money is bounded, then, when the money is approaching infinity, the utility function becomes arbitrarily close to a constant function, which violates non-satiation.
My question is, which economist argue that utility in real life must be unbounded, and who argue that a bounded utility is more normative, rational, or natural? Did economists reached a consensus that utility function must be bounded in real life? Any literature will be very helpful.

Sources for bounded utility: EU: Bounded expected utility, PC Fishburn (1967)

tl;dr: Short answer is that cardinal utility of rational person is in large part of a literature is derived from the von Neumann and Morgenstern expected cardinal utility framework. In such framework utility must be bounded by our definition of what rationality is. So in such framework the short answer is simply that utility has to be bounded for person to be considered rational.
There are also expected utility frameworks that allow expected utility to be unbounded (see review by Fishburn, 1976). However, these are not very widely used as they can often lead to paradoxes and do not seem to offer any special insight. I suppose this is due to the strong influence of instrumentalism on economic thinking. A researcher would prefer a utility framework that is able to provide some testable predictions rather one that just results in a paradox and hence offers no useful testable prediction. So even if someone could perhaps consider concept of unbounded utility more elegant its instrumental value in doing research would be close to none (if in particular case it leads to unresolvable paradox).
Full Answer:
The utility needs to be bounded in order to avoid paradoxes such as the St. Petersburg paradox (for more nuanced overview see this entry in Stanford encyclopedia of philosophy). As a matter of fact a rational person's utility should be bounded as suggested by Arrow (1970) precisely in reference to the paradox above.
More general actually cardinal utility will be bounded by the axioms that were used to derive the expected cardinal utility in the first place. Following Neumann and Morgenstern (1947) Theory of Games and Economic Behavior,  an expected utility from gamble can be described by the so called von Neuman-Morgenstern equation:
$$E[u(g_i)] = \sum_j u(X_{ij})p_{ij}$$
where $u$ is utility $g_i$ is gamble $X$ is an outcome and $p$ is a probability. Furthermore, for the above to be utility we must have some continuum of gambles for which:
$$g_i,g_j \in \mathbf{G}: g_j \succeq g_i \implies E[u(g_j)]\geq E[u(g_i)] $$
Now given this we can ask (as the author of the paper did) what would be properties of such utility function?
Now it turns out that basic rationality constraint where preferences satisfy transitivity, completeness, continuity and independence imply that the utility has to be bounded.
The completeness axiom states:
$$ \forall x,y \in \mathbf{X}: x \succeq y \vee y\succeq x \vee y \thicksim x $$
that is we can order all our options in terms of preference in some way.
The transitivity axiom states:
$$ \forall x,y,z \in \mathbf{X}, \text{ if } x \succeq y \wedge y \succeq z \implies x \succeq z$$
So if someone likes $x$ more than $y$ and $y$ more than $z$ then $x$ must be preferable to $z$
The continuity  $z \succeq y \succeq x$, then there must be some probability $p$ such:
$${px,(1-p)z} \thicksim y $$
This implies that no outcome $x$ is so terrible that you would not take up some gamble involving $x$.
by independence axiom if $y \succeq x$ then for $z$ and some probability $p$
$${px,(1-p)z} \preceq {py,(1-p)z} $$
This axiom states that if two outcomes have the same probability, we should evaluate the two alternatives independently of what we think that the outcome is.
The above axioms are how we define rationality in expected cardinal utility. There are of course different possible specifications of utility functions but most modern research relies on the von Neuman-Morgenstern type (or related utility functions).
Now these rationality requirements - which are axioms so they are by definition what rationality is in this context, simply demand that no outcome can produce infinite utility. In order to see this we can try to do proof by contradiction - suppose that there is a gamble wehere: $x = 1€$, $y=100€$ and $z= \infty €$ and that $u(X)=x$. In this case clearly $z \succ y \succ x$ but there is no $p$ for which the continuity axiom holds. Since the continuity axiom would be violated our basic axioms of what rationality is would not hold and a person with unbounded utility would cease to be rational (within the context of von Neumann and Morgenstern framework).


Instrumental variables for minimum wage I was wondering if there is a classic instrument for minimum wage as there is for schooling or other variables. If so, how does it fares with respect to most established designs like spatial differences http://davidcard.berkeley.edu/papers/njmin-aer.pdf or recent spatial regression discontinuity designs.
Assume even that one has panel data is it enough to control for its deep lags.
This is a reference question but if you have your own ideas feel free to post.

This Discussion Paper (PDF) suggests the use of political variables as an instrument for minimum wage.

See abstract (emphasis mine):

  Following the early 1980s apparent consensus, there has been a controversial debate in the literature over the direction of the minimum wage employment effect. Explanations to non-negative effects range from theoretical to empirical identification and data issues. An explanation, however, that has not been sufficiently explored is that a non-negative effect might be an upward biased estimate of a truly negative effect, resulting from the simultaneous determination of the minimum wage and employment. This paper estimates the employment effect of the minimum wage using a number of political variables – not previously used in the literature – as excluded exogenous instruments to control for the endogeneity of the minimum wage variable. The data used is an under-explored Brazilian monthly household survey from 1982 to 2000. Robust results indicate that an increase in the minimum wage has very small adverse effects on employment.

