Does free capital mobility invalidate the basic comparative advantage argument for free trade in goods? In Herman Daly's article "Economics for a Full World", Daly states that international trade must be regulated because free capital mobility would invalidate the principle of comparative advantage (Daly, 2015, p.12). As a reference, he cites John Stuart Mill's "Principles of Political Economy" IV.VII.I. However, there doesn't seem to be a chapter 7 in book 4, so I cannot check what he is referring to.

I would greatly appreciate your help in understanding the argument made by Daly here!

References

Daly, H. (2015). Economics for a Full World. Great Transition Initiative.

Daly actually does explain further what he means by that in footnote 7 of his paper:

  Capitalists are interested in maximizing absolute profits and therefore seek to minimize absolute costs. If capital is mobile between nations, it will move to the nation with lowest absolute costs. Only if capital is internationally immobile will capitalists bother to compare internal cost ratios of countries and choose to specialize in the domestic products having the lowest relative cost compared to other nations, and to trade that good (in which they have a comparative advantage) for other goods. In other words, comparative advantage is a second-best policy that capitalists will follow only when the first-best policy of following absolute advantage is blocked by international capital immobility. For more on this, see Chapter 18 in Herman Daly and Joshua Farley, Ecological Economics (Washington, DC: Island Press, 2004).

But IMHO, the absolute conclusion that  international trade must be regulated as following from that seems silly. After all, one can regulate capital flows too negating that first-best policy (argument). In fact there are plenty of barriers to capital flow, some implicit and some explicit.

Having said that, I cannot quite find the ultimate conclusion stated in those absolute terms by Daly, although he does say (we should) "Move from free trade and free capital mobility to balanced and regulated international trade." Which is frankly pretty vague. I mean doesn't the WTO do at least some of the latter?

The whole writeup of Daly smacks of a certain social agenda. Later he says

  Restore the US Full Employment Act of 1945 and its equivalent in other nations in order to make full employment once again the end, and economic growth the temporary means.

I think Bernie Sanders also said he wants something like that. Daly also says

  Un/under-employment is the price we pay for growth from automation, off-shoring, deregulated trade, and a cheap-labor immigration policy.

And finally, Dally says (we should)

  strengthen the original Bretton Woods vision of interdependent national economies, and resist the WTO vision of a single integrated global economy

That's basically a slogan in disguise, to put it diplomatically. You could just as well phrase it as "take back control of our economy/tariffs/borders/immigration". So his conclusions are more or less socio-political goals; it's hard to take them at face value as pure economic arguments. So there will undoubtedly be disagreement on such statements.

Perhaps to save his "ecological economics" creds Daly does say that in contrast

  climate change and arms control require global institutions

To use a political science neologism, that's an ambivalox with demanding no world-wide regulatory institutions for any other economic issues, like trade.

But to come back to the more serious economic topic, glossing over Daly's black-and-white approach, capital mobility as partially substituting for goods exchange is hardly a new discovery. See Nadel (1971) for example.

  It has long been recognized that commodity movements and factor movements [e.g. capital, my note] are, to a degree, substitutes for each other in international exchange [...] Yet, until recently, the dominant theory of international trade, the Heckscher-Ohlin model, had been rather thoroughly recognized under the rigid assumption of the immobility of factors. Only in 1957, with the publication of Robert Mundell's important article, was capital mobility in the H-O model explored.

(That important article being: Mundell, Robert, “International Trade and Factor Mobility,” American Economic Review 67
(1957):321–35. It has around 2800 citations in Google Scholar.)

What is somewhat novel (in ecology-related economics) is that under some models of pollution, capital movement is preferable to goods movement:

  Using a Heckscher–Ohlin model, this paper re-examines Robert Mundell’s famous thesis that free trade and
  unimpeded capital mobility are perfect substitutes. Under very general conditions which, according to many
  economists, have caused international convergence of factor rewards,we show that in a polluted environment
  free trade is inferior to free international investment.This happens even though commodity prices and factor
  rewards are the same with both policies.The practical side of our thesis is that the world will be better off by
  reducing the volume of trade while removing all barriers to foreign direct investment that at present hamper
  the service industries.

That paper Batra and Belladi (2012) does also say that

  Daly (1996), Batra (1992), and Batra
  et al. (1998) argue that transportation is highly pollution intensive, specially relative to production

That seems to be a cornerstone assumption of the model. It is [to me at least] an interesting separate question if economists outside of this narrow field of "ecological economics" agree with these premises.


Is free-trade beneficial if living costs are unequal between countries? Free trade, it is said by those who support it, makes the whole world richer. Yet it seems, that if things like minimum wage, taxes, or living costs are unqual between countries then free trade would only be advantageous to the poor countries and to the upper echelons of the rich societies.

For example, a factory in Antarctica would have higher living costs for the workers than a factory in China. Hence if the Antarctic peoples were formerly self sufficient, the upper classes would soon transfer all labour to the cheaper countries and the working classes would starve, and most likely freeze to death.

This seems like what happened in the EU where there was free trade but because the taxes were different in each country, it lead to a disaster.

How is it possible to make free trade work for the benefit of all people?

The classic answers is transfers through welfare programs, re-training etc. See this question which is almost a duplicate. I'm re-quoting from there, just with a different emphasis:

  But just because the size of the pie expands [due to free trade], it doesn’t mean that everyone is better off. There are going to be some losers whose slice of the pie is so much smaller that they would have been better off with less trade. However, because the overall size of the pie has got bigger, the government can compensate the losers which can still make everyone better off. [...] But remember: thanks to free trade, you can afford that [better welfare programs], because the overall size of the pie is bigger.

Or

  Trade enables countries to experience economic growth and a rising standard of living by increasing access to physical capital and export markets. However, not everyone is better off as a result of international trade. Some domestic businesses and industries fail in the face of foreign competition, which results in job losses for workers. Economists suggest, however, that policy solutions that impose trade barriers are harmful to the economy. Rather, they propose policies such as those that provide job training programs to assist those displaced by trade.

(If you want to ask about the Eurozone crisis, please ask separately, I don't want to get into details on that here. Suffice to say that it wasn't simply a matter of free trade, but also of a currency union etc.)


Understanding the construction of stochastic processes I've seen stochastic processes modeled/constructed in the following way.

  Consider the
  probability space $(\Omega, \mathcal F, Pr)$ and let $\mathbb S$ be the (measurable)
  transformation $\mathbb S: \Omega \rightarrow \Omega$
  that we use to model the evolution of the sample point $\omega$ over time.
  Also, let $X$ be the random vector $X: \Omega \rightarrow \mathbb R^n$.
  Then, the stochastic process $\{ X_t: t=0,1,...\}$ is used to model
  a sequence of observations via the formula
  $
X_t(\omega) = X[\mathbb S^t(\omega)]
$
  or
  $
X_t = X \circ \mathbb S^t.
$

How should I understand the sample points $\omega \in \Omega$ and
the transformation $\mathbb S$ in this construction? (Could $\omega$ be something
like a sequence of shocks in certain cases?)

For more concreteness,
how would I write these two processes in this notation?

Process 1:
$$
X_{t+1} = \rho X_t + \varepsilon_{t+1} \tag{1}
$$
where $X_0 = 0$.

Process 2:
$$
X_{t+1} = \varepsilon_{t+1} \tag{2}
$$

This construction you describe is not fully general. In fact it characterizes strictly stationary time series. You see that it's shift-invariant. This operator $S$ is essentially a shift operator.

For comparison, here's the usual definition of, let's say discrete-time, processes:

Definition A stochastic process is a sequence $\{ X_t \}$ of Borel measurable maps on a probability space $( \Omega, \mathcal{F}, \mu )$.

Now for what you're describing, you have a fixed Borel measurable map $X: \Omega \rightarrow \mathbb{R}^n$. It's the underlying measure that is evolving according to $S$. The map $S$ induces a new "push-forward measure" (in measure-theoretic parlance) on $\Omega$ by just taking preimages: define a measure $\mu_S$ by

$$
A \in \mathcal{F} \stackrel{\mu_S}{\mapsto} Pr(S^{-1}(A)).
$$

So the random vector $X: ( \Omega, \mathcal{F}, \mu_S) \rightarrow \mathbb{R}^n$ is $X \circ S$ by construction. They induce the same push-forward measure on $\mathbb{R}^n$. Do this with $S^t$ for each $t$ and you have your time series.

As for your question about $\omega$, inspecting the proof for the other direction should clarify this---i.e. any strictly stationary time series must necessarily take this form for some $( \Omega, \mathcal{F}, Pr)$, $X$, and $S$.

The basic point is that, from a general point of view, a stochastic process is a probability measure on the set of its possible realizations. This is seen in, for example, Wiener's construction of Brownian motion; he constructed a probability measure on $C[0, \infty)$. So in general, an $\omega$ is a sample path and $\Omega$ consists of all possible sample paths.

For example, take the two processes you named above. They are strictly stationary, if let's say the innovations are Gaussian. (Any covariance-stationary time series driven by Gaussian innovations is strictly stationary.) The construction would then start by taking $\Omega$ to be the set of all sequences, $\mathcal{F}$ the $\sigma$-algebra generated by coordinate maps, and $Pr$ the appropriate measure. For the white noise process (2), $Pr$ is just a product measure on an infinite product.

Reference This characterization/construction by shift of strictly stationary time series is mentioned in White's Asymptotic Theory for Econometricians.


What is money really? Say I have €1000 (or $1000) on a bank account. What is that money really?

Is it a value stored on some computer at the bank where I have the bank account, a value stored at the central bank of the currency (in the case of the euro the European Central Bank) or something else?

And if it is just a value stored on a computer somewhere, why do we give it so much worth?

Money is, in essence, debt. More broadly, it's a system of clearing and credit. That entry in the computer means that the bank owes you \$1000, which is worth whatever others are willing to exchange for that sum— one way of thinking about it is that if you have \$1000, you have a general claim on the rest of society for \$1000 worth of whatever society produces.

The fact is that most money is in the form of loans (debt), not currency. This is well-explained in a recent Bank of England paper.


What is was the total corporate Income earned in the United States in 2014? What is was the total corporate income earned in the United States in 2014?

The question may seem simple, but I have been looking for a reliable source to inform me of this figure, and I hope someone out there can help me find a reliable figure and source.

Not for 2014 but here is a useful 2012 report using 2007 data: Taxing Businesses Through the Individual Income Tax (CBO (2012))

It shows how taxed corporations like S corps have been in long run decline (in share terms) relative to pass through entities. Which makes it tricky because, increasingly, corporate income isn't taxable at the corporate entity and so  taxes paid on total corporate income might be a poor measure of the taxes on corporate profits because so much is taxed on individual tax returns.

