Derive demand function from utility function with constant elasticity Consider a $n$-good industry with a representative consumer with utility function for the differentiated goods given by,

$
U=\left(\sum^n_{i=1}q_i^\beta\right)^\theta
$

Suppose that the representative consumer is endowed with income $I$.

a. Derive the inverse and direct demands;

My solution: I am writing the lagrange as:

$
L=\left(\sum^n_{i=1}q_i^\beta\right)^\theta+\lambda(I-\sum^n_{i=1}p_iq_i)
$

FOC:

$
\theta \left(\sum^n_{i=1}q_i^\beta\right)^{\theta-1}\beta q_i^{\beta-1}-\lambda p_i=0
$

So the inverse demand function is:

$
p_i=\frac{\theta \left(\sum^n_{i=1}q_i^\beta\right)^{\theta-1}\beta q_i^{\beta-1}}{\lambda}
$

Is this right? Because the $\lambda$ seems a little bit strange. If yes, how do I isolate $q_i$, when there is this sum symbol to derive the demand function?

You stopped a bit too early.

Let me re-write the FOC for good $i$ as follows:

$$ \lambda=\frac{\theta \left(\sum^n_{i=1}q_i^\beta\right)^{\theta-1}\beta q_i^{\beta-1}}{p_i}
$$

As this is identical across goods, equalise for good $i$ and good $j$, where, after simplification, you get:

$$ \frac{q_i^{\beta-1}}{p_i} = \frac{q_j^{\beta-1}}{p_j} $$

This relation hold for any pair of goods. This means you can re-write the demand for any good in terms of $q_i$ and relative prices. Then, you can use the budget constraint to obtain the final demand for good $i$, in terms of income $I$ and all the prices.

Hopefully this information is enough for you to move forward and solve the problem.


Dif in Dif on countries, is it necessary to cluster by country? I have a question regarding Dif-in-Dif (DD) studies. If I want to compare a policy that is implemented differently in three different countries - thus three different treatment groups - using a DD approach, is it necessary to cluster standard errors by country (instead of for example by industry)?

From my understanding this would make a DD approach almost impossible as the amount of clusters can not be high enough (aka not higher than 42 or whatever number one likes to go by). With other words all DD studies comparing policy effects between 2 or 3 different countries (or states) would be invalid.

You should cluster on level where you believe the autocorrelation or heteroskedasticity occurs.

If you don’t have enough clusters at a given level, for example, if you believe the above mentioned problems occur on country level but you have only 3 countries, you are correct you should not be using clustered standard errors which by rule of thumb require at least about 40 clusters to be properly estimated. However, clustered errors are not the only type of error adjustment there is. For example, you can instead of clustered errors use Newey-West errors or bootstrapped errors (of course these have their own advantages and disadvantages as well). The above mentioned are just examples other ways of adjusting errors exist as well.


Is comparative advantage only beneficial with convex utility functions? I've been playing around with the numbers associated with the traditional comparative advantage problem provided by Ricardo.
(https://en.wikipedia.org/wiki/Comparative_advantage)

I looked at comparative advantage in my Econ 101 class, but I was surprised to find when reviewing it that it seems like comparative advantage is itself not enough to ensure trade. (I had thought this was sufficient to ensure trade for all optimizing agents.)

Am I correct in believing you'd need the utility function for at least one of the countries in the standard comparative advantage example to be convex, with a diminishing marginal rate of substitution (e.g., a Cobb-Douglass function of the form $U(x,y) = (x)^{0.5} (y)^{0.5}$)? Or am I missing something? It seems to me that without diminishing marginal rate of substitution (which isn't a huge assumption, of course), there's no benefit to trade.

What traditionally matters is a quasiconcave utility function (that is, the individual/country at least weakly prefers mixing such that all better sets are convex). I assume that's what you're referring to when you describe the Cobb-Douglass example.

Though I believe your comment about the functional form of utility is overall correct. If, for example, the utility function were
$$
u(x_{1},x_{2})=\max\{x_{1},x_{2}\}
$$
both countries would produce whatever they were more productive in, and neither country would be incentivized to trade.

(But again, I think the key is quasiconcavity of the utility functions, not convexity.)


Convert a sequential move game into a simultaneous move game A statement from Ponssard and Zamir "Zero-sum sequential games with incomplete information" at the bottom of the first page reads

  AM's result is for zero-sum two-person games in which the two players move simultaneously. This includes of course games in which the moves are made sequentially: Player I moves first, player II is informed of player I's move and then makes his own move. (Such a game can be looked at as a simultaneous game after redefining the pure strategies of player II.)

I am curious about the last statement in parentheses. How does one "redefine" the strategies of the follower to make the game simultaneous move?

This is basically the idea that any extensive form game has a normal form representation.

http://www.sfu.ca/~shihenl/302/Strategies%20Memo.pdf


How to find the long-run relationship using this regression (3rd time posted) This is an old exam question I can't figure out.

I thought to find the relationship you would sum the coefficients on the Ys, so it would be
0.80 + 0.70 - 0.10, giving you C = 1.4Y, but this isn't an option. Could someone tell me where I went wrong? Is it something to do with the fact it's in log form?

INITIAL ANSWER March 24

Ok. Let's answer this without answering. Your moral obligation to this community, in case it matters to you, is to report back with your work and your answer.

1) In Economics we use the difference of natural logarithms to express (approximately) something specific. It is essentially stated in the body of the exercise.

2) An estimated relation through regression is essentially an estimation of the expected value, which in turn can be thought of as some long-term average. So don't you think it should validate the assumed long-run values given in the exercise?

3)  Given the assumed long-run values in the exercise what is the relation between $C_{t-1}/Y_{t-1}$ ,  $C_{t}/Y_{t}$, and of $C/Y$, in the long-run? Or between $\Delta \log Y_{t-1}$ and $\Delta \log Y_{t}$ (in light of your answer in 1) above).

4) Given the assumed long-run values in the exercise, do you think that the answer will be of the form $C = a + bY$, or of the form $C = bY$?

The final step will require remembering your answer in 1).

ADDENDUM April 7th
Now that the question came to its proper home, and a two-weeks interval has passed, let's complete this:

Given the estimated relationship, in order to be consistent with our model, we accept that this relationship will also hold in the long-run. In the long-run some magnitudes are constant. Which ones, in our case? We are told that the long-run growth rate of Consumption and of Income are the same, constant, and equal to $0.25$. This means that in the long-run we will have the equalities

$$C_{t-1}/Y_{t-1}= C_{t}/Y_{t}=C_{LR}/Y_{LR}$$

$$\Delta \log Y_{t-1}=\Delta \log Y_{t} = \Delta \log C_{t} \equiv g =0.25$$

...since the difference of natural logs approximates the growth rate.
Given these, and given the estimated long-run inflation that is given and equal to
$$\Delta \log P_{t} \equiv \pi = 0.1$$
 the long-run relationship is transformed into an equation with a single unknown, $C_t/Y_t$. Specifically, we have, making first symbolic and then numerical substitution:

$$g = 0.8g+0.7g+0.1\ln(C_{LR}/Y_{LR}) -0.15\pi$$

$$\implies g(1-0.8-0.7) + 0.15\pi = 0.1\ln(C_{LR}/Y_{LR})$$

$$\implies  0.25\cdot (-0.5) + 0.15\cdot 0.1 = 0.1\ln(C_{LR}/Y_{LR})$$

$$\implies -0.11 = 0.1\ln(C_{LR}/Y_{LR})$$

At this point, it appears that the "old exam question" made a mistake, because the choices given for answering seem to "ignore" the existence of the coefficient $0.1$ attached to $\ln(C_{LR}/Y_{LR})$.

If the relation was $-0.11 = \ln(C_{LR}/Y_{LR})$, we would obtain by taking the exponential $e^{-0.11} = C_{LR}/Y_{LR} \implies 0.896 = C_{LR}/Y_{LR} \implies C_{LR} \approx 0.9Y_{LR}$, which is one of the choices given.

But with the coefficient $0.1$ present we obtain

$$... \frac {-0.11}{0.1} = -1.1 =\ln(C_{LR}/Y_{LR}) \implies e^{-1.1} = C_{LR}/Y_{LR} \implies C_{LR}\approx \frac 13Y_{LR}$$

which is not given as an option.

PS: The standard errors of the estimates are not involved in the above calculations. One could comment that their magnitude compared to the magnitude of the estimates indicates that the estimates are "statistically significant" for confidence $>95$%.


Lexicographic Preference Relation on the QxR I would like to ask for your help. I recently learned that the Lexicographic Preference relation can be represented by a utility function $u:X\to\mathbb{R}$ on $\mathbb{Q}\times\mathbb{R}$ (but not $\mathbb{R}\times\mathbb{Q}$).

To recall, a lexicographic preference relation says that on $\mathbb{R^2}$, $x\succeq y$x if and only if $x_1>y_1$  or $x_1=y_1$ and $x_2\geq y_2$ where $x=(x_1,x_2)$ and $y=(y_1,y_2)$.

Thus, I would have liked to see a proof of this statement and how is it possible to build such a utility representation. I guess that we must assume first that there exist a utility representation for the Lexicographic preference on $\mathbb{Q}\times\mathbb{Q}$ since the latter is countable, but I am lost after.

Infinitely many thanks for your help!

Note first that for each nontrivial (more than one point) compact interval $I$, there exists a strictly increasing function from $\mathbb{R}$ to $I$.

Let $\langle q_1,q_2, q_3,\ldots\rangle$ be an enumeration of $\mathbb{Q}$. We will define $u:\mathbb{Q}\times\mathbb{R}\to\mathbb{R}$ inductively, one $q_n$ after another.

Let $I_1$ be a nontrivial compact interval and $u_1:\mathbb{R}\to I_1$ be strictly increasing.

Now assume there are disjoint nontrivial compact intervals $I_1,\ldots,I_n$ that ordered on the line like $q_1,\ldots,q_n$, and strictly increasing functions $u_m:\mathbb{R}\to I_m$ for $m\leq n$. Since these intervals are closed and disjoint, there is space between any two consecutive intervals. So one can put a nontrivial compact interval $I_{n+1}$ in a place corresponding to $q_{n+1}$ among $q_1,\ldots, q_n$. Choose also some strictly increasing function $u_{n+1}:\mathbb{R}\to I_{n+1}$.