This article (PDF) (Which I like better anyway) uses the differences in the changes on minimum wages wrt to the federal minimum wages. It is worth noting that this paper has a pretty good reference list and useful introduction as well. I'd start here looking for further reading.

See abstract (emphasis mine):

  The magnitude of the impact of minimum wages on employment is a hotly debated topic in policy and academic circles. In this paper, we use cross-state differences in the impact of adjustments in federal minimum wages on effective minimum wages in each state - the maximum of federal and state minimum wages - to reassess this question and explain biases in past research. A rise in the federal minimum wage will have a larger impact on a state's effective minimum wage in states in which federal minimum wages are binding. Using CPS data for 1977-2007, we find notable wage impacts and large corresponding disemployment effects, yet only when we utilize the differential influences of federal minimum wages to instrument for state wage floors. State effective minimum wages are procyclical. Accounting for the endogenous determination of effective minimum wages at the state level turns out to be materially important for drawing accurate inferences about the impact of minimum wages on employment


What is it about the money market safeguards that increase volatility? In recent coverage of the Fed's repo operation, I was struck by this line:

  It also indicated Wall Street is struggling to absorb record sales of
  Treasury debt to fund a swelling U.S. budget deficit. What’s more,
  many dealers have curtailed trading because of safeguards implemented
  after the 2008 crisis, making these markets more prone to volatility.

I do not find this so intuitive, because increasing volatility seems to be an unlikely policy objective in the context of other initiatives at the time (TARP et all.)

Question

I hope I did not over-simplify the matter, and I would like to understand what is the regulation the article refers to and what is the logic behind the perceived "more prone to volatility?"

I don't know much about repo markets, but in dynamic systems in general, two things are likely to generate volatility:

Large shocks of any kind, corrective or not, especially when they are reactive (and therefore delayed and possibly out of phase with underlying cycles - think about pushing a child on a swing while standing at the edge, versus standing in the middle, of the arc).
Reducing the inertial mass of the system.  In this case, reducing the volume of trading.

You have both here. The large shock is the corrective policy (post-2008 actions like TARP), coming potentially years after the initial cause of the financial crisis. The reduced inertial mass can be partly explained by traders reacting to the disconnect between asset values and fundamentals due to actions like TARP, which was mainly about buying up worthless assets to keep banks afloat.


Credible Threat in the Perfect Bayesian Equilibrium Consider a simple game between P1 and P2 shown in Figure 1.

We consider a Perfect Bayesian Equilibrium. P1 uses a cutoff strategy based on his $c_1$ that has the Cumulative Distribution Function of $F$. If his $c_1$ is lower than a threshold $c_1^*$, which depends on P2's strategy, P1 takes the strategy $x$.

Similarly, P2 uses a cutoff strategy based on his $c_2$ that has the Cumulative Distribution Function of $G$. If his $c_2$ is lower than a threshold $c_2^*$, which depends on P1's strategy, P2 takes the strategy $a$.

We denote the optimal cutoff strategies as $F(c_1^*)$ and $G(c_2^*)$.

Suppose the game has slightly changed as shown in Figure 2.

Now P1 has one more turn. Suppose that, given the initial $F(c_1^*)$ and $G(c_2^*)$, we set P1's gain from the strategy j as always being equal to the strategy k. We assume that P1 takes the strategy j if P1 is indifferent between j and k.

In this case, does P2 still continue to use the same cutoff strategy $G(c_2^*)$? For P2, the node from the path $k$ is never reached while P2 cannot verify it. As long as P2 uses the same cutoff strategy $G(c_2^*)$, P1 will take the strategy $j$. I am wondering if P2's threat is credible.

In the new game, P2's gain remains unchanged. However, P2 may try to increase his gain by deviating from the optimal cutoff strategy $G(c_2^*)$ if P1 never use the strategy k. But, P1 will be aware of it and may use the strategy k again. If so, P2 will again use the same optimal cutoff strategy $G(c_2^*)$. I got stuck here.

I appreciate any help.

I am going to assume that $F$ and $G$ are continuous distribution functions (I.e. players are playing properly mixed strategies). If this is not the case there is not enough information to answer your question. Given that assumption, player 1 and 2 must be indifferent among their actions in game 1 given the strategies of the other player.

In the second game, you are assuming that the node given by $x,k$ is never reached (since $j$ and $k$ give the same payoff and when indifferent, player 1 always choose $j$).

Under that behavioral assumption (which must be verified to be consistent with equilibrium), player 2 must believe she is at the node "$y$" with probability 1. Since Player 2's beliefs have changed with respect to game 1, the mixed strategy given by $G$ is, in general, no longer optimal (unless $a$ and $b$ give the same payoff regardless of the action of player 1).

In short, player 2 will, in general, not use the same strategy in the first and the second game; so threatening to use $G$ is not credible.

Btw all threats are credible in a PBE since strategies are best responses given some beliefs that are Bayesian.


Do modern economists still believe balance of trade is an important concept in economics? My understanding is that discussions about a nation's balance of trade was largely seen as important by mercantilists, but isn't really part of modern economics. Am I right about that?

