Two variables: Which moves first? Say I have a time series of two variables, $X$ and $Y$, and want to find out which one of these two moves first. One example is the one of GDP growth and investment growth, where we usually tell the story that at a business cycle frequency, investment moves "earlier" than production or consumption.

I dont want to do eyeballing econometrics ("this thingy here clearly moved first"). What is the standard way of dealing with these things in the literature? What methodology can be used? Answers that allow for more than two variables are very welcome.

"Who moves first" can be conveniently detached from any causal inference, since there may be some third variable influencing both. Certainly one could build a logical and reasonable argument that links increases in investment to increases in GDP (or vice versa), but it is not necessary.

Then, examining cross-correlation coefficients on the levels or on an appropriate transformation (like first differences, or first log-differences) is a simple and valid way to examine the issue, as long as the chosen transformation will provide stationary series.

Specifically, one can examine (sample) ${\rm Corr} (X_t, Y_{t})$, ${\rm Corr} (X_t, Y_{t-k})$ and ${\rm Corr} (X_{t}, Y_{t+k})$, where, again, $X$ and $Y$ can represent the chosen transformation and not necessarily the levels of the variables. Also, what calendar time length will $t$ represent should also be decided according to the phenomenon under study. In turn, the distance represented by $k$ is a matter of experimentation, but it is advisable to start with $k=1$.

If there is a temporal order, then the contemporaneous cross-correlation ${\rm Corr} (X_t, Y_{t})$ should be negligible. Then, the magnitude and sign of the other two cross-correlations should provide statistical evidence as to "who moves first".


Difference between Nash equilibrium and Pareto Efficiency Nash Equilibrium is defined as a solution concept referring to a best outcome which players won't want to unilaterally deviate given the response of other players doesn't change. To me it seems like Nash equilibrium demands that there is no individual blocking (ie it is indivtually acceptable). So, in sense, it talks about individual level welfare.

While Pareto efficiency is an outcome where one or all cannot be made better off without harming someone. To me, Pareto condition is demanding two things - outcome should not be individually blocked (ie they are better off or at par with their endowments at this pareto outcome) and neither should it be jointly blocked ie it should be acceptable to all. So, in sense it talks about societal welfare.

My problem is Wikipedia page refers to Nash equilibrium as a broader concept. In what sense is Nash equilibrium broader?

I wouldn't say Nash equilibrium is broader than Pareto-efficiency I'd say its different. As all know the sole Nash equilibrium in the Prisoner's dilemma is not Pareto-efficient and the three Pareto-efficient outcomes are not Nash equilibria. That is to say there is no intersection between the two terms and hence none can encompass the other.

I think the main difference comes from the fact that Pareto-efficiency is only concerned with outcomes and not with the mechanisms of strategic interaction. The Nash equilibrium takes this mechanisms into account explicitly. I.e. you cannot obtain a Pareto-efficient outcome in the Prisoner's dilemma as the other player will preempt it.

My advice is: don't read about Game theory on Wikipedia! The first homework in the master's course on GT at my faculty is to find an error in a Wikipedia article on GT and correct it.


Why currency purchasing power is linked to confidence in central banks From the New Statesman, http://www.newstatesman.com/politics/economy/2016/02/coming-storm,

  "Ever since the collapse of the Bretton Woods system of pegged exchange rates in 1971, the sole guarantee that currencies will maintain their purchasing power, both domestically and abroad, has been confidence in central banks’ discretionary policies. A loss of faith in the consensus model of monetary policy would pitch us into the anchorless world that the architects of the Bretton Woods system always feared."

I cannot understand the reasoning behind why confidence in central banks' discretionary policies would help currencies maintain their purchasing power.

Moreover, what would be the possible consequences of markets losing their faith in modern central banking?

TL;DR Version:
The trust that money has value gives it its value. If money can be exchanged for gold, then this makes people trust that it will have value. If this is not the case (and it is not, although it used to be the case almost everywhere) then the only thing that can make people trust that money will not lose its value through extreme printing of money is having trustworthy people endowed with the power to print money. These people are called central bankers, hence their credibility matters here. The consequences of losing faith would be (hyper-)inflation.

Long Version:

First a few definitions. The purchasing power of money is basically its value. That is how many goods/services (e.g. bread) you can get for a dollar. Inflation is a price increase, which means that a dollar can now buy less things (as they cost more). Hence money loses its purchasing power when inflation occurs.

Further, the value of money is basically determined just like the value of anything else - supply and demand. So if you print a lot of money (supply increases) its value will go down. That's the reason the government doesn't just print a bunch of dollars and give them to everyone, because that money would lose value, i.e. it would lead to inflation (rising prices).

The reason that money has any value at all in the first place (today) is because people believe it has value. Also, people believe it has value, because it does. They observe that they can use it to obtain goods and services. That's pretty much the only thing distinguishing the dollar from monopoly money today. As is apparent from the reason money has value it is easy to get into vicious cycles. If people stop believing it has value then it won't, which will lead to more people believing it doesn't and so on.

This is why hyperinflation is so hard to stop. Once money loses a lot of its value the trust people have in this money is undermined. They panic and think it won't be worth anything soon. So they try to get rid of it by exchanging it for other things. As everyone tries to exchange money for other things, effectively the supply of money (really the velocity of money) increases, which undermines its value even more. Since everyone wants to get rid of money in this scenario, there is no one to give it to in order to trade with so it becomes worthless (as no one wants it). A german central banker once said that inflation is like toothpaste: once you get it out of the tube it's very hard to get back in again. The problem is, that governments have an incentive to print more money, to pay off debts and have more spending power, etc., which creates inflation.

So there are multiple equilibria possible, where all people (or a critical mass) believe in money and since all do there is no reason not to believe in it. Or nobody does and in this case there is no reason to in fact believe in money. It's also possible for many to believe in it and many not to (e.g. 50-50 or 60-40), but this is not a very stable equilibrium. For more on how money comes into existence at all, see the paper by Kiyotaki and Wright ("Money as a medium of exchange" and "A Search-Theoretic Approach to Monetary Economics" american economic review 1993) , who discuss these equilibria possibilites. There, basically money emerges, because barter (trading goods for other goods) is so inefficient as it requires a rarely occuring double-coincidence of wants. So if money is undermined, probably something else will emerge. E.g. in Germany after a crash people used cigarettes as currency.

Now it wasn't always the case that money only had value, because others believed it. On top of that, governments had what was called the "gold-standard". This meant that at any time, money could be exchanged for a certain amount of gold. Because of this, governments were restricted in how much money they could print, by how much gold they had in reserve. So this was meant to stopp excessive printing of money and to stop inflation panicks. This however came at a cost, because monetary policy could barely be used and it required governments around the world to frantically search for gold. Nowadays, we don't have the gold standard, so governments are free to do what they want. However, they don't abuse their power, which is evidenced by low inflation rates in the last 30 years and without the drawbacks of the gold standard.

If the central bank is not credible and the government does not guarantee to exchange money for gold, basically there is nothing to "anchor" the value of money. So if people expect the central bank to print too much money, then money will lose its value.

One last possibility through which the mistrust of the central bank is important here is because of wage-setting. When negotiating wages, unions take into account rising prices (inflation) so that they don't become poorer through price increases, which is why they demand higher wages. If they expect a lot of inflation to occur in the course of the year, they will demand high wages right now (as these contracts cannot be renegotiated every month). However the rising wages will lead to higher prices, which in fact is inflation and this spiral could get out of control. With a credible central bank, this won't happen of course, as the expectations aren't so wild.


Is there another name for marginal luxury? My coworkers and I were talking about the concept of voluntarily paying more than you need to for something. As an example, I can buy a locally grown organic apple from the farmers market for \$3 or a conventional one from the grocery store for \$0.50. We can say that the \$0.50 apple is a basic level of consumption- society agrees that I deserve that apple as a human right (or, we can expand the argument to a basic level of consumption including shelter, food, etc). Since I paid \$3 instead of \$0.50, I paid an extra $2.50 for the luxury if it being a special kind of apple I prefer.

We called this amount "marginal luxury". Does economics have a proper name for it? Is there a reliable source of how much of an economy, say the US, is marginal luxury?

The closest I can think of is Stone-Geary utility/preferences, where consumption is assumed to provide utility only above a specific level (the $\gamma_i$ parameter in the link), which is usually designated as the "subsistence level".

As for how much an economy is above this subsistence threshold, a way to roughly assess this is to calculate what would Total Income be if all people were at the poverty-line-income (each country determines its own poverty line). Then subtract this from the actual Total Income. What is left can be thought of as what the OP is looking for.

But calling it "luxury", implies that any consumption above the level guaranteeing mere survival is a luxury. Is it?


Convex rationalization when the budget sets are segments? Backgroud:
SARP can be defined on general budget set.

SARP: Assume for all $B$ the choice $c(B)$ is only one element. If $x_i,x_{i+1}\in B_i$, and $x_i = c(B_i)$, for all $i\in \{1,N-1\}$, then $x_1=c(B_1)\notin B_N$.

I learnt that, if the budget is this: $B_i=\{x\mid p_ix\leq p_ix_i\}$, then, SARP implies that the finite data is rationalized by convex preferece.
Motivation: most real life problems have more complicated budgets. For example, if the agent is allocating her money between risky security and riskless cash, then her budget will be a segment rather than a triangle.
My question: Let $y^i$ and $z^i$ be two points, and $\overline{ y^iz^i}$ is the segment connecting $y^i$ and $z^i$.
Let $B^i=\overline{ y^iz^i}$ be the segment budget set.
Let the data be $(x^i,B^i)^{i\in\{1,2,...,n\}}$ where $n$ is a natural number.
Can we still have a convex rationalization of the data?
That is, we are trying to find an Axiom, similar to SARP, such that the following two conditions are equivalent:

The data satisfies the Axiom,
The data is rationalized by a convex preference.