The BEA, as part of the NIPA publishes a number of corporate profit measures. You can see many of them on FRED. You may be particularly interested in Gross domestic income: Corporate profits with inventory valuation and capital consumption adjustments, domestic industries: Profits after tax with inventory valuation and capital consumption adjustments:


Stone-Geary utility function, derivation of Marshallian demand I am reading a paper on structural change. It has three sectors and it features non homothetic utility function, namely a CES with some thresholds for the consumption of the three goods. The UMP is as follows:
$$
\max_{C_k; k=1,2,3} \left(\sum_{k}\omega^{\frac{1}{\epsilon}}_k\left(C_k-\bar{C}_k\right)^{\frac{\epsilon-1}{\epsilon}}\right)^\frac{\epsilon}{\epsilon-1}
$$
Subject to the budget constraint
$$
\sum_{K}\left(P_k C_k\right)=W
$$
with $\omega_k$ summing up to 1.
What I find online is mainly a derivation of the log-utility case, which is not that suitable for my case. Also, in the paper authors use a price index which is really close to the one of the Dixit-Stiglitz case.

I'm currently stuck at the level of the FOC, and I wonder what are the steps to derive a proper demand function from these premises. Can anyone show me how to find this demand function?

If I understand your question correctly, you can take the log of the original utility function to simplify the calculations.  The demand derived will be the same as that which is derived from the original utility function.  This follows since the log function is a monotone function, and preferences are preserved under monotonic transformations of utility.  Thus, the "log-utility" case that you find online is exactly what you want to work with since it would simplify things quite a bit.


Quantitative Easing in Africa I am currently doing a research work on quantitative easing and can't find any example of it occurring in Africa. Have any African central banks ever used QE?

For Quantitative Easing to happen, a central bank needs to expand its balance sheet by, more or less, "printing money" from scratch. Quantitative Easing is a difficult policy in that you want to encourage inflation to force investment, but at the same time you need to control that inflation. For this reason QE should be used only when central banks believe economy is growing slower than it could/should be, which does not happen a lot in Africa.

For QE to be efficient, you need a strong central bank/currency, ie printing new dollars will create more dollars, but printing new 1920s Deutschmarks will only bring down the value of an individual Deutschmark.

To my knowledge, the only African country that wandered in Quantitative Easing is Zimbabwe. The success of this policy may by itself discourage any other comparable country to engage in such a policy.

QE is a last resort policy for stalling economies. Japan, Western Europe and the USA are countries where QE has been widely discussed because it is sometimes believed investment is delayed in hope of better days - QE should prevent this, but this is not a typically African problem, to my knowledge.

TL;DR: Even if African central banks were strong enough to engage in QE, African economies don't need such a policy to date.

Note that as mentionned in a comment, Quantitative Easing is a set of policies that has no standardized definition and that some examples above are anachronic with regard to the relatively recent introduction of the notion. While the term dates back to the early 2000s, what we know describe as QE was never practised as strongly as in the 1930s and 1940s against the Great Depression.


Electric Vehicle effects on family and macro-economics? What happens economically when cars last 1000,000 miles on cheap local energy?

EV's can save an average family 2000 dollars a year on energy costs, and 2000 per year on automotive investment.

That's equivalent to the national debt per capita figure of the West.

Does that mean the West will pay back its debt?

Will prices and taxes increase to reclaim civilian wealth spared by EV's for debts?

Will the car/lorry industries halve their revenues by producing thrice as durable vehicles?

Macro
One of the big issues with EVs is that several countries collect a lot of revenue from taxes on fossil car fuels. Those revenue streams will shrink, meaning that something else will have to be taxed to make up the shortfall.
Will the West pay back its debt? Well, that's barely a meaningful question. If you're thinking of government debt (which is not equivalent to Western debt), then EVs are neither good nor bad. If revenue drops from one source, it will be taken from another source instead.
The much bigger threat to car manufacturers is self-driving vehicles. Those could reduce vehicle demand by a huge proportion, if (as expected) they trigger a growth in shared ownership of vehicles. Most cars are used for only a tiny fraction of the time. And even at rush hour, only a minority of cars are in use at any one time.
Family
EVs currently differ from fossil cars in that they have higher capital expenditure, and lower operating expenditure. That will make household cash outflow much lumpier.
However, this also encourages the move towards shared ownership of self-driving EVs, which, for those households that choose it, will remove the capital expenditure element, making their cash outflow much smoother.


What does 'Health spending as a share of GDP' mean? I am watching a video essay talking about healthcare spending in different countries and one of the first graphs shown was titled: 'Health spending as a share of GDP'. After doing some reading, I think I understand now. It is saying the graph shows money spent on health as a percentage of GDP, but what is GDP. GDP is gross domestic product, which is the total value of goods or services produced and provided in a country in a year. So in my understanding, the phrase means: health spending as a percentage of the value of the entire nations economy. Is this correct? Also does this mean money spent on healthcare by citizens or by governments?

Here is the video. The graph is around 0:16.

Healthcare spending as a percentage of GDP is the measure of spending relative to the value of entire nations output at market prices in a given year. I suppose you can call the total output the value of the economy so you could say that although note that economy is a wider concept that would normally include things omitted by GDP which can only measure transactions for which there are market prices (hence economic activity such as housework and other non-market transactions are excluded).

According to the video they take the data from OECD data. OECD has multiple series on healthcare spending. Some series include only government spending and some include also private voluntary spending.

However,  the data in the video seem to closely match the total health spending % of GDP, 2013. There are some small discrepancies, for example the video says that the ratio was 11% in the Germany while the data show it was 10.9 - but more or less the data seem to match (these might have occurred due to some later corrections of the data or maybe the video is using different dataset - since they dont provide proper reference for the source its hard to know). See below:

Assuming its indeed the series above, according to the OECD the measure is defined as:

  Health spending measures the final consumption of health care goods and services (i.e. current health expenditure) including personal health care (curative care, rehabilitative care, long-term care, ancillary services and medical goods) and collective services (prevention and public health services as well as health administration), but excluding spending on investments. Health care is financed through a mix of financing arrangements including government spending and compulsory health insurance (“Government/compulsory”) as well as voluntary health insurance and private funds such as households’ out-of-pocket payments, NGOs and private corporations (“Voluntary”). This indicator is presented as a total and by type of financing (“Government/compulsory”, “Voluntary”, “Out-of-pocket”) and is measured as a share of GDP, as a share of total health spending and in USD per capita (using economy-wide PPPs).

So it would include both money spent by citizens as well as governments and all private organizations.


Central bank loss function (I did a solution, but it doesn’t totally make sense I guess) I have question on central bank loss function.

We know that the central bank loss function is

$$L(\pi, \bar{Y})= (\pi- \pi^e)^2+\beta \bar {Y}^2$$

And we know that fisher equation is $$i=r+\pi^e$$

where $r$ and $i$ Are respectively the real and nominal interest rate.

I want to minimize CB’s loss function by choosing $i$

——-

I tried to solve it. But it’s meaningless and so wrong:(

When I searched on the Net, I always saw that the CB loss function is minimized by substituting Phillips curve and takes derivative with respect to $Y$.

So, I substituted the fisher equation into the Phillips curve i.e. $\pi=a \bar{Y} +\pi^e= a \bar{Y}+i-r$

And then I substituted this equation into the loss function I.e. $L(\pi, \bar{Y})= (a\bar{Y}+i-r- \pi^e)^2+\beta \bar {Y}^2$

And take its derivative with respect to $i$

I got $2(a\bar{Y}+i-r-\pi^e)=0$

$i^*=\pi^e-a\bar{Y}+r$

But I think my way is wrong. Because this result doesn’t make sense.

Please let me show a way how to solve it. Any help would be appreciated.

Thanks a lot.

You need to differentiate with respect to Y, as you said! You substitute the phillips curve as you did (because it is a constraint for the central bank's optimization problem), then differentiate w.r.t $\bar{Y}$ (which I assume here stands for gap) and set this to 0 to obtain the optimality condition, which in turn will give you the monetary rule. Recall that once the optimal output-inflation combination is determined using the monetary rule, the central bank sets the interest rate to implement its choice.


How to calculate CRRA bounds from Holt and Laury (2002) type lottery? Lottery is between:

Option A: a certain choice of £5

Option B: £10 with probability 0.1 and £1 with probability 0.9

The probability of receiving £10 increases in each subsequent choice.

How do I calculate the CRRA bounds of this, using $U(x) = \frac{x^{(1-r)}}{1-r}$?

Let me rewrite your Option B as follows: £10 with probability $p$ and £1 with probability $1-p$ where $p\in[0,1]$ varies across the items in the list of options.

Let $\bar p$ be the point where the subject's choice switches. For example, subject chooses Option A for all $p<\bar p$ and Option B for all $p>\bar p$. Then we can use the indifference condition
\begin{equation}
U(5)=\bar pU(10)+(1-\bar p)U(1)
\end{equation}
to infer the risk aversion parameter $r$.

In experiments where $p$ is discretized, we can take $p_0,p_1$ as the values that are immediately before and after the switching point in choice list. For example, subject chooses Option A for all $p\le p_0$ and Option B for all $p>p_1$. Then the bounds on the risk aversion parameter can be inferred from the following inequalities:
\begin{equation}
U(5)\ge p_0U(10)+(1-p_0)U(1)
\quad\text{and}\quad
U(5)\le p_1U(10)+(1-p_1)U(1).
\end{equation}


inversely proportional utility functions If I have two products $x$ and $y$ and two users $A$ and $B$ whose utility functions for those products $u$ and $w$ are inversely proportional, would it be ok to express this relationship as: $u(x,y) = w^{-1}(x,y)$? Thanks.

Converting my comment to an answer...

I suppose the expression you wrote is almost correct, except perhaps for a notational issue. I would write $u(x,y)=[w(x,y)]^{-1}$, because $w^{-1}(x,y)$ is usually used to denote the pre-image of $w(x,y)$.

More generally, inverse proportionality between $u$ and $w$ is defined up to a multiplicative constant $K$; that is, $u(x,y)\cdot w(x,y)=K$ for some $K\in\mathbb R$. In the above case, you implicitly assumed $K=1$. So generally, you'd have
$$
u(x,y)=K[w(x,y)]^{-1}=\frac{K}{w(x,y)}.
$$


Real Income and a Fixed Money Supply What would happen to nominal income and wages if the money supply were fixed (100% reserve banking). Would real wages increase, even though nominal wages would stay the same or even decrease?

Roughly speaking nominal wages should remain fixed but things would still get invented and production would become ever ore efficient. So real wages would increase as deflation boosted the purchasing power of your wages.