This will give you a disjoint sequence $\langle I_1, I_2, \ldots\rangle$ of nontrivial intervals and a sequence of functions $\langle u_1, u_2, \ldots\rangle$ with $u_n:\mathbb{R}\to I$ be strictly increasing. Now define $u:\mathbb{Q}\times\mathbb{R}\to \mathbb{R}$ by $u(q_n,r)=u_n(r)$.

You can verify that $u$ represents the lexicographic ordering on $\mathbb{Q}\times\mathbb{R}$.

Warning: The existence of a countably infinite number of disjoint nontrivial intervals might appear very strange, but is perfectly fine.


Why are Hicksian demand curves unobservable I have read this paragraph in a book (Jehle, Reny: Advanced Microeconomic Theory):

I don't quite understand why Hicksian demand curves aren't directly observable? What does observable stand for in this context?
I can create a Hicksian demand function, which I then can differentiate for prices and so on, so why can I not observe them?

Observable just means directly measured by data. In that sense, Marshallian demand is observable because we can see people's optimal consumptions of a certain good for different prices and the same income.

In contrast, the Hicksian demand is the optimal consumption after a change in price and after adjusting income so that the same utility is achieved. Given that utility cannot be directly measured (i.e. is not observable) the Hicksian demand is also not observable. Anything we conclude about the Hicksian demand is due to the Slutsky equation that relates it to measurable things: the slopes of the Marshallian demand and the Engel curve ($\frac{\partial x_i(\cdot)}{\partial y}$), and the quantity demanded.


Laffer Curve Regression I am doing some research on a potential U.S. Nationwide Sales tax.  I found per-capita sales tax revenues and sales tax rates for each of the 50 states and conducted a quadratic regression on them.  I got a quadratic regression with a $R^2$ of approximately 0.4.  Is this $R^2$ sufficient to state a good correlation and are there any other statistical tests I may need to do?  Thank you in advance.

The Laffer Curve is a theoretical argument that feels strongly true the moment one hears about it. The complexities around it once one wants to have a closer look are many (just for a taste the wikipedia article can be consulted).

Even in the simplest econometric study, one has to make sure that what one does is consistent with the theory one wants to test (or the one on which one relies), otherwise it won't be an econometric study but an exercise in pure mathematical approximation devoid of economic content (after all any bounded continuous function can be approximated by polynomials as per Stone-Weierstrass theorem).

So what does the Laffer Curve (very) basic theory (and in its strongest form) asserts?
1) That output is a negative function of the tax rate.
2) That a tax rate of $100\%=1$ should result in zero output, and so zero tax revenue.
3) Moreover, logic says that if the tax rate is zero, tax revenues should be zero.
it appears then that we can start by an assumption that somewhere in between there is a point of maximum tax revenues (although one of the complexities mentioned earlier is that the curve may not be unimodal, i.e. it may also have a local maximum).

Let's see which conditions should the simplest "quadratic regression" satisfy in order to be consistent with the theory. We have

$$T(\tau, Y(\tau)) = \beta_0 + \beta_1\tau + \beta_2\tau^2 + u$$

where $Y$ is output (or sales), $\tau$ is the tax rate, $T(\tau, Y(\tau))$ is Total tax revenues, and $u$ is an error term, to account from deviations from the mean-value.

We can deduce the following:
A) In order to satisfy point 3) above on average, $T(0, Y(0)) = 0$, it must be the case that $\beta_0 =0$.

B) This equation, in deterministic terms has derivatives

$$\frac {{\rm d}T(\tau)}{{\rm d} \tau} = \beta_1 + 2\beta_2\tau, \;\; \frac {{\rm d^2}T(\tau)}{{\rm d} \tau^2} = 2\beta_2$$

and so it will have a maximum at the point
$\tau^* = -\frac {\beta_1}{2\beta_2}$ if and only if $\beta_2 < 0$.

C) Finally, in order for the equation to satisfy point 2) above, $T(1, Y(1)) = 0$, it must be the case that $\beta_1 = -\beta_2$.

But then we also obtain that the maximizer will be $\tau^* = 0.5$. This last consequence is not good: our tool (a specific mathematical functional form that appears convenient for our purposes), forces on us a very specific conclusion that is not predicted by the theory, something that should be left for the data to decide, even in the case were the data do indeed exhibit "Laffer-curve" properties. In other words, the quadratic regression postulates not "general Laffer curve properties", but a very specific Laffer curve (this essentially comes from the fact that the independent variable $\tau$ is restricted to lie in $[0,1]$).

But run the regression we must: so we found that for this specific "quadratic regression specification" to be valid, theory imposes three restrictions on the parameters,

$$\beta_0 =0,\;\;\; \beta_2 < 0,\;\; \beta_1 = -\beta_2$$

Since one of the restrictions is an inequality, one could use Inequality-Constrained Least-squares which requires an iterated algorithm, but I won't go there.

Otherwise, one should first run a regression with the coefficients unconstrained, and see whether at least, $\hat \beta_2 <0$.  Then run the regression imposing the two equality constraints, hope that in this restricted regression $\hat \beta_2$ remains negative, and conduct an $F$-test on the two specifications to determine which fits the data better.

Now assume that the restricted model does have a $\hat \beta_2 <0$ and that it outperforms the unrestricted model: one can then argue that this data set behaves like the Laffer-curve theory would predict, but also, that the tax revenue maximizer is around the value $0.5$. One cannot escape this last conclusion, if the restricted model prevails.

If it does not prevail, other aspects of Laffer-curve theory are not supported by the data, so to mechanically calculate a tax revenue maximizer based on the estimates from the unrestricted model will be rather shaky.

And there are also important statistical misspecification issues:
1) Can we argue that the sales and the tax rates of the various states come from the same distribution, and are independent? (this would be needed to have the "i.i.d. sample" framework)

and especially (which I believe is what @FooBar 's answer focused upon)
2) Is the tax rate uncorrelated with the error term, or is it endogenous? Are there factors that affect directly output/sales and are also correlated with the tax rate (e.g.: if a productivity or other mid-term range shock affects output, is there pressure to change the tax rates also, and do they adjust?)

In light of the above, I would say that the $R^2$ "fit criterion" is not the first thing to check, nor the primary method, in order to judge the quality of such a regression estimation.


market for lemons with signals - equilibriums vs constraints I checked online for a question similar to this but was unable to find one.  I understand the concept of pooling and separating equilibrium and can apply it to labourers having different qualities of work but how can it be applied to the market for lemons with signalling through warranty?
Also, is there a connection between separating / pooling equilibrium and participation / self-selection constraint?  I know one is related to signalling and the other to incentives from reading Hal Varians Micro book.  But is there more?
For example lemons are worth 20 to consumer and 10 to producer and peaches are worth 60 to consumer and 50 to producer.  Suppose a 50-50 split.  This means the expected value to consumers is 40.  The pooling equilibrium means all cars would be sold at the same value and the consumer will purchase at a maximum of 40 so only lemons will be sold.  How would I find the separating equilibrium for a warranty priced at w?
Is it solved like this?
60-w > 20   peaches under warranty
20 > 60-w   lemons not under warranty
Is solving the pooling vs separating equilibrium different from solving the participating vs self selection constraint?
Thank you in advance for any help.

The two questions you ask are related but distinct. First recall what a separating equilibrium is: its an equilibrium where distinct type takes distinct actions, supported by a system of consistent beliefs.
Now lets come to your questions one by one:

In the Lemons Market, a separating equilibrium would involve the seller setting different prices for the lemons and peaches. Can such an equilibrium exist? Think about what the buyer's beliefs would be and if the lemon can mimic the peaches?

I guess you mean Incentive Compatibility constraints instead of Participation Constraints. You must have encountered them in Principal Agent models. In these models, the agents play a (bayesian) game and the Principal can commit to design the rules of the game. The Participation Constraint ensure that the agents are willing to take part in the game designed by the Principal. The Incentive Compatibility Constraint ensures that the ensuing equilibrium of the game is a separating equilibrium - i.e. different types of agent will be choosing different actions in the game. The specific rules of the game designed by the Principal depends on the context.


Does it matter if your decision might not matter? I have read several experimental papers which ask people to make decisions which only matter with a certain probability. For example, individuals might be asked to submit bids in an auction, but told that their bids only 'count' with a certain probability $p$ (with probability $1 - p$, their payoff is 0 regardless of what they do). Alternatively, if we wanted to learn whether an individual's valuation for a good exceeds £10, we could offer to sell her that good for £10; but tell her that the good will be sold to her (and the payment taken) only with a certain probability. In both cases, the idea is that individuals should act as they would if $p = 1$ (i.e. the mechanism is 'incentive compatible') which then allows researchers to run these experiments more cheaply than they would be able to otherwise.

Is there any evidence about the general validity of this approach? More concretely, is there evidence as to whether the outputs of such experiments vary with $p$? Intuitively, I would have expected that subjects become inattentive if $p$ is very low (since in absolute terms, it doesn't matter much what they do), which could then add noise to the elicited estimates.

Interesting question. I don't have any empirical evidence to offer, so I can't answer your question if that's what you're asking for.

But it's easy to provide "theoretical evidence", as it were, that your concerns may be well-founded, even without leaving the EU model.

You simply need to add a decision cost --- or a cost to figure out your true WTP --- to the decision-theoretic model of your participants.
Then, as the EU stakes decrease (because $p$ decreases), participants are less likely to invest in the introspection cost of discovering their true WTP.
As a consequence, participants' behavior become a much noisier indication of their WTP:

Some of your participants will decide to buy the good although their true WTP is lower than the price. This could happen if the participant decided not to invest in introspection and therefore got a sufficiently upward-biased signal of their true WTP.
Other participants will decide not to buy the good although their true WTP is above  the price. This could happen if the participant decided not to invest in introspection and as a consequence got a sufficiently downward-biased signal of their true WTP.

Assuming the cost of introspection does not change with $p$, participants become less likely to invest in introspection as $p$ decreases (because decreasing $p$ decreases the stakes, and therefore the benefits of introspection), and you'll get more of this noise as $p$ decreases.


Does consumption decrease directly lead to a shift in Aggregate Demand curve to the left? Studying macroeconomics I began to wonder about the validity of a certain statement that I couldn't find a clear answer to:

"When Consumption decreases, Aggregate Demand curve will shift to the left."

First I thought this was obviously right. However, considering the components of AD (C, I, G, NX), when consumption decreases that would directly lead to the same amount of increase in Inventory, which results in the increase of Investment (I). So since the decrease in consumption is directly offset by the increase in Investment, Aggregate Demand wouldn't shift, and GDP wouldn't change at all right? At least, this is the answer I came up with.