If we could also get monotonicity, then it will be better. The focus is on convexity of preference.
My try: I've gone through the paper "Revealed preference analysis for convex
rationalizations on nonlinear budget sets". However, this paper requires that budget set $B$ is monotone, and a segment budget set is not monotone.
Any comments, long or short, will help. Any related reference will help, too. Thanks in advance.

Take a dataset $D = (B^t, x^t)_{t \in T}$ such that for all $t$, $x^t \in B^t$. I'll say that $D$ is rationalisable by the utility function $u$ if for all $t$ and all $x \in B$: $u(x^t) \ge u(x)$.
If you only impose convexity on $u$, then any dataset $D$ is rationalisable by the constant (convex) utility function $u(x) = k$. So this has not testable implications.
Assume now that you impose strict monotonicity on $u$ in the sense that $x > y$ implies $u(x) > u(y)$.
Consider a budget set $\overline{y^t z^t}$ and take the comprehensive hull:
$$
CH(\overline{y^t z^t}) = \left\{x \in \mathbb{R}^n: x \le w \text{ for some } w \in \overline{y^t z^t}\right\}.
$$
Then we can show that the dataset $D = (\overline{y^t z^t}, x^t)_{t \in T}$ is rationalisable by a montone utility function $u$ if and only if the dataset $D' = (CH(\overline{y^t z^t}), x^t)_{t \in T}$ is rationalisable by the same monontone utility function $u$.

For the proof: $(\to)$ Let $D$ be rationalisable by the montone function $u$. We want to show that for all $t$ and all $x \in CH(\overline{y^t z^t})$ we have $u(x^t) \ge u(x)$. Indeed, if $x \in CH(\overline{y^t z^t})$, we know that $x \le w$ for some $w \in \overline{y^t z^t}$. As such:
$$
u(x) \le u(w) \le u(x^t),
$$
where the first inequality comes from the monotonicity conditionon $u$ and the last one from rationalisability of D.

$(\leftarrow)$ Let $D'$ be rationalisable by $u$. Let us first show that for all $t$, $x^t \in \overline{y^t z^t}$. If not, then as $x^t \in CH(\overline{y^t z^t})$ there must exist a $w \in \overline{y^t z^t}$ such that $x^t < w$; Then, by monotonicity of $u$ and rationalisability of $D'$:
$$
u(x^t) < u(w) \le u(x^t),
$$
a contradiction. Now for any $z \in \overline{y^t z^t}$ it then follows from rationalisability of $D'$ that $u(z) \le u(x^t)$, so $D$ is also rationalisable by $u$.

This shows the following equivalence:

The dataset $D = (\overline{y^t, z^t}, x^t)_{t \in T}$ is rationalisable by a convex and montone utility function $u$.
The dataset $D = (CH(\overline{y^t, z^t}), x^t)_{t \in T}$ is rationalisable by a convex and monotone utility function $u$.

As the sets $CH(\overline{y^t z^t})$ are comprehensive, the revealed preference conditions for answering the condition 2) can be found in the JET paper that you refer to (Revealed preference analysis for convex rationalizations on nonlinear budget sets)


Fixed effects, first differences interpretation I am working with a fixed effects model to estimate the effect of enterprise zones on unemployment claims.

(1)  $log(uclms_{it}) = \theta_t + \beta_1 ez_{it} + c_i + \epsilon_{it} $ where $\theta_t$ are time specific effects and $c_i$ are city specific effects.

Another model is estimated that allows each city to have its own time trend:
$log(uclms_{it}) = \gamma_i t + \beta_1 ez_{it} + c_i + \epsilon_{it} $ and this model is then first-differenced to obtain

(3)  $\Delta log(uclms_{it}) = \gamma_i + \beta_1 \Delta ez_{it} + \Delta \epsilon_{it} $

I was asked to estimate (1) and (3) by fixed effects and comment on possible reasons for differences in the estimate of $\beta_1$

The estimates I got were;
from model (1) $\beta_1 = -0.1044$ with a t-ratio of -1.43 and p-value of 0.166.
from model (3) $\beta_1 = -0.252$ with a t-ratio of -2.41 and a p-value of 0.025.

So the estimate is relatively small in model (1) compared to model (3) and is insignificant in model (1), but significant in model (3) at the 5% level.

Am I right in thinking that, when (1) is estimated by FE, the city specific effects drop out, but the time specific effects remain. Whereas in (3) we only have city specific effects which drop out when estimated by FE. So the observed differences in $\beta_1$ arise because (1) includes time effects, but (3) does not. I'm also a bit confused about using first-differenced data in a fixed-effects model. Why would that be useful?

The biggest difference between (1) and (3) is that (3) has incidental linear trends while (1) has common time effects. Differencing (1) gives

(1a) $\Delta \log(uclms_{it}) = (\theta_t - \theta_{t-1}) + \beta_1 \Delta ez_{it} + \Delta \epsilon_{it}$.

Comparing this to (3) you see that (3) has $\gamma_i$ in place of $\theta_t - \theta_{t-1}$ in (1a). So three things are different: (A) As you said, it is FE vs FD; (B) the trend is free (using dummies) in (1), while linear in (3); (C) the trend is common in (1) but is individual-specific in (3).

It would be interesting how much difference is introduced by each of these three points.

About why FD is useful, well it is simple and informs us about functional relationship among variables in differences. So I'd say why not.


Properties of preference relation Let $\succeq$ be a preference relation on $X$. Is it true that $x \succeq y$ if and only if $\lnot (y \succ x)$?

I think it is true and my proof is as follows. To prove $\implies$ direction, we have $\lnot (y \succ x) \equiv \lnot(y \succeq x)$ or $x \succeq y$. So clearly if we assume $x \succeq y$, then $\lnot (y \succ x)$ is true. To prove $\impliedby$ direction, assume $\lnot (y \succ x)$ is true. Then either $\lnot(y \succeq x)$ or $x \succeq y$. If $x \succeq y$ then we are done. If $\lnot(y \succeq x)$, then since $\succeq$ is a preference relation it must be complete, which implies $x \succeq y$.

Is my proof correct? Also, in general, I just want to ask, is it true that whenever we have a preference relation $\succeq$, instead of proving all these facts, can we "informally" pretend $\succeq$ is like the inequality $\ge$, and everything works analougously? For example, we could prove that $\lnot (x \sim y)$ if and only if $x \succ y$ or $y \succ x$, but if we just wanted to use deduce this fact without actually proving it, we can clearly see it from $\lnot(x=y)$ if and only if $x>y$ or $y>x$.

If we define $\succeq$ on $X$ as the primitive, then the strict preference relation is derived as
$$ x\succ y ~\Leftrightarrow~ x\succeq y ~\text{ but not }~ y\succeq x.$$

Note that you can view this as a definition of $\succ$. Now we prove $y\succeq x$ iff not $x\succ y$:

$(\Rightarrow)$ If $y\succeq x$, by definition, $x\succ y$ is not true;

$(\Leftarrow)$ If not $x\succ y$, then there are only three possibilities: (i) $ x\succeq y$ and $y\succeq x$; (ii) not $x\succeq y$ but $y\succeq x$; and (iii) neither $x\succeq y$ nor $y\succeq x$. Case (iii) can be ruled out if we assume completeness of $\succeq$. Therefore, in both (i) and (ii), we have $y\succeq x$.

It's worth mentioning that Kreps (1990) introduces another approach to define preference relations on $X$. He takes $\succ$ as the primitive and then derives the weak preference relation as:
$$x\succeq y ~\Leftrightarrow~ \text{not }~ y\succ x.$$

In this case, there is no need to prove the equivalence since it is a definition.


What is the example of inaccurate impact due to endogeneity? When learning about endogenous variable, I found an answer in a topic on StackExchange very direct:

An Exogenous Variable is defined as a variable which is unaffected by
other variables within an model.
take a multivariable regression model as an example:
$y=\beta_0+\beta_1x_1+\beta_2x_2+u$
$x_1$ is called an exogenous variable when its determination is
unaffected by $x_2$ and error term $u$.
An Endogenous Variable is defined when $x_1$ is influneced by $x_2$ or
$u$.
This is important because when we run a regression we are producing a
function which assumes a dependent and independent variable. If we
find endogeneity we wont get accurate estimates for the effect of
$x_1$ on $y$.

Why in endogeneity case, we wont get accurate estimates for the effect of $x_1$ on $y$ . Is there any sample for that statement? In reality, I faced this problem that when I add some regressors to a regression equation, one of variable coefficient changed the magnitude or even flip the sign. But I want to know the reason behind.
One theoretical explanation is: $x_1$ is correlated with $u$ or $x_2$, producing a bias in $beta_1$ that depends on the direction and magnitude of the correlation