However, it may not be such a good idea to have a completely fixed money supply and deflation - it may become unstable if people noticed that storing money under your mattress was a perfectly effective way to save. If many savers started doing this then it could induce cycles of bubbles and crashes in the value of money. It would probably be better to deliberately increase the money supply by a few percent each year - just enough so that people were not inclined to save simply by storing money.


Turkish economy after 2013 Source.

Why did the Turkish economy plunge after 2013?
Why didn't it recover ever since?

I think I understand the problem here: you're thinking of exchange rates as "units", i.e you're thinking that looking at GDP numbers in dollars tells you the same thing as looking at the same numbers in the local currency after adjusting for inflation. Unfortunately, exchange rates need not reflect what you think they reflect at all. In a world without capital flows between countries and with floating exchange rates, exchange rates would adjust in order to ensure that the current account position of any given country is balanced. This adjustment means that exchange rates primarily reflect relative prices on the international market of tradable goods, like commodities, for instance. Services such as medicine, education, finance (the capital account is closed) are not easily traded, therefore the exchange rate would carry little information about their prices, which are relevant to any person living in the country.

However, the real situation is even worse, because in reality there are capital flows between countries; there's borrowing, there's portfolio investment, there's direct investment, etc. Therefore, the condition I mentioned above fails: instead, the exchange rate adjusts so that the balance of payments balances, i.e such that

$$ \textrm{Current account} + \textrm{Capital account} = 0 $$

This means that if investors in the US decide to cut exposure to Turkish assets in the face of increasing political risks, the lira would depreciate and the nominal GDP measured in dollars would fall. However, such a devaluation would likely be expansionary for exports, and if the country has no problems of inflation (which is not true for Turkey), and there is no currency mismatch on domestic balance sheets (which is, again, not true for Turkey) their central bank could maintain monetary policy at low interest rates, causing the depreciation to become expansionary. Turkey would be producing more goods and services, it would just be that their value measured in local currency and then converted to USD would be less than it was before.


Is money received from my mother every month an income? If my mother sends me some money every month, is that considered an income?

I usually fill in a sheet to track my expenses and display my savings for every month. For the past few months, I've been living on my mother's generosity to sustain myself while I'm studying.
I was categorising this as an income but felt it wasn't right.

The question is, What do you call the money you receive from a relative every month for a fixed period of time in exchange for basically nothing but your well being, education etc.?

I intend to share this sheet with students who might be receiving some sort of financial assistance from their relatives. The need for me to come up with a term that rightly describes this transfer of cash is to avoid any sort of confusion while using this sheet.

I will simply repeat what I've said in the comments, just so that there's a concentrated version of the argument.

What you are describing is not 'income' but a kind of 'transfer' payment. Your mother transfers an amount of money from her account to yours.

It is possible to consider it an 'investment' on her part; she would be investing in the increase of your human capital stock; such an approach would imply that she would have a claim on a part of your future income stream.

Since, usually, parents don't enter into contractual agreements with their children concerning their future income possibilities (that I know of) I would argue that from the viewpoint of you both, what you are receiving and what she is delivering is a cash transfer.


Second order stochastic dominance I have two very basic questions about second order stochastic dominance (SOSD):

Am I right in thinking that this is only a partial order, i.e. you can find a pair of lotteries such that neither SOSD the other?
Could it be that, if we only consider lotteries with equal means, SOSD is then a complete order? [I suspect not...]

The answer to 2. is no.
One way to see this is from MWG's Property 6.D.2: $F$ SOSD $G$ if and only if
\begin{equation}
\int_0^xF(t)\mathrm dt \le \int_0^xG(t)\mathrm dt \quad\text{for all }x.
\end{equation}
Dixit calls the two integrals super-cumulative functions of $F$ and $G$, respectively. Hence, a characterization of SOSD is that the super-cumulative of the dominating distribution always lies below the super-cumulative of the dominated distribution. (This is reminiscent of the characterization of FOSD as the cdf of the dominating distribution always lying below the cdf of the dominated one.)
For a counterexample, we only need to come up with distributions $F$ and $G$ such that their super-cumulatives cross. Here's one:
\begin{align}
f(x)&=\begin{cases}
0.1 & x\in\{0,6\}\\
0.4 & x\in\{2,4\}\\
0 & \text{elsewhere}
\end{cases}\\
g(x)&=\begin{cases}
\frac13 & x\in\{1,3,5\}\\
0 & \text{elsewhere}
\end{cases}
\end{align}
Both distributions have the same mean of $3$, but as the following figure shows, their super-cumulatives ($S_F$ and $S_G$) cross at several points, and so neither distribution SOSD the other.

Here, $S_F(x)=\int_0^x F(t)\mathrm dt = \int_0^x\int_0^tf(s)\mathrm ds\mathrm dt$, and $S_G$ is similarly defined. Since $f$ and $g$ are probability mass functions, the cdf's $F$ and $G$ are step-functions (shown below). Integrating the step-functions yields the continuous and piece-wise linear $S_F$ and $S_G$ above.

Edit
As OP noted in a comment, "ALL risk averse people with iso-elastic utility ($u=x^\alpha$, $\alpha\in(0,1)$) prefer gamble $G$ to gamble $F$". The negative answer above suggests that there must be a concave function with which $F$ is preferred to $G$. Here is an example:
\begin{equation}
u(x)=\begin{cases} 2x& x\le 2\\ 4& x>2 \end{cases}
\end{equation}
This function is concave, and $\mathbb E_F(u)=3.6>3.\overline{33}=\mathbb E_G(u)$.


What does 'intelligent money' mean? Is 'intelligent money' or 'smart money' an economic term, and if yes, what does it refer to?

"Intelligent money" or "smart money" is not an economic term per se, but a finance term.

It is colloquially used in the finance industry to describe the collective group of individuals who are paid to actively manage funds, rather than passively manage funds. Active management differs from passive management in that the former chooses how to invest money based on individual perceptions of expected return, whereas the latter follows a predetermined simple rule, such as "buy equities in a weighting equal to their individual market valuations amongst the largest x stocks".

More generally, 'smart money' refers to the subset of active managers that act as if they possessed an informational advantage, and/or the ability to adapt a fund's investment strategy to market conditions. In this sense, smart money consists of hedge funds and stock-picking mutual funds and 'dumb money' consists of passive mutual funds. (Passive funds are more likely to be ETFs, though it's not mutually exclusive).

However few economists would consider investing with active managers to be the intelligent choice (given equal risk, passive investment outperforms active investment on average, net of fees).

Since the term is colloquial, it is hard to find an example which provides a definition. Notwithstanding this, the following article's title lines up with this explanation, and further, explains why "smart money" isn't ordinarily a smart place for money.

http://time.com/money/3657009/indexing-investing-inflows-vanguard-blackrock/


Why do we need to "get the economy moving again"? Sorry I have no background in economics but as a computer programmer, I specialise in building models out of simple math and logic, so I hope we can speak the same language without having to get into too much economic jargon.

Consider the following scenario:

Kate is a hairdresser and Alice owns a restaurant. Every month Kate goes to Alice's restaurant and spends \$50 on a meal, and Alice spends \$50 getting her hair cut at Kate's. This generates $100 of GDP. Now say there is a global pandemic which makes it dangerous to meet each other, Kate decides it's safer to cook her own dinner and Alice cuts her own hair. They are both in exactly the same financial position as they were before but no GDP has been generated. After a while the government announces that we all need to do our bit to "get the economy moving again" (which I interpret to mean "generate GDP") even if it means putting ourselves in danger.

I understand that the government wants economic activity because that's how they collect tax revenues, and I also understand that some people do jobs that are essential for the functioning of society. I also understand that going to work conveys other psychological benefits than simply earning money, but let's assume for the moment that there are at least some people people who would rather just stay at home and where there is reduced natural demand for their services.

It seems to me that all the money that hasn't been spent in restaurants and hairdressers during the COVID-19 pandemic hasn't gone anywhere, it's still sitting in the bank accounts of the people who would otherwise have spent it.

If we could find another way of redistributing that wealth from the people who's jobs are essential (and are therefore still getting paid but aren't going to restaurants) to people who's jobs are not essential (and therefore don't need to work during the pandemic), is there any harm with putting the economy on hold for an indefinite period until people decide they want to go back to work again?

Edit 8 June

Thanks for all the great responses, this has really helped my understanding but I don't think anyone has hit the nail on the head so I've added this note to try and clarify what I was after. I’ve tried not to move the goalposts to the extent that previous replies look stupid (I haven’t edited anything above this line).

Firstly just to clarify my original question, I wasn’t questioning the benefit of economic growth over stagnation under non-covid circumstances; I was questioning whether covid + economic stagnation might be better than covid + enforced economic activity.

Also one thing I maybe didn’t make clear enough is that I wasn’t talking about an enforced lockdown in cases where people would rather go to work; I was arguing that people who wanted to consume or produce less shouldn’t be obligated to consume and produce more, just to fuel the engines of capitalism.

The effect of covid has been to push the cost of goods upwards (because of the risk of contracting covid while producing them) and the benefit of consumption downwards (because of the risk of contracting covid whilst consuming). This will put some markets into a state of oversupply, even without an enforced lockdown.

So let’s say my widget supplier says “I’m no longer willing to supply that widget for \$50; I’d rather lose my job and get paid \$30 on welfare” and I say “I’m not willing to pay \$50 anymore; I’d rather live without it, even if it means I have to pay \$35 more in taxes”.

In this scenario we’re both happier than we would have been had we traded, and the government gets $5 to administer the welfare. The only people who aren't happy are those that have a vested interest in ever-increasing GDP, who in turn are often those in powerful positions and might try to use their influence to "get the economy moving again" to the detriment of the average citizen.

Trade creates value.

Previously, Kate preferred spending \$50 on food at Alice's restaurant (rather than cook her own food). And Alice preferred spending \$50 getting her hair cut at Kate's (rather than cut her own hair). That Kate must now cook her own food and Alice cut her own hair means that value has fallen (where value is broadly defined as the degree to which individuals' desires are satisfied).

(Note though that the fall in value in the above example is probably not very large. In most other examples and cases, the fall in value will be much larger—consider for example the children who no longer go to school and are now supposed to be learning at home.)

Money is not the source of value.

You write:

  It seems to me that all the money that hasn't been spent in restaurants and hairdressers during the COVID-19 pandemic hasn't gone anywhere, it's still sitting in the bank accounts of the people who would otherwise have spent it.