If this statement ("When Consumption decreases, Aggregate Demand curve will shift to the left.") was one of the choices for an AP Macroeconomics question where you had to choose the right/wrong answer choice, would this statement be true, or false?

I couldn't get my head around this statement, and the above logic (Consumption decrease ---> Investment/Inventory increase by same amount ----> GDP unchanged) was the only one I could think of after pondering for hours.

Is there a clear answer to this statement if this were in an AP Macroeconomics question? Would a decrease in consumption really directly shift the AD curve to the left, or would it remain unchanged due to my logic? I would really appreciate a good explanation! :)

You mention here a crucial point that falls nowadays more and more in oblivion, that is the well-known aggregation issue across consumers. The described behavior of the individual and aggregate demand curve can only be expected to be observed when the essential properties of the individual demand functions can be bequeathed to the aggregated demand function. For this case one needs a particular type of utility function, it must be of Gorman form, that is, the utility functions of consumers must be quasi-linear, or to put it differently, they must be linear in the numeraire good to get an aggregate demand function that inherits their properties from the individual demand functions (cf. Varian Microeconomic Analysis 1992, third edition, pp.152-154).


Why are interpersonal utility comparisons not possible Why is it not possible to compare utility across individuals?

Is this only impossible when we consider ordinal utility where we have no numerical unit?

Whether `interpersonal comparisons of utility' are possible depends on what you mean by 'utility':

If you mean something like welfare, i.e. the extent to which a
person's life goes well, then interpersonal comparisons are
obviously possible. Example: if Anna is tortured on a daily
   basis, whereas Bob lives a life of luxury, then we would (given standard background assumptions) be justified in believing that Bob has a higher
   level of welfare than Anna. (If you don't like the example, feel
   free to change the details. The general point is that, in some cases
   at least, it is reasonable to believe that one person is better off
   than another person.)
In 'standard' microeconomics, however, the word 'utility' has come to
mean something rather different to welfare. Instead, utility is defined as whatever people maximise. To be more precise, a utility
function is simply a way of representing individual rankings over
outcomes; and the outputs of that function are termed utilities. Now,
if all utilities are supposed to do is represent rankings, it is
clear that there are many possible ways of assigning utility values.
For example, if I go prefer Paris to London, we could say that
$$u(\text{Paris}) = 2 > u(\text{London}) = 1;$$or instead that
$$u(\text{Paris}) = 7 > u(\text{London}) = 3;$$or more generally assign
any utility values such that $$u(\text{Paris}) > u(\text{London}).$$ And as a result, it is clearly meaningless to say that your utility
level is higher than mine. For utility levels are purely arbitrary: we can always make your utility higher than mine, but also rescale the utility functions so that my utility is higher than yours.
So if you are wondering whether utility levels can be compared across
individuals, you need to ask yourself a simple question: what do you
mean by 'utility'?


Learning about Debt and Credit I am very interested in learning about debt and credit - not personal debt and credit - but debt and credit of countries and the like. I have searched everywhere but it's difficult to find books that are related to these topics. One such book that I found was Alexander Graeber's "Debt: The First 5000 Years".

I was wondering if someone has a recommendations for books that would allow someone to get a much better idea of what exactly debt and credit are and how they affect the world around us.

Thanks!

P.S. I apologize in advance if this question is off topic but this was my last resort. :)

You might call Graeber's theory of money as something emerging from a system of compensation from the harm of others.

The Chartalist's say the state is what makes money, they demand taxes be paid in money, this gives money value, and then the state makes money which it spends on what it wants.

  The Chartalist contribution turns on the recognition that money cannot
  be appropriately studied in isolation from the powers of the state –
  be it modern nation-states or ancient governing bodies. It thus offers
  a view diametrically opposed to that of orthodox theory, where money
  spontaneously emerges as a medium of exchange from the attempts of
  enterprising individuals to minimize the transaction costs of
  barter. The standard story deems money to be neutral – a veil, a simple
  medium of exchange, which lubricates markets and derives its value
  from its metallic content. Chartalism, on the other hand, posits that
  money (broadly speaking) is a unit of account, designated by a public
  authority for the codification of social debt obligations. More
  specifically, in the modern world, this debt relation is between the
  population and the nation-state in the form of a tax liability. Thus
  money is a creature of the state and a tax credit for extinguishing
  this debt. If money is to be considered a veil at all, it is a veil of
  the historically specific nature of these debt relationships.
  Therefore, Chartalism insists on a historically grounded and socially
  embedded analysis of money.

  This chapter distinguishes between several broad Chartalist
  propositions about the origin, nature and role of money, and several
  specific propositions about money in the modern context. It offers
  only a cursory examination of the historical record to illumin- ate
  the essential characteristics of money emphasized in the Chartalist
  tradition. Chartalist ideas are not new, although they are most
  closely associated with the writings of Georg Friedrich Knapp of the
  German Historical School. Thus the chapter briefly surveys instances
  in the history of thought which have emphasized the chartal nature of
  money. The paper then expounds on Chartalism, clarifying aspects of
  the concepts and drawing out the implications for modern currencies.
  It concludes with a discussion of the various applications of this
  approach to policy.

Chartalism and the tax-driven approach to money

Economics (as a profession) generally focuses on another motive for money, solving the problem of the double coincidence of wants. That is, in barter we generally need to both want what the other has or we can't make a deal (unless we have credit, but consider barter among strangers). Money presents an alternative, a good that we don't want per se, but we can use for transactions because everyone else wants it and we can rely upon to want it later as well. Such a thing should be portable, hard to counterfeit, and easily identified. Then when Art wants to buy a Ball and Charlie has a Ball but wants to a Dog, Art can use his money to buy the Ball from Charlie so that later he can use money to buy a Dog from Eric who will then use it to buy Florence's Goat, and so on...

There is an accessible and justifiably famous paper on this sort of money, The Economic Organisation of a P.O.W. Camp,  about how cigarettes emerged as this sort of money in WW II POW camps. Graeber singles this paper out for scorn, saying these people already knew about money and so this is not a good example of a origin story for money, but it is a nice example of money as an emergent phenomenon to solve the double coincidence of wants problem.

I haven't read Ascent of Money, I recall it getting mixed reviews, but I really enjoyed a Ferguson's somewhat related The Cash Nexus,  which might help you understand the national aspect of your question. I also enjoyed The Origins of Value: The Financial Innovations that Created Modern Capital Markets, but that book covers much more than just money.  Famous Myths of Fiat Money has some nice examples of commodity money emerging to solve transactional issues. On Money as a Medium of Exchange is a famous (relatively modern) theory paper that covers the benefits of fiat over commodity money. The book What is Money? in many ways is a long answer to your question, with chapter 7 in particular covering a lot of these issues.


What factors allow manufacturing to succeed in a developed country? I am undertaking some research regarding differences between manufacturing sectors across countries.

I have noted that China has taken a lot of the less skilled manufacturing work away from developed countries. It clearly has a comparative advantage with regard to unskilled labour. Generally, it will be difficult for developed countries to compete with the wages of the lesser developed countries.

This has resulted in the decline of manufacturing in some countries such as Australia (12.6% of GDP in 2000 to 6.7% of GDP in 2015) or the US (14.2% to 12.3%). Whereas other developed countries are still able to successfully manufacture. Germany for example has had ~22% of GDP from manufacturing for the last 15 years.

What factors allow manufacturing to succeed in a developed country?

I am expecting it to be related to:

Regulation
human capital
size of domestic market
trade deals

I am interested in references in particular.

A massive simplification would to look at developed (high wage) countries as experiencing two forces.

There is the offshoring pathway. Low skill manufacturing can be offshored to lower waged countries. Output in the home country decreases.

Then there is the technological pathway. Automation and innovations can work to take the bottom out of employment, saving on wage costs. Manufacturing will become increasingly dependent on a more skilled employee. Output in the home country increases.

The expected trend is one away from the low skill manufacturing (think clothing) towards more complex, bespoke products (think 3D printed prosthetics).

The overall environment is notably more complicated with government subsidies, global supply chains and trade deals among others things all being important.

Deloitte Access Economics have released a manufacturing competitiveness report which covers elements of this.


What are the effects of abolishing the minimum wage? There's this one guy out there, Peter Schiff, and he aired on Joe Rogan a while back. One part of the podcast really caught my attention, and it was when Schiff said that the minimum wage should be abolished.
Without making this question subjective, I'll provide an overview of his arguments, however, that's where I need some help since I'm not so sure on how they stack up to the real world.

Here's the arguments he made:
1. Fixes unemployment rate
A company is not going to hire someone for 15 dollars an hour (or whatever the minimum wage is) if their skill level is only worth 5/h. The company will lose 10/h if they hire someone like that! So instead, reduce the minimum wage so that company's can now pay people 3/h, opening the market for everyone.
Think of a wage as a ladder. It starts at zero, making it accessible for everyone to climb. However, a minimum wage raises the ladder, making it unaccessible to people that don't have good skills. By abolishing the minimum wage, the ladder will be at the ground, so everyone can climb up.
2. Provides an alternative to college/university
If you don't go to college for whatever reason, then your skill level is probably not above the minimum wage. This will make it extremely difficult to find a job. However, with the minimum wage, you can start at the bottom, making 2/h, and work your way up. Even if it's a simple job like moving boxes, you still learn discipline.
3. A minimum wage limits the ability to sell labour
If you can only worth 5/h, you'll never get a job with a minimum wage of 15/h. You'll actually lose money for the company. However, with the abolishment of the minimum wage, then people can sell their labour based on whatever skill their at.
4. Brings jobs back to us
Most jobs will soon be automated, or moved overseas where it's cheaper (India or someplace). However, without a minimum wage, these jobs will start migrating back to us, the original country.
This will create thousands of jobs and create new opportunities for people.

There, that should be Schiff's view on things in chronological order if I did everything right.
Now what I'm wondering is if these arguments actually stack up against the real world.
However, I do have some specific questions:

1. Will this fix unemployment?
2. Would competition naturally raise, prices? And by how much?
3. Whould this bring jobs back to the country?

Anything would help. Thanks.

So this is a very broad topic. There are arguments pro and against minimum wages and there are many variables to consider.