Endogeneity can arise from several reasons and in each case the explanation will be slightly different. I won't show full review of all possible reasons but just two important examples:
Simultaneity
For example, following Verbeek a guide to modern econometrics pp 146, suppose that true model is given by system of equations:
$$y = \beta_1 + \beta_2 x_{2t}  + \epsilon_t \tag{1} $$
$$x_{2t} = y_t + z_{2t} \tag{2}$$
where $z$ will be exogenous $(cov(z,\epsilon)  = 0)$  but clearly $x$ is endogenous. We can see from the equations above that if $x$ increases not only does $y$ increase but $x$ increases again through effect of $y$ on $x$ given by $2$ which then again increases $x$.
Solving the 1 and 2 for $x$ and $y$ respectively we get:
$$ x_{2t} = \frac{\beta_1}{1-\beta_2} + \frac{1}{1-\beta_2} z_{2t} +  \frac{1}{1-\beta_2} \epsilon_t \tag{3} $$
$$ y_t = \frac{\beta_1}{1-\beta_2} + \frac{\beta_2}{1-\beta_2} z_{2t} + \frac{1}{1-\beta_2} \epsilon_t \tag{4}$$
It follows from 3:
$$ cov(x_{2t} \epsilon_t ) = \frac{1}{1-\beta_2} cov(z_{2t} \epsilon_t) + \frac{1}{1-\beta_2} V(\epsilon) = \frac{\sigma^2}{1-\beta_2} \tag{5} $$
The 5 just shows that $x$ will be correlated with $\epsilon$, but a direct consequence of this correlation is that:
$$ \text{plim } b_2 = \beta_2 + \frac{cov(x_{2t}, \epsilon_t}{V(x_{2t})}$$
So what you are estimating is not just your beta coefficient you want $\beta_2$ but you are estimating sum of the true $\beta$ coefficient together with ratio of covariance between $x$ and $z$ to variance in $x$ or  $\frac{cov(x_{2t}, \epsilon_t}{V(x_{2t})}$.  This indeed can even force coefficients to flip. For example, suppose true effect $\beta_2=5$ but $cov(x,z)=-20$ and $V(x)=1$ then if you just naively run model  $y = b_1 + b_2 x_{2t}  + \epsilon_t $ your estimated $\hat{b_2}$ will be $\hat{b_2} = 2 -20 = -18$ which has opposite sign and the magnitude of $b$ will be distorted. So you will be getting unreliable results.
Ommited Variable Bias
This would be example, where we do not observe (or fail to include) variable that should be in the model. Again following Verbeek pp 145 consider individual wage equation:
$$ y_ = x_{1i}' \beta_1 + x_{2i} \beta_2 +  u_i \gamma + v_i$$
here $y$ would be wage, $x_{1i}$ is vector of individual characteristics (e.g. gender, age, location etc), $x_{2i}$ years of schooling and $u_i$ some unobserved innate ability. We expect that $cov(x_{2i},u_i)>0$ because it makes sense that if you have higher innate ability you will have higher education as people with high innate ability should have easier time at the school/university.
Now let us suppose that because innate ability is not observable you are forced to estimate:
$$y x_i'\beta + \epsilon_i$$
with $x_i'=(x_{1i}', x_{2i}) $ and $\beta'= (\beta_1', \beta_2), $ and naturally since we omitted ability  $\epsilon_i = u_i\gamma + v_i$.
Now the $b$ estimates of $\beta$ are given by:
$$b= \beta +  \left( \sum_{i=1}^N x_i x_i' \right)^{-1} \sum_{i=1}^N x_i u_i \gamma + \left( \sum_{i=1}^N x_i x_i' \right)^{-1} \sum_{i=1}^N x_i v_i$$
Even assuming $E(x_i, v) = 0$ (i.e. there is no additional simultaneity or other endogeneity issues in the true model), we get:
$$\text{plim } b = \beta + \sum_{xx}^{-1}E[x_i u_i] \gamma$$
So as long either $\gamma \neq 0 $ (in which case it should not be in the first model to begin with as that would mean ability does not affect wage), or $E[x_i u_i] \neq 0$ which in our case wont hold because we assumed ability does affect education, your estimated beta is not going to be actual effect of the independent variable on the dependent variable but the actual effect plus term determined by correlation between omitted and included independent variable and $\gamma$. Again this can change both magnitude and sign of $\beta$ so you simply can't trust it at all.
Lastly, there could be other ways in which endogeneity arises in econometric setting, but exploring all of them is beyond scope of SE, and the two above mentioned ones are probably the most common ones and relevant.


How likely is a total economic collapse due to the potential coronavirus impact? Most signs show that lockdown could easily stretch through the summer. A freeze in consumer spending would cause multiple industries to fail causing a ripple effect.

To be specific, if lockdown lasts through the summer, and a second virus wave occurs in the fall as expected, then lockdowns will continue further into the year. The timeframe for a vaccine is 12-18 months earliest. Then, the vaccine must be manufactured and distributed. Since the virus is so widespread that it is now assumed that it will reach a global critical mass, this essentially guarantees the collapse of the restaurant, airline, tourism, and hotel industries as they cannot sustain prolonged losses in a capitalistic structure. If they fail, their suppliers fail, and so on. History has shown that large systems are prone to failure time and time again, esp. when accountability is obfuscated (e.g. the Titanic, the World Wars/Holocaust, and now this). In the past Egypt fell, and then Rome fell. What is to say our current systems won’t fail, even if as a slowly sinking ship?

EDIT: This question was closed, before I received enough good, thoughtful answers. As of tonight (April 4th) Bernie Sanders held a virtual address on the situation. He's looking at the unemployment projections that were posted by the St. Louis Fed's models and has spoken with a number of economists. Finally a voice of reason in this media circus. He has confirmed that a potential collapse is possible as another 47 million Americans may become jobless - this is unprecedented and would be absolutely devastating to American civilization.

As a disclaimer, this is not an answer, rather a long-form explanation of the difficulties of answering.

The first leg is uncertainty about the danger of the epidemic. Economists are not medical experts. For example, one could imagine that there is an amazing breakthrough where a common medicine saves patients. The economic effects of that scenario are very different than the scenarios presented by governments. More realistically, we do not know how strong activity restrictions have to be to control the epidemic.

The next leg of uncertainty is the government response. Governments have the capacity to bail out entities (firms, households) that get in trouble. We do not know what they will do.

Even if we knew all that, there is uncertainty about the best model that takes all this in. It is very unusual for governments to restrict economic activity in such a broad-based manner, and so there are no standard models. (There is a flood of research.)

Finally, “conventional” economics does not really spend much time looking into societal collapse scenarios. There are areas of academia that do this, and there is presumably studies in economic history. Experts in those subject areas are not normally visiting this website.


Is it necessary to have currency in an ideal centrally-planned economy? Under this condition, the price of goods are definitely meaningless.

How does the planner know that his central plan is the ideal one? The conventional story is that he's got an objective function that maximizes the sum of all the society's members' utility. He maximizes that sum by :

Setting the members' marginal utilities equal.
Allocating inputs efficiently so the output lies on the production possibility frontier (Production Efficiency)
Choosing the mix out outputs to put to their most valuable purpose (Product-Mix Efficiency)
Allocating outputs efficiently such that no resources can be redeployed to make someone better off without making anyone worse off.

How does he do this? He does this with prices. These may be shadow prices, relative prices without currency (barter), or they might be conventional prices quoted in the numeraire good. Explaining this is probably beyond the scope of a stackexchange article. This review may be of some use but the content in a microeconomics textbook would be similar.

So the price of goods are not only not "definitely meaningless" but essential to the planner's activities. However, you do not need currency in an ideal centrally-planned economy. It is possible to write down models with prices but without currency (credit models) or even money (barter models) which nevertheless have central planners that can easily maximize welfare.


Invading a country with high debt I thought about this question during the height of the Greek economic crisis several years ago. The media was saying that Greece had run out of money, having used funds that had been set aside for a natural disaster, and they really badly needed a loan.

Suppose that during this period, an alien spaceship crash-landed in Greece and the aliens proceeded to invade the country. Since Greece has no money (= cannot buy weapons, ammunition, pay their soldiers, etc), and it cannot borrow (since nobody being willing to lend Greece money was the cause of economic crisis) does it mean Greece will be easily conquered? If the answer is no, where will Greece get the money to defend itself from?

I'm asking this as an economics question, so I'm not thinking of stuff such as whether NATO intervenes or what the technological capabilities of the aliens are.

The situation in Greece is complicated because it is part of the euro area, and NATO. It would presumably receive external aid.

But if you want a historical example, you could look at the tail end of the Depression in the 1930s. Although debt levels were not high by modern standards, governments had difficulty because of the Gold Standard. As countries moved to build up their militaries, they broke their pegs to gold. This gave them the ability to run large deficits to pay for the military spending.

Eichengreen’s “Golden Fetters” gives an overview of that era.

(The problem Greece faces that it is locked into an exchange rate system,like the Gold Standard, but it is even harder to get out of.)

In summary, the usual response is to break any existing currency pegs, default on foreign currency debt, and use deficit finance (and inflation) to handle the emergency.


How to relate real rate of return on capital to bond interest rate: Lagrangian Suppose that household resource constrain equation is as follows:
$$P_tC_t + Q_tB_t+ P_tI_t \leq W_tL_t+R_tK_t+B_{t-1}+D_t$$
where $P_t$ is price at time $t$, $Q_t$ is the price of one bond quantity, $B_t$ is bond quantity, $I_t$ is investment, $W_t$ is wage, $L_t$ is labor amount, $R_t$ is nominal capital rental rate, $K_t$ is capital at tie $t$, $D_t$ is dividends.

Taking it into Lagrangian at $t=0$:
$E_0 \sum_{t=0}^{\infty}\beta^t U(C_t,L_t) - \lambda_t[P_tC_t + Q_tB_t+ P_tI_t - (W_tL_t+R_tK_t+B_{t-1}+D_t)]$

Taking partial derivative of lagrangian respect to $K_{t+1}$ where $K_{t+1} = (1-\delta)K_t + I_t$ seems to produce:
$$\frac{\lambda_t}{\lambda_{t+1}} = \frac{R_{t+1}}{P_{t+1}}$$ (Dropped expectation sign, but should be there)

And taking partial derivative of the lagrangian respect to $B_t$:

$$\frac{\lambda_t}{\lambda_{t+1}} = \frac{P_t}{P_{t+1}}\frac{1}{Q_t}$$

Equating these two,

$$R_{t+1} = \frac{P_t}{Q_t}$$

Taking $-\log Q_t = i_t$

$$\hat{R_{t+1}} = \hat{P_t} - \hat{Q_t} = \hat{P_t}+i_t$$
where $\hat{X} = \log X$.

This does not seem to be a right formula to me, and I must have made some mistake. What did I do wrong here?

Ignoring the expectations operator, your lagrangean has two mistakes: first the constraint is per-period so it is also multiplied by the discount factor. Second,  the way you have wrote the time indexes is inconsistent, as regards their interpretation for capital and bonds. If $K_t$ denotes "capital at the beginning of period $t$" (as it does), you should also write $B_{t}$ instead of $B_{t-1}$, to denote bonds held at the beginning of period $t$. This takes with it also the time index on $Q$.