This expresses a common misconception among non-economists. Money is not the source of value.†

Value is the satisfaction of people's desires—and such value arises through production and consumption. If everyone is sitting at home and not producing anything, then no desires are satisfied, no value is produced, and all the money sitting in banks is worthless.

†The mercantilists of the 17th and 18th centuries likewise believed that gold and silver were the sources of value and that one's country should try to accumulate as much gold and silver as possible. Adam Smith pointed out that this was mistaken--value comes from production and consumption, not precious metals, pieces of paper, or numbers in a bank account.


The Federal Reserve is only issuing cash money? When the Federal Reserve is issuing money, they are only printing cash money (coins and banknotes)?

If not, then what other types of money they are issuing?

Deposits at the Federal Reserve largely count as money, at least as far as the depositing commercial banks are concerned.

Apparently on March 1 2016, the Federal Reserve Banks' liabilities included $\$1475$ billion of Federal Reserve notes, net of F.R. Bank holdings, and $\$2530$ billion of deposits, together with $\$412$ billion of other liabilities. See the second part of table 5 of https://www.federalreserve.gov/releases/h41/current/ for more details

Coins are not issued by the Federal Reserve, but by the United States Mint


What is the logic behind that one can "grow out of debt" via increase in GDP? As we all know the US has a big debt and increasing deficits. The head of FED J. Powell commented that the US was on an unsustainable path w.r.t some debt to GDP ratio. A few commentators I listen to argue that if the US increases it GDP, then they can "grow out of" this problem that Powell mentioned.

Could someone explain this logic to me?

If they invest in productivity-enhancing stuff, GDP could grow at a faster pace than the [increase in] debt. Then the debt to GDP would decrease.


Name of phenomenon where migrant workers receive decent wage but absolutely no chance of getting any government benefits Not sure if the title reflects the question very accurately but my question is specific to the Gulf countries which have a huge population of migrant workers, like Saudi and UAE. So, let's say Raj is an expat living and working in RandomGulfCountry with his family. He has a decent job which also pays for a modest apartment and for his kids to go to an okay-ish school. The economic activity created by Raj brings in wealth for the RandomGulfCountry government which then uses it to fund free healthcare, education, utilities etc. that is accessible by only its citizens. It is literally free because there's no income tax (at least for citizens). Most citizens don't really 'work', as they either own the companies or are employed in high positions because of a law requiring a quota of employees to be citizens so they're just figureheads; meaning most of the economic activity is created by expatriates like Raj.

Now, Raj could access these programs but becoming a citizen is almost next to impossible. But Raj is still happy, his job in RandomGulfCountry is paying 5x the salary he'd have gotten back in his home country. However, his continued residence in RandomGulfCountry is at the mercy of his employer. If he gets fired and doesn't find another job soon he has to leave, there is no path to permanent residence or citizenship. The government also charges a high fee for renewing his residence permit and that fee increases with the number of family members staying with him.

So by continuing to work in RandomGulfCountry, Raj is effectively subsidizing the social programs which he can never access. He still has to pay his utilities bill while the citizens don't have to. He has health insurance from his employer but he still has to pay his co-pays while citizens don't need to pay a single penny. Raj still has to fund his own kids higher education but the fruits of his labor go into funding RandomGulfCountry kids to go study abroad for college without them having to pay a single penny.

This example might be a bit too simplistic and people like Raj are very privileged unlike most of the actual migrant workers in the Gulf. So I want to know what is the most appropriate term for this phenomenon, where you contribute to a foreign economy directly and your productivity is exploited to increase the luxury of the citizens who already live quite luxuriously and you never have a chance to receive any of the benefits because you will always be considered a temporary resident.

I was thinking something like wage slavery but you do get good wages, just not the full outcome of your productivity I guess? While it takes into account the fact that you're at the mercy of your employer for your continued well being, it's not really the wages that are responsible for your well being. Also what term would also take into account that the foreign government not only exploits you but also charges you to stay in the country?

There's a lot going on in this question, so I'll focus on the labor-economics part of the question rather than the political-economy part of the question.

If it is the case that these migrant workers are being paid considerably better than their alternative labor options, but they are at the same time being deprived of rights they might value (access to social services, citizenship), then this is an example of a compensating differential.

The theory of compensating differentials says that, in order to get people to take a job that they'd rather not take (perhaps because taking it means they'd have to live as a second-class citizen), you have to pay them a little extra in order to convince them to take the job, "compensating" them for accepting the downsides of the job.

This explains, from a labor-econ perspective, why the workers might accept this arrangement. It doesn't explain the political system that deprives the workers of rights.


I'm looking for a reviewed source on the amount of money in the world As in title, I'm looking for a paper estimating the amount of all money in the world, sum of value of all national currencies or something like this.

When I google it, I find only pop-science curiosities, but I need hard data to quote.

If you're looking for total value of banknotes and coins in circulation, then the Bank for International Settlements provides some useful statistics. While the BIS only collects data on ~20 countries including the EU, the noted countries cover almost all of the value of banknotes and coins in circulation as of now. At the end of 2017, the total amount in USD is $6.458 trillion.


What strategies can the president employ to deflate the dollar United States president Donald Trump has publicly declared a desire to deflate the value of the dollar.  I have read in news reports that he has asked aids to find ways to decrease the dollar's exchange rate.

I understand that attempting to influence the Fed to lower interest rates could achieve his goal of a lower exchange rate.

What are other methods a president could undertake to weaken the dollar?

Direct intervention by the U.S. Treasury in the foreign exchange market offers one option for the president.    The Treasury would use dollars to buy foreign currency bonds, bidding up the relative prices of foreign currencies and weakening the dollar.

Another option is  imposing taxes on the foreign purchase of U.S. assets as a way of weakening the dollar and reducing the trade deficit.


Wealth transfer by Social Planner in GE I am reading the definition of a price equilibrium with transfer in MWG on page 548, 524-5.

Consider two-consumer exchange economy. If social planner wants to transfer wealth, how does she achieve this?

Two consumers are born with some apples and oranges. So, the social planner lets these consumers sell at the going market place of what they are endowed with.  Then, does she collect taxes and transfer wealth in this way?

It seems like this wealth transfer can be achieved also by directly reallocating the apples and oranges distributed among consumers.

I am not exactly getting the terms like "there be some wealth distribution" or "equilibrium with transfers", "wealth transfers". What does it mean to say, "there is an assignment of wealth levels with ...."?

We have an allocation $(x^*,y^*)$ and a price system $p$ forming a price equilibrium with transfers.The assignment of wealth levels $(w_1,\ldots,w_I)$ has to satisfy $$\sum_i w_i=p\cdot\bar{\omega}+\sum_j p\cdot y_j^*.$$
One way to interpret the wealth levels is that the planner hands out coupons that can be traded at existing prices for commodities and chooses the production plans of the economy. But one can interpret the wealth distribution also as a distribution of the initial endowments and of firm shares. Let $w=\sum_i w_i$ and for each consumer $i$, let $m_i=w_i/w$, which is just the share consumer $i$ has in the aggregate wealth. Now give each consumer an endowment $\omega_i$ of $m_i \bar{\omega}$ and for each firm $j$ a share $\theta_{ij}$ equal to $m_i$. For the resulting private ownership economy, $(x^*,y^*)$ and $p$ constitute a Walrasian equilibrium, so one has reduced redistributing wealth to redistributing endowments and shares in firms. To see that everything works out, note that
$$w_i=m_i w=m_i\bigg(p\cdot\bar{\omega}+\sum_j p\cdot y^*_j\bigg)=p\cdot m_i\bar{w}+\sum_j m_i p\cdot y_j^*=p\cdot \omega_i+\sum_j\theta_{ij} p\cdot y_j^*.$$


Does Not Having a Fractional Reserve System Cause More Inflation? It is my understanding that countries without fractional reserve requirements still have capital requirements, but what I do not understand is how equity can be used to satisfy these requirements without causing large amounts of inflation in the housing market.

If banks are not required to have currency reserves, then what is to prevent them from extending themselves effectively unlimited credit based on their equity?  In the short term, they may be limited by debt to equity ratios, but in the long term, wouldn't this lead to a consistent rate of near constant inflation?

Every time a bank issues credit to buy a house, (in aggregate, of course) the price of housing increases, which increases equity, which allows them to issue more credit..

Does anyone else not see a problem with this?

Canada abolished bank reserves in 1992. Canada has had very similar inflation rates as the United States since then.

Increases in house prices do not improve bank equity. Banks make a profit based on being paid a rate of interest above their cost of funds. Increasing house prices just reduce losses in the case of default. Threfore, the relatively steady profits that come from interest rate spreads slowly builds up equity, with the result that bank balance sheets only exhibit moderate growth rates (similar to nominal GDP growth rates).


Adam Smith and universal opulence Adam Smith seems to be saying that the goal of governing is "universal opulence which extends itself to the lowest ranks of the people," which he appears to think achievable in capitalism with the minimalist government. Clearly, things did not work out the way he thought, prompting Karl Marx, 90 years later, to assert that state-protected capitalism is the legalization of thievery. What are some defenses economists make on behalf of Smith? References appreciated.

The irony of Marx's criticism is that Communism is just as, if not more, available to become a "legalization of thievery", due to the elimination of the "invisible hand" of the market.

To your question, I would point to the Chicago School's consideration of Antitrust government intervention as a defense of the intuitions of Adam Smith, albeit a modification of strict faith in the ability for the "invisible hand" to unrestrictedly manage the fairness of the markets.

Michael S. Jacobs discusses the rise of the Chicago School's antitrust perspective, in his 1995 article in the North Carolina Law Review, "An Essay on Normative Foundations of Antitrust Economics". For Chicagoans, Antitrust actions are a tool to protect the free market. This is aligned with Adam Smith's concept of economic systems, via the application of the strict guideline that "consumer welfare, narrowly conceived in explicit economic terms, should be the only object of inquiry" in considering antitrust intervention (Jacobs, 1995. e.g. Herbert Hovenkamp, 1985). These tools are only to be used with the strict attention to preserving efficiencies of the market - an allusion to the foundational premises of Smith.

The topic of Antitrust Legislation provides an example of the role of government to intervene in the free market, while respecting the need for it to be enacted in a minimized way.

Additional reference material can be found in the article - it is highly notated.

LINK: "An Essay on Normative Foundations of Antitrust Economics". Michael S. Jacobs, North Carolina Law Review, 1995.