As for your question, arguments 1-3 are basically argument 1. A higher minimum wage can limit employment / increase unemployment among people whose hourly value of labor to the employer is less than the minimum wage. As a result, those people may also miss out on increasing their value of labor, by missing out on work experience. That much is true. However, it does not mean that there would be zero unemployment without a minimum wage. For example Germany did not have a minimum wage for many years and still had unemployment. This is because there are other reasons for unemployment as well, like skill mismatches, search costs (frictions), reservation wages, etc.

Argument 4 is basically speculation. There is no guarantee that jobs would return to the US without a minimum wage. People will still have reservation wages below which they will not offer their labor and those reservation wages could still be above the current wage in another country. There is also no guarantee that automation would be significantly halted if the minimum wage were to be abolished (although the speed might slow down a bit).

For the sake of fairness, there are reasons economists would favor a minimum wage. One reason could be for example the presence of a monopsony (one dominant employer) and some would argue that is what Walmart has in certain regions.

Suffice to say that there is no clear answer on whether the minimum wage should be abolished or not.


How do you find out how much money is in circulation? I was watching a video about how money gets its value.  They say the answer has to do with how much money is in circulation.  But how does one find out how much money there is in circulation as set by the Fed?

The video gives the impression that the Fed "sets" the money supply. However this is not true at all. Surprisingly the money supply is mostly determined by private banks and the amount of lending that they do. The Fed then has some things it can do to influence the money supply. It's a system called fractional reserve banking and its very hard to get your head round. For a less technical explanation, watch this.

You will learn that there is more than one possible definition of "the money supply" (M1, M2 etc). The amount of each can be found at the St Lois Fed website - try doing a search for "money".


Marginal rate of substitution This is a homework question.

Suppose a consumer has preferences over two goods that can be represented by the utility function $U(x,y) = 2\sqrt{x} + y$

The marginal rate of substitution of $x$ for $y$ in this case is $\frac{1}{ 2\sqrt{x}}$, which is the negative of the slope of the indifference curve. It's well defined only for $x > 0$

The question asks to plot the indifference curve with $x$ on the horizontal axis and y on the vertical axis, and indicate if the graph of indifference curve will intersect either or both axes.

I was thinking that since slope of the indifference curve tends to infinity as $x$ approaches $0$, therefore the indifference curve should not intersect the y-axis. However, the solution provided by the lecturer says "since it's possible to have positive utility when either $x$ or $y$ is zero, the indifference curve intersects both axes", and I kinda agree this statement as well...

So what should be the answer?

There is more than one indifference curve. There is one belonging to every utility level. So for any utility level $c$, the points $(x,y)$ that satisfy
$$2\cdot \sqrt{x} + y = c$$ are an indifference curve.

For example let $c = 2$. Can you find a point $(x,y)$ that satisfies
$$2\cdot \sqrt{x} + y = 2$$
and is on the $y$-axis or the $x$-axis?


Why do the GDP baskets of different countries have different percentages? Why might the housing part of the US GDP basket 40% of the basket, but only 17% of China's?

The “shopping baskets” of items should be representative of consumer spending patterns. The general principle is to apply a fixed set of weights to price changes for each of the items such that their influence on the overall index reflects their importance in the typical household budget.
In 2015, housing on average accounted for about 22 percent of consumption expenditure in China, and it represented about 33 percent of household expenditure in the U.S. in 2016 (same percentage in 2018 according to the US Bureau of Labor Statistics). These consumption patterns may explain the difference between the 40% in the U.S. and the 17% in China.


DSGE models (Dynare) are only based on simulations and approximations? (without data) I'm beginner in DSGE models. Are they only based on simulations and approximations? Don't we have any real data-sets (for example interest rate, labor force, etc) to estimate the equations? I opened some .Mod files and I can only see equations, variable names and other functions. If yes, why do we have this structure in DSGE models and why can't we use real data-sets in these models?

Short answer

It doesn't seem like you've tried very hard to find estimation using Dynare (google results of "Dynare estimation"). Dynare is in fact capable of doing estimation and typically people use some sort of data to estimate the parameters that govern their model.

Longer Answer

What is a DSGE model?

A DSGE model is a series of equations (and variables and parameters) that describe a "model" economy. Once you write everything down and take into consideration the optimizing decisions made by the agents, it is simply a system of stochastic difference (differential) equation that you can imagine writing in some form along the lines of:

$$ E_t F(y_{t+1}, y_t, y_{t-1}, u_t) = 0$$

What does Dynare do?

The majority of introductory examples only use Dynare to solve the model and run some simple simulations. In addition to being able to solve the model, Dynare is also capable of doing Bayesian estimation of the parameters that make up the model by feeding in data.

Solves and simulates the Model

Dynare takes this system of equations (and the given parameter values) and solves them using perturbation methods. One of the outputs of the solution is a law of motion for all of the variables in the economy -- i.e. one can write something along the lines of

$$y_{t+1} = F(y_t, u_{t+1})$$

This law of motion allows you to generate model analogues of the data that you are interested in -- i.e. capital, labor, consumption etc...

Estimates the model

Once Dynare has a law of motion and has obtained simulated moments, it can compare the output of the model to data that you have provided. Dynare uses Bayesian estimation (though it is possible it does other types, but I'm not familiar with it) to estimate parameters which means that you need to provide it with a prior for each variable that you would like to estimate. It then uses a simple Metropolis Hastings algorithm to obtain estimates for the distribution over parameter values.

References

I would recommend you read both of the following references.

Tommaso Mancini Griffoli. Dynare User Guide: An introduction to the solution & estimation of DSGE models. 2007-2008. found here
Stefanie Flotho. DSGE Models - solution strategies. December 2009. found here


What is aid money for natural disasters spent on? It's often said that the best thing you can do to help after a natural disaster is to give money.

I have a simple question about how and where that money is sent. I imagine often resources can be donated, but money is still required to utilise them.

Is there a study showing the breakdown?

One thing such funds get spent on is corruption:

Do Public Fund Windfalls Increase Corruption? Evidence from a Natural Disaster
(Nikolova and  Marinov (2015))

  We show that unexpected financial windfalls increase corruption in
  local government. Our analysis uses a unique data set on flood-related
  transfers, and the associated spending infringements, which the
  Bulgarian central government distributed to municipalities following
  torrential rains in 2004 and 2005. We build an index of corruption
  using information from the publicly available audit reports, and
  exploit the quasirandom nature of the rainfall shock (conditional on
  controls for ground flood risk) to isolate exogenous variation in the
  amount of funds received by each municipality. Our results imply that
  a 10% increase in the per capita amount of disbursed funds leads to a
  12.2% increase in corruption. We also present suggestive evidence that more corrupt mayors anticipated punishment by voters and dropped out
  of the next election race. Our results highlight the governance
  pitfalls of non-tax transfers, such as disaster relief or assistance
  from international organizations, in weak democracies.

Weathering Corruption (Leeson and Sobel (2006))

  Could bad weather be responsible for U.S. corruption? Natural
  disasters create resource windfalls in the states they strike by
  triggering federally-provided natural disaster relief. Like windfalls
  created by the ìnatural resource curseî and foreign aid, disaster
  relief windfalls may also increase corruption. We investigate this
  hypothesis by exploring the e§ect of FEMA-provided disaster relief on
  public corruption. The results support our hypothesis. Each additional
  $1 per capita in average annual FEMA relief increases corruption
  nearly 2.5 percent in the average state. Eliminating FEMA disaster
  relief would reduce corruption more than 20 percent in the average
  state. Our Öndings suggest that notoriously corrupt regions of the
  United States, such as the Gulf Coast, are notoriously corrupt because
  natural disasters frequently strike them. They attract more disaster
  relief making them more corrupt.


How can a free market be operated in a way that significant social and environmental costs are intrinsically covered? More precisely, is there any practical way to operate a free market so that external costs, namely negative social and environmental impacts, become naturally (intrinsically) covered (paid for or mitigated) by the market itself?
History suggests that capitalism inherently incentives production processes which externalize as much of the cost of production as possible.
This economic tendency to externalize costs wasn't a big problem in a world of seemingly infinite resources. More recently, however, globalization appears to both intensify and conceal the externalization tendency, as large international corporations seek to increase profits and/or stockholder earnings through any available means, including unethical and/or illegal means which remain concealed by the sheer size and complexity of the global marketplace.
[The next two paragraphs are probably not necessary for the question, and may be inflammatory.]

But the damage being done by externalized costs is also global, and is apparent to us all. We call them "wicked problems". We are becoming like the laboratory rats that, under conditions of severe crowding, go crazy and start eating their young. For all of its incredible efficiency and historical success -- creating a huge increase in global wealth -- free market capitalism in its current form is like a cancer, sacrificing the host in its pursuit of unlimited growth, both environmentally (e.g. global warming) and socially (e.g. the middle class shrinks while the financial sector expands).
There is hope, and there is still time. Perhaps all that is needed is a tweak to our economic system. At the local level externalized costs can be identified, controlled and mitigated by government regulation. But at the national level, regulatory mechanisms are expensive and inefficient, and regulators will always be playing catch up to corporate ingenuity. The regulatory challenge is even greater at the global level.

It would be far more efficient and sustainable if the tendency to externalize costs were managed by market mechanisms that, ideally, were built into the economic system, rather than imposed from the outside.

As far as we can tell, no, there is no way to do it using only a free market.

Coase postulated that within a free market, agents would negotiate private contracts to internalise the externalities.

In reality, this didn't happen. It turned out that humans aren't perfectly informed hyper-rational beings. And as Coase himself had inferred, the transaction costs are typically too high.

There are well-documented ways in which markets have been adjusted for externalities: sometimes taxes or subsidies are sufficient; other times, prescription or proscription has been necessary.

There are even well-documented ways in which the commons have been protected, meaning that the destruction of them is no inevitable tragedy: Elinor Ostrom won the Nobel Economics Prize for her work showing how empowered stewardship by a group of custodians had repeatedly protected the custodians' commons.

So the relative efficiency of market mechanism versus planned mechanism is nowhere near clear enough to claim that "It would be far more efficient and sustainable if the tendency to externalize costs were managed by market mechanisms ... ". Each of the alternatives has inherent inefficiences: planned mechanisms have dead-weight costs. market-mechanisms have transaction costs and failures due to imperfect information and bounded rationality. There's a lot of evidence, particularly when it comes to the wicked problems you describe, that the market inefficiencies are far worse than the planning inefficiencies.