Also  I would advise to write your constraint in "normal form" (as they say in micro), namely with the constraint as "higher than or equal to zero".

Let's try this, up to a point.

$$\Lambda = \sum_{t=0}^{\infty}\beta^t \Big[U(C_t,L_t) + \lambda_t\big(W_tL_t+R_tK_t+B_{t}+D_t - (P_tC_t + Q_{t+1}B_{t+1}+ P_tI_t)\big)\Big]$$

$$ = \sum_{t=0}^{\infty}\beta^t \Big[U(C_t,L_t)\\ + \lambda_t\big(W_tL_t+R_tK_t+B_{t}+D_t - P_tC_t - Q_{t+1}B_{t+1}- P_t\big[K_{t+1} - (1-\delta)K_t\big]\big)\Big]$$

Then

$$\frac{\partial \Lambda}{\partial K_{t+1}} = 0 \implies -\beta^{t}\lambda_t P_t + \beta^{t+1}\lambda_{t+1}[(1-\delta)P_{t+1} +R_{t+1}] =0$$

and

$$\frac{\partial \Lambda}{\partial B_{t+1}} = 0 \implies -\beta^{t}\lambda_t Q_{t+1} + \beta^{t+1}\lambda_{t+1} =0$$

Equating we get

$$\frac {[(1-\delta)P_{t+1} +R_{t+1}]}{P_t} = \frac 1{Q_{t+1}}$$

Now, $R_{t+1}$ is the nominal gross return to capital, so a $P_{t+1}$ is implicitly in there. If we set $r_{t+1}\equiv R_{t+1}/P_{t+1}$ the relation becomes

$$\frac {[(1+(r_{t+1} -\delta)]P_{t+1}}{P_t} = \frac 1{Q_{t+1}}$$

Taking logs, we get the Fisher equation written for period $t+1$.


What is the “entry price” in relation to tariffs? I see the term “entry price” and “price entry system” in relation to tariffs.

What do these means?

For example this document: https://ageconsearch.umn.edu/bitstream/10095/1/sp06go22.pdf

Entry price system (EPS) is a EU-specific term relating to their food import tariffs, more specifically to fruits and vegetables. It's a somewhat complicated system designed to strongly discourage imports below a certain price. This is a summary from 2009 paper:

  The EU protects growers of 15 kinds of selected fruits
  and vegetables against international competition not
  only by the means of ad valorem tariffs of up to 20%,
  but also by the EPS. The EPS came into effect on 1
  July 1995, replacing the former RPS. Analogous to a
  minimum import price, the EPS is designed to restrict
  imports below the product-specific, politically
  designated EP plus ad valorem tariff (Table 1). If the
  EP is undercut, an additional specific tariff is levied,
  which proportionally varies depending on the gap
  between the product’s actual import price and the EP.
  When the EP is undercut by 8% or more, the
  maximum specific tariff, referred to as the maximum
  tariff equivalent (MTE), of up to 80% of the EP is
  charged. For example, the EPS is applied to oranges
  during the EU orange harvest season in the time period
  December 1 to May 31. The MFN tariff for oranges
  seasonally varies between 3.2% and 16.0% whereas
  the MFN EP remains constant at a level of 354 €/t. If
  oranges are exported to the EU at a price of 336.3 €/t,
  the EP is undercut by 5%. This implies that the
  exporter has to pay an additional specific tariff of 17.7
  €/t which is equal to the gap between the import price
  and the EP. If the entry price for oranges is undercut
  by 8% or more, an additional specific tariff at the level
  of the MTE of 71 €/t is charged. [...]

  Monitoring compliance with the EPS faces the
  difficulty that a large share of fruit and vegetable
  imports in the EU is on commission, implying that the
  import price is not determined until the product is sold
  in the EU market. Therefore, the EC calculates a
  synthetic import price, the standard import value
  (SIV). Fruit and vegetable prices, surveyed for each
  product and export country individually, are collected
  on representative fruit and vegetable wholesale
  markets in all EU Member States. The daily SIVs are
  calculated as a weighted average of collected
  wholesale market prices, less a marketing and
  transportation margin and applied tariffs.
  The EPS can be circumvented (both legally and
  illegally), so that some product is finally sold at prices
  below the EP (García-Álvarez-Coque, 2002).
  According to information from importers, illegal
  circumvention (e.g. based on false invoicing) is more
  prevalent in small-scale trading, particularly between
  related trading partners. Storage can offer a means of
  legal circumvention, as storable products can be
  imported at any time while customs clearance is
  delayed until some later date when the SIV is above
  the EP. Once cleared at a favourable SIV, the product
  can be sold later on EU markets at any price (Cioffi
  and del' Aquila, 2004).

There were some 2014 changes (not covered in that quote).


What is a "modified IS-LM framework"? Recently in a test I was asked to describe the modified IS-LM framework. I assumed I was being asked the IS-LM-BP model, since it modifies the traditional IS LM model by adding a BP curve.

I looked up on a couple of references (Macroeconomics by Dornbusch, and Macroeconomics by Olivier Blanchard) but they have no reference to it. Looking the term up on a search engine only throws results about papers that suggest a modification to the IS LM model.

What exactly is a modified IS-LM framework?

There is no universal definition of a modified IS-LM framework. There are several modifications out there. Some such modifications include adjusting the model to capture the last financial crisis or opening the economy with the BP curve as you said, or more explicitly considering the role of banks. Another modification is the IS-MP model, which represents a more realistic version of monetary policy.


Are there more historical examples of big change in prices thanks to demand/supply changes like the tulip mania? I'm currently searching for historical changes in prices as a result of a big/sudden change in demand/supply, like the tulip mania in Holland. Are there any notable examples?

Every price change of a good is due to a change in supply/demand. Based on your example are you maybe thinking of sudden price changes due to a bubble? For example with the tullip mania the price of the tullips was completey detached from the utility that anyone actually got from owning tullips. In a nutshell people were willing to pay exorbitant prices for these tullips because they expected to be able to sell them for an even higher price in the future.

Another example would be the dotcom bubble where there was a sudden drop in the value of internet based companies. I want to mention that the people spending a years salary on a tullip bulb weren't necessarily stupid or naive. Think about it like a time bomb where you don't know when it is going to explode. Holding the bomb(owning the asset) allows you to make money and you can hand off the bomb anytime you want. If you are however holding it when it explodes you lose all of your money.

Another example would be the cryptocurrency market.


Velocity of M1 versus M2 money According to Pablo Kurlat's textbook on Macroeconomics, the graph of Ch 13 compares the velocity of M1 and M2 over the years. I don't understand why M1 velocity exceeds M2 even though M2 includes more variables such as M1+ money market mutual funds + time deposits + savings deposits. I thought M2 velocity would exceed M1 velocity. I also understand that according to the Quantity equation: money supply * velocity = price level * real GDP

You may be confusing money velocity with money supply. From Wikipedia, the velocity of money is "measure of the number of times that the average unit of currency is used to purchase goods and services within a given time period." There is indeed more M2 than M1 but the velocity of M1 is often higher than that of M2. The shared portion of M1 and M2 will have the same velocity: this is the same thing as saying the velocity of M1 is the same as the velocity of M1. However, the portion unique to M2 will have a lower velocity: for example, saving deposits are usually moved around less than credit in demand deposits (checking accounts). Hence, overall M2 will often have a lower velocity than M1.


Effect of lower Government spending on Loanable Funds Market I'm having trouble with understanding what the results would be...

Let's suppose the situation where the newly formed government act to cut government spending and, by doing so eliminate the current federal government budget deficit.
Does this shift the demand curve or the supply curve in the loanable funds market?

I watched a Youtube video and it said demand would increase (crowding out) but my lecture notes contradict that by saying supply will decrease (crowding out) or does that result to the same thing?

If the opposite were true and the government proposes spending $1 trillion on infrastructure spending we will see a shift outward of the demand curve and rates will tick upward to a new equilibrium point. The crowding out occurs when we have movement along the demand curve (from the old interest rate --> new demand curve intersection up to the new intersection of the S and D curve).

With a decrease in government spending your demand curve for the loan-able funds market will shift inward and push the interest rate lower. When a fall in the interest rate leads to higher investment spending, the resulting increase in real GDP generates exactly enough additional savings to match the rise in investment spending.

It is somewhat agreed upon that contractionary fiscal policy leads to a surplus and the government can act as a creditor rather than a debtor. It will also leave more money for private investments for people such as small borrowers.

(There are some economists that believe that under the right circumstances that expansionary government policies may produce crowing in instead of crowding out. Keynesian economists may suggest that if the policy is strong enough to change the economic climate then businesses may find it profitable to add capacity -induced investment- which works to counteract and possibly out weigh the crowding out effect.)


About intertemporal elasticity of substitution The inter temporal elasticity of substitution between two periods of time is $$\sigma=-\frac{d[\ln(c(s)/c(t))]}{d[\ln(U'(c(s))/U'(c(t)))]}$$ I need to prove that $$\lim_{s \to t}\sigma = -\frac{U'(c(t))}{U''(c(t))c(t)}$$
So, I have the following by the definition of total differential:

$$\sigma=-\frac{ \frac{dc(s)}{c(s)}-\frac{dc(t)}{c(t)}}{ \frac{U''(c(s))}{U'(c(s)}dc(s)- \frac{U''(c(t))}{U'(c(t)}dc(t)  }$$  Then if $s$ tends to $t$ we have an indetermination $0/0$ so, we use L'Hôpital Rule. That is my problem, I don't know how to derivate with respect to $c(s)$.

To close this one: As I wrote in my initial comment, one should consider the derivative with respect to $s$, not $c(s)$. This first means that anything containing $t$ has a zero derivative. So we have

for the numerator

$$\frac {d\ln(c(s)/c(t))}{ds} = \frac {c'(s)}{c(s)}$$

and for the denominator

$$\frac{d[\ln(U'(c(s))/U'(c(t)))]}{ds} = \frac {U''(c(s))\cdot c'(s)}{U'(c(s))}$$

Forming the quotient of the two we get after simplifying and adding the minus sign the desired

$$\lim_{s \to t}\sigma = -\frac{U'(c(t))}{U''(c(t))c(t)}$$


Why are required reserves so trivially low? We know that required reserves are the reserves that central bank requires banks to hold in reserves.

