Elasticity of intertemporal sustitution with composite CRRA function In the usual CRRA $\frac{c^{1-\sigma}-1}{1-\sigma}$ function we have that the intertemporal elasticity of sustitution  $\partial\frac{c_{t+1}}{{c_{t}}{\partial r}}$ is $\frac{1}{\sigma}$.
But how can i calculate the IE of S when the CRRA function is the composite:
$\frac{(c-G())^{1-\sigma}-1}{1-\sigma}$
Thanks in advance

Suppose $c_t$ is some composite function of interest rate $r$, e.g. $c_t(G(r_t))$.
First the intertemporal elasticity of substitution is actually (IES) given by $\frac{\partial \ln(c_{t+1}/c_{t})}{\partial r}$ (or also $\frac{\partial \ln(c_{t+1}/c_{t})}{\partial \ln( u'(c_{t+1})/u'(c_t))}$).
You can take the derivative above using chain rule for composite functions which says that $dF(G(x))/dx = \frac{dF}{dG}\frac{dG}{dx}$.
So in the above case we would get:
$$\frac{\partial \ln(c_{t+1}(G(r))/c_{t}(G(r)))}{\partial r} = \frac{\partial \ln(c_{t+1}(G(r))/c_{t}(G(r)))}{\partial G(r)} \cdot \frac{\partial G(r)}{\partial r} $$
You can directly apply this to the problem you mention in your question.


Finding the conditional input demand function Find the conditional input demand function and cost function for the given production function $$f(a,b,c,d)=\min\{ a,2b\} + \max\{3c,4d\} $$
In The solution, The production function is defined as $f(x,y)=x+y$ which is perfect substitutes.
Therefore, when $P_x >P_y$, $x=q$ and $y=0$. And when $P_x < P_y$, $y=q$ and $y=q$.
So far, everything is okay. The point that I don’t understand is how to define $P_x$ and $P_y$. In the answer, these are defined as follows
$P_x= P_a+(P_b/2)$ and $P_y= P_c/3 $ if $P_d/P_c >4/3$ and  $P_y= P_d/4 $ if $P_d/P_c <4/3$
Why does he sum of the prices of goods a and b to find the $P_x$? But while finding $P_y$, he separates it under a condition? What is the difference ? In short, how to define Px and Py? My question is this.

Output $z$ is given as $z = x + y$ where $x=min(a,2b)$ and $y = max(3c,4d)$.
So assume that you want $x=12$ then $a=12$ AND $b=6$. Since this part of the production delivers only the minimum of serveral production processes $a$ and $2b$ the producer must get insure that ALL subproductionprocesses $a$ and $2b$ deliver the minimum.
The producer therefore has to buy both $a$ and $b$ in the required amounts and therefore the price for $x$ is composite including both the price of $a$ and $b$.
However, when you want $y=12$ you must have $12=3c$ OR $12=4d$ implying that $c=4$ OR $d=3$. Since the productionprocess $y$ delivers the max of the subproduction processes the producer only has to make sure that AT LEAST ONE of the subproduction processes delivers the wanted amount $y$.
The producer will therefore always produce $y$ using the "cheapest" input and as dependig on input prices. The input price will therefore only depend on the factor $c$ or $d$ chosen to achieve the max.


How can I know whether a good is inferior or normal? I can't determine elasticity with this? I just need to make sense out of elasticities and how to determine if a good is normal or inferior.
I have determined by $X_1$ which is in the form $m/p_1 - p_1/p_2$, that I should just take the derivative with respect to $m$ to get a value, which is always negative, and by that logic a normal good. But what does it mean when the demand of a good doesn't have $m$ in its function?

Suppose we have a function of income for a particular good, $f(x)$ for income $x$. Then its derivative is the income elasticity of the good (at a certain level of income, though for linear models it's all the same). The consumption of a normal good grows with income while the consumption of an inferior good decreases with income: we have $f'(x) > 0$ for a normal good, $f'(x) < 0$ for an inferior good and $f'(x) = 0$ when the consumption of the good does not depend on income.
That the consumer income doesn't appear in the demand function means just that, that demand isn't affected by changes in income.


Weak Axiom of Revealed Preference Maybe this is a well-known fact that I have somehow overlooked or forgotten etc., but I found myself curious recently if there are any conclusions about WARP holding over different dimensions for a given choice structure.

So, if I have a utility function, $N$ agents, $L$ commodities and price vectors in $R^L_+$, and I want to determine if WARP holds here, is it enough to assume that $L=2$ and prove WARP. Meaning, is it true that if WARP holds for $L=2$ it also holds for $L=N$, $N \in \mathbb{N}$

Edit : I feel like I should add that I know, generally, proving something for a specific case does not allow one to generalize the result. However, there are unique cases where such proofs can work. The first example that comes to mind is that whenever the excess demand function is homogeneous of degree zero we can reduce the problem to the simplex and it is sufficient to show that only n-1 markets clear.

Why I am asking?

I am trying to determine whether or not WARP holds for an adaptation of the (1999) Fehr & Schmidt Inequality Aversion utility function. I thought it might be easier to do by considering $L=2$

I can shed some light on the question, but am not sure I can answer it as I am not sure it is really even well defined.

(1) The Weak Axiom of Revealed Preference is a decision theoretic concept regarding the choices of a single agent. So I do not understand how having $N$ agents is relevant to the problem.

(2) Generally speaking, if $U: X \to \mathbb{R}$ is a utility function and $\mathscr{C}$ is a choice correspondence over $X$ such that $\mathscr{C}(A) = \{x \in A \mid U(x) \geq U(y), \ \forall y \in A\}$ then $\mathscr{C}$ will satisfy WARP. This is a straightforward exercise in using the definitions, and the dimensionality of the space should play no role (its true over an abstract $X$).

(3) If the consumption space is $\mathbb{R}^l$ then preferences over defined $\mathbb{R}^l$. How you project preferences into $\mathbb{R}^2$ matters.

(4) If I interpret your question a la denesp, so that you ask: fix the $2 < k \leq l$ dimensions of consumption and only let dimensions 1 and 2 vary (of course, what we fix the other dimensions of still may make a difference), and assume that this restricted choice correspondence satisfied WARP will the choice correspondence in general satisfy WARP.

To answer (4): if the choices comes from a utility function then yes, trivially (see point (2)). If the choices are more general, then no. This fails severely. Take as a counter example a preference over $\mathbb{R}^3$ such that fixing the 3rd dimension, the consumer is indifferent over all elements (i.e., the first and second dimensions are null). WARP holds as $\mathscr{C}^{x}(A) = A$ for all $A \in \mathbb{R}^2 \times \{x\}$. This leaves the 3rd dimension wholly unrestricted. Letting the choice function over this last dimension be cyclic (i.e., fail WARP) and we see that the original choice would as well.

(5) What if we instead interpret your question as: we see every two dimensional projection of choice. (That is for every $i,j \leq l$, $i \neq j$, we see the projection of choices over the dimensions $i$ and $j$ fixing the other dimensions arbitrarily. Well, if the way we fix the other dimensions matters to the restricted choices (e.g., $\mathscr{C}^{x}$ over $\mathbb{R}^2 \times \{x\}$ is not the same as $\mathscr{C}^{y}$ over $\mathbb{R}^2 \times \{y\}$). Then we are back to the same type of problem as (5)---$\mathscr{C}$ could be cyclic when the dimensions are fixed differently.

What if how we fix the dimensions doesn't affect the restricted choice (so we have separable preferences, a la Koopmans). Then WARP will hold over $\mathscr{C}$ if it is rationalized by a preference relation. But, the result is not very interesting, since from the restricted choices know the choice of out of $\{x,y\}$ for all $x,y \in \mathbb{R}^l$. It is well known that only a binary choice is necessary to verify a rationalization. Without this additional constraint, I believe you could still cook up a counter example in the spirit of (4) where cyclically kicks in when certain elements (at least 3, pairwise distinct over 3 different dimensions) are present.


What is the difference between a free trade agreement and a preferential trade agreement? What is the difference between a free trade agreement and a preferential trade agreement?

What is the difference between a free trade area and a free trade agreement?

A free trade agreement stipulates free (cero tariff) trade between countries/states. In practice, this also includes broader provisions, such as agreements on movement of capital, goods and people (such as NAFTA). A free trade agreement will also mostly include all or a large portion of goods.

In contrast, a preferential trade agreement is much less broad covering preferential (i.e. low or lower other countries) tariffs for a set of products or services. A preferential trade agreement can also just be unilateral or for a particular amount of years, etc.

A free trade area is an area inside a country or state where free-trade rules (in general, but depending on the country and circumstance) apply. These areas are intended mostly for the import and export of goods, and are useful for a country that imports a good as an input by which another good is produced, thus lowering tariff costs for the producers.

A free trade agreement is, of course, not a physical place (see explanation above).

Further, I recommend simply wikipedia in this case...


Question on Human Capital Accumulation Model by Acemoglu/Autor I was reading the lecture notes by Acemoglu and Autor on Labour Economics. https://economics.mit.edu/files/4689

I was able to understand equations 1.1 to 1.8 of the notes; however, I am unable to understand how equations 1.9 and 1.10 were derived from equations 1.8 and 1.9 respectively. I understand that integration and differentiation was applied, but I am not able to figure out the exact steps involved.

For the transition from equation 1.8 to 1.9, I tried to understand in terms of general power rule and general exponential rule of integration, but there are so many terms involved that I am unable to think how these rules apply.

For the transition from 1.9 to 1.10, I tried to understand in terms of general product rule and quotient rule of differentiation, but I am unable to figure out exact steps.

I would deeply appreciate if anyone could help me understand these steps. Please let me know if any other info is required from me.

Thank you.

The FOC from (1.9) is (I'm skipping the content of the $\exp()$ expression for brevity):

$ \frac{1}{r+\nu+g_h + g_w} \left(\eta'(S)w(0) \exp(\cdot) + \eta(S) w(0) (r + \nu - g_w)\exp(\cdot)\right) \overset{!}{=} 0$

This makes use of product rule.
Since the first term can't be 0 due to the last equation on p.~11, it must be second one

$ \eta'(S)w(0) \exp(\cdot) = \eta(S) w(0) (r + \nu - g_w)\exp(\cdot) $

$ \eta'(S) = \eta(S) (r + \nu - g_w) $
yielding Eq. (1.10):

$ \frac{\eta'(S)}{\eta(S)} = r + \nu - g_w $


Economics and Stock Market/Bond Market In this link, we can read "The revised reading of second-quarter gross domestic product growth beat analysts’ expectations triggering a stock-market rally and a bond selloff." Well, why can we assume that the upward pressure on the nominal interest rate won't be enough to decrease the stock values by counteracting the increasing nominal dividends that stocks provide?(i.e. the LM curve is flat)

Consider an investor who splits up his portfolio into stocks and bonds according to some ratio that considers all things that need to be considered. These include returns etc. Assume the portfolio is "correct" i.e. in equilibrium. Through the GDP revision, stocks become more attractive compared to bonds for the individual investor, so each individual investor has to adjust his ratios and increase the nr. of stocks, which means he has to sell bonds. The individual investor does not expect his action to actually influence government bond yields as he is small compared to the market. If all investors do this, then we get the result mentioned in the link.