What does Hayek mean at the end of the first paragraph of The Use of Knowledge? I reproduce here the first paragraph of Hayek's well-known essay The Use of Knowledge in Society:

  What is the problem we wish to solve when we try to construct a rational economic order? On certain familiar assumptions the answer is simple enough. If we possess all the relevant information, if we can start out from a given system of preferences, and if we command complete knowledge of available means, the problem which remains is purely one of logic. That is, the answer to the question of what is the best use of the available means is implicit in our assumptions. The conditions which the solution of this optimum problem must satisfy have been fully worked out and can be stated best in mathematical form: put at their briefest, they are that the marginal rates of substitution between any two commodities or factors must be the same in all their different uses. [emphasis added]

I have bolded the part that I don't quite grasp, not being a trained economist. Can anyone explain this in layman's terms? (I understand marginalism quite well, so no need to go in depth on that, though it could help others understand better. Of course, perhaps I don't understand marginalism as well as I thought.)

Your marginal rate of substitution between (say) eggs and wine is the number of eggs you'd be willing to trade for one additional bottle of wine.  This marginal rate of substitution can reflect your preferences (if you're a consumer) or the state of technology (if you're a producer who can, for example, substitute three eggs for one wine in your production process).

Suppose your MRS is three eggs per wine and my MRS is two eggs per wine.  Then there's an opportunity for a mutually beneficial trade:  You give me two and a half eggs, and I'll give you a wine.  You thought the wine was worth three eggs, and you got it for two and a half --- that's a win.  I thought the wine was worth two eggs, and I sold it for two and a half --- that's also a win.

Whenever your MRS differs from my MRS, there's an opportunity for a mutually beneficial trade.

Therefore, if our MRS's differ, it means that an opportunity for mutually beneficial trade has been missed.

So in order for resources to be used efficiently --- that is, in such a way that all opportunities for mutually beneficial trade have been exploited --- the MRS between any two commodities must be the same for you as it is for me or anyone else, regardless of how we're using those resources.


Is this use of a Law of Large Numbers correct? The usual LLN I've seen, the theorem states that $1/n \sum u_t \rightarrow^p E(u_t)=\mu$,where the expected value is independent of t. However, I cannot apply it to the exercise below.

In the picture, the author seems to be using $ \displaystyle \frac{1}{n} \sum u_t \rightarrow^p \lim_{n \rightarrow \infty}\frac{1}{n} \sum E(u_t)$

Result (3.44) is $Var(\hat u_t^2)=E(\hat u_t^2)=(1-h_t)\sigma^2$, and it's also the result they refer to as 'in the previous exercise', and (3.46) is just the first equation, without the plims.

So, what LLN can I apply?

Any help would be appreciated.

Are the $\hat{u}_t^2$ independent? If yes, the result is indeed a version of the law of large numbers due to Kolmogorov, and that deals with independent (but not necessarily identically distributed) processes.

Here is the formal statement. Suppose that $\{u_t\}_{t=1}^{\infty}$ is a sequence of independent real-valued random variables that satisfies
\begin{equation*}
\sum_{t=1}^{\infty}{\dfrac{Var(u_t)}{t^2}}<\infty
\end{equation*}

Then the random variable
\begin{equation*}
\dfrac{1}{n} \sum_{t=1}^{n}{[u_t-\mathbb{E}(u_t)]}
\end{equation*}
converges to 0 almost surely.

Edit: the assumption of independence seems stronger than needed, and the following result (an adapted version of the law of large numbers for non-independent processes) might be useful. If $\sigma_{n,m}=Cov(u_n,u_m)$ exists, and if there is $0< \alpha <1$ and $M \in \mathbb{R}$ such that $\sigma_{n,m} < M \alpha^{|n-m|}$ for all $(n,m)$, then
\begin{equation*}
\mathbb{P}(|\dfrac{1}{n}\sum_{t=1}^{n}u_t- \dfrac{1}{n}\sum_{t=1}^{n}\mathbb{E}(u_t)|>\epsilon] < \dfrac{M}{n \epsilon^2}
\end{equation*}
for any $\epsilon$.


What does long-run level mean for exchange rate I am reading a paper by the economist Dornbusch. It says that exchange rate will converge to its long-run level. The rate appreciate if prices are initially below their long-run level, and, conversely, if prices are initially exceed their long-run level.

Now what does long-run level mean?

The long-run in economics is a technical term. It means, roughly "without any short-run constraints". What are short-run constraints? Well they're fixed costs like any contracts you've signed (like, say, your lease, your employment contract) and any capital that you've accrued or lack would be short-run constraints.

To give an illustrative example, a barbershop may want to increase profits and considers potential options. In the short-run he can increase the prices of haircuts or decrease his hours of operation. In the long-run he can move to another location where he'll have more room for additional chairs and such.

For currency exchanges, I'd imagine fixed costs would include trade contracts and debt. At any rate hopefully this answers your question.

edit: and "level" in this context just means the exchange rate itself. Since it is numeric, it can be said to have a level. You could change the word 'level' for 'rate' and it'd be the same meaning.


Second Order Derivatives in Becker's Crime and Punishment I'm trying to understand Becker's seminal paper Crime and Punishment (1968) particularly the parameter of cost of apprehension and conviction and their second order partial derivatives.
The paper states the costs of various activities to apprehend is given by the function $C = C(A)$ where $C' = \frac{dC}{dA}$ and that activities can be approximate by the clearance rate $(p)$ and number of offences $(O)$ by the formula $A ≅ pO$
Now, partially differentiating once with respect to each $(p)$ and $(O)$ gives the following
$$C_p=\frac{∂C(pO)}{∂p} = C'O \quad \textrm{and;} \quad C_O = C'p \quad \textrm{respectively} \quad$$
Becker then says if $pO ≠ 0$ then an increase in either probability of conviction or number of offenses would increase total costs. This is where my confusion begins, when he discusses the marginal cost of increased activity given by second order differentiation where:
$$C_{pp}= C''O^2;\\
C_{OO}= C''p^2\\
C_{pO}=C_{Op}= C''pO + C'$$
Put simply, why is there an added $C'$ for the cross-partial differentiation results? I went through my calculus books and tried to figure out the chain rule application but to no avail.

You have to apply both chain and product rule for derivatives here. In this case:
$$C_p'=\frac{\partial C(pO)}{\partial p}=C_p'(pO)O$$
But note when calculating cross-derivative you take the 2nd order derivative wrt O:
$$\frac{\partial C_p'(pO)O}{\partial O} =  \frac{\partial }{\partial O}[C_p'(pO)]\cdot O +  C_p'(pO)  \cdot\frac{\partial}{\partial O} [O] \\
= C_{pO}''(pO) \cdot pO + C_p'(pO)  \cdot 1 $$
Omitting subscripts this is equivalent to: $C'' pO + C'$.
To sum up, $C'$ comes from the product rule for derivatives (i.e. $\frac{d}{dx}[f(x)g(x)]= f'(x)g(x)+ f(x)g'(x)$ - you can learn more about this rule in standard math textbooks such as EMEA by Hammond et al.).


Cointegration and imposing AR terms I am dealing with what I believe to be cointegrated statistics (Johansen says cointegration is present) however, when regressing the model the error terms are not stationary.

One of the causes of this is autocorrelation in the dependent regressor. So by imposing an AR structure on the model, I do get stationarity of the error terms, but is this cooking the equation to make it stationary?

Thanks!

Johansen cointegration will usually yield more than one cointegrating vectors (cointegration regression coefficients). By definition, for a cointegrating vector, residuals must be stationary. And a stationary process can take any stationary ARMA form. So, adding AR term is cheating. What you shall do is to test for stationarity of residuals obtianed from cointegration vector. I do not mean to be rude, but you must be doing something wrong. Perhaps, your original variables are not I(1), or you need to include a determinsitc or stationary trend in your stationarity test, and the like. Just for comparison purposes, how do your Johansen results compare to Engel-Granger test. This might shed some light.
Best,


What will be the effect on velocity of money when demand for real money increases? Suppose that a change in government regulations allows banks to start paying
interest on checking accounts. The money stock is the sum of currency and demand
deposits, including checking accounts.
(a) How does this change affect the demand for money?
(b) What happens to the velocity of money?
(c) What will happen to the LM curve?
(d)If the price level is fixed, what will happen to the output and interest rate? Use the
IS-LM framework to explain your answer.

This was the question given. According to my understanding:
(a) interest on checking accounts means lower cost of holding money so money demand goes up.
(c)Since demand for money has gone up interest rate will go up, hence LM curve shifts to the left.
(d) due to the leftward shift of LM curve interest rate go up and output goes down.
Are my answers correct? How do I insert velocity of money in ISLM model?

(a) The effect of this policy change sounds theoretically ambiguous to me. It ultimately depends on the consumers' preferences.

An increase in interest payments lowers the opportunity cost of having cash, which might make some consumers better off by saving more and some might see this is a relief and hold more cash. We need an utility function in order to know how consumers would react to the policy change.

(b) Again, ambiguous. It depends on the liquid effect of the policy change on money demand. Let's first remember the Equation of Exchange:

$$MV=PQ$$

If consumers deposit more money on checking accounts, money supply goes up. Given the price level and output are fixed (we're in the short run), an increase in $M$ makes the money velocity $V$ decrease. On the other hand, if consumers deposit less on checking accounts, money supply goes down and velocity of money increases.

(c) The correct answer - at least in my understanding - is that it's ambiguous. If the money supply increases, the LM shifts to the right and if it decreases, to the left.

(d) If the LM shifts to the right and the price level is fixed, output goes up and interest rates go down, if it shifts to the left, output goes down and interest rates go up.


Determining Another Possibility For a Microeconomics Question If new, more advanced equipment reduces the amount of labor needed to produce an increased level of output, then

The AVC curve will shift upward
The MC curve will shift upward
The ATC curve will shift downward
The AFC curve will shift upward

The textbook states the correct answer is 3, however my teacher tells me that there is another possibility.

My thinking is that it could be the 1.The Average Variable Cost will shift upwards. My reasoning is that because the new equipment adds to the cost, including ordering the equipment, installing it, maintaining it, and training people to operate it. All of that would contribute to the cost.

Am I grasping the concept of AVC correctly. And is 1. a good alternative?

Usually capital costs are deemed fixed rather than variable costs. Probably your teacher is thinking that the AFC curve will shift upwards, although this depends on the cost of the new equipment relative to that of the old.


How does the Federal Reserve reduce "excess reserves"? Over the last few years, the amount of currency is circulation (and the corresponding liability on the Fed's balance sheet) has been growing; however, the asset side of the BS hasn't increased. By basic accounting, that means one of the other liabilities (either required reserves or excess reserves) has been shrinking.