Reserves= Required Reserves +Excess reserves.

But I see that in 2017 Total Reserves (RESBALNS) = 2000 Billion whilst Required Reserves (RESBALREQ) are only 124 Billion.

If required reserves are so low how could changing it possibly effect anything? Am I not using the right indicators?

The world changed in 2008, and commercial banks substantially increased their reserves held at the central banks in many countries including the US, mainly because they did not want to lend to each other in the unsecured interbank market

At that point, required reserves failed as a policy measure for fine-tuning money markets in many countries, since it amounted to pushing on a piece of string; the Bank of England removed them entirely in 2009.  Several central banks moved to alternative instruments, including:

quantitative easing
interest on excess reserves (in the US they were small and positive but some cases such as Euroland the equivalent could be negative)
bank capital ratios, as a solvency regulation


Let the utility function $U = a + b \min\{x,y\}$. Are $x$ and $y$ perfect complements? It is possible to have a monotonic transformation on this type of utility function, but what about $a$ and $b$? Usually a function with perfect complements is $U(x_1, x_2) = \min \{a x_1, b x_2 \}$

Consider a typical car, which is made of one car-body (for lack of a better word) and four tires. Let $x_1$ denote the number of car-bodies and $x_2$ denote the number of tires. Most consumers would prefer cars in the form of one car-body with four tires, and not in any other combinations. So we may represent their preference as
$$U(x_1,x_2)=\min\{4x_1,x_2\}.\tag{1}$$
Thus two cars are preferred to one car can be expressed as
$$
(2,8)\succ(1,4)\quad\Leftrightarrow\quad U(2,8)=8>4=U(1,4). \tag{2}
$$
One car with two extra tires does not increase one's utility:
$$
(1,4)\sim(1,6)\quad\Leftrightarrow\quad U(1,4)=4=4=U(1,6).  \tag{3}
$$
Equation $(1)$ is the utility function associated with a perfect complement preference. In particular, it is a special case of the general form $\min\{ax_1,bx_2\}$ where $a=4$ and $b=1$.

Let's now apply an affine positive transformation to $U(x_1,x_2)$. To avoid notational confusion, let's use $\alpha\in\mathbb R$ and $\beta>0$ as the parameters:
$$
V(x_1,x_2)=\alpha+\beta U(x_1,x_2).
$$
For concreteness, suppose $\alpha=1$ and $\beta=0.5$. And we can verify that the preference illustrated in $(2)$ and $(3)$ is preserved:
$$
(2,8)\succ(1,4)\quad\Leftrightarrow\quad V(2,8)=5>3=V(1,4).
$$
$$
(1,4)\sim(1,6)\quad\Leftrightarrow\quad V(1,4)=3=3=V(1,6).
$$

Therefore, while $\min\{ax_1,bx_2\}$ represents some perfect complement preference, its monotonic transformation, $\alpha+\beta\min\{ax_1,bx_2\}$, also represents the same preference.


Why do we spread knowledge across nations? We have access to lots of knowledge on paper sharing platforms, open course platforms, open-source platforms and question asking platforms and etc, and Tesla opened all its electric car patents in 2014 starting from which year XPeng and FF and many others in China and other countries were founded.
I don't know why we are not afraid of the backfires of knowledge sharing or the late-mover advantage? Does a company need the often mentioned technical barrier to be competitive? In China there was a saying "师夷长技以制夷" which means literally "learn from foreigners to compete with them", then I thought those platforms are very dangerous to be utilized by enemies/competitors.
I am sorry if I asked this in the wrong place again(if so, please kindly let me know where I can post this question). I asked this question somewhere else on StackExchange and somebody suggested that I should consider comparative advantage and I learned the term here but cannot still get my head around how to answer my question using that. Any suggestions? Thanks in advance.

This is a long comment that is too long for the comment box.
In fact, many research projects in US are secretive, especially the ones related to military. At the same time, much, much more research projects in China are secretive, including some agricultural ones, which are not military-related but considered as national security-related by Chinese government.
There has always been a China-threat theory in US, and a US-threat theory in China. The majority of US military are nationalists which could be considered as right-wing, while the majority of US academia are left-wing globalists who think China is less threatening. So the later care more about free-market and free knowledge while the former might want to put some restrictions on China.
By the way, there is a culture difference on "world order" between the East and the West. For thousands of years, the Western world is comprised of hundreds of smaller yet independent states, while almost all of the Far East nations could have been a tributary subject of the "Center Empire". People from the "Center Empire" could naturally believe that there will be only one major leader in the world, while the westerners might believe that the world is consist of many equal entities. The latter is of course less concern about knowledge-sharing.
The globalists believe that the global challenges faced by all human are more threatening than China. This could be one of reasons why the globalists have gained more support in the special year of 2020.


How to derive the standard euler equation from the Expanding Variety Model In the standard expanding variety model where the representative household faces the following CRRA utility function
$$
\int_{0}^{\infty} \exp(-\rho t) \frac{C(t)^{1-\theta}-1}{1-\theta}dt
$$
and final goods that is produced competitively with the following production
$$
Y(t) = \frac{1}{1-\beta} \left( \int_{0}^{N(t)}x(v,t)^{1-\beta}dv\right)L^{\beta}
$$
with the following resource constraint
$$
C(t) + X(t) + Z(t) \leq Y(t)
$$
where $X(t)$ is the total spending on machines, and $Z(t)$ is the total expenditure on research and development.
The innovation possibilities frontier takes the form
$$
\dot{N}(t) = \eta Z(t)
$$
The intermediary goods firm faces the following problem where
$$
r(t) V(v,t) - \dot{V}(v,t) = \pi(v,t)
$$
The thing I don't understand about the model is how the Euler Equation is derived. In almost everywhere I look the Euler Equation is the standard
$$
\frac{\dot{C}(t)}{C(t)} = \frac{1}{\theta}(r(t)-\rho)
$$
I don't understand how you would derive this equation.

The way you would go about solving this problem is as the ChinG said is by setting up the Hamiltonian. In this case this is:
$$\mathcal{H}:e^{-\rho t} \frac{C(t)^{1-\theta}-1}{1-\theta}+\mu(t)\left[Y(t)-C(t)-X(t)-Z(t)\right]$$
Taking the first order condition for this problem we get:
$$\frac{\partial \mathcal{H}}{\partial C(t)}:e^{-\rho t}C(t)^{-\theta}-\mu(t)=0 $$
or
$$e^{-\rho t}C(t)^{-\theta}=\mu(t)$$
Taking the natural logs of this equation and differentiating with respect to time we get:
$$\ln\left[\frac{\partial \mathcal{H}}{\partial C(t)}\right]:-\rho t -\theta \ln [C(t)]=\ln[\mu(t)]$$
$$\frac{\partial\ln\left[\mathcal{H}_{C(t)}\right]}{\partial t}:-\rho-\theta\frac{\dot{C}(t)}{C(t)}=-\frac{\dot{\mu}(t)}{\mu(t)}$$
Rearranging the above and noting that $\frac{\dot{\mu}(t)}{\mu(t)}=r(t)$
we get:
$$\frac{\dot{C}(t)}{C(t)}=\frac{1}{\theta}(r(t)-\rho)$$
Which is the Euler equation.
Hope this helps.


Difference between two ways of calculating real return I've just learned the following way of calculating the real return rate $R$ of an investment:

  $$R=\frac{P(1+N)-P(1+I)}{P(1+I)}$$

Where $P$ is the initial value invested, $N$ is the nominal interest rate and $I$ is the inflation rate.

However, I've seen an alternative formula for calculating the same thing, which is

  $$R=N-I$$

So my question is, which one gives a better result for the effective rate of return of an invesment and why? Thanks very much in advance.

First, it's better to cancel $P$ in your first definition. Then
$$
R=\frac{N-I}{1+I}
$$
And the second expression is
$$
R=N-I
$$
Actually, it is the famous $\textit{Fisher Equation}$.

The difference that there is a $1+I$ on denominator. Of course they are different. But economists sometimes use both since they are approximately equal when $R$ and $I$ are small. If you look at the data, both real interest rate and inflation rate are just a little above 2%.

Instead of using your first definition, let's start from an alternative form
$$
1+N = (1+R)(1+I) = 1+R+I+R\cdot I
$$
When $R,I$ are both small, their product can be ignored. Say $2\%\times 2\%=0.0004$. Hence, you can say
$$
N= R+I \Leftrightarrow R= N-I
$$

Here is the Wikipedia Link.
https://en.wikipedia.org/wiki/Fisher_equation


Does a Robinson Crusoe economy have a substitution effect and an income effect? Consider a Robinson Crusoe economy. Let $c$ be consumption and let $l$ be leisure. Our utility function is defined as

$$U(c,l)$$

Geometrically, I think we can say his indifference curve should be concave up, so therefore $\frac{dc}{dl} >0$ and $\frac{d^2c}{dl^2} >0$.

Typically we have a production function $$y = f(\ell)$$
where $\ell$ is labor, $f'>0$,$f''<0$ and $c \leq y$.  Also, I think $l = 1 - \ell$.

Also, note

$$MRS = MPL$$

WHY INCREASING PRODUCTIVITY MIGHT INCREASE LABOR

Suppose $f(\ell)=A \sqrt{\ell}$. Then
$$MPL = f'(\ell) = \frac{A}{2\sqrt{\ell}}$$
So then if $A \rightarrow \lambda A$, then for fixed $MPL$ we must have
$$MPL = \frac{\lambda A}{2\sqrt{\lambda^2 \ell}}$$

In other words, if $A$ increases, Crusoe works harder if we assume $MPL$ is fixed.