Further dividends are not the only reason stocks have value. Many companies don't pay out dividends, because the shareholders then have to pay tax on them, but rather re-invest the profits which increases the stock value, which can then be sold.

Also its not clear that the government bond interest rate is the relevant interest rate for discounting for these investors (the effect you are referring to).


Is this a joke by Galbraith or did he have something more serious on mimd? In the Sydney Morning Herald, May 1982 Galbraith is on record for saying:

  Wealth, in even the most improbable of cases, manages to convey an aspect of intelligence.

As an economist Galbraith would have had a chance to have to observe men with great wealth at close quarters, so one supposes that this acerbic little comment is drawn from life. But did he mean something more important by it, or was it simply a joke on his part at the expense of the wealthy?

note: I’ve tagged it as macroeconomics as I couldn’t hink of the right tag this should be filed under. Any sensible suggestions will be appreciated.

Not having read the article, I do not know the context in which this quote was made. But I believe it is in line with a view he also expressed elsewhere — that people mistake wealth for intelligence.
In e.g. A Short History of Financial Euphoria (1993 edition, pp. 13–16), he writes:

The basic situation is wonderfully clear. In all free-enterprise (once called capitalist) attitudes there is a strong tendency to believe that the more money, either as income or assets, of which an individual is possessed or with which he is associated, the deeper and more compelling his economic and social perception, the more astute and penetrating his mental processes. Money is the measure of capitalist achievement. The more money, the greater the achievement and the intelligence that supports it.
Further, in a world where for many the acquisition of money is difficult and the resulting sums palpably insufficient, the possession of it in large amount seems a miracle. Accordingly, possession must be associated with some special genius. This view is then reinforced by the air of self-confidence and selfapproval that is commonly assumed by the affluent. On no matter is the mental inferiority of the ordinary layman so rudely and abruptly stated: "I'm afraid that you simply don't understand financial matters. " In fact, such reverence for the possession of money again indicates the shortness of memory, the ignorance of history, and the consequent capacity for self- and popular delusion just mentioned. Having money may mean, as often in the past and frequently in the present, that the person is foolishly indifferent to legal constraints and may, in modern times, be a potential resident of a minimum-security prison. Or the money may have been inherited, and, notoriously, mental acuity does not pass in reliable fashion from parent to offspring. On all these matters, a more careful examination of the presumed financial genius, a sternly detailed interrogation to test his or her intelligence, would frequently and perhaps normally produce a different conclusion. Unfortunately the subject is rarely available for such scrutiny; that, too, wealth or seeming financial competence often excludes.
Finally and more specifically, we compulsively associate unusual intelligence with the leadership of the great financial institutionsthe large banking, investment-banking, insurance, and brokerage houses. The larger the capital assets and income flow controlled, the deeper the presumed financial, economic, and social perception.
In practice, the individual or individuals at the top of these institutions are often there because, as happens regularly in great organizations, theirs was mentally the most predictable and, in consequence, bureaucratically the least inimical of the contending talent. He, she, or they are then endowed with the authority that encourages acquiescence from their subordinates and applause from their acolytes and that excludes adverse opinion or criticism. They are thus admirably protected in what may be a serious commitment to error.


Why doesn't anyone talk about GNW (Gross National Wealth)? I just noticed a very interesting fact.

GDP of the United States: $18.5B

GDP of China: $11.4B

If we look at national wealth...

GNW of the United States: $84.8B

GNW of China: $24.1B

The margin of the GNW is 8.5 times higher of that of the GDP! Why is GDP so paraded and why do we never hear about national wealth?

Sources: https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(nominal), https://en.wikipedia.org/wiki/National_wealth

Historically, the distinction between GDP and GNW goes back (at least) to Adam Smith. Before Smith, it was quite common to measure a country's economic power by its wealth. For example, this was very characteristic of the Mercantilistic school in the 17th century. Following the motto "you are what you have", mercantilists suggested that countries should try to accumulate as much wealth (for them: gold) as possible. This was to be achieved by a combination of an export oriented economy and political measures to limit imports such as tariffs. Selling goods abroad and keeping one's currency (again, gold) they hoped would result in having more money and thus being more wealthy. This idea is reasonable for the middleages where the difference between having and not having money can decide about which country is able to hire more mercenaries and has the potential to decide wars.

For more modern societies a country's wealth (read assets) becomes less important.  Adam Smith was the first to realize that the "Wealth of Nations" is not so much about how much money they have but rather about how much economic welfare they can generate. This is measured in the number of goods and services produced in a given year, nowadays known as GDP.

From today's perspective, why do we use GDP rather than GNW:

Actual production is much more important to determine a country's productivity than its wealth
Accumulated wealth (GNP) measures past wealth while this years production of goods and services (GDP) is a good indicator of future wealth
There is probably also some path dependency. Given that hardly anyone ever hears about GNP, I agree with you that (despite all arguments against it) GNP is slightly underrated.


Check for concavity, quasi-concavity with given value of function I am studying for an upcoming exam in microeconomics and I have always struggled with proving concavity, convexity in different exercizes. This one I can't solve for the life of me. It is kind of hard to find the exact point I struggle with, because I'm pretty confused on this one overall.

We are given sets of points for which the value of the function is f(x) = 1, 2, 4.

We are then asked if these curves are consistent or inconsistent with the function being either concave or quasi-concave.

We are given tips:

Write down the definition of concavity:

$f: D -> \mathbb R$ is concave if for all $ x, x' \in D, t \in (0,1):$

$f(tx + (1-t)x') \geq tf(x) + (1-t)f(x')$

Select two points in the domain (1,3) and write down the convex combination for the points.

???

Evaluate the value of the function.
Evaluate the value of the convex combination for each of the points for this function.
Use the defintion to show where the function is concave and/or quasi-concave

What throws me off here is that there is no actual function given, but only values for the function. If I had a function, say $f(x,y) = x^\beta y^{1-\beta}$, I could choose a point and check with a certain t against the concavity defintion, right?

I hope this doesn't fall under the no homework-clause. I don't have to turn this in, I'm just lost :)

First look at the shape of the indifference curves. (I assume that $f$ is a utility function here.) The better-sets are convex, so this is consistent with quasi-concavity of the function $f$.

Second, consider the convex combination $(2,2)=\frac{1}{2}(1,1)+\frac{1}{2}(3,3)$. You have $f(2,2)=2$, but $\frac{1}{2}f(1,1)+\frac{1}{2}f(3,3)=\frac{1}{2}1+\frac{1}{2}4=2.5>2$, which is inconsistent with the function being concave.


Why hasn't JPE formally retracted Emily Oster's article "Hepatitis B and the Case of the Missing Women" (2005)? Amartya Sen (1992) argued that there were more than 100M "missing women" worldwide.
In "Hepatitis B and the Case of the Missing Women" (2005), Emily Oster argued

that hepatitis B can account for about 45 percent of the “missing women”: around 75 percent in China, between 20 and 50 percent in Egypt and western Asia, and under 20 percent in India, Bangladesh, Pakistan, and Nepal.

Oster was heavily criticized. And later, Oster et al published what amounted to a full retraction: "Hepatitis B does not explain male-biased sex ratios in China" (2008, 2010).
Klassen (2008) gives a short account of the above story.

What I found strange is that Oster (2005) still appears on the JPE website (and also JSTOR). There is no retraction, errata, or any other clue to the uninformed reader that there might be anything wrong with the article.
Why hasn't JPE formally retracted Oster (2005)?

Why hasn't JPE formally retracted Oster (2005)?

In this case there simply is no reason to retract the paper.
Academic papers are typically retracted for one of the following reasons:

Retraction for error: For example, if paper claims that if $3+x=15$ then $x=10$ and such error significantly changes conclusions from the study (usually the mistake has to be severe). However, this has to be some serious error not something like well when your regression errors have just heteroskedasticity it might be better and more appropriate to use white errors instead of HAC errors - this can also sometimes change result of a study but people are allowed to make some judgements when setting up their models.
Retraction for fraud or misconduct: For example, plagiarism, falsifying data or falsifying result. Some ethical issue (e.g. it was later uncovered data for the paper was collected unethically and so on).
Retracting Paper on Request of an Author: Sometimes authors will ask publication to retract the paper. This can happen even if the paper has no issues. For example, recently a paper on police killings was retracted by authors who did not liked how their paper was portrayed in media.
Retracting Paper Due to Public Relations: It sometimes happen readers or wider public wants the article to be retracted. For example, PLOS One retracted one biology paper after readers complained it had reference to "creator"  - although retracting paper for this reason is always controversial, and not all journals will do such thing (and the journal was criticized for this retraction heavily).

In the case above 1 and 2 does not seem to apply. As written in by Levitt in his blog (also mentioned in the comments) [emphasis mine]:

Emily wrote a paper arguing that high rates of Hepatitis B in China explained a large part of the missing women puzzle. Medical data suggested women with Hepatitis B gave birth to more sons — many women in China are infected, thus too many sons. It seemed like a crazy theory when I first heard it, but she put together extremely compelling evidence from a variety of sources to support her argument. Eventually we published it in the Journal of Political Economy, where I was an editor.

Then along came a host of other academics, including my friend and former student Ming-jen Lin, who gathered data from new sources that didn’t support Emily’s conclusions. Usually, these debates become quite acrimonious and linger on until no one cares any more. Certainly no one would admit they were wrong.

Consequently, in this case there is no evidence that there was any error in the study, or fraud or other misconduct. From what I understand study was overturned thanks to new better data.  Next, obviously the author did not requested retraction otherwise the article would not be still listed. In addition, there does not seem to be any 'mob' pressure to retract it (the point 4) and as mentioned under the point 4 many journals would not just succumb to mob pressure.

And later, Oster et al published what amounted to a full retraction: "Hepatitis B does not explain male-biased sex ratios in China" (2008, 2010).

No that was actually not retraction that was new publication with new method and new data that did not confirmed the result of original publication. Authors will usually specialize in a single area of research. It is always possible, and in fact in empirical studies its not too rare, to see that new and better data and statistical techniques change conclusions of a study.
For example, if a researcher conducts randomized control trial with 30 participants they might find positive effect that is publishable and publish it. However, even if the results are interesting having just 30 participants is a weakness (which can be criticized but might not necessary be reason for rejection of paper). Later in their career the scientist might decide to repeat the experiment  with bigger sample lets say 1000 participants and it might happen that new study will show previous study was wrong. That new study subsequently can still get published, and the old one wont get either retracted or any errata.