The economics of trade can broadly be divided into two parts.  There is a microeconomic part concerned with patterns of trade in particular kinds of goods, their causes such as factor endowments and costs, and effects on welfare, key concepts being comparative advantage and the gains from trade.  Then there is a macroeconomic part concerned with overall volumes of trade and payments for traded goods, and their relations with exchange rates and domestic macroeconomic conditions.  The two parts can be linked, as in the Dekle et al paper referred to by emeryville, but more often are considered separately.

The concept of balance of trade belongs in the macroeconomic part, although
economists often use the more precise term balance on current account, which includes trade in goods and services and certain other items. It is generally considered that a continuing deficit on current account is harmful because the net outflow of funds cannot indefinitely be met by running down the country's international currency reserves, and must eventually be balanced by an inflow of funds associated with increasing international debt and/or foreign ownership of domestic assets.  The moderate aim of a balance on current account avoids two disadvantages of mercantilism, which aimed to achieve a surplus: firstly, it led to conflict because it was impossible for every country to have a surplus, and secondly, it reduced welfare, because restrictions on imports meant that the (microeconomic) gains from trade were not fully achieved.

Thus the balance of trade or balance on current account remains an important concept in the macroeconomics of trade.


Correlated Equilibrium for Rock Paper Scissors Consider the game of Rock, Paper, Scissors (RPS), with payoffs given as follows:

Is there a correlated equilibrium in this game?

Consider, for example the signal given to both players not to play the third strategy. In this case, the game (conditional upon one's opponent following the signal) becomes:

Which has a NE of playing the second strategy for both. This seems like a correlated equilibrium? On the other hand, if you know that your opponent follows the signal and plays the second strategy, you should respond by playing the third strategy. Hence, intuitively, as the signal reveals information on your opponent's play (conditional upon her following it) you should be able to exploit that by violating correlated equilibrium.

No, the unique Nash equilibrium is the unique correlated equilibrium by a general property of two-player zero-sum games pointed out in:

  Forges, Françoise. "Correlated equilibrium in two-person zero-sum
  games." Econometrica (1986-1998) 58.2 (1990): 515.,

For every action of player 2 that is played with positive probability, the conditional distribution over player 1's actions is an optimal strategy for player 1 and vice versa. Since optimal strategies are unique in RPS, the conclusion follows.


Negative long term effects of wage cap, especially on purpose of money? It can be figured that a wage cap could have some noticeable short term effects - mainly, those who are higher paid will not receive as much money anymore, meaning less spending by the richest in the economy (who also happen to own a large portion of the economy's wealth) and more economic downturn for companies.

However, the market could normalize after this as the money earnt by a nation's richest would eventually be more evenly distributed amongst others, hence they would spend more, canceling the downturn.

My question is how will a wage cap (a limit on the amount of income that can be possibly earnt in a year) have negative long term effects that will not be countered by more equal spending in the economy, as provided in the example?

Mainly, I am interested in how will this affect the purpose of money. Would the power of money possibly be restricted in a noticeable way that leads to negative effects in the long-term? Would there also be other negative effects, both on the macroeconomic and microeconomic scale, that would last in the long-term and prove difficult to counter?

Sources, links and further reading is welcome. Thank you in advance.

However, the market could normalize after this as the money earnt by a nation's richest would eventually be more evenly distributed amongst others, hence they would spend more, canceling the downturn.

Wage cap is not an redistribution measure. It’s an measure aimed at reducing inequality but without any direct redistribution.

For example, suppose you have Peter and Paul, Peter earns 10000\$ per month and Paul 1000\$ per month. If there is wage cap 5000\$, Peter will earn 5000\$ and Paul is still earning only 1000\$. Hence there is no direct redistribution effect even though inequality is now lower.

So there will not necessarily be any more spending in an economy. That assumption is completely false and would hold for income tax that redistribute money from rich to poor but not for wage cap. In fact most likely there will be less spending in the economy as result of wage cap.

Regarding other long term effects of wage cap, it would severely depress the labor supply of people to whom it applies to. Wage cap is de facto equivalent of confiscatory tax that confiscates any income above certain level, but it is even worse as government does not even get any revenue, from it. If a person does not earn any income for their labor above certain level they will have no incentive to work anymore (aside from maybe the fact that they enjoy their work). Hence their labor supply will be depressed. They will spend less time at work and more time enjoying some leisure activities.

This can have serious impact on economy as usually people who earn more in market based economies are those people who are more productive. Highly skilled doctors, managers, scientists etc, decreasing overall productivity of the economy. Moreover, such measure would create a permanent supply shock (as long as it would be in effect) permanently lowering the level of GDP and hence also the material welfare of people in given country.

It could also impact the growth of the economy, as endogenous theory of economic growth says that human capital formation can be very important driver of economic growth and since people tend to earn more the more human capital they have this would depress the human capital formation for the very brightest who would be affect by such a measure.

Also as a side note, I don’t really know any public economists who would approve of wage cap. The reason for that is that in fact if you care about redistribution you want as many people with high incomes as possible so then you can tax their incomes and raise the welfare of the poor through redistribution.