WHY INCREASING PRODUCTIVITY MIGHT DECREASE LABOR

But increasing $A$ would also mean essentially that Crusoe gets more production per unit of labor consumed. This gives him more $c$ available. This will mean his $MU_c$ goes down.

Recall $$MRS = \frac {U_l} {U_c}$$ If we assume $MRS$ remains constant, then $MU_l$ must go down to offset this change. This implies $l$ goes up and therefore, $\ell$ goes down.

So one could also argue changing $A$ results in $\ell$ going down.

MY QUESTION

What is the income effect and substitution effect in the case of changing $A$?

According to what my instructors have said (and I don't think they explain it well at all), the income effect is the latter change I described due to $A$ (i.e. decrease in $\ell$) whereas the substitution effect is due to the former change (increase in $\ell$).

But these don't match the income and substitution effects I learned about in my class on Marshallian and Hicksian demand functions. It seems very confused. Can someone define these explicitly or explain why my instructor has misused these two terms?

I don't see why equilibrium $MPL(\ell)$  would be fixed.

I think Robinson's income is measured by what he can get using his total time $t = l + \ell$.

Assume that given the original $A$ and total time $t$ his optimal choice was $(c_1,l_1)$. If the technology improves to $A'>A$ he can reach $(c_1,l_1)$
 (or $U(c_1,l_1)$ if you take the Hicksian approach)
 by only using total time $t' < t$.

Let us denote the optimal consumption bundle given technology $A'$ and time $t'$ by $(c_2,l_2)$. This is the intermediate step separating the income and substitution effects. The difference between $l_2$ and $l_1$ would be the substition effect. The 'income' in the two situations is considered equal as $(c_1,l_1)$  (or $U(c_1,l_1)$ if you take the Hicksian approach)  is barely feasible in both cases. Any difference in leisure consumption is due to the different transformation rate between leisure and consumption.

Let us denote the optimal consumption bundle given technology $A'$ and time $t$ by $(c_3,l_3)$. The difference between $l_3$ and $l_2$ is the income effect. The technology is identical in both cases, so any difference in consumption is due to the difference in 'income'.

Perhaps your instructors are trying to say something about the backward bending labor supply curve. It is difficult to tell from the available information.


Energy saving technology and energy service price I want to assess the effects of energy saving technologies on output growth using time series data. My work would benefit from time series data on patents for energy saving innovations, but this is hard to find. I have time series data on energy service prices (not energy prices), which I am thinking of using as a proxy for energy saving technologies. Energy service prices appear to have declined over time and this is due to the improvement in energy technologies, mainly. Thus, I assume the energy service price data reflects the improvements in energy technologies.

Do you think the idea of proxying energy technologies with energy service prices is appropriate in an empirical analysis?

Edit: Price of energy refers to the price of energy carrier, say oil. Energy service price refers to the cost of providing an energy service, say heating or lighting etc.

A problem with using energy service prices is that they might reflect competition conditions (e.g. monopoly/oligopoly, or the big six in the UK) rather than the true cost of energy to firms.

A problem with using energy prices is that they might reflect demand and supply issues. For example, no one would say that the drop in oil prices from 140 to 50 was due to technological improvement. Instead, it was driven by a shale oil revolution, and perhaps geopolitical aspects.


Moral hazard with linear effort and two possible outcomes Suppose you have a risk averse principal and a risk averse agent with utility functions $v(q_i - w_i)$ and $u(w_i)$, respectively, where $i = \{H,L\}$, and $q$ is output and $w$ is the wage. The probability that output is high is given by $p(e)$ with $p'(e) > 0 \geq p''(e)$ and effort is given by the linear function $e$. How do you prove that in the second-best case, the agent receives a larger (smaller) share of the profits when output is high (low) relative to the fist-best case? Bolton and Dewatripont (2005) mention this result but do not prove it.

principal: $\max_{w_h,w_l,e}p(e)v(q_h-w_h)+(1-p(e))v(q_l-w_l) $ subject to

(IR)       $~~~~~p(e)u(w_h-c(e))+(1-p(e))u(w_l-c(e))\geq \bar u$

(IC)$~~~~~~e\in arg\max_{\tilde e}p(e)u(w_h-c(e))+(1-p(e))u(w_l-c(e))$

Replace the IC with the FOC approach:

(IC'))$~~~~~~p'(e)u(w_h-c(e))+p(e)u'(w_h-c(e))(-c'(e))-p'(e)u(w_l-c(e))+(1-p(e))u'(w_l-c(e))(-c'(e))=0$

Now consider the principal's foc wrt $w_h$:

$p(e)v'(q_h-w_h)(-1)+\lambda(p(e)u'(w_h-c(e))+\mu [p'(e)u'(w_h-c(e))+p(e)u''(w_h-c(e))(-c'(e))]=0$

So the difference between this and first best is that third term in the FOC. Using the standard assumptions, we know that that third term is positive and so:

$v'(q_h-w_h)_{first best}<v'(q_h-w_h)_{second best}$

Now v concave and (assuming inverse exists):

$q^f_h-w^f_h>q^s_h-w^s_h$

So the spread decreases,


Problem with a Hal Varian Question from chapter 5 Remember our friend Ralph Rigid from Chapter 3? His favorite
diner, Food for Thought, has adopted the following policy to reduce the
crowds at lunch time: if you show up for lunch t hours before or after
12 noon, you get to deduct t dollars from your bill. (This holds for any
fraction of an hour as well.)

(a) Use blue ink to show Ralph's budget set. On this graph, the horizontal
axis measures the time of day that he eats lunch, and the vertical axis
measures the amount of money that he will have to spend on things other
than lunch. Assume that he has 20 total to spend and that lunch at
noon costs 10. (Hint: How much money would he have left if he ate at
noon? at 1 P.M.? at 11 A.M.?)

(b) Recall that Ralph's preferred lunch time is 12 noon, but that he is
willing to eat at another time if the food is sufficiently cheap. Draw
some red indifference curves for Ralph that would be consistent with his
choosing to eat at 11 A.M.

The answer is given as

My question is, shouldnt the graph be perfectly parabolic? with both tangents at Time = 11 and 1.
Shouldn't eating at 11 be exactly as preferable to eating at 1?

Thanks for the help.

I think the answer to your question is that it would be a matter of Ralph's preferences. Perhaps he is indifferent to eating at 11:00 am or 1:00 pm, as you suggest. But he might have non-parabolic preferences (for reasons unspecified), and both this situation and the one you describe are consistent with his eating at 11:00 am, so the answer provided is a correct solution to the question asked. Perhaps the particular indifference curves drawn are a way to avoid multiple solutions (the author might have thought it simpler).

I'm going exclusively off the information in your post though, so I'm assuming that we do not know if Ralph has any preferences over time independent of how it implicitly affects the price he pays.


Why imports increase if higher relative inflation? I'm reviewing a previous AP Macroeconomics exam and I saw the following question:

  The United States and South Korea are trading partners, and the United
  States has a zero current account balance. Assume now that the
  inflation rate in the United States decreases relative to the
  inflation rate in South Korea.

Based on the decrease in the inflation rate in the United States, will United States exports to South Korea
increase or decrease?

The answer is that US exports to South Korea will increase.

But my intuition says the opposite. If South Korea has high relative inflation, their currency will not be worth as much compared to the U.S. dollar, so it will depreciate. Thus, the South Korean currency cannot buy as much from the U.S. and will thus not be able to import as much, so I would think exports from the U.S. would decrease to South Korea. Why is my intuition wrong?

At first, U.S. exports increase because US exports become cheaper due to the low inflation rate. Inflation itself only influences the exchange rate indirectly through its effect on supply and demand for currency. That effect goes through trade. For that to happen, trade must first take place and so US exports must first increase.

So at first the exchange rate doesn't adjust at all (no difference in supply/demand of the currencies just yet). US goods become cheaper so they're exported more. As US exports increase the demand for dollars by South Korea increases. This will later on lead to the south korean currency to depreciate and for US exporte to go down again (if the Marshall Lerner condition is fulfilled).


What does the value of an industry mean? In product pitches, a timeless line is "this is a $____ industry", but what does that really mean? Is that how much money the industry typically produces in a year? In a quarter? As some ratio of the annual/quarterly sales or profits? What does it mean?

If I'm understanding your question, this typically means the amount of revenue that an industry generates. Usually, the statement "this is a ____ industry" is labeled. For example, "this is a $1,000,000 a year industry." Although recognizing how much revenue an industry generates is nice and is helpful, it may not apply to a person looking to break into an industry. It's important to note that profit and revenue are not the same things.


What are the prerequisites to study Mathematical Economics? I am a high school student with keen interest in mathematics and economics. I wish to study mathematical economics, but most of the books I have encountered begin with quite advanced mathematics. In particular, Mathematical Economics by Akira Takayama begins with Nonlinear Programming [Concave Programming, Differentiation and Unconstrained Maximum Problem and Quasi Saddle Point Charecterization]. Frankly, I find myself at sea while trying to understand this content. Could someone please recommend what prerequisites one must have in order to fully understand books of such caliber.

In the preface, Takayama writes that the book was written with the intention to keep the prerequisites to a minimum: elementary calculus and matrix algebra.

Perhaps he was exaggerating a little, but I suspect, after skimming the table of contents, that knowledge of the aforementioned subjects and experience working with (i.e. reading/understanding and independently constructing) mathematical proofs should be enough.

I'm assuming you've taken calculus and linear algebra -- in which case you might want to get more experience with working with proofs. I'm quite fond of Axler's Linear Algebra Done Right, and I've heard good things about Abbott's Understanding Analysis.

If you haven't studied those two subjects, work on learning those first. You can try the two textbooks I suggested to do so, but that might be a bit rough-going. I'm sure your math teacher might have more helpful suggestions for a first reference to learn calculus and matrix algebra from.

I think with a bit of what mathematicians like to call 'mathematical maturity', you should be able to manage Takayama just fine.