I'm guessing the growth in currency volume has been offset by declining excess reserves, but I don't understand the mechanics of that. Does the fed send $100 bill to a bank and then reduce that banks' excess reserves by 100 dollars? If so, how does the Fed decide which banks' account will be reduced by how much?

As you point out excess reserves have indeed been going down since around 2014.

The Federal Reserve doesn't force member banks to withdraw excess reserves, although the Fed can provide incentives to do so by lowering interest rates on those reserves. In other words, excess reserves have been going down because member banks have chosen to withdraw reserves to, for example, purchase financial assets.


Public debt and GDP in post-socialistic countries Why is public debt in % of GDP in post-socialistic countries of Eastern Europe is less than in countries of Western Europe.

Some arguments, opinions or articles?

The statement is not generally true. If you look at gross debt, the Western countries of Finland, Denmark and Norway have lower debt ratios (53%,50%,34%) than post-socialistic Croatia (80%) and Hungary (79%). If you look at net debt, these Western countries have even better numbers.

So right now the correct answer is that your premise is not true.

Your statement is probably true in some form (e.g. on 'average', whatever that would mean in this context, or given some specific Western countries), but please make it exact and back it up with a source. (Perhaps in a new question, seeing that I put effort into answering your current one. Changing it post-answer would be somewhat unsporting.)


How good is a forecast? (Many outputs) I have several macroeconomic models (eg two DSGEs and a VAR). They each produce forecasts for GDP, inflation and unemployment, and I have data to test them on, going back years.
How can I say which model has the "best" overall performance?
I realise this is vague, so here's more detail:
Assume that model X performs better than model Y on GDP, but worse on inflation.
If I'm just looking at GDP, I could just ask something like "which model has the smallest mean square error?" (predicted GDP - actual GDP, squared)
Similarly, if I only care about inflation, I could do the same thing.
But I actually care about forecast accuracy over all three variables (GDP/inf/unemployment).
Is there a way to assess accuracy over all three variables, without just assigning weights to each MSE value and adding them up?
Thanks for your help!

The MSE is essentially a squared Euclidean distance between two vectors, say $\mathbf y$ and $\hat{\mathbf y}$, where $\mathbf y$ is the actual economic data over $T$ periods and $\hat{\mathbf{y}}$ the predicted values. A natural extension of this to matrices $\mathbf Y=(y_{it})$ and $\widehat{\mathbf Y}=(\hat y_{it})$ where $i=1,\dots,n$ and $t=1,\dots,T$ ($n$ variables over $T$ periods) would be
\begin{equation}
\text{MSE}^*=\frac{1}{nT}\sum_{i=1}^n\sum_{t=1}^T(y_{it}-\hat y_{it})^2.
\end{equation}
But beware of the pitfall. Of course there are other matrix norms available as well.


How do Marxist economists solve the Diamond-Water Paradox? For class surveying different economic systems, I read a book on Marxism and its core beliefs.  As I read, I came to learn that the Marxist view of economics depends heavily on the Labor Theory of Value since Marx believed that the value of a good was determined by the amount of labor.
But, from what I understand, the economic community no longer accepts the Labor Theory of Value due to its inability to explain the Diamond-Water Paradox.
How is it then, that certain economists still adhere to the Marxist view of economics?  How do they have Marxism explain the Diamond-Water Paradox?

The Labor Theory of Value has been replaced by the theory of Marginal Utility, which was already accepted by Marx time. In fact he acknowledged:

  "nothing can have value, without being an object of utility"

-Wikipedia: Marginal Utility - The Marginal Revolution and Marxism

Marginal Utility addresses the diamond - water paradox by explaining that the more of a resource or commodity one has ready access to, the less one needs access to even more. The declining marginal utility means that because water is nearly ubiquitous and easily accessed it has very little "value" per unit to an individual because they know they have access to many many units.

"Modern" analytical Marxists, including John Roemer have built a strong foundation (if somewhat heterodox) based on the theory of marginal utility.


Conditional probability in Kaplan, Menzio (2014) This is question about Kaplan and Menzio's shopping time model.

Pages 7,8: Unemployed search once or twice (for a seller).

$\psi_u$:probability of searching twice, searching once with prob $1-\psi_u$
$\nu$ is the probability of finding a seller.
Searches are independent. An unemployed who searches twice, hence has the probability of finding two sellers of $\nu^2$.

Now here's the problem, on page 10, they look at it from a seller's point of view. Conditional of the seller of being matched with a buyer, what is the probability of the buyer being matched with another seller?

$$ Prob(\text{being matched second seller} | \text{being matched with first seller}) = \frac{Prob(\text{being matched with first and second seller})}{Prob(\text{being matched with first seller})} \\
= \frac{\text{search twice and find both times}}{\text{search once and find a seller or search twice and find one or two sellers }} \\
= \frac{\psi_u\nu^2}{((1-\psi_u) * \nu) + (\psi_u)*(\nu + \nu)}\\
= \frac{\psi_u\nu}{1+\psi_u}\\
$$

However, what they get is

$$ \frac{2\psi_u\nu}{1+\psi_u}$$

They compute some "intermediate probabilities" on page 8, but I don't see how they help get their result. How does one get their result?

The first / second seller terminology can be confusing here (does it relate to time or to conditionality?). It's safer to focus on a particular seller.

Let the probability that a buyer finds a particular seller, $s$, via single search be $\nu_s$. The probability that a buyer is matched with $s$ and (either before or after) another seller is then (assuming that $\nu_s$ is small so that the probability of finding $s$ twice in at most 2 searches can be ignored):

$$\psi_u(\nu_s\nu+\nu\nu_s)= 2\psi_u\nu_s\nu$$

The probability that a buyer is matched with $s$ via either a single or a double search is (again ignoring the probability, given a double search, of finding $s$ twice):

$$(1-\psi_u)\nu_s + \psi_u(\nu_s + \nu_s)=\nu_s(1+\psi_u)$$

The conditional probability of a buyer being matched with $s$ and another seller, conditional on $s$ being matched with that buyer, is therefore:

$$\frac{2\psi_u\nu_s\nu}{\nu_s(1+\psi_u)}=\frac{2\psi_u\nu}{1+\psi_u}$$

But the latter formula does not depend on $\nu_s$. Hence the same formula applies to any seller.


Delegation with Discreteness Consider a game of delegation. An uninformed principal must delegate some task to an informed agent with preferences imperfectly aligned.

I'm aware of plenty of literature that studies these kinds of problems when there is a continuous action space, Alonso and Matouschek (2008) for example. Their lit review also seems to feature papers with continuous spaces. Quadratic loss utilities are very popular.

Are there any papers featuring delegation of a decision which is constrained to some discrete space? Do qualitative results change?

I believe this is the basic case discussed in the Laffont-Martimort textbook "The Theory of Incentives". The choice of the agent is either 0 or 1. You can find a complete description in "The Moral Hazard" chapter, section 4.2. The results are listed later, and while I am not sure, I do not think there should be qualitative differences.


What are the books usually called for studying the computation of GDP? What are the books usually called for studying the computation of GDP?

It seems that the economics growth by Barro doesn't discuss about that.

The ultimate reference is the UN's SNA 2008 manual. SNA stands for System of National Accounts. The SNA 2008 is the international statistical standard for the national accounts


If $a$ and $b$ are two pure rationalizable strategies, can $0.5a+0.5b$ fail to be a rationalizable strategy? It is easy to see that if $\sigma$ is mixed rationalizable strategy, then a pure strategy $a$ such that $\sigma(a)>0$ is also rationalizable, but it seems not vice versa.

For a two-player finite game, let $P_1$ be the set of all pure rationalizable strategies for player 1, then the set of her rationalizable strategies is simply $\Delta(P_1)$, which can be seen as a corollary of equivalence of iterated strict dominance and rationalizability for two-player finite games.

What is an example for a finite game with more than two players such that the set of rationalizable strategies is strictly smaller than the mixed extension of the set of pure rationalizable strategies?

Yes. Consider a two player game described by the following matrix

\begin{array}{|c|c|c|}
\hline
&  L & R   \\
\hline
a & 3,0 & 0,0   \\
\hline
b & 0,0 & 3,0    \\
\hline
c & 2,0 & 2,0    \\
\hline
\end{array}

If only pure strategies are allowed, only $a$ and $b$ are rationalizable because they are best responses to $L$ and $R$ respectively while $c$ is not a best response to anything. But if you look at the mixed extension of the game then $c$ strictly dominates 0.5$a$+0.5$b$, hence 0.5$a$+0.5$b$ is not rationalizable. As a result, in the mixed extension all $a$, $b$ and $c$ are rationalizable.

If you insist on an example with three players I can add a third one to this. This third player has exactly one possible strategy, so it does not really matter what his payoffs are and what he does.
If you think that is cheating, the third player can have multiple strategies that do not at all influence the payoff of the first two players.


Interpolation of Gini Index? Is there a conventional curve used to interpolate the Lorenz curves that model the distribution for calculating the Gini coefficient? Is it polynomial? But why? Which degree?

A Lorenz curve is a P-P plot, so the shape of the curve depends on the underlying probability distribution. Depending on what probability distribution you're using for your model (uniform, normal, exponential, etc.), you'll end up with a different functional form for the Lorenz curve.
Given an underlying cumulative distribution function $ F(x) $ with inverse (if it exists) $ x(F) $, the Lorenz curve is given by
$$ L\big(F(x)\big) = \frac{\int_0^F{x(G)}dG}{\int_0^1{x(G)}dG} $$
In practice, when you're looking at Lorenz curves and Gini coefficients, it's common to use a Pareto distribution as the underlying probability distribution.
Here's a derivation for the functional form of the Lorenz curve for the Pareto distribution as an example of the process. Starting from the CDF of the Pareto distribution:
$$ F(x) = 1 - \bigg(\frac{x_m}{x}\bigg)^\alpha , $$
we can invert it to
$$ x(F) = x_m (1-F)^{-\frac{1}{\alpha}} . $$
Then, inserting the inverse of the CDF into the definition of the Lorenz curve above, we have
$$ L(F) = \frac{\int_0^F{x_m (1-G)^{-\frac{1}{\alpha}}}dG}{\int_0^1{x_m (1-G)^{-\frac{1}{\alpha}}}dG} $$
$$ =
\frac{\bigg[-\frac{x_m}{1-\frac{1}{\alpha}}\big(1-G\big)^{1-\frac{1}{\alpha}}\bigg]^F_0}{\bigg[-\frac{x_m}{1-\frac{1}{\alpha}}\big(1-G\big)^{1-\frac{1}{\alpha}}\bigg]^1_0} $$
$$ =
\frac{\frac{x_m}{1-\frac{1}{\alpha}}\bigg[1-\big(1-F\big)^{1-\frac{1}{\alpha}}\bigg]}{\frac{x_m}{1-\frac{1}{\alpha}}} . $$
So, for the Pareto distribution with parameters $x_m$ and $\alpha$, the corresponding Lorenz curve has the functional form
$$ L(F) = 1 - (1 - F)^{1-\frac{1}{\alpha}} . $$
Now, if you want to find the functional form of the Lorenz curve given data on some measure, like wealth or income, you would first have to fit the distribution of your data to the Pareto distribution first and estimate its two parameters, $x_m$ and $\alpha$ (see here).
Once you have your estimate of $\alpha$ ($\hat{\alpha}$), you can simply plug that into the Lorenz curve for the Pareto distribution we found above:
$$ L(F) = 1 - (1 - F)^{1-1/\hat{\alpha}} . $$


If all quantities produced rise by 10 percent, and all prices fall by 10 percent, which of the following occurs? I am having a hard time deciding for this question:

If all quantities produced rise by 10 percent, and all prices fall by 10 percent, which of the following occurs?