Why are the same set of controls used for both OLS and 2SLS? I have been reading several papers that use 2SLS. These papers usually also show the OLS regression results. I noticed that when authors report results for 2SLS, they also include control variables that were used in the OLS regression.

If 2SLS is supposed to solve the omitted variable bias, couldn't we omit the control variables that are included in OLS because we do not have to worry about omitted variable bias? For what reason would authors include those variables?

The reason for that is that 2SLS does not solve omitted variable bias without its cost.

First, for every omitted variable you would have to find suitable instrument. Finding instruments is incredibly hard so why would you purposely create more omitted variable bias? Unless you are trying to challenge yourself for fun or doing it as a practice exercise for students it does not make sense.

Second, actually 2SLS still has bias - the advantage of 2SLS is that bias decreases as strength of the instrument increases, so with good instruments 2SLS is better than OLS in terms of bias. But in practical applications you rarely have perfect instruments- so even in case you could feasibility instrument the other variables you omit on purpose you will be just adding to the bias of your model.

Hence you should always include all relevant controls that you can include


Marshalian and Hickisian Demands and Slutsky Equation everyone.

I have the following question:

A consumer has the following indirect utility function:

$ V(p_1,p_2,b) = (p_2k-b)p_1^{-1} \left[ \frac{2p_2k - 2b}{p_2} \right]^{-2}, x_2 < k$

a) Find the Marshalian demand for good 2.

b) Find the Hicksian demand for good 2.

c) Show that the Slutsky equation holds for good 2.

d) Why is it necessary to have $x_2 < k$

For a) I found:

$ \boxed{\boxed{ x_2(p_1,p_2,b) = \frac{2b-p_2k}{p_2} }} $

For b):

$ \boxed{\boxed{ x_2^c(p_1,p_2,\bar{U}) = k - \frac{P_2}{2P_1 \cdot \bar{U} }}} $

For c) after replacing $E(p_1,p_2, \bar{U})$ with $p_1 \cdot x_1(p_1,p_2,b) + p_2 \cdot x_2(p_1,p_2,b)$ I found $\bar{U} = \frac{p_2^2}{(p_2k-b) 4p_1}$ and using that in

$\frac{\partial x_2(p_1,p_2,b)}{\partial p_2} = \frac{\partial x_2^c(p_1,p_2,\bar{U})}{\partial p_2} - \frac{\partial x_2(p_1,p_2,b)}{\partial b} \cdot x_2(p_1,p_2,b)$

I was able to show that both sides are equal.

For d) here's what I've tried:

using Roy's identity we can find

$x_1(p_1,p_2,b) = \frac{p_2k - b}{p_1}$

assuming the demand for good 1 is positive, we must then have:

$ \frac{p_2k - b}{p_1} > 0  $

Since $p_1 > 0$, we can re-write the inequality as

$ p_2k - b > 0 $

but

$b = p_1x_1 + p_2x_2$,

so

$ p_2k - p_1x_1 - p_2x_2 > 0 \therefore p_2 \cdot (k - x_2) > p_1x_1 \therefore k-x_2 > \frac{p_1x_1}{p_2}$, because $p_2$ is positive.

Now, since $p_1 > 0$ and assuming $x_1 > 0$, we have $\frac{p_1x_1}{p_2} > 0$, which in turn implies that

$k-x_2 > 0 \therefore \boxed{\boxed{x_2 < k, Q.E.D.}} $

Are my answers correct? In c) is there a faster way to find $\bar{U}$ so I can replace it in the Hickisian demand and show that the Slutsky equation holds for good 2?

I appreciate any inputs.

Have a good one,
Pedro.

Although my teacher has yet to verify my solution for d) (which I believe is incorrect), he shared his answer and the condition $x_2<k$ derives from the positivity of $V(p_1,p_2,b)$ and from the budget inequality $p_1x_1+p_2x_2≤b$. The other answers are correct.


Imperfect vs incomplete information What's the difference? To illustrate, please give examples of

A game with perfect but incomplete information; and
A game with complete but imperfect information.

Related.

You are at a decision point and you don't know what strategy the other player has taken. But you still know that which game you are in, you still know the other players' strategy sets etc.
Under incomplete information you might not even know what game you are into.

For example: Two firms are taking up R&D projects sequentially. One is the first mover. It decides whether to take up R&D or not. Now the second firm has to decide but does not know what first firm has decided. This is imperfect information.

Now imagine ypu are playing a card game and need to throw a card but you don't know whether you are playing poker or sweep. This is incomplete information.


How does one interpret the usda wholesale market price reports? For example: http://www.ams.usda.gov/mnreports/nx_fv010.txt

The data for mangos is :
MANGOES:  MARKET STEADY.  flats 1 layer HT Francis (Francine) 9s 11.00 10s
12.00 12s 10.00-12.00 MX Keitt 7s 5.00-6.00 few 6.50 8s 5.00-6.00 few 6.50-7.00
9s 5.00-6.00 few 6.50 10s 5.00-6.00 few 6.50 12s 5.00 occas higher Kent 6s
6.00-7.00 fr appear 4.50 7s 5.00-6.00 8s 5.00-6.00 9s 5.00-6.00 10s 5.00-5.50
few 4.00 12s 5.00 Ataulfo 18s 12.00 25 lb cartons DR Banilejos 36.00

What exactly do these numbers mean?