Why did the Fed raise interest rates between 2004 and 2006? Between June 2004 and August 2006, the Fed raised interest rates again and again, because they were "...growing more uncomfortable about inflation".

Looking at the graph below, inflation did increase, but not in any totally insane way (note that it clearly didn't respond to the rate rises!):

Given that high interest rates are bad for mortgage-holders (particularly those with high loan-to-value ratios), you'd think quindrupling rates within 18 months would be bound to lead to a wave of defaults.

Were there accusations at the time that the Fed was blindly following its inflation targeting rule without thinking about the consequences in the rest of the economy?

Or was it about something other than inflation?

Good question!

It seems that one of the reasons was precisely that inflation did not respond. They kept raising interest rates,  hoping it would respond at some point. In fact, nominal interest rates have to increase more than expected inflation for the real interest rates to go up, so it made sense.

The other reason is also related to the question. It seems that they were aware that a relatively long period of low interest rates was potentially fueling "asset price bubbles",  such as in housing, but also in asset backed securities, corporate bonds and equities. These also did not seem to respond quickly to the rate changes.

Of course, apparently, they did not realize that it was dangerous moment to increase rates quickly. It would have potentially been a good idea to raise the rates very very slowly, so that leveraged agents had a chance to de-lever as the prices of their assets slowly came down... Alternatively they could have slowly tightened the regulation on lending instead of raising the rates at all. This last point seems to be the key to avoiding a new crisis: having a good too to increase and decrease economy wide leverage distinct from interest rates.


What is the difference between a loan and an investment? IMF, WB, ADB, IDB, AIIB are known to give loans. On the other hand, China is said to be investing in Pakistani project termed as CPEC.

What is the difference between these two terms in these two particular cases?

A loan is an agent lending funds to another agent. This money can be used for investment spending, or it can be used for personal consumption expenditures. It can be used to buy fixed assets like real estate, which may or may not be "investment" depending on how you use the terminology. In the case of the IMF, the role of the institution is to ensure financial stability by providing funds to countries in an emergency; for example, a country which becomes insolvent and is unable to service its sovereign debt is likely to seek help from the IMF. The IMF would then provide a bailout loan along with a stabilization program aimed at improving the country's public finances. This is not investment, in the sense that it does not grow the country's capital stock; it just allows it to meet its obligations to past creditors.

Investment is an expenditure which will yield revenue in the future, and hopefully amortize itself through that revenue. In the case of a household, investment can take the form of acquiring financial assets; in the case of an economy, investment often refers to actions which improve the country's productivity. This can be the construction of new factories, higher wages at state subsidized education institutions, higher research and development spending by the private sector, etc.

The reason the two are related is that quite a lot of investment is done through borrowing. A corporation can borrow to ramp up capital expenditures, a country can borrow on international capital markets to invest more in infrastructure, an individual can take out a mortgage to acquire a house. All of these can be legitimately described as "investment".

China is said to be investing in Pakistan (and quite a lot of other countries) under its Belt and Road Initiative because of two reasons: these expenditures are aimed at boosting domestic productivity in those countries, and China expects to reap benefits from its program. The potential benefits for China are plentiful. China is still very much an export-oriented economy and a global manufacturing hub. Strong growth in underdeveloped countries is likely to increase demand for Chinese goods, allowing the Chinese economy to experience faster growth. China also hopes to get direct revenue from its investment operations under this program, and they have the additional goal of expanding their political clout. Contrast this with the case of the IMF, whose founding goal is to ensure financial stability and to prevent crisis contagion and panic. The two forms of lending are evidently quite different in their desired goals.


Predicted recessions that never happened It seems generally accepted that recessions are hard to forecast, in both onset and intensity, but the bias seems to be toward rosy outlooks:

  The main finding is that, while forecasters are generally aware that recession years will be different from other years, they miss the magnitude of the recession by a wide margin until the year is almost over. Forecasts during non-recession years are revised slowly; in recession years, the pace of revision picks up but not sufficiently to avoid large forecast errors. [...] Strong booms are also missed, providing suggestive evidence for Nordhaus’ (1987) view that behavioral factors—the reluctance to absorb either good or bad news—play a role in the evolution of forecasts.

Of course, this may be put in simpler terms as forecasting having a bias towards things staying on the current course.

I'm curious if there are historically significant examples where the consensus forecasting (or at least that of some major institutions) predicted a [bad] recession that failed to materialize.

One example is this UK Government analysis:

  "Britain’s economy would be tipped into a year-long recession, with at least 500,000 jobs lost and GDP around 3.6% lower, following a vote to leave the EU, new Treasury analysis launched today by the Prime Minister and Chancellor shows…Speaking at B&Q in Eastleigh, Hampshire, the Prime Minister and Chancellor set out the Treasury’s analysis of the impact on the nation’s economy over the immediate period of two years following a vote to leave. This analysis shows that such a decision would cause an immediate and profound economic shock across the country"

But growth has been consistently positive in the almost three-year period since the vote.

I'm not sure this a very good example, because there are clear political incentives surrounding this forecast, which might mean it was less than sincere.


Necessary indifference conditions in mixed equilibrium Suppose we are playing a game where the Action set for Player 1 is $(a,b)$, for Player 2 is $(c,d)$, and for Player 3 is $(L,M,R)$. Assume that for Player 3, the action $M$ is weakly dominated by some mix between $L$ and $R$. I am attempting to find all of the possible mixed equilibria.

Let $p$ be the probability that Player 1 chooses $a$, let $q$ be the probability that Player 2 chooses $c$, and let $r_1, r_2, r_3$ be the probabilities that Player 3 choose $L, M, R$ respectively.

I have two questions:

First, because action $M$ is weakly dominated for Player 3, does everyone assume that $r_2=0$?

Second, the probabilities $p$ and $q$ are subject to the constraint that Player 3 be indifferent between his/her own actions. Does Player 3 need to be indifferent between $L$, $M$, and $R$, or just between $L$ and $R$, since $M$ is weakly dominated?

First, because action $M$ is weakly dominated for Player 3, does everyone assume that $r_2=0$?

Without seeing the game you're considering, it's hard to tell. But the general answer is No. Weakly dominated strategies can be played in a Nash equilibrium (either mixed or pure). In the following game, both $B$ and $C$ are weakly dominated strategies for both players. But each player randomizing between them in any proportion is still a NE.

\begin{array}{|c|c|c|c|}
\hline & A & B&C\\\hline
A&1,1&0,0&0,0\\\hline
B&0,0&0,0&0,0\\\hline
C&0,0&0,0&0,0\\\hline
\end{array}

  Does Player 3 need to be indifferent between $L$, $M$, and $R$, or just between $L$ and $R$, since $M$ is weakly dominated?

The indifference condition for MSNE applies to pure strategies in the support of the equilibrium mixed strategy. If $M$ is played with positive probability in equilibrium, then you'd need indifference across all three. If $M$ is played with zero probability, then you'd need $u_3(\sigma_1,\sigma_2,L)=u_3(\sigma_1,\sigma_2,R)\ge u_3(\sigma_1,\sigma_2,M)$

More generally, the necessary and sufficient conditions for a Nash equilibrium (either pure or mixed) are summarized in the following theorem:

  A strategy profile $(\sigma_1,\dots,\sigma_n)$ is a Nash equilibrium if and only if for all $i=1,\dots,n$,
  \begin{equation}
u_i(s_i,\sigma_{-i})= u_i(s_i',\sigma_{-i}), \qquad \forall s_i,s_i'\in\mathrm{supp}(\sigma_i)
\end{equation}
  and
  \begin{equation}
u_i(s_i,\sigma_{-i})\ge u_i(s_i',\sigma_{-i}), \qquad \forall s_i\in\mathrm{supp}(\sigma_i)\text{ and }\forall s_i'\notin\mathrm{supp}(\sigma_i).
\end{equation}

Hence, we see that the indifference condition is only required for pure strategies in the support of the equilibrium mixed strategy but not necessarily outside it.


Studying growth in US and Sweden, what variables should I watch out for in a regression? I've be assigned a project on growth paradigms in US vs Sweden as part of my introductory course in econ. Can somebody please help me out with regression ideas?

"Solow's Growth Accounting"

A first pass idea is what MIT's Bob Solow proposed many decades ago: to do a growth accounting exercise. You'd like to know how much physical capital changed and how much human capital changed and then with some assumptions or estimation of the relative importance of each of these then estimate how much total factor productivity changes. One way to do this is by running a regression of (log) output on (log) human capital, and (log) physical capital, for data from both the US and Sweden. The errors are the "total factor productivty" component or "Solow residual"....


The most frequent causes of economic downfall? In retrospect what are the major parameters, most frequently causing countries' economy to reduce its size and/or growth.

Global Financial Crisis?
Regional instability?
Local Banking Sector failure?
Long-term inefficient governmental fiscal, civil, law policies, corruption?

Interestingly, Romer and Romer (2014) show that financial crises are typically not causing major downfalls in economic activity, if you restrict your sample onto the developed countries post WWII.

An advantage of their method is that they look at a real time narrative, so they don't try to judge ex-post what was a crises. So historians winner writes history criticism doesn't apply here.

It is certainly worse if the financial crises is global, but that's pretty infrequent.


Owner occupied public housing What is Owner occupied public housing?
This text says "in Singapore at present about 86 per cent of the population live in public housing, of whom 90 per cent are home-owners."
https://www.jstor.org/stable/43196729?seq=1
How can you be the owner of you live in an apartment owned by the state?
Maybe the government sells the apartments to the people living in it, if they chose so?