A) Real GDP rises by 10 percent, while nominal GDP falls by 10 percent.

B) Real GDP rises by 10 percent, while nominal GDP is unchanged.

C) Real GDP is unchanged, while nominal GDP rises by 10 percent.

D) Real GDP is unchanged, while nominal GDP falls by 10 percent.

I think it is either A or B, because I know that real GDP rises but i'm not sure what happens to the nominal GDP. if anyone can help, it would be much appreciated.

It helps to write out things as (simple but) proper equations. Denote production as $Y$ and prices as $P$

It is given that

$$Y_{t+1} = 1.1 Y_t \\
P_{t+1} = 0.9 P_t$$

Nominal GDP is given by $P_t Y_t$

$$ P_{t+1}Y_{t+1} = 1.1 Y_t \cdot 0.9 P_t  \\
= 1.1\cdot 0.9 \cdot Y_t P_t$$

So nominal GDP changed by $1.1 \cdot 0.9 = 0.99$ - it dropped by one percent.

So which answer is it?

I assumed that the initial value is base value for the description of the relative changes. If, instead, we have that the larger value is base for the relative change,

$$0.9 Y_{t+1} = Y_t \\
P_{t+1} = 0.9 P_t$$

we get that
$$ P_{t+1}Y_{t+1} = \frac{1}{0.9} Y_t \cdot 0.9 P_t = Y_t P_t  $$

nominal GDP does not change.


Bank rate and Repo rate Please explain the difference between Bank rate and Repo rate. Do the Bank and Repo rates affect each other?

The Bank Rate / Discount rate is the interest rate charged by the central bank to member institutions for loans from the central bank. These are typically thought of as emergency funds to meet the liquidity needs of solvent banks with illiquid assets, thought since Bagehot to be properly set at a penalty rate to discourage abuse.* In contrast, the repo rate is the interest charged on repurchase / rehypothecation transactions, which are short term over-collateralized (e.g. \$100 collateral to borrow \$95) loans where a much larger set of institutions including banks, insurance companies, hedge funds, and others can participate on similar financial terms.

The discount rate is a policy rate where the repo rate is an emergent market price for funds. These rates are linked but not in a mechanical way. For example, if the discount rate were set very low, banks would prefer to borrow from the central bank than the collateralized loan market at the repo rate and therefore quantities and rates in the repo market would likely fall. Or it would if there weren't generally speaking a stigma to using the discount window to borrow at the discount rate. But if it were profitable maybe that stigma could be overcome. And there may be other differences like changes in terms or the suitable assets usable as collateral that make comparisons of rates imperfect.

* -

  This penalty explains the positive difference between the fed funds
  rate and the discount rate. If there were no penalty, banks would be
  indifferent between borrowing from other banks and the Fed’s discount
  window.

Is the Discount Window Necessary? A Penn Central Perspective (Calomiris (1993))

That is, banks would rather borrow from the Fed than each other, so the Fed sets its policy rate higher to push banks back into market sources of funds. Then only those shut out of such markets will avail themselves of such funding.


Competitive equilibirium of max utility functions Apologies in advance if my terms aren't exact, I'm learning "Mathmatical Economoics" in the hebrew language and some of the terms don't translate well.

I was given the following question:
Two sellers are a part of an exchange market with two goods, each has the utility function $u(x,y)=\max(x,y)$. Assume the first seller starts with two units of product $x$ and one unit of $y$.

Find $(a,b)$ s.t seller two starts with $a$ units of $x$ and $b$ units of $y$, for which there is a competetive equilebrium.

Any guidence will be of great help! Thanks in advance

I might be wrong so feel free to point out any mistakes.

Both of them have the same utility function $u(x,y)=max(x,y)$
This means when $Px > Py$ , they'll choose to consume $Y$ instead of $X$ since they get higher satisfaction by selling all units of x and purchasing y.

Take the case of First seller, If he sells all X and purchases Y, His total demand for $Y$ will be $2(Px/Py) + 1$ and since Px/Py >1, total demand will be higher than 3. If he had done the opposite, his total demand will be less than 3.
 Since the utility function is $max(x,y)$ He will choose the former strategy

Hence, the demand for $X$ will be zero but the supply is $a+2$. Also, there is excess demand of $Y$. Hence, this is not a competitive equilibrium.

Similarly, then $Px <Py$, there will be excess demand for $X$ so that isnt a competitive equilibrium either.

The only case we have left is $Px=Py$ where the seller will be indifferent in consuming  either good. Here, each seller consumes all of 1 good each. There will be 2 cases.

Case 1. If seller 1 consumes all $X$, His demand is $2 + (1)Py/Px = 3$ since Px=Py and the supply of X is $a+2$. When we equate this, we get $$a=1$$
Notice that this is the only condition that needs to hold here, B can take any non negative values in this case.

Case 2 is where seller 1 consumes all $Y$ and, His demand is $1+ (2)Px/Py = 3$ and the supply of $Y$ is $b+1$. Since they have to be equal, we get $$b=2$$ And again there's no restriction on $a$ and it can take any non negative values.


Fixed-income investment in a low interest-rate environment From an investment perspective, it seems to me that a low interest-rate environment can yield to some relatively "un-risky" profits.

As the interest-rate can barely go lower, we now it should rise again at some point (take for instance the recent interest-rate hike in the US).

In this case, what would be the corresponding investment vehicle/product to invest in? My guess would be to just short-sell positions in bonds, as an interest-rate rise corresponds to a decrease of bond prices, but this seems too obvious.

Am I missing something, for instance that short-selling of bonds is not permitted?

Your assumption that low interest rates will "eventually" have to rise is not warranted.

Indeed, we are currently witnessing prolonged periods of low interest rates that do not obviously seem to be coming to an end.

Example 1. For 7 years, the US FOMC's target federal funds range remained unchanged at 0–0.25% (from Dec 2008 through Dec 2015). From Dec 2015 through Oct 2018, there have been 8 increases so that it is now 2.00-2.25%. But even after 8 increases, this rate range remains historically low.

Example 2. A more dramatic example is the case of Japan, where the 10-year government bond yield has remained closed to 0% for two decades now (and indeed is under 0% now).

You predict that since interest rates are so low now, they must rise. You might very well turn out to be correct, but this is hardly a certainty and there are many others taking the opposite bet.


Why solving the model for a benevolent social planner gives an efficient allocation? Probably this question is really dumb - and I'm sorry if it is - but why solving the model for a benevolent social planner, gives an efficient allocation?

What's the criteria for this efficiency?

I'm asking this because in several NK models in macro, when we're comparing the 'desirability' of simple rules, we take as efficient the allocation obtained from solving the model as stated above.

Any help would be appreciated.

I think the general proof is in this paper.

Thinking in a simple exchange Edgeworth Box, a competitive economy involves prices, which mediate the relationship between consumers relative valuation of goods - the marginal rate of substitution. A (benevolent) social planner does not need those prices, as goods will not be traded in the market, but simply allocated to whom it "corresponds", based on the same optimality conditions. Such equilibrium is simply found by equalising consumers marginal rate of substitution.

In other words:

equilibrium in competitive economy through exchange/markets:

$$ MRS^1_{X,Y} = \frac{P_x}{P_y} = MRS^2_{X,Y} $$

equilibrium via allocation from benevolent social planner:

$$ MRS^1_{X,Y} = MRS^2_{X,Y} $$

(the formulas above can be trivially extended to $n$ consumers and goods)


Piracy/File sharing - Why aren't songs, movies or ebooks given for free (+ads) like TV? Update: I have spent 750 reputation points for bounties on this 6 year old question, and it looks like ONLY NOW this question might be closed. LOL. this must be such a huge guinness book of stackex records: longest duration of post or most reputations points spent for bounties (or both) on question that is supposed to be closed before question is actually closed.

Question: Why aren't songs, movies or ebooks given for free (+ads) like TV?

i. Sub-question: Every minute, people are pirating and there is no stopping that. If people see 0.99 for a song on iTunes and 0.00 for a song on a torrent site, I don't see anything stopping majority of people from going to that torrent site in the same way I don't see anything stopping them from going to a library or asking a friend to borrow a book instead of buying the book in Borders or taping a song off the radio. In particular, there's betamax. It was thought illegal until this case or something.

(Anyway that's about legality not economic benefit/loss. Also betamax is more like is or positive rather than should or normative, I guess.)

So, why don't companies, like the RIAA or MPAA, release their songs, movies or ebooks for free but put in ads kind of like how cable TV was/is done? In my opinion, companies incur a huge opportunity cost

eg 'JK Rowling has lost millions of dollars, because she refused to let Harry Potter come out in ebook form. Newsflash: you can get ebooks of all the Potter books from pirate sites. She didn't cater to her fans, so her fans catered to themselves.'.

ii. Sub-question: What I guess is that they think they can actually stop piracy with things like DRM or scaring people into believing that they will be caught even though such is unlikely so as to keep making money on iTunes, Netflix or whatever.

However, I read that in a documentary, Chairman and CEO of the Motion Picture Association of America (MPAA) Glickman 'concedes that piracy will never be stopped, but states that they will try to make it as difficult and tedious as possible.'