What I found strange is that Oster (2005) still appears on the JPE website (and also JSTOR). There is no retraction, errata, or any other clue to the uninformed reader that there might be anything wrong with the article.

Well this is actually not strange at all. This is how scientific publishing normally works. Older results are getting challenged every day in science. For example, you will still find literally hundreds of old physics, economics, biology articles discussing results or theories that were proven wrong. That is no reason to retract those old articles as they are and should still remain part of the corpus of scientific literature.
This is the reason why any scientist will tell you that if you want to understand some topic you have to do a literature review on the issue. You cannot ever in any field of science just take any single paper at face value, no matter who wrote it and in what journal it is published in. Any paper has to be properly placed in the mosaic  of wider literature to be properly understood. This is why it is not enough for a layman to simply read a paper on lets say some medication and then start prescribing it.


Chow test of parameter constancy A bivariate regression is fitted to 20 sample observations on y and X. I know the following:
$X'X=\begin{pmatrix}
                             20 & 10\\
                             10 & 30 \\
                             \end{pmatrix}$,
$X'y=\begin{pmatrix}
                             30\\
                             40 \\
                             \end{pmatrix}$,
$y'y=75$.

I received that $\beta=\begin{pmatrix}
                             1.4\\
                             1.3\\
                             \end{pmatrix}$.

Then a new observation was obtained: $X=2$, $Y=4$.
I should perform a Chow test of parameter constancy.
In fact I know the formula for the test: $F=\frac{(RSS_{pooled}-RSS_{1}-RSS_{2})/(k+1)}{(RSS_{1}-RSS_{2})/(n-2k-2)}$. Unfortunately, I have no idea how to calculate the RSS for any of these regressions. Help is needed.

This should help you figure out how to compute RSS for the different models.

Let's begin with what we have:

We know that

$y$ is an $n \times 1$ vector that has observations of the endogenous variable
$x$ is an $n \times 2$ matrix of observations of the exogenous variables
$\beta$ is a $2 \times 1$ matrix of coefficients

Unfortunately (or fortunately depending on how you look at it), we don't know what $x$ and $y$ look like in this equation. Instead we are given $(x' x)$, $(x' y)$, and $(y' y)$.

Using your comment about what RSS actually is -- Namely, that

$$\text{RSS} = (y_{\text{observed}} - y_{\text{estimated}})' (y_{\text{observed}} - y_{\text{estimated}})$$

First notice that $y_{\text{estimated}}$ is simply $x \beta$. Then replacing this in the previous formula gives us

\begin{align*}
  \text{RSS} &= (y_{\text{observed}} - y_{\text{estimated}})' (y_{\text{observed}} - y_{\text{estimated}}) \\
  &= (y_{\text{observed}} - x \beta)' (y_{\text{observed}} - x \beta) \\
  &= y'y - 2y'x\beta + x \beta \beta' x'
\end{align*}

Now this is almost what we want. We want things to ultimately be in terms of $(y'y)$, $(x'x)$, $(x' y)$, and $\beta$. The first term is exactly $y'y$, but other terms look like they have pieces we want and we just have to find a way to get them.

Now, notice that each of the elements in our equation above is simply a scalar (aka sizes are such that they are $1 \times 1$). The determinant of a scalar is itself, then by using properties of determinants we can say:

\begin{align*}
  2y'x \beta &= \det(2y'x\beta) = \det(2 \beta' x' y) \\
  x \beta \beta' x' &= \det(x \beta \beta' x') = \det(\beta' x' x \beta)
\end{align*}

I will leave the linear algebra itself as an exercise.


What policies are in place to police financial speculation in the modern era? Maynard Keynes in section VI in chapter 12 of his General Theory of Employment, Interest & Money writes:

If I may be allowed to appropriate the term speculation for the activity of forecasting the psychology of the market, and the term enterprise for the activity of forecasting the prospective yield of assets over their whole life, it is by no means always the case that speculation predominates over enterprise. As the organisation of investment market improves, the risk of the predominance of speculation does, however, increase.
In one of the greatest investment markets in the world, namely, New York, the influence of speculation (in the above sense) is enormous. Even outside the field of finance, Americans are apt to be unduly interested in discovering what average opinion believes average opinion to be; and this national weakness finds its nemesis in the stock market...
...Speculators may do no harm as bubbles on a steady stream of enterprise. But the position is serious when enterprise becomes a bubble on a whirlpool of speculation. When capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done.
The measure of success attained by Wall Street, regarded as an institution of which the proper social purpose is to direct new investment into the most profitable channels in terms of future yield, cannot be claimed as one of the outstanding triumphs of laissez-faire capitalism - which is not surprising, if I am right in thinking that the best brains of Wall Street have been in fact directed towards a different object.
These tendencies are a scarcely avoidable outcome of our having successfully organised 'liquid' investment markets. It is usually agreed that casinos, in the public interest, be inaccessible and expensive. And perhaps the same is true of stock exchanges...
The introduction  of a substantial Government transfer tax on all transactions might prove the most serviceable reform available, with a view of mitigating the predominance of speculation over enterprise in the United States.

One such transfer tax is the Tobin Tax but this seems very specific in that it is applied to 'spot conversions of one currency into another'; what other specific proposals in line with Keynes suggestion are there? And have any been implemented and if so what have been the results?

I am afraid that "speculation" can be policed only very indirectly, since it is impossible to tell what "speculation" is and isn't. Look at Keynes' definition: speculation for the activity of forecasting the psychology of the market
In other words, you know the INTENTION of the speculator. You must see inside his head. I am not aware of any agreed-upon distinction of "enterprise" and "speculation," that can be perceived and judged objectively, from the outside. One activity can be speculation in one context and not in another.


What are the advantages and disadvantages of second price auctions? I am reading https://en.wikipedia.org/wiki/Vickrey_auction about second price auctions.

It seems counterintuitive to me that the winning bidder pays the
bidding price of the runner-up bidder, rather than their own winning
bidding price as in first price auction. What is the purpose of
that?
What are the advantages and disadvantages of a second price auction?
Especially when it is compared to a first price auction?
The wikipedia article also says

  Vickrey auctions are much studied in economic literature but uncommon
  in practice. A slightly generalized variant of a Vickrey auction,
  named generalized second-price auction, is used in Google's and
  Yahoo!'s online advertisement programmes.

Why does the internet advertising industry use second price auction,
instead of other auction types e.g. first price auction?

A lot of questions here. Might be helpful to split them into different posts, but let's take a crack at them.

The reason why the second price sealed auction is set up this way is simple. Imagine you have a set of individuals/bidders, thinking of what $b_i$ to bid. They all have independent values, $v_i$ of a single object up for auction (their enjoyment does not depend on others). The optimal strategy in a second price auction is to bid however much you value that object, that is,

$$b_i = v_i$$

Since you won't pay as much as you bid if you win, you have a chance to get a positive benefit from the auction, or if someone bids the same as you, you also get a payoff of zero, which is an, "oh well", but no big deal.

If you unilaterally change your bid so that $b_i > v_i$, then you increase the chance of winning, but if you're still the top bid, then you still pay the same amount, so it seems kinda useless. If you happen to beat out someone's bid, $b_j$, where $b_i > b_j > v_i$ then you win! But now your payoff is negative. You can think similarly for the case of underbidding. It decreases the chance of winning AND it doesn't increase the chance of paying less for your object, so that's two bad things.

Basically, in theory, second price auctions induce truthful bidding.

Compare that to the first price auction. If you simply bid $v_i = b_i$, then your expected payoff is exactly zero. Very unfun. So instead you "underbid" your "true value". It decreases the chance of winning, but if you do, then you actually have a positive payout. The amount you underbid is obviously based on what you think other people's values are. So bidding here in first price auctions is strategic, rather than truthful.

But the big result you should know is that, in theory:

  First price and second price auctions are revenue equivalent for the auctioneer, given independent private values for a single object without budget constraints.

In theory. But in real life, people's bids are interdependent. You can imagine a bunch of big-wig types in a room for an auction of a priceless piece of art, where part of the value of the object is winning it and beating out the competition because you're the coolest kid on the block (with lots of cash to throw around). In this case, you can imagine a first price auction would be better suited for the house than a second price sealed auction.


If two variables are not cointegrated, can one still cause the other? For part of a project, I wanted to see if electricity consumption causes GDP in Colorado. I initially intended to follow the approach of Mozumder and Marathe (2007), who use a VECM approach, but that requires cointegration.

I'm not sure what to do now. I tried the Toda-Yamamoto method but my errors seem to be serially correlated...

Causality between time-series variables does not require the two to be cointegrated.

First, cointegration requires that each series be $I(1)$. It is certainly possible for two $I(0)$ series to follow a causal relationship (or two $I(d)$ variables for that matter).

Second, cointegration implies a long-run equilibrium among the series, which is not required for a causal relationship. A long-run equilibrium between two time series variables $x$ and $y$ implies that
$$y_t-a-bx_t$$
is a stationary process. In other words, if shocks are 'turned off', the values of $x$ and $y$ will converge such that $y_t=a+bx_t$.


Production function and elasticity Let $y=x_1^\alpha x_2^\beta$ where $\beta=1-\alpha$ be a Cobb-Douglas production function.
Find the elasticity of the optimal demand functions (for minimizing production cost) for both goods wrt. $w_2/w_1$ ($w_1,w_2$ are the respective prices of the inputs). What does this say for our spending on $x_1$  compared to the total cost?
My try
I found the elasticity of $x_2^*/x_1^*$ wrt $w_2/w_1$ to be 1. Now, I have to find a value for the ammount spend on good $x_1$. How can I do that with my elasticity? I think it has to be constant, but still no clue on how to find such a value even though I have found the elasticity to be 1.
edit: I know it has to be constant.

The first order conditions equate marginal revenue per factor to the price of that factor:
\begin{align}
p\cdot\alpha\frac{y}{x_1} &= w_1\\
p\cdot\beta\frac{y}{x_2} &= w_2,
\end{align}
Where I used the property of power function $(x^n)'_n = n \frac{x^n}{x}$.
Divide the second FOC by the first to get the relation between the relative prices and the relative factor demands:
$$\frac{\beta}{\alpha}\frac{x_1}{x_2} = \frac{w_2}{w_1}. \tag{A}$$
From this relation we can draw two conclusions:

Rewrite (A) in log form:

$$- \ln \frac{x_2}{x_1} + \ln \frac{\beta}{\alpha} =\ln \frac{w_2}{w_1},$$
And using the log definition of elasticity $\epsilon_y^x = \frac{\mathrm{d}\ln y}{\mathrm{d}\ln x}$ we come to the conclusion, that relative factor demand is decreasing in relative factor prices with unit elasticity:
$$\frac{\mathrm{d}\ln x_2/ x_1}{\mathrm{d}\ln w_2/w_1} = -1.$$

Multiply both sides of (A) by $\frac{x_2}{x_1}$ :

$$\frac{\beta}{\alpha} = \frac{w_2x_2}{w_1x_1}. \tag{B}$$
Rearrangement (B) says that the expenditures on different factors are proportional to their respective input elasticities, i.e. if our total spending on factor 1 is $\\\$\alpha$ then we must spend $\\\$\beta$ on factor 2.
The total cost $C$ is allocated in the same proportion, i.e. for a general Cobb-Douglas production function, spending on factor 1 is
$$w_1 x_1 = \frac{\alpha}{\alpha+\beta}C,$$
or simply $w_1 x_1 =\alpha C$ if $\alpha+\beta=1$, i.e. if the production function is homogeneous of degree 1.