How do tax payers have to pay for the tax deductions someone else receives due to a charitable donation? "A USD 1,000 donation from a donor in the highest tax bracket costs that donor only USD 604. The federal government kicks in the remaining USD 396 in the form of a reduction in taxes", writes Ray D. Madoff in a piece for the New York Times.
Similarly, Paul Vallely argues in an article for The Guardian, that, for a tax-deductible donation, "the highest-rate taxpayer would need to pay out only £55, because the state would provide the other £45", hence "taxpayers contribute part of the gift".
While I do understand, that the government loses money in tax incomes, I don't understand how this directly increases the tax burden on other tax payers (except for, in the long term, the government might raise taxes to make up for lost tax revenues).
Can anyone explain how this works?

Well you actually answered this question yourself. It is because of this:

While I do understand, that the government loses money in tax incomes, I don't understand how this directly increases the tax burden on other tax payers (except for, in the long term, the government might raise taxes to make up for lost tax revenues).

To be more precise an alternative is also for government to spend less but I think that the articles are arguing that ceteris paribus keeping government spending fixed government will have to somehow eventually collect the resources from economy in one way or other. In a long run government has to respect its intertemporal budget constraint. If someone pays less, taking government spending as fixed, someone will have to pay for that shortfall either directly or indirectly eventually at some point.


Why does the retiree to contributor ratio matter when discussing the solvency of Social Security? Whenever the topic of Social Security solvency comes up, the consensus is that benefits for future generations have to be cut, mainly because of two reasons:

People are living longer.
There are more people retiring than people contributing to the system.

I understand the first reason, but the second doesn't make sense to me, mathematically speaking: the retirement of an older generation should not be affected by the number of contributors in the younger generation.

In simplistic terms, if the older generation is composed of 100 people, those 100 people paid payroll taxes during their working years, so by the time they retire, there should be 100 people's worth of reserves to fund their retirement. The number of contributors in the younger generation is irrelevant.

Inflation should not be a factor either since, at least in the United States, reserves are invested in intra-government bonds.

So, why do I constantly hear the retiree to contributor ratio as a reason why Social Security benefits will have to be cut for future generations?

Pay as you go vs Fully funded pension plan distinction is relevant here. Also known as Defined benefit vs Defined contribution.

If everyone saved for their own pension via payroll taxes or otherwise (Pay as you go/ Defined contribution), then the ratio of retiring to contributing people indeed would not matter.

However, most governments pay current retirees from taxes on current workers. If there are fewer current workers relative to retirees, then either each has to pay more tax (discouraging working, eventually leading to declining tax revenue) or each retiree gets less pension. Governments typically do not save the current taxes to pay pensions when the current workers retire. Instead, governments are typically borrowing against future tax revenue.

See also the Overlapping Generations Model (OLG).


Name of example of irrationality of proportional and absolute cost I am trying to give a puzzle from behavioral economics illustrating on the irrationality of thinking of costs in proportional rather than absolute terms. I remembered vaguely an example like this but could not find the exact term or if another more salient example exists:

  You can buy a computer nearby for \$1k or 1 hour away for \$950. Most people think that \$50 is only 5% of the cost and so would not drive 1 hour  away.

  You can buy a stereo system nearby for \$100 or 1 hour away for \$50. Most people think that \$50 is 50% of the price and so would drive 1 hour to get the cheaper item.

  The problem is that it's the same 1 hour away and the same \$50.

What is the name of this puzzle or irrationality?

I think you're referring to the jacket-calculator problem, first proposed by Tversky and Kahneman (1981) as their Problem 10. The paper illustrates the idea of mental accounting with several problems regarding uncertainty, and problem 10 illustrates "the temporary devaluation of money":

  The following problem, based on examples by Savage and Thaler, further illustrates the effect of embedding an option in different accounts. Two versions of this problem were presented to different groups of subjects. One group ($N = 93$) was given the values that appear in parentheses, and the other group ($N = 88$) the values shown in brackets:

    Problem 10: Imagine that you are about to purchase a jacket for (\$125) [\$15] and a calculator for (\$15) [\$125]. The calculator salesman informs you that the calculator you wish to buy is on sale for (\$10) [\$120] at the other branch of the store, located 20 minutes drive away. Would you make the trip to the other store?

  The response to the two versions of problem 10 were markedly different: 68 percent of respondents were willing to make an extra trip to save \$5 on a \$15 calculator; only 29 percent were willing to exert the same effort when the price of the calculator was \$125. ... By the curvature of $\nu$, a discount of \$5 has a greater impact when the price of the calculator is low than when it is high.

  ...

  Many readers will recognize the temporary devaluation of money which facilitates extra spending and reduces the significance of small discounts in the context of a large expenditure, such as buying a house or a car. This paradoxical variation in the value of money is incompatible with the standard analysis of consumer behavior.


Ricardo's theory of comparative advantage The aim of this question is to better explore the mathematical economics model behind Ricardo's theory of comparative advantage and the claims that can be made based on this model. This seems necessary because of this question and some of the answers given to it. Following is a description of the model as I understand it.

Suppose there are two countries (England and Portugal, denoted by E and P) producing two goods (good x and good y). The only input needed to produce these goods is labor. The economics of scale are constant in both industries of both countries and the labor requirement to produce good $m$ (where $m \in \left\{x,y\right\}$) in country $i$ is denoted by $a_{m,i}$. Without loss of generality I will assume that England enjoys comparative advantage in producing the good $x$, meaning
$$
\frac{a_{x,E}}{a_{y,E}} < \frac{a_{x,P}}{a_{y,P}}.
$$
Let us denote the size of the English labor pool by $L_E$, that of the Portuguese by $L_P$. Denote the produced quantities by $\left(q_{x,E},q_{y,E}\right), \left(q_{x,P},q_{y,P}\right)$. So England may choose any production $\left(q_{x,E},q_{y,E}\right)$ as long as
$$
q_{x,E} \cdot a_{x,E} + q_{y,E} \cdot a_{y,E} \leq L_E.
$$
The income of a country is determined by the value of its production. Denote the equilibrium prices by $p_x, p_y$.

Now follow some assumptions that do result in some loss of generality, but I think these are necessary for simple illustrations.
Assume that the English public's consumption (denoted by $c_{m,E}$) preferences of said goods, $\left(c_{x,E},c_{y,E}\right)$, are described by symmetric a Cobb-Douglas utility function. Assume the same for Portugal, where Portuguese consumption is denoted by $\left(c_{x,P},c_{y,P}\right)$.

A discussion of how England can maximize her profit is probably useful, but I seek to focus on the following claims and whether they are true given this model:

England will always produce good $x$ (in some positive quantity).
England will never produce good $y$.
England will never export good $y$.

In case you are wondering: No, this is not a homework question. But because you do not have to take my word for this I tried to phrase the question in accordance with the current guidelines for exercises.

The solution concept used in Ricardo's modell is the competitive equilibrium. Let the set of countries $N$ be defined as $N = \left\{E,P\right\}.$ (England, Portugal) Then the competitive equilibrium is a vector
$$
\left(p,\left(q_{x,i},q_{y,i}\right)_{i\in N},\left(c_{x,i},c_{y,i}\right)_{i\in N}\right),
$$
where $p$ is the equilibrium price ratio of the goods $x$ and $y$, so $p = \frac{p_x}{p_y}$, and $\left(q_{x,i},q_{y,i}\right)$ and $\left(c_{x,i},c_{y,i}\right)$ are the production and consumption vectors of country $i$. The equilibrium vector has the following properties:

Profit maximization:
Each country choose a production that maximizes her profit given her production capabilites and the equilibrium price ratio. The set of possible production vectors $T_i$ is defined by the size of the countries labor pool $L_i$ and the labor requirements $a_{x,i},a_{y,i}$ as defined in the question
$$
q_{x,i} \cdot a_{x,i} + q_{y,i} \cdot a_{y,i} \leq L_i.
$$
A production vector $\left(q_x^i,q_y^i\right)$ is profit maximizing if
$$
\max\limits_{(x,y)\in T_i} p \cdot x + y = p \cdot q_{x,i} + q_{y,i}.
$$
Utility (welfare) maximization:
The vector $(c_{x,i},c_{y,i})$ maximizes country $i$'s utility if
$$
\max\limits_{p \cdot x + y \leq p \cdot q_{x,i} + q_{y,i}} U_i(x,y) = U_i(c_{x,i},c_{y,i}).
$$
The good markets are in equilibrium, i.e. in the market of each good demand equals supply (technically only the values are equal, but here, i.e. with Cobb-Douglas preferences, prices are always positive in equilibrium, so there is no difference). The equations for these are
$$
\sum\limits_{i\in N} q_x^i = \sum\limits_{i\in N} c_x^i \hskip 20pt \sum\limits_{i\in N} q_y^i = \sum\limits_{i\in N} c_y^i.
$$