So he ADMITS piracy cannot be stopped, which makes my guess wrong. So what, are the RIAA and MPAA actually irrational?

Question: What are some economic concepts or theories involved in file sharing/piracy besides opportunity cost and free rider problem?

Notes:

This can also extend to games, apps, etc.

To clarify, I don't mean to ask why songs, movies and ebooks are not given ONLY for free. They should continue to be given for payment since there will still be demand. If people want to buy CDs, DVDs or ebooks, attend concerts or go to cinema before songs, movies and ebooks would be given free, they would likely not want to do less if ever songs, movies and ebooks would be given free, I think because it seems that if people like the cinema or concert experience, don't have Internet access or like smelling books, they will continue to purchase as much.

My question is not 'Why do people go to netflix instead of torrent?', a question focused on the consumers given the law and the companies' decisions. My question is instead 'Why aren't songs, movies or ebooks given for free?', a question focused on the law and the companies' decisions given, well:

Pirate Coelho's 'Sharing is part of the human condition. A person who does not share is not only selfish, but bitter and alone.'

Btw I just discovered artificial scarcity.

Edit: in re my badge, thanks for the upvotes everyone! This is so weird that this has only 3 downvotes. I could've sworn this was at 0 score sometime in the past year or so with like at least 10 downvotes. I got a lot of 'user was removed' in notifications recently, so maybe that's relevant.

It's called a Principal-Agent Conflict.
The RIAA/MPAA act as agents on behalf of the people who actually produce content (and consequently end-consumer value).
To maintain relevance to their principals', the RIAA/MPAA must signal value to them (i.e. claim loudly and repeatedly that they do something good for them [regardless of the validity of that claim]).
Firstly, this signaling is demonstrably an example of the Principal-Agent problem, in that it diverts resources away from actually advancing the principals' interests, but more so in that it creates a perverse incentive for lobbying groups to fight imaginary fires.
The impact of piracy on the broad economy is believed to be near zero, so IP laws are effectively just rent-seeking $^{[2]}$ anyway.
Whether or not that particular type of rent-seeking is always a drain on the broad economy (in that it distorts markets producing deadweight loss in excess of the externalities corrected) is up for discussion, though it is known to be possible (insofar as the existence of an optimal tax [or government induced market distortion] is necessarilyy proof of the existence of an excessive tax).


What is the meaning of the weights in a CES-production function? In different paper I offen encounter two types of CES production functions

$y=\left[\left(1-\omega \right) x_{1}^{\frac{\sigma -1}{\sigma}}+ \omega x_{2}^{\frac{\sigma -1}{\sigma}} \right]^{\frac{\sigma}{\sigma -1}}$

or

$y=\left[\left(1-\omega \right)^{\frac{1}{\sigma}} x_{1}^{\frac{\sigma -1}{\sigma}}+ \omega^{\frac{1}{\sigma}} x_{2}^{\frac{\sigma -1}{\sigma}} \right]^{\frac{\sigma}{\sigma -1}}$

the only difference being the exponents of the weights.

What is the difference in meaning and interpretation of the two weights (on an intuitive and a theoretical level). Does it matter which version to use in a paper?

The weights are usually called "distribution parameters" (top of page 12 of linked document), as they correspond, in the case of a Cobb-Douglas, to each factors share in total output. For example, if the two factors were labour and capital respectively, $(1-\omega)$ would be the labour share, and $\omega$ would be the capital share. Because in the case of a Cobb-Douglas ($\sigma=1$) both specifications are identical, the weights refer to the distribution parameters in both specifications.

To see this, take the second equation. First, define the share of $x_1$ in total output as

$$ \lambda_1 \equiv \frac{w_1x_1}{py} $$

where $\frac{w_1}{p}$ is the real return to factor $x_1$ (e.g. real wage).

Under competitive conditions, the firm(s) employ $x_1$ until its marginal product equal $\frac{w_1}{p}$. This marginal product is:

$$ \frac{\partial y}{\partial x_1} = (1-\omega)^{\frac{1}{\sigma}}\left(\frac{y}{x_1}\right)^{\frac{1}{\sigma}} = \frac{w_1}{p} $$

Combining the later equality with the definition of the factor share, you get that

$$ \lambda_1 = (1-\omega)^{\frac{1}{\sigma}} \left(\frac{y}{x_1}\right)^{\frac{1-\sigma}{\sigma}}  $$

In the case of a Cobb-Douglas ($\sigma=1$):

$$ \lambda_1 = (1-\omega) $$

Equivalently,

$$ \lambda_2 = \omega $$

which means that $\lambda_1 + \lambda_2 = 1$, in line with the assumption of constant returns to scale, in both specifications.

Regarding the difference between the two, according to my calculations, the second specification does not encompass the Leontieff case ($\sigma = 0$). This is because, whereas in the first specification you can solve the limit of $(1-\omega)x_i^{\frac{\sigma-1}{\sigma}}$ when $\sigma \rightarrow 0$ (using the minimum of $x_i$, see equation (23) here), you cannot do the same for $(1-\omega)^{\frac{1}{\sigma}}x_i^{\frac{\sigma-1}{\sigma}}$, because the first component goes to zero (provided the standard assumption $0<\omega<1$).

Thus, if you want to be as general as possible, I would recommend the first specification. Additionally, whereas the first specification is imo "very common", the second is not, which would require further justification as to why you choose it. If there is no extra benefit of it, then, by Occam's Razor, the first one is definitely preferred.


Do banks pay for deposit insurance? Under deposit insurance, if my bank goes bankrupt, the government reimburses my deposit up to a specified maximum.

Do banks pay for this insurance, and does it depend on their risk-taking?  If not, what is to stop banks from taking very high risks with deposits from private citizens (the ones unimportant enough to be below the threshold), knowing that the government takes the risk (and will likely opt to rescue the bank rather than repay all account-holders, should the bank fail)?

(Relevant: two main problems with deposit insurance)

There's additional information in this answer, but in the US, banks pay into the FDIC Deposit Insurance Fund, and regulation and capital requirements are used to stop banks from taking excessive risks with deposits. In the event of a bank failure, depositors below the insured limit are repaid in full, but equity-holders are generally wiped out and other creditors must often take losses as well.

The DIF premiums do vary somewhat with risk (see page 2 here):

  The FDIC charges premiums based upon
  the risk that the insured bank poses, and it inspects, or examines, banks to further manage that
  risk.


At forecasting, should I calculate inflation rate daily, monthly or annualy? For example, 100 dollars is going to be worth less in 30 years, how much less depends on the inflation rate. if we assume a constant annual inflation rate of 3%, should I compound the inflation rate daily or monthly or yearly?
I'm debating mostly between daily and monthly, since the data of inflation rate is collected on monthly  basis. But isn't it happening in real life on a daily basis??
Can someone help me to answer this question and please provide some explanation is possible

Thank you!

Inflation is the percent change in a price index per unit time. You should compound at the same frequency as the units in the inflation measure. Many reported measures of inflation are year over year measures, which means that even though they may be reported monthly or quarterly they overlap substantially between observations. You want to be sure to handle this properly by choosing non-overlapping intervals.


Is perfectly inelastic demand always coupled with inelastic supply? In the case of perfectly inelastic demand, the price is always infinite. Does it mean that the supply curve is also inelastic?

I assume you are talking about Price elasticity of demand/supply and not cross elasticity or income elasticity of demand/supply.

Not necessarily.

Perfectly inelastic demand means that a change in price leads to no change in quantity demanded. Imagine a country where, say, tomato is super crucial to survival, any change in its price will not make people want to buy more/less of it.

Inelastic supply can exist separately from perfectly inelastic demand. This is just how responsive supply is to changes in price. Just because the price increases/decreases, doesnt mean producers can make more/less of it more easily, even if they wanted to, e.g. think about sudden weather changes for crop production as an example.

In conclusion, no perfectly inelastic demand is not always coupled with inelastic supply, but it can be.


What is establishment-level data National level or aggregate level data and firm-level data are self explanatory. I have seen certain papers on productivity analysis as well as other topics which refer to "establishment-level" data. Can someone please explain what is meant by this term?

Establishments are firms at the facility level. Think about it like branches: If a firm has three different branches, each of these branches counts as an establishment. If a firm has no branches, the firm itself is the (sole) establishment.


Relation between incomplete contracting and the principal agent problem? I have read about incomplete contracts in the context of vertical integration of firms, in which the two contracting parties are relatively "symmetric" (we cannot say that one is the agent and the other the principal. Both take hidden actions that influence the other party)

In principal agent theory, I have not read anything that explicitly talks about "contractual incompleteness" as a source of agency problems. Yet it seems intuitively that they are related.

How is contractual incompleteness related to the principal agent problem?

Are all principal agent problems the result of incomplete contracting?
is incomplete contracting merely one example of a source of principal agent problem?
How, in general, are they related?

EDIT: In particular, the term "admissible contract" or "feasible contract" is used in the context of principal-agent problems. Does "incompleteness" of contracts simply mean that "the set of admissible/feasible contracts is restricted in some important senses"?

Not all principal-agent problems are the result of incomplete contracts, no. In fact, in most principal-agent problems, complete contracts are assumed.

An incomplete contract is one that cannot be contingent on every possible outcome that could occur after the contract is signed. You can't write a contract that gives out a different payment to each party under every possible circumstance, because you can't imagine every possible circumstance. For example, an American agricultural firm's profits might be affected in miniscule ways by weather in Peru. But a contract related to that firm might offer the same payouts regardless of Peru's weather.

A principal-agent problem arises when the incentives of the principal and of the agent are not aligned, and so the agent may not act as the principal desires. For example, putting in less effort than the principal would find optimal because the agent will be the primary benefactor of additional effort. A lot of the problem arises here because the principal cannot perfectly and costlessly observe what the agent does, and so must write a contract contingent on the outcome of the project, rather than contingent on the agent's actions, which cannot be observed.

You could, colloquially, say that the principal-agent problem is an example of incomplete contracts in the sense that you can't contract on the agent's actions. But that's not what economists mean by incomplete contracts. Incomplete contracts refers to the fact that your contract is not sensitive to every possible contingency, even though everyone will know what that contingency is after it happens, as opposed to principal-agent problems, which refer to the fact that you can't include unobservable actions of the agent in your contract, which are hidden to the principal.

As for how they're related, they're both examples of problems that can make it difficult to write a contract. There are certainly models that combine the two (for example this), but one doesn't subsume the other.