Why is there consumption sharing in Arrow-debreu time-zero complete markets trading model? Specifically, I am looking at this paragraph

    The fractions of the aggregate endowment assigned to each individual are
    independent of the realization of s^t . Thus, there is extensive cross
    history and cross-time consumption sharing. The constant-fractions-of
    consumption char- acterization comes from two aspects of the theory: (1)
    complete markets and (2) a homothetic one-period utility function.

The paragraph is taken from paragraph from section 8.6 in Sargent and Ljungqvist.

I understand that the fractions are independent of $s^t$, the state/complete history of realizations. However, I don't see how this leads to the second sentence -- there is extensive cross-history and cross-time consumption sharing.

So my question is: why does the fractions of aggregate endowment assigned to each individual being independent of $s^t$ lead to cross-time and cross-history consumption sharing?

Thanks

I guess it just follows by definition.

Assume that in the high state (for household $i$, aggregate endowment is 10, and household $i$ consumes $1/5 = 2$ of this, while having an endowment of $5$. Now consider what happens if we were in the low state (for household $i$), where household $i$ only gets $1$ of whatever endowment. However, if this is a high state for some other household(s), such that the aggregate endowment is still $10$, since the fraction is constant household $i$ still consumes $2$, even though they have a smaller endowment.

Similarly for across time consumption sharing (although a bit weird since the model has no storage...). I guess it works that, if aggregate endowments are the same across two time periods, a household will consume the same amount regardless of whether their endowment was large or small (basically, they contribute to others when they have a lot (they lend), and they take contributions when they have little (they borrow). Thus, consumption smoothing.


The Economics of Coronavirus People are concerned about the economic impacts of the virus. How severe will the economic downturn be? Will the coronavirus cause a global recession worse than the 2008 crisis?
I'm not looking here for speculative answers, but references with a solid economic background. For example, I found these:

Flattening the Pandemic and Recession Curves, March 13 2020, by Pierre-Olivier Gourinchas, Berkeley.
Economics in the Time of Covid-19, by Vox CEPR.

Any other (academic) references?

Economics podcasts are also welcome. I found those:

Russ Roberts and Tyler Cowen on COVID-19
The Side Effects of Social Distancing by Freakeconomics
And a bunch of recent episodes by Planet Money.

Update.

Some nice references on Following the economic impact of COVID-19 by Stanford (SIEPR) experts.

Last update: On the weekly NBER Working papers released by April 13, 2020, there is already a lot of material on covid-19!

The Geographic Spread of COVID-19 Correlates with Structure of Social Networks as Measured by Facebook,  T. Kuchler, D. Russel, and J. Stroebel.
How Are Small Businesses Adjusting to COVID-19? Early Evidence from a Survey, A.W. Bartik, M. Bertrand, Z.B. Cullen, E.L. Glaeser, M. Luca, and C.T. Stanton.
Covid19 and the Macroeconomic Effects of Costly Disasters, S.C. Ludvigson, S. Ma, and S. Ng.
Optimal Mitigation Policies in a Pandemic: Social Distancing and Working from Home C.J. Jones, T. Philippon, and V.Venkateswaran #26984
COVID-Induced Economic Uncertainty, S.R. Baker, N. Bloom,
S.J. Davis, and S.J. Terry.
Social Distancing, Internet Access and Inequality, L. Chiou and
C. Tucker.
A Simple Planning Problem for COVID-19 Lockdown, F.E. Alvarez, D. Argente, and F. Lippi.
Firm-level Exposure to Epidemic Diseases: Covid-19, SARS, and H1N1,    T.A. Hassan, S. Hollander, L. van Lent, and A. Tahoun.
U.S. Economic Activity During the Early Weeks of the SARS-Cov-2
Outbreak, D. Lewis, K. Mertens, and J.H. Stock.
Demographic Determinants of Testing Incidence and COVID-19 Infections
in New York City Neighborhoods, G.J. Borjas.
Triage Protocol Design for Ventilator Rationing in a Pandemic:    Integrating Multiple Ethical Values through Reserves, P.A. Pathak, T. Sönmez, M. Utku Unver, and M. B. Yenmez.
Polarization and Public Health: Partisan Differences in Social
Distancing during the Coronavirus Pandemic, H. Allcott, L. Boxell, J.C. Conway, M. Gentzkow, M. Thaler, and D.Y. Yang.

With the right keywords (and author searches) from earlier papers, I actually found some academic output already; this might not be peer-reviewed yet, i.e. preprints:

McKibbin and Fernando (2 March 2020) The Global Macroeconomic Impacts of COVID-19: Seven Scenarios

  examines the impacts of different scenarios on macroeconomic outcomes and
  financial markets in a global hybrid DSGE/CGE general equilibrium model.
  The scenarios in this paper demonstrate that even a contained outbreak could significantly
  impact the global economy in the short run. [...]
  These results are very sensitive to the assumptions in the model, to the shocks we feed in and
  to the assumed macroeconomic policy responses in each country.

And that's already cited by Wang et al. COVID-19's Impact on China's Economy Based on Data of Spring Festival Travel Rush

  this paper starts with the analysis of the daily railway passenger volume data during the Spring Festival travel rush, and establishes three time series to model the railway passenger volume, GDP in the first quarter model, and GDP in the last three quarters respectively. The forecast results indicate that: (a) Affected by the epidemic, China’s economy will lose 4.8 trillion yuan in the first quarter of 2020, which is an expected decrease of 20.69% and a year-on-year drop of 15.60%; (b) China's expected GDP growth rate for the full year of 2020 will reduce from 6.50% to 1.72%. However, there are some positive factors not taken into account in these models, which means that the forecast results may be underestimated. With the global spread of the epidemic, the instability of the world economy will in turn impact China’s economy.

A more recent (March 30) paper, Greenstone and Nigam that emphasizes/quantifies the benefits of the lockdowns, in the US:

  Using the Ferguson et al. (2020) simulation model of COVID-19’s spread and mortality impacts in the United States, we project that 3-4 months of moderate distancing beginning in late March 2020 would save 1.7 million lives by October 1. Of the lives saved, 630,000 are due to avoided overwhelming of hospital intensive care units. Using the projected age-specific reductions in death and age-varying estimates of the United States Government’s value of a statistical life, we find that the mortality benefits of social distancing are about \$8 trillion or $60,000 per US household. Roughly 90% of the monetized benefits are projected to accrue to people age 50 or older. Overall, the analysis suggests that social distancing initiatives and policies in response to the COVID-19 epidemic have substantial economic benefits.

JP Morgan has put out some estimates already, although they don't detail their methodology as much as a peer-reviewed publication would (have to).

  The U.S. economy is projected to contract by 14% in the second quarter, after experiencing a 4% contraction in the first quarter, before recovering to 8% and 4% growth in the third and fourth quarters. Euro area GDP will suffer an even deeper contraction, with double-digit declines of 15% and 22% in the first and second quarters, before rebounding by 45% and 3.5% in the third and fourth quarters.

  “There is no longer doubt that the longest global expansion on record will end this quarter. We now think that the COVID-19 shock will produce a global recession, as nearly all of the world contracts over the three months between February and April,” said Bruce Kasman, Chief Economist at J.P. Morgan. Initially, the expectation was the novel-recession may generate limited labor market damage, but J.P. Morgan Research is now forecasting the unemployment rate for developed markets as a whole will rise 1.6 percentage points in the next two quarters.

  “The rise in unemployment will be sharper in the U.S. than in the Euro area. Most immediately, U.S. initial jobless claims should spike above 400,000 in the coming weeks,” said Michael Feroli, Chief U.S. economist at J.P. Morgan.

McKinsey has a somewhat spread-out (March 25) presentation, but a couple of slides with their scenarios/estimates I could fish from there:

Likewise, PWC has a March [white]paper mostly focused on Australia... but which does come with a global map attached of their estimates of GDP losses, alas in absolute figures only (and I think over one year based on what they say on the previous slide):

Before the COVID-19 outbreak, there has been a niche academic domain of estimating the economic impact of pandemics already, typically using a CGE model. Results depend of course on the assumptions used. E.g. Smith, Keogh-Brown et al. had a series of papers approximately a decade ago. Quoting from a later one that covered more than one European country:

  Results suggest GDP losses from the disease of approximately 0.5–2% but school closure and prophylactic absenteeism more than triples these effects.

So they went as high ~10% GDP losses. While they did not envisage government mandated lockdown(s), they modelled "prophylactic absenteeism" in response to ~3% death rate media reports as the most severe case. An earlier paper of theirs, on UK only is open-access in the BMJ. Quoting their assumption from there

  almost everybody in the population will know someone who has died once the mortality rate reaches one death per 300 people, triggering prophylactic absenteeism.

The same authors (Keogh-Brown and Smith) also published in 2008 a fairly detailed post-hoc account of how economic predictions for SARS fared in hindsight... which generally wasn't all that good, meaning that most models overestimated the economic impact of SARS. It cites positively an 2003 ADB paper of Fan that hedged its bets on two different scenarios (early containment being one of them).

Another paper Verikios et al. (2015) in a similar vein but attempts a global estimate (GTAP CGE), and also discussed prior/related work:

  The two pandemic scenarios modelled give quantitatively and qualitatively different
  results. [...] Our results show that the peak GDP effects on the world economy of an influenza pandemic are in the range 0.06 to 1.01 per cent in the peak year depending on the nature of the pandemic. Our results are smaller than the only previous estimates of the global economic effects of influenza pandemics by McKibbin and Sidorenko (2006). They estimate reductions in global GDP of between 0.8 and 12.6 per cent depending on the severity of the pandemic. Our results are not directly comparable to McKibbin and Sidorenko as they did not model a continuum of pandemic scenarios across the virulence-infectiousness continuum. Rather, they assume a given reproducibility of the virus (infectiousness) and vary virulence across their four scenarios. Further, they implicitly assume multiple waves for all their scenarios as they presume that
  new infections continue to occur for greater than one year. This is likely to characterise only more extreme pandemics (such as the 1918–19 flu) rather than milder pandemics. Differences in the range of influenza pandemics modelled by us and McKibbin and Sidorenko are justifiable given the uncertain nature of future pandemics. Our results thus build upon the findings of McKibbin and Sidorenko by extending the estimation of potential GDP estimates over a further range of potential pandemic threat scenarios.