MANGOES: MARKET STEADY. flats 1 layer [[cargo type]] HT [[Haitii]] Francis [[variety]] 9s [[9 fruits in 1 layer flat]] 11.00 [[price for 9 fruits]] 10s [[10 fruits in 1 layer flat]] 12.00 [[price for 10 fruits]] MX [[Mexico]] Keitt [[Variety]] 7s [[count]] 5.00-6.00 [[price]] few 6.50 [[a few at a different price]] ...etc... 25 lb cartons [[cargo type]] DR [[dominican republic]] Banilejos [[variety]] 36.00 [[price]]


GDP with Intermediate Production I'm a total noob.  Please be kind.  :)

GDP is only calculated using "end products".  This seems terribly difficult to me.  For example, is a truck an end product or a method for production?  If I'm driving myself and my family around, then it seems like an end product.  But if I'm using it on my farm, then it doesn't.

How about a computer?  If I'm using it to play video games, then it seems like an end product.  But if it's used in a hospital to manage medical records, then it seems like an intermediate product.

How are these multiple uses taken into account with GDP?

I want some metric that is the total amount of goods produced (regardless of whether or not the good produced is an end product or not).  What is the best metric for this?

Thank you!

You’re looking for gross output; GDP is final output.

Per the BEA:

  Economy-wide, real gross output—principally a measure of an industry's sales or receipts, which includes sales to final users in the economy (GDP) and sales to other industries (intermediate inputs)

For calculation purposes, it’s generally assumed that a firm purchasing a good (for example, a computer) is using it as an intermediate input, while a household purchasing the same good is using it as consumption (so it’s a “final sale” counted in GDP), though corrections are applied in particular cases where this assumption doesn’t hold well. Cases where households act as producers, like farms and real estate, are prime areas for these corrections.


Acemoglu - Introduction to Economic Growth - Existence of a one-to-one relation between human and physical capital In the book the author claims that equation $(1)$
$$
f_x(x(t),y(t)) - f_y(x(t),y(t)) = a - b \hspace{10mm} (1)
$$
where $f_x(\cdot)$ is the partial derivative of $f(\cdot)$ with respect to $x$ and $a,b$ are constants, along with condition $(2)$
$$
f_{xy}(x(t),y(t)) > 0 \hspace{10mm} (2)
$$
implies that there is a one-to-one relationship between $x$ and $y$ of the form
$$
y = \xi(x)
$$
where $\xi(\cdot)$ is uniquely defined, strictly increasing and differentiable.
How would I go about seeing that? I understand that if I replace this generalized version for one using a Cobb-Douglas production function, for instance, I could see it more clearly, but I wanted to understand how it works in general.
Thanks!

I think this needs little bit context to be answered, because in your question you missed a whole host of background assumptions - this is not a result that will hold for arbitrary function.
The equations actually describe are derived from first order optimality condition for a steady state from a Hamiltonian
$$f_k(k(t), h(t)) − f_h(k(t), h(t)) = \delta_k − \delta_h,$$
where $f$ is production function, $k$ per capita capital and $h$ per capita human capital and $\delta_k$ and $\delta_h$ are the depreciations respectively. Furthermore, as stated in the first paragraph you omit host of many important assumptions about the production function.
These assumptions are too many to be listed here (the assumptions take several pages to explain in the textbook itself in ch 3.3 on pp 85 and following pages), but the main important assumptions (and their implications) are:

$f$ has constant returns to scale
$f$ is strictly concave in $k$ such that: $f (k^∗, h^∗)>f_k(k^∗, h^∗)k^∗ + f (0, h^∗) \implies f (k^∗, h^∗)>f_k(k^∗, h^∗)k^∗$
$f_k(k(t), h(t))>0, f_h(k(t), h(t))>0$ and $f_{kh}(k(t), h(t))> 0  $ implies function is monotonically increasing.
Inada conditions.

These imply that if you double the factors of production output will double  and that one would always want to use human capital and capital together. This means that one would always want to increase usage of capital together with human capital rather than just usage of one factor.
Since whenever we increase use of $k$ we want to also increase use of $h$ and since difference between marginal productivity of both of them will be always constant, there should be some one-to-one mapping between $k$ and $h$ described by some function $k=\xi(h)$. Also this is why the textbook assumes that $\xi(\cdot)$ is strictly increasing, unique and differentiable. It has to be strictly increasing because the more human capital $h$ we use the more we will want to use regular capital $k$. It is unique given that from all conditions we impose on the model there will always be some unique equilibrium $(k^*,h^*)$ combination, and differentiable simply because this is obviously continuous function.    Also this result would not hold for any arbitrary function $f$.


To input equation from eviews to excel Eviews,

Just want to know how we can use the below estimation equation using MS-Excel.

Estimation Equation:

CLOSE = C(1)*D(CLOSE) + [AR(3)=C(2),MA(3)=C(3),BACKCAST=1/29/2016,ESTSMPL="1/29/2016 5/27/2016"]

Let's begin by fleshing out what the EViews code is saying.