Let us examine what these properties imply. The set $T_i$ is a triangle. As goods have positive value in equilibrium so all the labor is used up and the production vector is chosen from the production possibility frontier. Which industry ($x$ or $y$) can employ labor more lucratively? In industry $x$ a unit of labor produces value $\frac{p_x}{a_{x,i}}$. Similarly the value produced in industry $y$ is $\frac{p_y}{a_{y,i}}$. If $\frac{p_x}{a_{x,i}} > \frac{p_y}{a_{y,i}}$ only good $x$ is produced, if $\frac{p_x}{a_{x,i}} < \frac{p_y}{a_{y,i}}$ only good $y$ is produced, if $\frac{p_x}{a_{x,i}} = \frac{p_y}{a_{y,i}}$ it does not matter how labor is allocated among the industries as long as all labor is used. So the profit maximizating quantities are
$$
\left(q_{x,i},q_{y,i}\right) = \left\{
\begin{array}{cc}
\left(\frac{L_i}{a_{x,i}},0\right) & \frac{a_{x,i}}{a_{y,i}} < p \\
\alpha \cdot \left(\frac{L_i}{a_{x,i}},0\right) + (1 - \alpha)  \cdot \left(0,\frac{L_i}{a_{y,i}}\right)
 & \frac{a_{x,i}}{a_{y,i}} = p \\
\left(0,\frac{L_i}{a_{y,i}}\right) & \frac{a_{x,i}}{a_{y,i}} > p.
\end{array}
\right.
$$
The optimum condition for the utility maximization problem is
$$
MRS_i(c_{x,i},c_{y,i}) = \frac{c_{y,i}}{c_{x,i}} = p.
$$
Because the utility functions in England and Portugal have the same form we can take this further. From
$$
\frac{c_y^A}{c_x^A} = p = \frac{c_y^P}{c_x^P}.
$$
we get
$$
\frac{c_{y,A}}{c_{x,A}} = p = \frac{c_{y,P}}{c_{x,P}}.
$$
we get
$$
c_{y,P}  = \frac{c_{y,A}}{c_{x,A}} \cdot c_{x,P}.
$$
Using this
$$
\frac{c_{y,A}+c_{y,P}}{c_{x,A}+c_{x,P}} = \frac{c_{y,A}+\frac{c_{y,A}}{c_{x,A}} \cdot c_{x,P}}{c_{x,A}+c_{x,P}} =  \frac{c_{x,A}}{c_{x,A}} \cdot \frac{c_{y,A}+\frac{c_{y,A}}{c_{x,A}} \cdot c_{x,P}}{c_{x,A}+c_{x,P}} =
\frac{c_{y,A} \cdot c_{x,A} + c_{y,A} \cdot c_{x,P}}{c_{x,A} \cdot \left(c_{x,A}+c_{x,P}\right)}.
$$
so
$$
\frac{c_{y,A}+c_{y,P}}{c_{x,A}+c_{x,P}} = \frac{c_{y,A} \cdot c_{x,A} + c_{y,A} \cdot c_{x,P}}{c_{x,A} \cdot \left(c_{x,A}+c_{x,P}\right)} = \frac{c_{y,A}}{c_{x,A}} = p.
$$
What this says is that the relative demand ($\frac{c_{y,i}}{c_{x,i}}$) is not only equal to the price ratio for individual countries but also the relative aggregate world demand is equal to the price ratio. (Again, this is only true if the individual countries have Cobb-Douglas utility functions with identical parameters.) We now have a relatively easy way to find the equilibrium price ratio: we calculate relative aggregate supply. As aggregate supply equals aggregate demand in equilibrium, relative aggregate supply will equal relative aggregate demand, and as we have just shown it will also equal $p$. We get relative supply from the profit maximizing productions of the individual countries. Let us first discuss the aggregate of the profit maximizing productions, which I will denote by $(q_x,q_y)$. So $(q_x,q_y) = (q_{x,E} + q_{x,P},q_{y,E} + q_{y,P})$ which means
$$
(q_x,q_y) = \left\{
\begin{array}{cc}
\left(\frac{L_E}{a_{x,E}} + \frac{L_P}{a_{x,P}},0\right) & \frac{a_{x,E}}{a_{y,E}} < \frac{a_{x,P}}{a_{y,P}} < p \\
\left(\frac{L_E}{a_{x,E}} + \alpha \cdot \frac{L_P}{a_{x,P}} , (1 - \alpha) \cdot \frac{L_P}{a_{y,P}} \right) & \frac{a_{x,E}}{a_{y,E}} < p = \frac{a_{x,P}}{a_{y,P}} \\
\left(\frac{L_E}{a_{x,E}} , \frac{L_P}{a_{y,P}} \right) & \frac{a_{x,E}}{a_{y,E}} < p < \frac{a_{x,P}}{a_{y,P}} \\
\left(\alpha \cdot \frac{L_E}{a_{x,E}}, (1 - \alpha) \cdot \frac{L_E}{a_{y,E}} + \frac{L_P}{a_{y,P}} \right) & \frac{a_{x,E}}{a_{y,E}} = p < \frac{a_{x,P}}{a_{y,P}}  \\
\left(0, \frac{L_E}{a_{y,E}} + \frac{L_P}{a_{y,P}} \right) & p < \frac{a_{x,E}}{a_{y,E}} < \frac{a_{x,P}}{a_{y,P}}  .
\end{array}
\right.
$$
The relative aggregate supply is the ratio $\frac{q_x}{q_y}$. It is perhaps best described by this image:

The relative aggregate demand is the ratio $\frac{c_x}{c_y}$. As we have discussed $\frac{c_y}{c_x} = p$ so
$$
\frac{c_x}{c_y} = \frac{1}{p}.
$$
As a result one can draw the relative aggregate demand in the previous graph as  hyperbole. The intersection with the relative aggregate supply curve will give yield the equilibrium price ratio and will also yield information about the production of individual countries. Where this intersection occurs depends on the parameters $L_E,L_P,a_{x,E},a_{y,E},a_{x,P},a_{y,P}$. I will distinguish between three types of equilibria, each represented in the following figure:

In the 1. equilibrium the price ratio is $p = \frac{a_{x,E}}{a_{y,E}} < \frac{a_{x,P}}{a_{y,P}}$. Thus Portugal specializes and only produces good $y$, but England does not specialize but produces both good $x$ and $y$. Producing either good gives her the same value. The exact equilibrium quantities England produces are determined by the value the aggregate demand curve takes at price $p$, because
$$
\frac{q_x}{q_y} = \frac{c_x}{c_y} = \frac{1}{p}
$$
and
$$
q_x = q_{x,E} + q_{x,P} = q_{x,E} + 0 \hskip 20pt q_y = q_{y,E} + q_{y,P} = q_{y,E} + \frac{L_P}{a_{y,P}}.
$$
In this case England will still not achieve a net export of good $y$. The preferences tell us that Portugal will consume both goods $x$ and $y$. But the only way it can pay for the goods $x$ consumed is by trading some of its goods $y$, so Portugal, not England, will be a net exporter of good $y$ while England is a net exporter of good $x$.
In the 2. equilibrium both countries specialize: England produces only good $x$, Portugal produces only good $y$. This is usually presented as the textbook case.
The 3. equilibrium is like the 1. equilibrium, but here England specializes and produces only good $x$ while Portugal does not specialize and produces both.

So to answer my original questions:
Given that England has a comparative advantage in producing good $x$,

England will always produce good $x$.
England may also produce good $y$.
England will never export good $y$.


How to find Marshallian demand of $u(x,y,z)=x+y^2+2z^2$? Consider the utility function $u(x)=x+y^2+2z^2$. How to derive Marshallian demand for a consumer with these preferences?

Just compare the utilities of these three bundles: $\left(\frac{M}{p_X}, 0, 0\right)$, $\left(0, \frac{M}{p_Y}, 0\right)$ and $\left(0,0, \frac{M}{p_Z}\right)$ and consume the one that yields highest utility.


Is it possible to repay the world debt? If not, why do we care? Let me apologize if my questions sound stupid to experts. I have no training in economics. I am just curious and puzzled. I couldn't find any answer to the questions below.

As far as I have understood, broadly speaking, money is created by central banks and landed to governments with interest and creating debt.

Now, let's take a simple example. Let's imagine a world with 10 countries and 1 central bank. The central bank gives 10B (billions) to each country (100B in total) at a 1% interest rate. At the end of the year, the world owes 101B.

Where is this extra 1B coming from?
Since 1B was never created in the
first place, how can the 1B be paid back?
If it turns out that   the world cannot actually ever pay back the full debt, then why do we care? What is the use of the 1B in debt?

Of course, the countries are in business with each other. During the year some will gain money, some will lose money. The countries that managed to gain that 1% can pay back the interest, but hardly the full debt. In general, for each 1% gained by some country, others must have lost that money.

So it appears to me that with such a design 1) the debt cannot ever be paid back, 2) someone must go bankrupt in the long run and 3) the debt can only grow over time (since it cannot be fully paid back). Is that true or am I missing something?

Just to be clear, I get why we need money. I don’t get why we need debt. Wouldn’t capitalism work as well if central banks could just distribute money around as needed without asking them back?

I don't think this question duplicates  this one. While the linked question does explain the mechanism of money and debt creation, it doesn't shine light on WHY we care about debt, nor whether  it is possible to ever pay back the world debt if it is destined to steadily increase over time.

So there are a couple of things you want to consider:

1st: It is not true that if some country gains 1% some other country must have lost that 1% of economic growth. The economy is not a zero-sum game where the gains of one person are the losses of another one. In fact, usually, it is the opposite. Think about it this way, if the US grows by a lot it also means that they will buy more things from other countries so these countries will probably also grow faster.

2nd: Money is just the means by which we keep track of, and do transactions. At the end, what really matters is how much stuff is produced (goods or services). That is why if some country produces more things, everyone can benefit from it.

I do understand your logic that if the Bank produces 100B of coins how can they expect to get back 101B? Once you think of it in terms of stuff, the puzzle is resolved as follows:

The bank lends you the money so you can buy and plant seeds (these are the 10B), they expect to get back some of the benefits from this productive project after you produce apples (they could directly ask to pay back in apples, but this would be impractical, that's one of the reasons we use money, so instead  they ask you for the 10.1B). Of course, if the bank does not print more money where will the .1B come from? Well, indeed the bank will never ask for 1% interest if they know there is no physical way to actually pay it back.
What really happens is that the bank understands that if an economy is growing, she needs to constantly be printing money, so people can easily do and keep track of all the transactions they do. Therefore, when they ask for the 1% interest, first this is possible, because there is more money out there in the economy, and second, they choose how much interest to charge in order to reflect that they expect you to do something productive with the money (interest also depend, of course, on how risky is your project, and other factors).

I am over-looking the whole issue of inflation to keep things simple and explain the main logic of why banks (including the central bank) charges interests. Whenever you think about whether a debt can be paid or not; the relevant question is not if there is enough money out there to pay it. Rather the relevant question is if the money loaned is being used in a productive way so that it can later pay the interests. And if the answer is no, we care because that means that the money loaned is being wasted, instead.


What, in the most literal sense, are eurodollars? There are readily available "definitions" including on this site, but I want to know what they are in a concrete sense.  Because the definitions make them basically sound like just electronic bank deposits in dollars at a foreign commercial bank, but in a literal sense this seems nonsensical unless those foreign banks (or the central bank in their country) have accounts at the US Fed. After all, to a commercial bank, electronic deposits are just a local accounting fiction, the movement of which gets accounted for at the end of the day by a net transfer of central bank reserves. So are they US treasury securities? or physical cash? or do foreign banks indeed have accounts at the fed?

They actually literary are a deposit accounts of US dollars outside US. Also no those foreign banks will not generally have accounts at Fed. In fact one of the reasons why eurodollar deposits pay higher interest than a dollar deposit in US as they are more risky since they are neither subject to FDIC insurance and those banks will not get liquidity from Fed if there is run on them.

After all, to a commercial bank, electronic deposits are just a local accounting fiction, the movement of which gets accounted for at the end of the day by a net transfer of central bank reserves.

But there is no 1:1 correspondence between amount of dollars in circulation and Fed reserves. You can have a look at Fred data for volume of reserves and money stock $M2$ and you can see that at any point in time money stock is several orders of magnitude larger than volume of reserves.
If you want to know how eurodollars work on conceptual level then have a look at Niehans, & Hewson (1976).
Actually a good primer was also provided by Milton Friedman (1971). Friedman, also includes concrete example.


What do the numbers in the ISO 4217 currency codes mean? The International Organization for Standards (ISO) has a ISO 4217, which delineates currency codes, country codes, etc. for, well, international currency.