  [...] Our results show that the global macroeconomic effects of an influenza pandemic may be significant but are also likely to be short-lived. The largest economic impacts of an influenza pandemic are driven by reduced international tourism, due to risk-modifying measures by households and travel restrictions imposed by health authorities, and lost workdays, due to illness or formal social distancing measures designed to contain the virus. This is consistent with the work of Keogh-Brown et al. (2009, 2010). [...]

Verikios seems to work for KPMG Australia nowadays and they have released a COVID-19 model that is fairly detailed in explaining its assumptions, for example it has separate pre- and post-stimulus arms/scenarios, but it mostly covers the Australian case, in particular only models the government response of that country.

KPMG uses a NiGEM (New-Keynesian) macro model, and they've basically tweaked some parameters of this using estimates of shocks in four areas: reduction in productivity due to additional sick leave by workers, reduction in productivity due to additional carer’s leave by workers, incremental investment premium, capacity utilisation adjustment (i.e. supply chain disruptions). The first two were informed by fairly detailed labour & health statistics, the latter two seem a bit more arbitrary to me, e.g. they added a flat 1% investment premium.

I was hoping the IMF would have something more concrete than this, but I guess
they are weary of advancing anything more detailed yet:

  The COVID-19 pandemic would cause a global recession in 2020 that could be worse than the one triggered by the 2008-2009 global financial crisis, but world economic output should recover in 2021, the IMF said on Monday.

  Georgieva issued the new outlook after a conference call of G20 finance ministers and central bankers, who she said agreed on the need for solidarity across the globe. [...]

  The outlook for global growth is negative and the IMF expects “a recession at least as bad as during the global financial crisis, or worse,” Georgieva said.

  Earlier this month, Georgieva had warned that 2020 world growth would be below last year’s 2.9 percent rate, but stopped short of predicting a recession.

  Georgieva on Monday said that a recovery is expected in 2021, but to reach it, countries would need to prioritize containment and strengthen health systems.

  “The economic impact is and will be severe, but the faster the virus stops, the quicker and stronger the recovery will be,” she said.

The CBO has now posted its own assessment for the US economy. It disclaims that it is "highly uncertain, especially for later periods", but basically, for the second quarter of 2020 it predicts 10 percent unemployment and the economy to contract by "more than" 7 percent.

The WTO Secretariat has posted this self-explanatory chart on April 8:


What's the difference (if any) between "fixed assets" and "fixed capital" in the UN SNA? From my reading of the UN System of National Accounts (2008 update), "fixed assets" and "fixed capital" seem to be completely synonymous. Yet strangely there seem to be these two different terms. So what, if any, is the difference between them?

I can find a definition for "fixed assets" but not for "fixed capital":

  Fixed assets are produced assets that are used repeatedly or continuously in production processes for more than one year (p. 196).

I can also find a definition for "consumption of fixed capital":

  Consumption of fixed capital is the decline, during the course of the accounting period, in the current value of the stock of fixed assets owned and used by a producer as a result of physical deterioration, normal obsolescence or normal accidental damage (p. 198).

Elsewhere, I find a statement which, together with the above, would seem to identify "fixed assets" with "fixed capital":

  consumption of fixed capital, a figure representing the decline in value
  during the period of the fixed capital used in a production process. (p. 3)

Put on your institutional hat. And make a distinction between fixed assets, like land, and the ownership of fixed assets: capital. See the European System of National Accounts 2010 p. 73.


Why did creating the Eurozone cause the cost of labor to rise in Greece? As I understand the implementation of the Euro as a common currency caused labor prices to spike in certain countries, Greece being one of them. Why did this happen? Why did it affect certain countries more than others?

I think we should ask why didn't Germany's labor cost increase, while everyone else's did:

The eurozone had economic growth before 2008, so appreciating labor was expected, especially due to increasing labor mobility. Wages were converging to Germany's.

In addition, Southern Europe saw an influx of capital (this is how they caught the debt crisis). Capital triggered some speculative economic growth — 4% in Greece — and an increase in wages.

One more thing. When the crisis hit in 2008, the private sector fired a lot of people. But high-paid employee remained. Which lead to this 12% pike in the business sector alone, as the average wage of the remaining workers increased:

Unit labor cost, year-to-year change: Business sector services only

Data source

The public sector kept its employees, so on average you have no peaks in 2010 (the first figure). And after 2010, you see a decline — basically caused by the same determinants, now working in the opposite direction.


Price elasticity of demand of CES Anyone would like to help me show the following ( or a book/paper reference would be a great help)
" The price  elasticity of demand is equal to $\sigma$ for the demand function of CES preference, $d(p_i,I,P)=\dfrac{p_i^{-\sigma} I}{P^{1-\sigma}}$, where $P=\left(\sum_{j=1}^N p_j^{1-\sigma}\right)^{\dfrac{1}{1-\sigma}}$ and $I=\sum_{j=1}^Np_jx_j$."
The formula for the price elasticity of demand is given by $\epsilon_i(p_i,I,P)=-\dfrac{\partial d(p_i,I,P)}{\partial p_i}\dfrac{p_i}{d(p_i,I,P)}$.
I have tried many times but couldn't get the desired answer. Thank you very much in advance.

Assuming that $p_i \neq p_j$ you just apply the formula;
$$\epsilon_i(p_i,I,P) =-\dfrac{\partial d(p_i,I,P)}{\partial p_i}\dfrac{p_i}{d(p_i,I,P)} \\ = -\left( \frac{-\sigma p_i^{-\sigma-1} I}{P^{1-\sigma}} \right)\frac{p_i}{\frac{p_i^{-\sigma} I}{P^{1-\sigma}}} =\sigma$$.
The way how you gave the problem neither $P$ or $I$ contain $p_i$ so you treat them as constants during differentiation.


study question: change of Expenditure in terms of price and quantity I am learning the Economic class and I have a very specific question regarding a basic economic concept: change of expenditure in terms of change of price and change of quantity.

I'v learnt below:

1. Expenditure = Price x Quantity (by definition)
2. change of Expenditure = change of Price + change of Quantity

I am really confused about how #2 above is inferred. I thought change of Expenditure is defined as

E - Expenditure, P - Price, Q - Quantity

(E2 - E1) / E1 = (P2 x Q2 - P1 x Q1) / P1 x Q1

But this is really not equal to

change of Price + change of Quantity = (P2 - P1) / P1 + (Q2 - Q1) / Q1

Can someone show me how does the formula "change of Expenditure = change of Price + change of Quantity" hold please?

Many thanks

Adopting your notations, $E = P \times Q$. Taking natural log for both sides, we have $\log E = \log P + \log Q$.

When the percent change of some quantity, $\Delta x / x$, is small, we can approximate this percent change with $\Delta \log x$,  the change in $\log x$. This is because when $\Delta x / x$ is small,

$$
\log (x + \Delta x) - \log x = \log \frac{x + \Delta x}{x} = \log (1 + \frac{\Delta x}{x}) \approx \frac{\Delta x}{x}
$$

Now we come back to the equation $\log E = \log P + \log Q$. When the change is small, we can loosely say that the percent change in E is the sum of the percent changes in P and Q. But you are right, this relationship is not exact, and may not be appropriate when the percent change is large.


Auction and best response Consider an auction in which $k$ identical objects are sold to $
n>k $ bidders. Each bidder $i$ needs only one object and has a valuation $v_{i}$  for
  the object. In the auction, simultaneously, every bidder $i$ bids $ b_{i} $ . The highest $k$
  bidders win. Each winner gets one object and pays the $k+1 ^{st}$ highest bidder (i.e.,
  the price $p$ is the highest bid among the bidders who do not get an object). (The
  ties are broken by a coin toss.) Each of the losing bidders gets a gift of value $w$
  for their participation. (The winners do not get a gift.) Show that the game has
  a dominant strategy equilibrium, and compute the equilibrium.

It has a solution on page 9 here, but I cannot understand it.

Can someone explain me the answer or provide one? Also, do the losing bidders pay their bid amount here? And what does this line mean: "Each winner gets one object and pays the $k+1 ^{st}$ highest bidder"?

Hint: I will talk through a simpler case, and let you extend it to the generic case.

Let's say there's only two bidders and only the top 1 bidders win. Whoever wins pays whatever the loser bid. This situation is basically a second price auction.

You, player 1, like the object up for auction with a value of $v_1$, but the consolation prize of $w$ is also nice. The solutions you gave say that the optimal bid is $b_1^* = v_1 - w$. Let's confirm this.

If you win this auction with this bid, that means the other bidder bid less than you, $b_1^* > b_2^*$. The total value of winning is $v_1 - b_2^*$. If you lose, then the other bidder bid higher than you, and you receive $w$. So the difference between winning and losing is

$$v_1 - b_2^* - w > v_1 - b_1^* - w = v_1 - (v_1 - w) - w = 0$$

So hooray! There is value in winning compared to taking the consolation. :)

What happens if you unilaterally deviate from this proposed strategy (so your opponent doesn't change their bid) and bid higher up to  $b'_1 = v_1 + \epsilon - w$? Well, if you win when you were going to win anyway compared to the above case...you still get $v_1 - b_2^*$ as the total reward. If you lose when you were going to lose anyway, then you still get $w$. The interesting part is when you bid high enough to then win when you would have previously lost.

That implies we would have $b_1^* < b_2^* < b'_1$. You win and receive $v_1 - b_2^*$, so seems like nothing is different...or is it?

$$v_1 - b_2^* - w < v_1 - b_1^* - w = v_1 - (v_1 - w) - w = 0$$

So now you've won...but you should've just taken the consolation prize. :(

You can do a similar thought experiment for bidding lower. If you bid lower and win, then what you pay doesn't change from bidding the proposed strategy. If you lose when you would've lost anyway, then nothing changes. If you lose when originally you would've won, then you're taking a relative loss again.

So there is no outcome that makes you better off by unilaterally deviating from the proposed strategy of bidding $b_1^*$. You can extend this to realize it is a dominant strategy for all players to follow this line of reasoning.

What about with three players with two winners? Three players with one winner? This question is really just a weird extension of a second price auction. If you understand that, that will help, but otherwise, try following the intuition above and re-reading your solutions given to you.


Correct scientific term to describe this system property I am from a non-economic background so please bare with me.

I have a crowdsourcing system that enables businesses to request individuals to perform certain tasks in exchange for a monetary payment. For any task t, the business pays an amount of p units as long as the participant is taking on only one task. If a user wishes to multi-task, the system pays an amount p-x where * x < p* and both are nonnegative. This motivates users to take on multiple tasks as it will achieve higher profitability to each user. At the same time, the incurred costs for businesses will be reduced. Is there a scientific term that describes this mechanism? Is the term "cost-efficiency" correctly describes what the business is trying to do?