The EViews code says that the variable CLOSE depends on its first difference and there is also an ARMA(3,3) error term included in the model. Supposedly, the ARMA error process is to whiten the residuals, which can be, and has been, argued against as a modelling strategy. It's also worth noting that there is no constant term in the equation. The reference to BACKCAST indicates how the MA process is initialized - the details of which can be found in the EViews documentation. ESTSMPL typically refers to the estimation sample.

Having understood the EViews code, the question is now: how does one estimate a linear regression model with ARMA errors using MS-Excel?

The easiest solution would be to find an existing add-in that provides this feature. An alternative method would be to write the code yourself using the MS-Excel programming language (VBA). Beware though, what makes this application tricky is the MA term; AR processes are easier to program and more common in certain fields, e.g. VAR models appear more frequently in economics than VARMA models. Another approach, if you are willing to delve into some code, would be to look at some R source code (either base code or from some time-series package) to get a sense of the task ahead if you do decide to program from scratch. Programming this from scratch seems like overkill, though, as this sort of estimation has been around for decades. Why bother if all you're interested in are the estimated parameters and not the underlying routines? It doesn't answer your question, but my advice would be to use R if EViews is not available to you. Or, seek out an MS-Excel add-in that will do the job for you.

A useful thread from the EViews forum is here: http://forums.eviews.com/viewtopic.php?f=7&t=465. Note: "Estimation, and forecasting of MA processes is complicated, especially when backcasting is used to obtain starting observations for the error terms."

Good luck!


Why are stock prices so time sensitive? It seems like the vast majority of all goods and services don't change price so often.

I guess I should be careful the way I say this, because as far as I understand, they're actually very information sensitive.

So what I really mean is, why do they have 2 second ticks where the price might change, rather than changing daily to adjust for information? It seems like a 2 second tick is a little over the top.

If it is really necessary to have such a frequent possible update of prices, why do other goods and services not need that? Or which ones also do?

Prices changing so frequently is simply the result of an adjustment between demand and supply in the market. Demand and supply change all the time, because market venues allow them to change very frequently, and so does the prices. This does not mean that the fundamentals of the underlying assets are also changing, this is just the way market process (what it perceives as) new information.

Say the price of a stock is $x_0$ and I'm about to buy 1,000 units of that stock. Effectively, I will buy those 1,000 units at a price $x_1>x_0$ because at a given point in time demand increases so the price adjusts. However, if there is no new information, it's likely that somebody else would want to sell 1,000 units after that, and then the price would adjust downward at $x_2<x_1$. Note that we do not necessarily have $x_1=x_0$ though. It depends on much more factors that in my simple example, but the idea is there.

The price changing a lot, also means that you, as an investor, are able to buy/sell at any point in time. If, as you said, prices were updated once a day, that means that you would be able to make a transaction only once a day. Actually this exists on some market, and in general the price is set through an auction process. But obviously, if possible you want to be able to buy/sell at the moment you take the decision, and in general you would dislike to wait until the daily batch processed.

Regarding, the high frequency that the most liquid markets have reached now, this is the result of the competition between market venues. Indeed, in current days, there are often several places where you can buy/sell a particular stock for instance. Since market venues are seeking to attract the largest possible amount of transaction on their market, for liquidity reasons, this results in market competing on the frequency they offer to market participants.

Actually, this is a bit more complicated, let me just sketch up some words. Algorithmic traders are the type of market participants that provide a lot of liquidity because their are able to buy/sell extremely fast, there are the new market makers in a sense. The people who set up those algorithms (large banks mostly) are also seeking for profit. They know that high-frequency will make them more efficient than classic human investor, so they are looking for the fastest possible way to make transaction on a market. And market platforms, wanted to attract those liquidity traders (the algorithmic traders), have increased (a lot) the frequency of their market. This is not necessarily bad, actually if you buy/sell something on a exchange-market, it's likely that your counterparty will be an algorithm. The question of whether it's efficient or not, especially in time of crisis, is more opinion-based and there are some research on that issue.


Definition of capitalism Does the discipline of economics have an accepted rigorous definition of capitalism?
 I.e. not something like "some economists would quote Hayek and say that so and so constitutes capitalism" but an if and only if definition that most economists would agree on.

The dictionary definitions of capitalism (currently the most upvoted answer) have been critiqued as inadequate, in the sense that they are too broad, by Geoffrey Hodgson in his treatise, Conceptualising Capitalism (University of Chicago Press, 2015).

  Definitions proliferate. Most dictionaries stress private
  ownership and markets; many add the profit motive. The entry in The
   New Encyclopaedia Britannica (1998, 2:831) is typical: “Capitalism, also
  called free market economy, or free enterprise economy: economic system
  . . . in which most of the means of production are privately owned
  and production is guided and income distributed largely through the operation
  of markets.”