Alongside this, each country is given a three-digit numerical code number.  I've been trying to figure out what kind of designation process this has, but it appears to be random.  Why is it oddly (mostly) random?

They appear to somewhat progress alphabetically with new ones added to sometimes newer countries that appeared after the 1973 designations, but not always.  And there are way too many gaps for those countries that may have fallen off the map since then, so to speak.  What is the meaning of the numerical designation for ISO 427 labels on currency?  I find it hard to imagine it is just sloppiness.

From the ISO homepage this answer can be found:

The three-digit numeric code is useful when currency codes need to be understood in countries that do not use Latin scripts and for computerised systems. Where possible the 3 digit numeric code is the same as the numeric country code.
For currencies having minor units, ISO 4217:2015 also shows the relationship between the minor unit and the currency itself (i.e. whether it divides into 100 or 1000).
ISO 4217:2015 also describes historical codes in List three as well as the codes representing certain funds in List two.


Dynamic programming problem with dimension over 1000 I am working on a project which need to solve a dynamic programming problem with dimension over 1000. In past literature, there exist several methods like Smolyak algorithm and Sparse grid method that can solve dynamic programming problem with dimension no more than 100. My question is that does there exist such a brute force method that can solve problem with high dimension efficiently. Or I need to apply some approximation or reduce dimension.

Numerical Dynamic programming is always an approximation when any of the variables are continuous....

Depending on the structure of the problem, some people claim that you can apply linear programming techniques to approximate a solution. These guys MIT paper, claim that they have experiments that show that their linear reprogramming approximation is good enough.


Flexible lab experiment in otree I am building a lab experiment through otree, ``a Django-based framework for implementing multiplayer decision strategy games."

Basics about otree's forms

Here is an example of how otree gets the players to report their choices (based on the "matching_pennies" game which is part of the templates provided by otree).

In a file named model.py, one finds the following code

class Player(otree.models.BasePlayer):

[...]

penny_side = models.CharField(choices=['Heads', 'Tails'])

[...]

Then in views.py one finds

class Choice(Page):

form_model = models.Player
form_fields = ['penny_side']

Finally, the form is displayed to the end user through choice.html by inserting

{% formfield player.penny_side with label="I choose:" %}

What I would like to do

is create a flexible experiment in which the number of choices that players have to make varies with a parameter x. That is, I want the whole framework to generate x possible choices by just setting a parameter x, and not having to go update all the files manually. This is in order to make my life easier if we ever change the experimental design, and to make the code useful to others with different experimental design (I plan to release it on Github at some point).

It seems like it should be fairly easy to do with a couple of loops, but I am having trouble using lists given the way otree is structured.

From what I understand,  I only see one very nasty way to have the number of choices depend on a parameter x. I first give each choice a different name in model.py, e.g.

class Player(otree.models.BasePlayer):

[...]

for i in range(x):
        exec("""choice%d = models.IntegerField(
        choices= ['Heads','Tails'])""" %i)

[...]

then pass the name of all those choices along to view.py, e.g.

class Choice(Page):

all_forms = list()
for i in range(x):
    all_forms.append('choice%d' %i)

form_model = models.Player
form_fields = all_forms

and finally, find a way to loop through all the forms in Choice.html; something like (I know the code below does not work, just to give the gist of it)

{% for p in range(x)  %}

{% formfield player.choice{{p}} with label="I choose:" %}

{% endfor %}

My question are:

This is all very dirty, and looks overly complicated : lists have been invented to avoid this kind of crazy naming process. Do you see a way to make this work with lists instead?
If that's the only way to hack into otree and have the number off choices depend on a parameter x, so be it. But I am still unable to figure out a way to generate the desired set of forms via a loop in Django (obviously the example above does not work, for many reasons.).

I found an answer to the second part of the question here https://github.com/oTree-org/otree-docs/issues/2.

It turns out that in oTree,  the variable form which is passed to the template is iterable. Thus one the following code does the job:

{% for field in form %}
        {% formfield field %}
    {% endfor %}

Regarding the first part of the question, I contacted a programmer working at oTree. He confirmed that, in its current version, oTree can only define a fixed number of field. He advised to define in model.py a large maximal number of fields and then use get_form_fields in views.py to dynamically return a list with desired subset of fields.

Notice that if you want to create a really large maximal number of fields, the trick presented in the question using loop and exec remains — I believe — the easiest way to proceed.


Sequential Game is Extensive form game? Dynamic, Sequential, Stochastic, Extensive form and Evolutionary games.

I know what all of them mean very roughly.

I want to clarify them.

As I understand Extensive form is a description of a game, not the type of a game. But Some use Extensive form game as a type of game.
So, is Extensive form game sequential game?

Can anybody clarify the definitions of all these terms and relationships/differences?

First of all, you can differentiate between static (essentially all players move simultaneously and only once) and dynamic (essentially non-static) games.

An extensive-form game is essentially a game tree. This form of presentation makes sense when looking at games where players move sequentially. However, you could also represent a simultaneous-move game in a game tree. It just doesn't add any insights over the normal form (matrix).

Game trees are a great tool to present dynamic games such as standard sequential-move games with perfect and complete information (player 1 moves first, player 2 observes the move and reacts, and so on), and they can also be used to present games of incomplete information or games of imperfect information.

Repeated games are dynamic games in which the same static stage game is repeated multiple times. Such games are dynamic but usually not represented in extensive-game form. If the stage game is not always exactly the same, but instead the game to be played in each period depends on a state, we speak of a stochastic game. How the state transitions from one state to the other can depend on the actions played before (and pure chance). Strictly speaking, A repeated game is a stochastic game with only a single state.

I have never heard the term "evolutionary game" without "theory" following. I am not sure if there is a definition of "evolutionary games". However, I see evolutionary game theory as a subfield of game theory that deals with certain forms of dynamic games and also different underlying assumptions. In particular, there is often no "common knowledge of rationality" and often players find their "optimal" strategy by trial and error without really knowing what they are doing.


What is the point of the indirect utility function? Where does this have application? I understand how the demand function may be arrived at using the utility maximization problem but I don't understand where the indirect utility function is used and I think the two are somewhat related... Please excuse me if this is a very fundamental question. I have only started Intermediate Microeconomics.

Recall that if $x$ and $y$ are consumption bundles, $u(x)$ is the consumer's utility function, and $u(x)>u(y)$ means the consumer strictly prefers bundle $x$ to bundle $y$.

The indirect utility function $v(p,w)$ is the highest value of the utility function when $u$ is evaluated over all affordable bundles given $(p,w)$. In other words, $v(p,w)=max u(x)$ subject to $p\cdot x \le w$.

So the indirect utility function tells you the consumers preferences over price-wealth pairs: $v(p,w)>v(p',w')$ means the consumer gets to consume a strictly better bundle when prices are $p$ and wealth is $w$ than any other affordable bundle when prices and wealth are $p'$ and $w'$.


Why people respond to surveys like that of Purchasing Managers' Index? A lot of data, including indexes, rely on surveys. For example, Purchasing Managers' Index.

(1) Why people answer these surveys (is there any benefit)?

(2) How to make sure the data is correct? What if people randomly fill in the survey, or intentionally give incorrect data?

For your first question:

Some have noted that surveys make people feel like they are a part of something bigger than themselves and that their opinion matters.

According to Ed Halteman (survey expert) two reasons why people participate in surveys, ,  are that they feel their participation will affect something they care about, and they want to share their opinion with someone who will listen and act on the information.

For your second question:

Once the surveys(or census) are collected there are two stages that typically takes place to ensure that the data products are of high quality.  They are data processing and statistical adjustments.

In data processing, a survey statistician or analysts,   use codes to capture data from their raw state to an edited data file that can be used within the survey organization for quality assessment in preparation for statistical adjustment and dissemination.

They use coding to classify survey responses into categories with associated numeric values. They also decide how coding and data capture will be conducted and monitored. A survey statistician or analysts will edit the data to check for errors throughout the survey lifecycle.

Statistical adjustments:  Consideration will be made for missing data or data values that are obviously wrong using single or multiple imputation methods.

Analysts will use codes to calculate outcome rates based on available data according to the agencies methodology(s).  They will also develop survey weights for each interviewed element on the sampling frame.

Throughout the above processes, documentation is done during both data processing and statistical adjustment steps.


Preference for consumption smoothing and actual smoothing The typical dynamic consumption-saving under certainty model can be written as:

$$
\max V(c)=\sum_{t=1}^{T} \beta^{t-1}\; u(c_t)
$$
Subject to the intertemporal budget constraint
$$
\sum_{t=1}^{T}\frac{y_t}{1+r}=\sum_{t=1}^{T}\frac{c_t}{1+r}
$$

Where $T\leq \infty$ (finite or infinite horizon), $\beta \in (0,1)$ is the subjective discount factor, $y_t$ is the individual's income and $c_t$ is the individual's consumption in every time period. Finally, $u(\cdot)$ is the agent's subutility function, with $u^{\prime}>0$ whose concavity is usually related to the agent's preference for consumption smoothing. The argument is equivalent to the one justifying that an individual will reveal risk aversion iff his utility function over wealth is strictly concave.
The argument that leads to consumption smoothing is the following:
The first order condition for the problem is the well known Euler equation

$$
\frac{u^{\prime}(c_t)}{u^{\prime}(c_{t+1})}=\beta \; (1+r)
$$
It is assumed that $\beta^{-1}=(1+r)$ so that
$$
u^{\prime}(c_t)=u^{\prime}(c_{t+1}) \quad \Rightarrow \text{by strict concavity of} \; u \quad c_t=c_{t+1}
$$

I have two questions regarding this argument which are somehow related:

The result of consumption smoothing seems to be independent of the preference for such smoothing: one needs the condition $\beta =(1+r)$ to hold in orther to obtain the result.
It seems to me that the implication
$$
u^{\prime}(c_t)=u^{\prime}(c_{t+1}) \quad \Rightarrow c_t=c_{t+1}
$$

Would still hold for a strictly convex utility function, as one needs a much general condition to the implication to hold, namely that the derivatives of the utility function will be unique for any increasing utility function.. it seems to be that the uniqueness of $u^{\prime}$ (i.e $u^{\prime}(a)=u^{\prime}(b) \quad \Rightarrow a=b$) will hold irrespective of the sign of $u^{\prime \prime}$ provided it is not equal to zero.

If my thinking is correct this would imply that the desire for smoothing doesn't play any role on what the individual does at the end, as this possibility is open only when $\beta =(1+r)$ holds, and furthermore, it would be optimal to smooth out consumption even to an agent with a strictly convex utility function.