The term is "volume discounting", where a supplier offers/accepts a lower unit price in exchange for higher volume of business.
Here, it is the firm/buyer that asks for this volume discount, rather than the suppliers/users that offer it as a commercial policy.

Note that  when the buyer demands a volume discount (when it sets $x$) some conditions must be satisfied in order to be even feasible.
Assume $m$ tasks identical as regards the costs that the user has to incur (time etc). Denote the cost per task $c_a$.

For a single task the user is paid $p$, so its net payoff is $p-c_a$.

Taking on multitasking, the user will be paid in total $m\cdot (p-x)$ and its costs will be $m\cdot c_a$.
In order to take on multitasking it must hold that

$$ m\cdot (p-x-c_a) > p-c_a$$

A necessary but not sufficient condition for this to hold is that

$$p-x-c_a > 0 \implies  x < p -c_a$$

which places an uper bound on $x$, a bound that depends on supplier costs $c_a$. So the firm/buyer that sets $x$  must have a good idea about what $c_a$ might be.

Assume that this holds. Then we need

$$m > \frac {p-c_a}{p-x-c_a}$$

The higher the reduction $x$  in price per task the more tasks a user must take on. This may seem like providing an incentive to the buyer to set the requested $x$ as bigger as possible, but it may be the case that the reduction in unit price is so large that the user cannot take on the necessary number due to physical constraints. Let a maximum possible number of tasks that the agent can hanlde be $\bar m$.

Then we need as a necessary condition

$$\frac {p-c_a}{p-x-c_a} < \bar m$$

so that there exist feasible number of tasks $m$ below the maximum, and above the minimum number required to have higher profitability of the supplier/agent.

Re-arranimng for $x$ we obtain

$$x< \left(1-\frac 1{\bar m}\right)(p-c_a)$$

which is tighter than the previous necessary condition on $x$. So the fimr/buyer must also have a good idea about what the value of $\bar m$ is. Otherwise the whole plan runs the risk of not being adopted by the user.

A situation where the above becomes more feasible is when $c_a$ is not fixed per task but at least initially declines with multi-tasking.


Variable cost as the sum of marginal cost We learned in class that variable cost is the sum of marginal cost. I am given the following question.

Assume you are a profit-maximizing firm in a perfectly competitive market. Marginal cost is MC(qi) = 10 + qi/4 and the market price for you output is P= $60.

Calculate variable costs. So the teacher goes ahead and solves for the area of a trapezoid to get a variable cost of 7000 (when q=200) and that's fine. But why do I get a different answer when I try to calculate the sum of a series? My attempt:

$$VC=(10+1/4)+(10+2/4)+...+(10+200/4)=2000+(200)(201)/8=7025$$

Clearly 7025 doesn't equal 7000, so what is going on here? Also I thought MC isn't supposed to include fixed costs so is the equation MC(qi)=10+qi/4 only defined when qi is at least 1? Thanks

You can obtain variable cost as the sum of a series in this case because the given formula for marginal cost is linear. But there is a much simpler way.

First the series approach.  The first term of your series was $10+1/4$ which is the marginal cost at $q=1$. This ignores the fact that, according to the formula, marginal cost is less than that whenever $0 \leq q < 1$. The first term should instead be the average marginal cost over the range $[0,1]$. Since marginal cost at $q=0$ is $10$, this is given by:

$$(1/2)[10 + (10 + 1/4)] = 10 + 1/8$$

Now the idea of a marginal cost for a quantity of less than one unit may seem nonsense if one thinks of marginal cost as the additional cost attributable to the marginal unit. But it does make sense for a good that can be produced in quantities that are not exact numbers of units of measurement (eg liquids, powders, measured in units of capacity or volume).  In such a case, and given linearity, marginal cost can be defined as $\Delta C/\Delta q$, where the $\Delta$'s indicate changes in cost $C$ and $q$ respectively, and $\Delta q$ may be less than one unit.

By a similar logic, the second term in the series should be the average marginal cost over the range $[1,2]$ which is:

$$(1/2)[(10 + 1/4) + (10 + 2/4)] = 10 + 3/8$$

Continuing in this manner up to the final term which is the average marginal cost over the range $[199,200]$ we have:

$$VC = (10 + 1/8) + (10 + 3/8) \dots + (10 + 399/8) = 2000 + (100)(400)/8 = 7000$$

(The formula $(100)(400)$ comes from summing $100$ pairs: $1+399$, $3 + 397$, and so on.)

Now the simpler way. Given linearity, there is no need to consider intervals of one unit.  The averaging formula can just be applied to the whole range $[0,200]$ as below:

$$\text{Variable cost = No. of units x Average marginal cost}$$

$$VC = (200)(1/2)[10 + (10 + 200/4)] = (200)(35) = 7000$$

Note however that neither of these methods would work if the formula for marginal cost were non-linear.  Given a non-linear formula you would need to calculate an integral as illustrated in Herr K's answer.


CV, EV for additive utility; confirm or deny I'm currently a TA for a class and recently graded a midterm. I gave the answer key back to the teacher, after going over part of the exam in a study hall. I was going to go over the rest of it tomorrow, but while making my own answer key in office hours, I seem to have come to a different answer than the teacher.

We maximize
$$u = 2x_1^{1/2} + 4x_2^{1/2}$$
with a normal budget constraint where $p \cdot x \leq w$. We arrive at the Walrasian demand:

$$x^*(p, w) = \left(\frac{p_2 w}{p_1(4p_1 + p_2)} , \frac{4p_1 w}{p_2(4p_1 + p_2)}\right)$$

Suppose $w = 10, \vec p = (1, 4), \vec p' = (3, 2)$.

Thus, $x(p', w) = (\frac{10}{21}, \frac{30}{7})$, and $x(p, w) = (5, \frac{5}{4})$ for our new and old bundles respectively.

So to find compensating variation we find the original utility:

$2 \cdot 5^{1/2} + 4 \cdot (5/4)^{1/2} = 4 \sqrt 5$

and find $w'$ that would get old utility and new prices:

$4 \sqrt 5 = 2(\frac{w'}{21})^{1/2} + 4(\frac{3w'}{7})^{1/2} = 2(\frac{w'}{21})^{1/2} + 12(\frac{w'}{21})^{1/2} = 14(\frac{w'}{21})^{1/2} \implies \\
4 \sqrt 5 = 14(\frac{w'}{21})^{1/2} \\
80 = 14^2 \cdot \frac{w'}{21} \\
\boxed{w' = \frac{60}{7}}$

Thus $\boxed{CV = w - w' = 10 - \frac{60}{7} = \frac{10}{7}}$

To find equivalent variation we find the new utility:

$2 \cdot (10/21)^{1/2} + 4 \cdot (30/7)^{1/2} = 2 \cdot (10/21)^{1/2} + 12 \cdot (10/21)^{1/2} = 14 \sqrt {\frac{10}{21}}$

and find $\hat w$ that would get new utility at old prices:

$14 \sqrt {\frac{10}{21}} = 2(\frac{\hat w}{2})^{1/2} + 4(\frac{\hat w}{8})^{1/2} = 4(\frac{\hat w}{2})^{1/2} \\
14^2 \cdot \frac{10}{21} = 16 \cdot \frac{\hat w}{2} \\
\boxed{\hat w = \frac{70}{6}}$

Thus $\boxed{EV = \hat w - w = \frac{70}{6} - 10 = \frac{5}{3}}$

The problem is if I recall correctly, the CV and EV are supposed to have the opposite sign so that the change in welfare is ambiguous. Where have I gone wrong, if anywhere? (Worth noting that if you do Slutsky decomposition for this question, you find that good 2 is inferior.)

Questions with numbers are usually not as good as questions without numbers. If you had written down the formula for CV and EV you would probably have noticed that your premise is false.

CV and EV are not supposed to have opposing signs. You can see this from their definitions where
$$
CV = e(p_1,u_1) - e(p_1,u_0), \hskip 20pt EV = e(p_0,u_1) - e(p_0,u_0).
$$
Either $u_1 > u_0$ and then a larger income is needed to reach $u_1$ given any price or the opposite is true.

In your final comment you also note that good 2 is inferior. As can be seen from your demand function

$$
x^*(p, w) = \left(\frac{p_2 w}{p_1(4p_1 + p_2)} , \frac{4p_1 w}{p_2(4p_1 + p_2)}\right)
$$

this is not true. If income were to increase $x_2^*(p, w)$ would increase as well.


Axiomatic Bargaining: Kalai-Smorodinsky and Nash solutions coincide Under standard assumptions on the domain of bargaining problems like Pareto Optimality, Symmetric, Scale Invariance and Independent of Irrelevant Alternatives / Individual Monotonicty, in which conditions (on feasible set S, or disagreemnt point d) that characterize the domain in which Kalai-Smorodinsky and Nash solutions coincide?

My idea is that when feasible set is symmetric, both solutions should coincide but it should be other cases..?

Another sufficient condition for the two solutions to coincide, which is not necessarily the same as symmetry, is that the feasible set $S$ be rectangular. That is,
\begin{equation}
S=\text{convex hull}\{(d_1,d_2),(d_1,\overline x_2),(\overline x_1,d_2),(\overline x_1,\overline x_2)\},
\end{equation}
where $d_i$ is $i$'s reservation utility and $\overline x_i$ is $i$'s best possible utility from the bargaining. Both Nash and KS solutions are at $(\overline x_1,\overline x_2)$.

Using the property that the KS solution can be obtained at the intersection of a ray from the disagreement point $d$ and the (northeast) boundary of the feasible set $S$, we can derive the following necessary condition for KS and Nash solutions to match: let $(x_1^N,x_2^N)$ denote the Nash solution to bargaining problem $(S,d)$; the KS solution $(x_1^{KS},x_2^{KS})=(x_1^N,x_2^N)$ only if
\begin{equation}
\frac{x_2^N-d_2}{x_1^N-d_1}=\frac{\overline x_2-d_2}{\overline x_1-d_1}.
\end{equation}


Perfect Bayesian Equilibrium I've been given a question which I'm struggling with:

Take the standard Prisoner's Dilemma game and consider it is played twice. (Players observe the outcome of the first game before playing the second). Consider beliefs in terms of which node player 2 is in their information set.

Find a weak perfect bayesian equilibrium (strategies and beliefs) where the strategies aren't a sub-game perfect equilibria.

So in the Prisoner's Dilemma:

(Defect, Defect) is unique nash and so is also the unique sub-game perfect equilibrium.

But how can we get a weak perfect bayesian equilibrium that doesn't involve Defect? Surely this is strictly dominant . . .

Is the question wrong?

It then goes on to ask for sequential equilibria (where we consider the sequence of mixed strategies).