  But, if we consider systems based largely on private ownership, the
  profit motive, and markets, we can find many examples before the medieval
  era. [...] trade has existed for tens of
  thousands of years, markets may have appeared as long as five millennia
  ago in China, and they were evident in several locations in the eastern
  Mediterranean and the Middle East around 600 BC. Private ownership,
  the pecuniary calculus, and the profit motive have similarly played
  a prominent role in leading economic regions for thousands of years.
  Hence, prominent dictionary definitions of capitalism make it a system
  that has lasted for multiple millennia. If we adopt such definitions, then
  we need to find another word to describe the institutional structures that
  were consolidated in the eighteenth century and gave rise to spectacular
  economic growth and ongoing technological innovation.

And he does have his own definition (which I will not try to argue that is mainstream); its premise is that:

  Capitalism [...] requires special forms of state that cannot confiscate property arbitrarily at will, that are effectively restrained by laws, that have internal
  checks and balances, and that are faced with countervailing (democratic
  or other) powers that help protect a relatively autonomous legal system.
  Such states are necessary to legitimate and protect property rights and
  to enforce contracts. They required peculiar circumstances and a long
  time to evolve. Foreshadowed in the Italian city- states, they did not appear
  on a national scale until the seventeenth century, in Britain and the
  Netherlands. [...]

  I argue that, while markets are central to capitalism, capitalism is not
  simply a market system: unavoidably it contains different subsystems of
  governance, production, distribution, and exchange. Furthermore, capitalism
  cannot in principle have markets for everything or bring everything
  within the orbit of commodity exchange.
  In particular, under capitalism there can never be a complete set of
  markets for future labor power. For there to be full futures markets for
  labor, all workers must enter into contracts for their expected working
  life. This would be tantamount to voluntary bondage, limiting the freedom
  of workers to quit their employment. Paradoxically, pushing markets
  to their limits would mean the return of slavery for the workforce.

He goes on to semi-formalize a list of tenets that constitute capitalism first according to [his interpretation of] Marx and then similarly for Schumpeter

  M[arx]-capitalism

  A legal system supporting widespread individual rights and liberties to own,
  buy, and sell private property
  Widespread commodity exchange and markets involving money
  Widespread private ownership of the means of production by firms producing
  goods or services for sale in the pursuit of profit
  Much of production organized separately and apart from the home and
  family
  Widespread wage labor and employment contracts

  Most dictionary and encyclopedia definitions emphasize conditions
  (1), (2), and (3), albeit often without emphasis on the legal system. More
  than Marx, the notion of M-capitalism emphasizes the legal system and
  individual rights. Regarding condition (4), the separation of much production
  from the family and the domestic sphere was emphasized by Weber
  (1968) and is implicit in Marx’s writings. Weber rightly argued that
  this separation was important to subject production to systems of rational
  accounting and pecuniary motivation. Marx emphasized condition
  (5) because it flows from the nature of capitalism as generalized commodity
  production and encapsulates the driving antagonism between
  the employing class and the working class. [...]

  A problem [...] is that the addition of
  condition (5), widespread wage labor, to the preceding four does not effectively
  demarcate modern industrial capitalism from the four preceding
  centuries when wage labor was widespread in rural England.
  M-capitalism, as specified above, gives us a better-than-average definition,
  but not one that is sufficiently sharp in terms of historical specificity.

  Further problems of historical demarcation arise with the first four
  conditions. As noted in section 4.4 above, the idea that secure property
  rights were first established in England in the seventeenth century is a
  myth. Furthermore, money, markets, and private ownership have existed
  for millennia. The fourth condition is helpful but hardly sufficient as an
  explanation of massive expansion of capitalism around 1800. The five
  conditions are inadequate to demarcate historically the explosion of capitalist
  productivity even if they are necessary for that system.

As for S[chumpeter]-capitalism, he argues that it contains all of the above, except for #5, but that additionally it has

  A developed financial system with banking institutions, the widespread use
  of credit with property as collateral, and the selling of debt

  The addition of condition (6) takes seriously the monetary definition
  of capital and institutions promoting collateralization and the salability
  of debt. Capitalism is thus marked by “the predominance of ‘capital’”
  (Sombart 1930, 196). This definition points to the development of institutions
  of clearer historical specificity. According to this definition, the
  emergence of capitalism in England is marked by developments in financial
  institutions in the eighteenth century.

  Note that condition (1) in the definitions of M-capitalism and
  S-capitalism rules out (at least widespread) slavery. Consequently, both
  M-capitalism and S-capitalism involve missing futures markets for labor.
  With S-capitalism, there may be self-employment or worker cooperatives
  but not extensive slave labor. M-capitalism rules out an economy
  with predominant self- employment or worker cooperatives.

As you can probably guess, by synthesis, he argues that the definition of capitalism should include the superset of 1-6 from both M- and S-capitalism (which already have a lot in common).

  But there is a cost to the exclusion of condition (5) from this definition. [...] the advantage of retaining
  the employment contract in the definition of capitalism is that it demarcates
  the system from economies involving self-employed producers or
  worker cooperatives. Furthermore, the introduction of wage labor gave
  important incentives for labor-saving innovations and led to increases in
  productivity. Consequently, the definition of capitalism that is favored
  here— and described simply as capitalism, without any prefix— involves
  all six of the above conditions. [...]

  Conditions
  (5) and (6) serve as fuzzy historical bookends, together demarcating
  capitalism from preceding systems and possible successors. [...]