The argument relayed in the question as regards consumption smoothing is flawed. Consumption smoothing does not mean consumption equality over periods, but rather, tendency to avoid corner solutions, or near-corner solutions. So it has nothing to do with whether, in the context of this family of models, $\beta (1+r) =1$ or not (after all, in a more comprehensive model, this condition is the long-run equilibrium one, and it does not hold for the transition towards equilibrium).

Consumption smoothing in the intertemporal setting has similarities with "variety in consumption" in a static setting with more than one goods: there, with a concave utility function, we get convex indifference curves and so interior solutions, i.e. a solution where the consumer consumes a mix of goods available, not just one, or very few of them, given the linear budget constraint

As general equilibrium theorists point out, timing of consumption can be seen as just one more feature of a good, and so, when the same good has a different "consumption time stamp", it is a different good after all.

So, in the basic two-period setting, we have a bivariate intertemporal utility function

$$U(c_1, c_2) = u(c_1) +\beta u(c_2)$$

To examine its indifference curves we fix the value of the function at $\bar U$ and we examine the second derivative of $c_2$ with respect to $c_1$:

$$c_2 = u^{-1}\left (\frac 1 {\beta} \cdot \big[\bar U - u(c_1)\big]\right)$$

$$\implies \frac {\text{d} c_2}{\text{d} c_1} = \frac 1 {\beta} \frac {-u'(c_1)}{u'\left (\frac 1 {\beta} \cdot \big[\bar U - u(c_1)\big]\right)}$$

and

$$\frac {\text{d}^2 c_2}{\text{d} c^2_1} = \frac 1 {\beta}\frac{-u''(c_1)\cdot u'\left (\frac 1 {\beta}  \big[\bar U - u(c_1)\big]\right) - (1/\beta)u''\left (\frac 1 {\beta} \big[\bar U - u(c_1)\big]\right)\cdot [u'(c_1)]^2}{\left[u'\left (\frac 1 {\beta} \cdot \big[\bar U - u(c_1)\big]\right)\right]^2}$$

For the indifference curve to be convex we need this derivative to be positive, and so we need the second derivative of the period-utility function $u$ to be negative, $u''()<0$.

Then with a linear budget constraint with negative slope (say for exogenous endowments per period),

$$c_2 = y_2 +(1+r) (y_1-c_1) = \big[y_2+(1+r)y_1\big] - (1+r)c_1$$

we can get the familiar graphical solution of interior tangency at the optimum, which excludes corner solutions we would have obtained if the indifference curve between present and future was concave (and so the period-utility function was convex).

So it is all about the utility function and has nothing to do with the Euler equation taking a specific value.


What does it mean "non-Walrasian" or "quasi-Walrasian"? In a recent NBER workshop, Robert Hall started a discussion with his first slide summarizing the macro literature.

I am not very familiar with either DMP model or New Keynesian model and have no idea about any of his statements in this slide. Can anyone explain them without going to the very detail of the models?

Well non-Walrasian is an model that is not Walrasian so to explain that we should explain what  a Walrasian model is. Generally speaking in macro context when we talk about a Walrasian model it is a Walrasian general equilibrium model.
A Walrasian general equilibrium has the following characteristics see MWG pp 579:

Definition 17.B.1: Given a private ownership economy specified by
$$ \{(X_i, \succeq_i) \}^I_{j=1}, \{Y_j \}^J_{j=1},\{(\omega_i, \theta_{i1}, ... , \theta_{iJ})\}^I_{i=1}$$
an allocation $(x^*,y^*)$ and a price vector $p=(p_1, ..., p_L)$ constitute a Walrasian (or competitive, or market, or price -taking) equilibrium if:
(i) For every $j,y^*_j \in Y_j$ maximizes profits in $Y_j$ that is, $p\cdot y_j\leq py^*_j$ for all $y_j \in Y_j$
(ii) For every $i,x^*_i \in X_i$ is maximal for $\succeq_i$ in the budget set $\{ x_i \in X_i:p \cdot x_i \leq p \cot \omega_i + \sum_j \theta_{ij} p \cdot y_j^*\}$
(iii) $\sum_i x_i^* = \sum_i \omega_i + \sum_j y^*_j$

Slightly different definition holds for pure exchange economy, but for more detail you can have a look at the rest of the chapter in MWG. The gist of what is a Walrasian general equilibrium (and thus if model is Walrasian) is given by the authors in the brackets, it is a model characterized by competitive, or market, or price-taking equilibrium. A non-Walrasian model would be some general model that is not characterized by such equilibrium.
Following Calvo (1978)  quasi-Walrasian model is (emphasis mine):

These [quasi Walrasian models] are models
where agents perceive themselves as infinitesimal micro units, unable to exercise any kind
of "market power"; the agents set the variables under their control in order to maximize
their objective functions (utility, profit, etc.).
In contrast to the so-called "disequilibrium"
or "fix-price" models (see Allan Drazen)
there is no exogenous rationing or price
inflexibilities. However, they differ from standard Walrasian models (for example, see
Kenneth Arrow and Frank Hahn, chs. 1-5) in
that agents are not necessarily price takers
and, typically, markets are incomplete

The explanation above is pretty much self explanatory.
Lastly, New Keynesian general equilibrium models are quasi-Walrasian precisely because they allow for market power (in fact that is what in some NK models creates price rigidities/stickiness), or incomplete markets and so on. You can see nice overview of NK models in Woodford Interest & Prices, you will see that virtually all of them have some twist where there is market power, or similar market imperfection.


Research question formation I am in the process of starting a research paper (for those in the IB Board, this is the Extended Essay) and I had previously formed my research question like this:

To what extent will factor x impact the economic growth and development of country y.

But then I thought I should narrow it down more so I made it:

To what extent will factor x impact the economic growth and development of city y.

I want to know if it's valid to talk about the economic growth and development of a city instead of a country. I have this confusion because I have never read the analysis of the economic growth and development of a city.

I mean development on a city basis is usually considered, but will looking at these macro concepts (growth and development) be viable for an economics research paper?

If yes, when I talk about growth, do I talk about the increase in AD/GDP or the increase in government revenue for city y etc?

I want to know if it's valid to talk about the economic growth and development of a city instead of a country

In principle there is nothing wrong with narrowing your research question down to municipal level. There are studies that look at economic growth on urban level. Here is just an example that came out of quick google scholar search:

Ding, Chengri, and Erik Lichtenberg. "Land and urban economic growth in China." Journal of Regional Science 51.2 (2011): 299-317.

However, it is not possible to give more specific answer without knowing what $x$ is. There is no guarantee that something that determines growth of an economy as a whole will be also important determinant at municipal level and vice versa.

  If yes, when I talk about growth, do I talk about the increase in AD/GDP or the increase in government revenue for city y etc?

Ideally you would look at growth of metropolitan GDP. In some countries it is possible to get Urban/Metropolitan level GDP data. Here is an example of such data set from US Bureau of Economic Analysis. However, not all countries provide metropolitan level GDP so you might have to use some proxy, like average incomes or nighttime light is often used as a proxy for economic activity (see for example this paper). The list of possible proxies is not exclusive, what will make the most sense will depend on specifics of your research.


Is money supply affected by the stock market? Do stock prices have any effect on the money supply of an economy? Please provide a simple example if possible.

Intuition suggests there is more money around when prices are high (consider for instance the dotcom boom). I guess the answer may be dependent on what definition of money supply one uses (M0-M4).

They may, but probably not much. Because stocks cannot be used as a substitute for money in most transactions there is no direct channel. However, because stocks can act as collateral for loans, and loans have the capacity to create money through the money multiplier mechanism they can have some effect, just as anything that relaxes borrowing constraints could increase the money supply.

Collateralized loans make up the vast majority of bank debt. Suppose, for example, that banks only made collateralized loans. Then when stock prices go up, some borrowers formerly at the limits of borrowing constraints due to limited collateral, would be able to take out additional loans. These loan proceeds could then be deposited in banks or spent, either way likely ending up in banks eventually where, through the mechanism of fractional reserve banking, they could be used to create additional money. However, as you can see in the figures below, margin debt is a very low fraction of GDP in contrast to say household overall debt. So in general this is not going to be a big channel.

Source: Ominous Sign as Margin Debt Continues to Rise

Source: Wikipedia Subprime mortgage crisis page


Symmetric mixed-strategy equilibrium: Entering markets [Solved] Question: Suppose three identical, risk-neutral firms must decide simultaneously and irreversibly whether to enter a new market which can accommodate only two of them. If all three firms enter, all get payoff 0; otherwise, entrants get 9 and firms that stay out get 8.

My attempt: Arbitrarily choosing firm A, firm A is deciding whether to enter the market or not. Hence, the Nash equilibrium occurs when $\text{payoff of not entering = entering}$. Let $p$ be the probability of each firm entering the market. Then
$$\text{not entering = P(only firm who enters) + P(second firm to enter) + P(third firm to enter)}\\
8=9(p)(1-p)^2+9(p^2)(1-p)+0(p^3)\\
8=9(p-p^2)
$$

and I get a complex number as the answer. The correct equation should be $8=9(1-p^2)$, but I'm not sure how to get that.

Any help is greatly appreciated!

Edit: Solved it an hour later. I was being silly. I'm leaving my partial answer below for anyone who is curious.

I solved it, haha. Turns out I was being silly. I had completely neglected the fact that this was a 3-player game, and $\text{not entering}$ still had probability values attached to it. Let $A$, $B$, and $C$ be the three firms. So the game looks like this:
$$
\text{P(A enter;B,C enter)+P(A enter;only B enter)+P(A enter;only C enter)+}\\
\text{P(A enter;neither enters) = P(A dne;B,C enter)+P(A dne;only B enter)+}\\
\text{P(A dne;only C enter)+P(A dne;neither enters)}
$$
It's a giant mess of $p$'s and $(1-p)$'s, but at the end of the day, the final version $8=9(1-p^2)$ is derived.


Does the Marginal Propensity to Import = negative Marginal Propensity to Tax? the multiplier $= \frac{1}{(1-MPC)}$

and

the multiplier $= \frac{1}{MPW} = \frac{1}{MPS+MPM+MPT}$.

Now since $MPC + MPS = 1$ it follow that $1-MPC = MPS$,

therefore the multiplier = $\frac{1}{(MPS+MPM+MPT)} = \frac{1}{MPS}$

and so $MPS = MPS + MPM + MPT$

from this, we can see that $MPM = -MPT$

Therefore, Marginal Propensity to Import = negative Marginal Propensity to Tax

I am unable to see what the flaw in the logic is or if there is something I am missing. Any explanation or help would be great.

Hint. Is it always the case that MPC + MPS = 1?  Or does this hold only in a certain type of model with assumptions that simplify from reality?