Is this question wrong or am I misunderstanding these concepts?

Let the strategy of player 1 be represented by $(x1_1,xDD_1,xDC_1,xCD_1,xCC_1)$ where $x1$ is the first round action of player 1, $xDD_1$ is the action taken at the information set where both players have defected in the first round, $xDC_1$ is the action taken at the information set where player 1 has defected and player 2 has cooperated in round 1, etc.. Note that something like $(x1_1,x2_1)$ (with $x2_1$ being the action taken in round 2) is never a full specification of the strategy of player 1, since we need to specify behavior at each information set separately. Define the strategies of player 2 similarly. However, a perfect Bayesian equilibrium must also specify the beliefs of the player, $\mu_1,\mu_2$. This is an important part of the specification of an equilibrium. As we will see below, the question is geared towards understanding that a different equilibrium does not require the strategies to differ. A difference in beliefs is sufficient to count as a different equilibrium.

The perfect equilibrium is given by: $((D,D,D,D,D),\mu_1)$ for player 1 and $((D,D,D,D,D),\mu_2)$ for player 2, where $\mu_1$ and $\mu_2$ are consistent beliefs at all information sets.

As has been noted in the comments, since "defect" is a dominated strategy irrespective of beliefs, even in a weak perfect Bayesian equilibrium the strategy profiles must be $(D,D,D,D,D)$ for both players. However, the following is now also a weak perfect Bayesian Nash equilibrium: $((D,D,D,D,D),\mu_1')$ and $((D,D,D,D,D),\mu_2')$ with $\mu_1'$, $\mu_2'$ consistent on the equilibrium path.

Thus, the question is not wrong, it simply shows that two weak perfect Bayesian Nash equilibria can have identical strategies as long as they differ in beliefs off the equilibrium path.


Did Bitcoin increase the money supply of the world? I was reading about M2 and it somehow got me asking this question: did Bitcoin, by merely popping into existence, increase the money supply of the world? Is it classified as "near money"?

The concept of “money supply of the world” is vague. I think there’s at least two ways of looking at it.

Economics is normally concerned with the formal definition of “money”. Money is associated with a currency. One key property of money that its value is (nearly) fixed (some broad money definitions allow short-term debt instruments that have a fixed value in the near future). Bitcoin does not have a fixed value in any country’s currency, and will not be part of the money supply. If we somehow aggregate all countries’ money supplies (not obvious how to do), it would not change.
The obvious response to the above is that Bitcoin is a new currency. One could argue that it should be added (somehow) to all the other money supplies. The problem with this is that the domestic money supply figure has some theoretical relationship to transactions in a country. There is no obvious relationship between the supply of Bitcoin to any country’s domestic transactions, nor is there any reason to believe that a “global money supply” figure is meaningful.


Why is the social value curve NOT the supply curve shifted downwards? Abbreviate 'Social Value' as SV. In some other resources such as this, the SV curve is known as the Social Marginal Benefit curve.

The following quotes explain [1.] why the SV curve is the demand curve shifted upwards, but they don't explain [2.] why the SV curve is NOT the supply curve shifted downwards.

Here's my rationale for [2.]: Assume $SV > 0$. Because SV benefits society, the suppliers of this SV can consider the SV supplied, as follows:
Suppliers' true cost  $=$ their original costs $-$ SV, $\qquad$ for all quantities supplied.
So the new supply curve must underlie, and be parallel to,   the old supply curve.

Source: pp 179-180, Modern Principles of Economics (2 ed, 2011) by Tyler Cowen, Alex Tabarrok

  [See Figure 10.3.]
  The social value curve counts all the benefits of vaccine
  use, the private value plus the external benefits, so the efficient quantity is
  found where the social value curve intersects the supply curve.

  A final way of illustrating the underuse of vaccines is to notice that if people
  who got a flu shot did receive all the benefits of vaccination, then their demand curve would shift upward by $20 and would be the same as the social
  value curve. ...

  The last way of thinking about the problem of external benefits also suggests
  one potential solution. If every time someone was vaccinated, they were given
  a subsidy of $\$20$, the monetary equivalent of the external benefit, they would
  demand the amount $Q_{Efficient}$. Recall from Chapter 6 that we can analyze a subsidy
  by shifting up the demand curve by the amount of the subsidy. Thus, in
  Figure 10.3, notice that a subsidy set equal to the level of the external benefit
  would shift the demand curve up and increase the market quantity from $Q_{Market}$
  to $Q_{Efficient}$.

Footnote: I was reading p 201, Principles of Microeconomics (7 Ed, 2014) by N G Mankiw, when I encountered this problem. I don't quote Mankiw's book because it's brusquer than Cowen's above.

Here is how I interpret your question: "Why when modeling positive externalities do we shift the marginal benefit curve upward instead of shifting the marginal cost curve downward?"

Either way of thinking about it is fine. Positive externalities can be thought of as resulting in a social marginal benefit curve that's above the private marginal benefit curve, or as resulting in a social marginal cost curve that's below the private marginal cost curve. Which side you place it on is only a matter of accounting, since

Private Marginal Benefit + Externality - Private Marginal Cost = Private Marginal Benefit - (Private Marginal Cost - Externality).

Your question doesn't make sense in some ways though and I think it's important you understand why. You say "Because SV benefits society, the suppliers of this SV can consider the SV supplied, as follows: Suppliers' true cost = their original costs − SV, for all quantities supplied.
So the new supply curve must underlie, and be parallel to, the old supply curve."

The positive externality in this case cannot shift the producer's supply curve downward, because the producer's supply curve is his private marginal cost. Importantly, externalities only affect social marginal cost.

Remember: The supply curve is a function that tells you what quantity a supplier will produce at any given price, whereas the marginal cost curve is the cost per unit of producing an additional unit. These two things only happen to coincide in the absence of externalities.


How to interpret fixed effect regression R-sq. results for panel data? I runned a fixed effect regression in Stata (xtreg, fe) for panel data. I obtained below R-sq. results. How should I interpret them? Which one is my main interest(within,below or overall)? How can I derive the exact Adjusted R-sq. by using these 3 values?

R-sq:
     within  = 0.8226
     between = 0.4727
     overall = 0.5311

Thanks a lot!

In panel regressions you have multiple dimensions and that is why also you have 3 different $R^2$. The within $R^2$ tells you how much variation within your panel variables is on average explained by your model. The between $R^2$, tells you how much variation between your panel variables is explained by the model, and overall $R^2$ gives you the combination of both and tells you how much variation in the whole panel data your model explains.

According to the stata manual you should get adjusted $R^2$ for fixed effects by ereturn list it will be the r2_a scalar. However, there are no simple adjustments for within and between $R^2$, those are most often reported unadjusted.


Efficient market hypothesis and different performances between countries When comparing historical gains (I used the "adjusted close" data on yahoo) of major indices in different countries it is clear that the US outperformed most of these by quite a bit (see for example also https://www.visualcapitalist.com/worlds-major-stock-markets-same-scale-1990-2019/). From US based sources you often read that the expected average yearly return on investments is around 10%. This figure is based on historical data of for example the Dow Jones Index. However, other major indices had much lower performances (on the extreme end: the Nikkei 225 had basically no gain in the last 30 years).
Is this just a matter of the US having been the (unpredictable) "winner" over the last 100 years (or decade or most time intervals in between)? Just like having picked Apple around 2005 would have been very lucky. If so any prediction on the new average return on investments should clearly not be based just on this "winner" from previous years right? Would it not be more accurate to base the estimate for the average expected return on more (all) markets?
Or does the US predictably outperform other markets for some reason? That would beg the question why all markets are not emptying out and pouring their money into american stocks.
Is there some tax, regulatory, currency or inflation related reason that a consistent predictable gap in the average gain between US markets and other markets would not close?

Efficient market hypothesis does not in itself predict that stock market returns will equalize among different stock markets so it should not really be part of the question (efficient market hypothesis only refers to informational efficiency of markets). Rather this is something that would be predicted by trade/international macro models that predict factor return equalization (i.e. Rybczynski, Stolper-Samuelson, and factor-price
equalization theorems).
These theories would predict equalization of expected returns to capital due to capital flows between countries. If a country's stock market performs better than some other country capital should flow from the worse performing country to the better performing country until supply and demand for capital equalizes expected returns.
However, in real life expected returns wont always be equal even if they will exhibit tendency to equalize. As you mentioned in your question this can be due to various institutional reasons (Schularick, & Steger, 2008), but it can also be due to imperfect capital mobility, due to market failures, some investments might be geographically specific and so on. The literature on this is extremely broad I suggest looking for keyword factor price equalization on google scholar.
Furthermore, note that link you provided from that site just shows nominal ex post observed returns from stock markets between different countries. That in itself does not actually provide any evidence that ex ante expected returns are not equal between those countries.


Is there a measure of similarity for economies? Is there a measure of similarity for economies?

For example, I would like to find the world economies most similar to the UK.

To the best of my knowledge, there isn't. Ant that is actually a good thing, the economic structure of a country is usually a fairly complicated thing to be able to simplify it with a single number. You could, on the other hand, create an aggregate of measurements and try to look for patterns, e.g. you can see the behavior of macroeconomic variables such as gdp, inflation rate and unemployment, and based on those decide which countries are similar to each other.

And that is why clustering analysis is for. In the plot below I used Principal Component Analysis (just to reduce the dimensionality of the problem and be able to graphically display what's going on) to show 4 clusters fo countries. Each color is a k-means cluster, the axis are just the two firs principal components $x_1$ and $x_2$

I also added some of the countries on each cluster so you can see their similarity. For example, the $\color{blue}{\rm blue}$ cluster has large gdp, low unemployment, whereas countries in the $\color{green}{\rm green}$ cluster are not doing so well: high inflation, high unemployment and low gdp.