  Explicit reference to social class is also absent from the definition offered
  above. In his review of different definitions of capitalism, Michael
  Merrill (1995) argued that capitalism is much more than simply a market
  economy. He was right about that. But he wanted to define capitalism as
  “a market economy ruled by, or in the interests of, capitalists” (322). A
  problem [...] is that the basis of class itself has to
  be defined, and Marx and Engels were obliged to use legal terms such as
  ownership to do so. Being a capitalist or a worker is not a congenital attribute:
  it is the occupation of a social role that is determined in part by
  legal relations. Class-related legal terms appear in all points above, except
  condition (4).

  Marxists have abused class-centered definitions of capitalism. They
  see class struggle, where the destiny of one class is to seize control of the system from another. But, notwithstanding the power of capitalists over
  workers, capitalists do not control capitalism: it is more the other way
  round. Such large and complex systems cannot be fully controlled, as if
  from a single chamber of power.

And while he disses that idea that capitalists control capitalism itself as a caricature, he nevertheless argues that it is an integrated economic and political system (and in this he is not that original, as he acknowledges):

  The central role of the state within capitalism means that we must
  address politics as well as economics. [...] Douglass C. North, John J. Wallis,
  and Barry R. Weingast (2009, 269) argued: “The seeming independence
  of the economic and political systems on the surface is apparent, not
  real. In fact, these systems are deeply intertwined.” I also concur with
  Bruce R. Scott (2009, 4) in his claim that capitalism is both “a political
  phenomenon” and “an economic one” and that “specifically it requires
  the visible hands of political actors exercising power through political
  institutions.” Capitalism always involves legal and political institutions:
  pure “anarchocapitalism” is an unrealizable fantasy.

And since the Austrians (Hayek actually) got mentioned in the question, Hodgson has this to say about their approach to defining capitalism:

  The Austrian economists had
  little to say about the sphere of production—conditions (4) and (5)—
  including the employment contract. Although they mentioned money
  many times, they paid insufficient attention to the use of property as collateral
  or to the selling of debt—condition (6). Their theory of money
  downplays the vital constitutive role of the state. At best, they stressed
  three of the six conditions only. The first three conditions are insufficient to identify the institutions of the capitalist system that were responsible
  for the explosive production of wealth in the last three hundred
  years.

While this may not be any sort of consensus statement, it is at least a comparative analysis of various definitions (from fairly prominent sources).


If a business charges more for a product than the cost to make it, how is our economy not inevitably doomed for debt? The analogy would be stirring water in a bucket; without adding more water to the bucket, there is no gain...

Obviously the various resources to create say an iPod came from different countries... but this general concept of x = 4x therefore the company made 3x (as an over simplification) so where did the 3x come from? From people yes, but if it's always subtracting then how do we get to positive?

To continue your example:
Resources (including labor) cost $x$, product sells for 4$x$. The fat cat business owner makes 3$x$. What does he do with it? If he spends it, for example plays golf or gets his hair done then the people providing those services get the money. Thus there need not be debt, the hairdresser can use these earnings to buy the product the fat cat's business was selling. The usual water analogy is of a circulatory system: water (money) flows from one vessel to the other.


Merging Panel data with two different splits. Is it possible? I have two data frames with panel data. The first contains data on companies on a yearly basis. The layout is as below:

ID Year x1  x2  x3
A1 2000 10  11  12
A2 2000 13  25  20
A1 2001 13  58  13

and so on.
The second data set contains the same companies, but data that is split by state AND year.

ID  Year  State  xx1  xx2  xx3
A1  2000   AL    581  135  1.22
A1  2000   FL    584  51    1.5
A2  2000   AL    5138 84   1.7
...

Now, I am wondering if and how I can merge these two?
Economically, it makes sense to have these different data panels as some data is only available on an overall company level (total assets, debt, income) and some data can be split for example: revenue in state; customers in state and so on...

I am very grateful for any idea on this!

p.s. using R

I would just merge them horizontally... so that the main dataset is the second one, and you include country-wide statistics into each row:

ID  Year  State  xx1  xx2  xx3   x1  x2  x3
A1  2000   AL    581  135  1.22  10  11  12
A1  2000   FL    584  51   1.5   10  11  12
A2  2000   AL    5138 84   1.7   13  25  20
...


What is the definition of exogenous and endogenous preferences? Wikipedia states:

Exogenous Preference -- one that comes from outside the model and is unexplained by the model.
Endogenous Preference -- preferences then cannot be taken as given, but are affected by individual internal responses to the external state of affairs.

Can someone clarify what these two terms mean? Specifically, what does it mean to be "inside" (or internal) or "outside" (or external) of a model?

Exogenous variables are believed to have some value given by nature. They are not caused by your theory's variables of interest. This is why they are said to be outside the model.

Endogenous variables have values dependent on your theory's variables of interest. They both cause, and are caused by your topic.

Example: In the study of wages, some individuals are born superior, genetically, perhaps. They are superior exogenously. Because of their superior innate quality, they may choose to seek additional education knowing they will get higher returns for their investments. So the amount of education is endogenous to wages, because a person's expected earnings informs their education.