The cluster that you are interested in has these values (as of 2017)

                 country     gdp  inflation  unemployment
---------------------------------------------------------
9              Australia   55692       1.95           5.3
13               Austria   47347       2.08           5.1
17               Belgium   43488       2.13           6.2
15                Canada   45094       1.60           5.6
8                Denmark   56630       1.15           4.8
14               Finland   45927       0.75           7.2
20                France   39932       1.03           8.9
16               Germany   44769       1.74           3.3
3                Iceland   70248       1.76           2.9
4                Ireland   68710       0.34           5.3
19                Israel   40272       0.24           3.7
22                 Japan   38448       0.47           2.4
0             Luxembourg  105863       1.73           5.0
11           Netherlands   48555       1.38           3.5
18           New Zealand   41572       1.85           3.9
2                 Norway   75389       1.88           4.0
5                  Qatar   61024       0.40           0.6
12            San Marino   47595       1.05           8.0
10                Sweden   52925       1.79           6.3
1            Switzerland   80637       0.53           2.4
23  United Arab Emirates   37732       1.97           1.6
21        United Kingdom   39800       2.69           4.0
6          United States   59792       2.13           3.9


What is the returns to scale of the production function q = min {K, L^(1/2)}? I learned that when there is decreasing returns to scale, the average cost is always increasing.
But the professor told us today that the other way around might not always be true. So if average cost is increasing, it might not necessarily mean that there is decreasing returns to scale.
The production function $q = \min \{K, L^{(1/2)}\}$ was one he gave us as something to think about as a possible counterexample.
we assumed that the input prices are 2 for capital and 1 for labor.
If we solve for this using cost minimization, we get $C(q) = 2q + q^2$ and the $AC(q) = 2 + q$ which is an increasing function.
And if I input $kK, kL$ in the production function where $k > 1$ , then the function becomes
$q = \min \{kK, (kL)^{1/2}\} = \min \{kK, k^{1/2} * L^{1/2}\}.$
How do I know what returns to scale this is showing?
if the min function was simply $q = \min \{ K, L \}$, then I could definitely tell that this is showing constant returns to scale since $\min \{kK, kL\} = k*\min\{K,L\}$,  but how do you mathematically solve for returns to scale for a function like the one above, $q = \min \{K, L^{1/2}\}$ ?
I don't know what step to take next after arriving at $\min \{kK, k^{1/2} * L^{1/2}\}$. I don't know what to extract out of the min function from this point on.
I would appreciate advice on how to continue to determine the returns to scale for this kind of example.

You have a Leontief production function and in optimum you will always have $K=\sqrt{L}=q_1$.  Now increase both inputs by factor $k>1$ and you arrive at $k*K > \sqrt{kL}=q_2$ where the first inequality follows from $k>\sqrt{k}$ for $k>1$ and the second ineqality from the fact that only the minimum matters in your production function.
Therefore you have $F(kK,kL)= \sqrt{kL}<kK=k\sqrt{L} =k*F(K,L)$ with any optimal input combination $(K,L)$ and therefore decreasing returns to scale.


By what means do prices change? The classical supply and demand theory states that prices and quantities of a given good (in a perfectly competitive market) are determined by the supply and demand of that good, a shift in the demand curve, for example, would change the equilibrium prices, but how exactly does that work, can't imagine a firm owner saying 'Ok guys, the supply curve for our product shift to the right, time to raise prices"

I can grasp how a price above the equilibrium would go down (the producers would not sell, so they lower the price because less profit is better than no profit)

But how can an increase in demand drive prices up?

The simplest method would be to watch how quickly your inventory is depleted.  If your baseline is that you sell 1000 widgets a day at a dollar per widget and suddenly you're selling 1250 widgets a day (or selling out of the 1000 widgets your factory can produce a day by early afternoon), it is reasonable to believe that the demand curve has shifted to the right (there demand at a price of $1/ widget has risen by 25%) and to respond by raising prices.  From that same baseline, if you're suddenly only selling 750 widgets a day, it is reasonable to assume that the demand curve has shifted to the left and that you need to respond by lowering prices.

In the real world, think of the hot toy every Christmas.  If your supply of Tickle Me Elmo dolls fly off the shelves minutes after you get them and grown adults are fighting each other in the store to get their hands on one, it's a pretty safe bet that you're selling them at below equilibrium prices.  If the Furbies on the same shelf sit there for months without selling, you've probably priced them above the equilibrium price.

Of course, in reality, stores may have additional methods.  They can look around at what other people are selling items for.  They can do market research to survey customers and potential customers to determine the demand.  Online, they can show people different prices for the same product and see how that impacts purchase decisions.


Why monthly present in on line monthly payment calculator calculates as annual percent divided by 12? Why monthly present in on line monthly payment calculator calculated as annual percent divided by 12? I think it's wrong, it should be exponential. For instance annual percent 4%. To calculate monthly percent we need to 1.04^(1/12). So monthly percent should be 0.327%, but if we use approach on on line calculators it is going to be 0.333.

Basically the way that APR is calculated varies depending on the industry and who quoted it. On a car they calculate the APR by taking the monthly percent and multiplying by 12, the calculator is actually right.

You probably want to calculate APY (annual percentage yield). Check this article out: http://www.finweb.com/loans/how-do-they-calculate-your-car-loan-apr.html#axzz3lTowC0op


Cournot's game profit maximisation first order condition question My question is about the last part (I attached the rest for context). I don't understand the final line at all. I thought the first order condition would just be to set the derivative = 0. Very confused! Any help would be greatly appreciated! Thank you :D

To elaborate on @HerrK’s comment:

The product rule of differentiation is
$$\frac{d}{dx}fg=f’g+fg’$$
The text in your question states that you are trying to maximize the quantity
$$[a-Q-c]q_i$$
So, as you predicted, we must differentiate this and find when the derivative equals $0$. If we differentiate this with respect to $q_i$ and use the product rule, setting $f=a-Q-c$ and $g=q_i$, we obtain
$$-\frac{dQ}{dq_i}q_i+[a-Q-c]$$
since the derivative of $a-Q-c$ with respect to $q_i$ is $\frac{dQ}{dq_i}$ (since $a,c$ are constant) and the derivative of $q_i$ w.r.t $q_i$ is $1$. Setting this equal to zero gives
$$-q_i\frac{dQ}{dq_i}+[a-Q-c]=0$$
or, equivalently,
$$a-Q-c=q_i \frac{dQ}{dq_i}$$
which is the last line of the text.


How does a bank create new money when it pays its own staff? I am reading Ryan-Collins et al. (2013, Where Does Money Come From? A Guide to the UK Monetary and Banking System). I think I understand how banks create new money whenever they make a loan.

Using their example in 4.2, when a bank loans say £10,000 to Robert, their assets increase by the £10,000 loan and their liabilities also increase by £10,000 in the form of a deposit into Robert's new account. The latter deposit is the new money created by the bank.

However, I do not understand how:

  the bank creates new money when it ... pays its staff salaries or bonuses.

Say the bank pays its own staff Jane £5,000. What happens to the bank's balance sheet?

I think a deposit of £5,000 is made into Jane's bank account -- this is the new money created and is recorded under the bank's liabilities. But is there any corresponding change in assets?

If an employee performed work there is a liability called "current liabilities". Paying into the employee's account is just changing one kind of liability into another kind of  liability of the same size so total liabilities is unchanged and total assets is unchanged. The new liability is a recorded as a deposit.

Paying the employee with an amount of cash reduces assets and reduces liabilities.

@IñakiViggers is correct, of course, that part of the assets were the result of interest earned and fees charged. My answer addresses only what happens at the instant in time the employee is paid.


Empirical Data on Demand for Minimum-Wage Jobs in the USA The idea of a minimum wage and its effects in terms of supply and demand are well-known in mainstream economic theory.

I'm constructing an argument regarding the minimum wage, and what I'm curious about is whether there is actual empirical data that indicates that demand for minimum wage jobs is greater than their supply, and if so, by how much? I'm looking for data particular to the U.S., but if such data exists for other countries, that would be helpful too.

Neumark and Wascher have a paper that surveys recent empirical work on the effects of the minimum wage in detail. It includes a number of tables that nicely summarise the results of a large number (102!) of studies.

They conclude the paper with the following remarks:

  Nonetheless, the oft-stated assertion that the new minimum wage
  research fails to support the conclusion that the minimum wage reduces
  the employment of low-skilled workers is clearly incorrect. Indeed, in our view, the preponderance of the evidence points to disemployment
  effects. For example, the studies surveyed in this monograph correspond
  to 102 entries in our summary tables. Of these, nearly two thirds
  give a relatively consistent (although by no means always statistically
  significant) indication of negative employment effects of minimum
  wages, while only eight give a relatively consistent indication of positive
  employment effects. In addition, we have highlighted in the tables
  33 studies (or entries) that we regard as providing the most credible
  evidence, and 28 (85 percent) of these point to negative employment
  effects. Moreover, when researchers focus on the least-skilled groups
  most likely to be adversely affected by minimum wages, the evidence
  for disemployment effects seems especially strong. In contrast, we see
  very few – if any – cases where a study provides convincing evidence of
  positive employment effects of minimum wages, especially among the
  studies that focus on broader groups for which the competitive model
  predicts disemployment effects.


What's quantitative easing? From what I understand after reading mainstream media, quantitative easing increases the supply of money in the economy without direct government spending (fiscal policy).

It seems to have all the benefits of monetary policy (decreasing interest rates), but can still be done with rock-bottom interest rates.

Is my understanding correct? What's the downside I'm missing?

Before the edit, you wrote "qualitative easing", but I think you refer to quantitative easing. I'll discuss both.
Quantitative Easing
Quantitative easing corresponds to the central bank (CB) expanding its balance sheets by "buying" assets. This is typically done in secondary markets. It mainly injects liquidity into the system. To the extent that there is an additional buyer of assets now, the price of assets/investment (interest rates) decreases. However, the quantitative impact should be negligible: Through its demand, the CB increases value and liquidity in the markets it is operating. However, the scale of its operations should be too small  to affect the aggregate interest rate.
Qualitative Easing
Qualitative easing is a relatively new expression and refers to the riskiness of the stocks that the CB is investing in. In contrast to quantitative easing, which is about the magnitude of assets on the CB's balance sheets, qualitative easing is about the riskiness on the CB's balance sheets, and hence the decrease in aggregate risk (on the banks' balance sheets).
Downsides
Independence of a central bank
When the CB holds assets, it is interested in their value. This may lead it to commit policies that infract its primary directive (e.g. inflation stability). Even if it does not do so, effectiveness of a CB comes from its capacity to control expectations. It suffices for households and firms to expect the CB to commit "bad" policies, to decrease the effectiveness of the CB.
Number of Goals
I don't have sources on this, but I seem to remember that central banks with one clear goal (i.e. monetary stability) are more effective than those with a basket of goals (i.e. monetary stability, GDP growth, decrease of unemployment rate). A general criticism can be that QE are not operations that help with the important margin, monetary stability - and that the central bank should focus on that instead.
Note that these are not just esoteric points. In fact, the academics and central bankers at the "Rethinking Macro Policy" conference agreed that (quoting Blanchard)

Throughout the conference, e.g., in Gill Marcus’ talk, and actually throughout the various meetings which took place during the IMF meetings in the following days, policy makers remarked and complained about the heavy burden placed on monetary policy in this crisis, and the danger of a political backlash against central banks. Even as the crisis recedes, it is clear that central banks will end up with substantially more responsibilities—whether they are given in full or shared—for financial regulation, financial supervision, and the use of macro prudential tools.
While even the use of the policy rate has distributional implications, these implications are much more salient in the case of regulation or macro prudential tools, such as the loan-to-value ratio. The general consensus was that these distributional implications could not be ignored, and that while central banks should retain full independence with respect to traditional monetary policy, this cannot be the case for regulation or macro prudential tools.