In Singapore, a government agency called the Housing and Development Board (HDB) builds housing (mostly apartment buildings). HDB is not meant to be profitable. It loses money every year and is subsidized from the government budget.
HDB ensures that its buildings have access all the standard infrastructure nearby - mass transit, retail stores, schools, medical and recreational facilities, etc before tenants move in.
HDB also ensures that the tenant population is diverse and no ethnic group is disproportionally overrepresented in any location (i.e. they will reject a prospective tenant in a location belonging to an ethnic group that they already have too much of).
About 80% of the Singapore population lives in HDB apartments.
The tenants have an option to sign a 99-year lease. About 90% of the tenants choose this option. They're not quite "owners" (the government is the owner and the landlord), but close enough with the 99-year lease - they can re-sell the apartment, hopefully at a profit. The remaining ~10% tenants rent short-term, usually because they can't afford the 99-year lease.
The government has a Central Provident Fund (CPF). CPF withhold 37% of everyone's income into 3 accounts: retirement (like U.S. Social Security), medical care, and housing. for most people, the money accumulated in their CPF account is enough to cover downpayment and most of mortgage payments. Singapore citizens (but not permanent residents) receive certain government-funded subsidies when buying the 99-year leases.
This Wikipedia page has more details and history.


Competition between utilities like ports I was reading about the frequent congestion in US ports and the resulting effect on the US economy. I feel there are unique features to this setting. When ports face congestion, they levy charges, and these are transferred on to the buyers by the shippers. On top of this, costs of delayed reception of goods are also borne by the retailers only. The only 'catch' for ports arises if the congestion is so high that firms shift to air transport or reroute through a farther port and incur road transport expenses.

Are there papers which model the economic interactions like competition between ports, or the interactions between firms, ports and labour unions?

In America, on the West coast, unions negotiate a common contract:

  Ironically, the International Longshore and Warehouse Union is a
  beneficiary of the same forces that are killing unions everywhere
  else: Its workers are the folks who unload the stuff that comes in
  from abroad. Those workers are sitting right at the bottleneck through
  which all that foreign competition flows to the U.S., and due to some
  smart planning by the union in earlier decades -- such as insisting
  that the West Coast ports would bargain as a bloc so that they can't
  play different locals against each other -- they can cork that
  bottle anytime they want. That gives them the ability to extract a
  little tariff on all that trade. Their rake-off is a tiny fraction of
  the overall flows, but that still translates into substantial sums for
  the few thousand workers who are holding onto that cork. The more
  trade, the better the concessions the ILWU is able to extract -- and
  the worse workers in other unions do.

Where Have All Our Wages Gone? by Megan Mcardle

There used to be a pre-anti-trust era railroad cartel in the USA:

  The [Joint Executive Committee (JEC)] was a cartel formed by the
  railroads which controlled eastbound freight shipments from Chicago to
  the Atlantic seaboard in the  I  88os. The agreement was publicly
  acknowledged, as it preceded the passage of the Sherman Act (1890)
  and the formation of the Interstate Commerce Commission (1887). ...
  The JEC cartel agreement took the form of market share allotments
  rather than absolute amounts of quantity shipped. Firms set their
  rates individually, and the JEC office took weekly accounts so that
  each railroad could see the total amount transported. Total demand was
  quite variable, and the actual market share of any particular firm
  depended on both the prices charged by all the firms and unpredictable
  stochastic forces.

On the Incidence and Duration of Price Wars (Porter (1985))


MICROECONOMICS: Optimal quantity produced in a Perfect Competition Market Suppose the Total Cost function of a firm in Perfect Competition is
  given by: $$C(q) = 450 + 15q + 2q^2$$

  The market price is $P = 15$ per unit

  Determine the optimal quantity produced by the firm

The trouble I'm having with this is a friend suggests the optimal quantity is q = 25 but that doesn't make sense to me.

Because when we calculate Marginal Cost = Marginal Revenue we get:

$$4q + 15 = 15$$

Which will yield an optimal quantity of 0 and not 25 when we solve for q.

The only way I can see it being equal to 25 is if the price is 115 and not 15 because of some typo. Any thoughts?

A typo seems very probable; more importantly, your procedure and concepts of setting MC=MR to solve for profit maximisation is definitely correct, regardless of the numbers being plug into the question.


Impulse response functions? I have a very basic model about a small open economy. This is a summary:

  $$
E_0\sum_{t=0}^{\infty}\theta_t U(c_t, h_t)
$$
  utility function:
  $$
d_t = (1 + r_{t-1})d_{t-1} - y_t + c_t + i_t + \Phi(k_{t-1} - k_t)
$$
  evolution of foreign debt:
  $$
y_t = A_t F(k_t, h_t)
$$
  output:
  $$
k_{t+1} = i_t + (1 - \delta)k_t
$$
  stock of capital evolves according to:

  The first order conditions of the household's maximization problem are:
  \begin{align}
\lambda_t = \beta(c_t, h_t)(1 + r_t)E_t\lambda_{t+1}\\
\lambda_t = U_c(c_t,h_t) - \eta_t\beta_c(c_t,h_t)\\
\eta_t = -E_t U(c_{t+1}, h_{t+1}) + E_t \eta_{t+1} \beta(c_{t+1}, h_{t+1}) \\
-U_h(c_t,h_t) + \eta_t\beta_h(c_t,h_t) = \lambda_tA_tF_h(k_t,h_t)\\
\lambda_t[1 + \Phi'(k_{t+1} - k_t)] = \beta(c_t,h_t)E_t\lambda_{t+1}[A_{t+1}F_k(k_{t+1},h_{t+1}) + 1 - \delta + \Phi'(k_{t+2} - k_{t+1})]
\end{align}
  Law of motions of the productivity shock:
  $$
\ln A_{t+1} = \rho \ln A_t + \epsilon_{t+1}; ~~~~ \epsilon_{t+1} \sim { NIID}(0,\sigma_\epsilon^2); ~~~~ t\ge 0
$$
  we parametrize this as
  \begin{align}
U(c,h) = \frac{[c - \omega^{-1}h^\omega]^{1 - \gamma} - 1}{1 - \gamma}\\
\beta(c,h) = [1 + c - \omega^{-1}h^\omega]^{-\psi_1} \\
F(k,h) = k^{\alpha}h^{1-\alpha} \\
\Phi(x) = \frac{\phi}{2}x^2; ~~~~ \phi>0
\end{align}
  $$
\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline
\gamma & \omega &  \psi_1 & \alpha & \phi & r & \delta & \rho & \sigma_{\epsilon} \\\hline
2 & 1.455 & 0.11 & 0.32 & 0.028 & 0.04 & 0.1 & 0.42 & 0.0129 \\ \hline
\end{array}
$$

I have computed the steady state, but how can I compute the impulse response function?

Start by establishing $ \epsilon _1 = \epsilon , \epsilon_{t>1}=0$ . Now, epsilon will be your impulse.
You can calculate an expression for $A_t,\bar{A}_t\ \forall t$ . From here, you can either:

Work recursively with each variable and provide an analytic function for them, for every moment on time.
Calculate a value if you are simulating it, using the policy functions at each step.

Notice that, if you log-linearized your equations, $\epsilon=1$ would mean a 1% deviation from the steady state.


Does utility in economics also refer to producer's surplus ? How to balance the consumer surplus and producer surplus? I am confused about the use of utility in economics and how it relates to allocative efficiency.

At 4:35 and 5:07 in this video (https://www.youtube.com/watch?v=9a3wXj1o91k) he talks about how at the left and right of the equilibrium, total utility is not maximised.

I am unsure of what is meant by "total utility". Is it the consumer surplus added to the producers surplus?

Utility is not the same as consumer surplus. Consumer surplus is the difference between price an individuals pay and their individual reservation price.

Utility is a measure of gratification that can be completely different from consumer surplus and depending on what kind of utility we are talking about it might not even be possible to assign integer value to it. For example, with ordinal utility you can’t say some good gives you 20 utils from its consumption but with cardinal utility you can.

However, utility should be monotonically increasing function of consumer surplus so it is valid to say that at a point where total surplus is maximized also utility should be maximized.

Also producers also get utility because the higher producer surplus implies larger difference between actual price and their reservation price. Again utility should monotonically increasing function of this.


Consumption smoothing in RBC Model I have the following inter temporal utility function:

$U(t)=(\frac{s(t)}{1-\sigma})(c_t/c_{t-1}^\gamma)^{(1-\sigma)} - \chi*h(t)$

where $h(t)$ is the hours worked.
I know that gamma is responsible for consumption smoothing as I have achieved the following results after a positive shock on $s(t)$:

The problem is i do not know how to prove mathematically that when gamma=1 consumption is smoother

Have you tried solving the maximization problem? Normally you do this taking into account some market clearing condition or budget constraint and you should be able to solve for equilibrium prices to get future consumption as a function of present consumption. Consumption smoothing will simply show the path of consumption.

Getting this equation you can show how consumption varies for different levels of $ \gamma $ (in your case = 0 and = 1)


Why is AC = MC in the monopoly? Using the Microeconomic Theory Basic Principles and Extensions, Nicholson, W. and Snyder, C., I've reached to the point where Monopoly and Imperfect Competition is discussed (Chapter 14 and 15 to be more specific).

It's kind of easy to deduce that Marginal Cost equals Marginal Revenue at the point of profit maximization. In the imperfect competition in the long-run (or in the perfect competition) no one can surpass the point where price equals marginal cost equals average cost, because above this point firms will have negative economic profit.

The main question is why (and not only the graphic explanation please) the firm will choose AC (average cost) = MC (marginal cost)?

Graphically, it looks like the slope of the Demand Curve makes this choice the best one, but why in imperfect competition is this choice not pursued by the firm instead of the Supply Curve?

Suppose the marginal cost is constant and equal to $c$, that fixed costs are $K>0$, and that revenue is $R(q)$. You seem to understand that MR=MC must be true for profits to be maximized: $R'(q)=c$. We also know that average costs are given by $AC=(K+qc)/q$. But note that $AC=(K+qc)/q>c=MC$. Thus, when profits are maximized we have $AC>MC=R'(q)$. So it is not true that $AC=MC$ when profits are maximized in this example. We can conclude that $AC=MC=R'(q)$ holds only in certain special cases.


How to estimate a constant elasticity of substitution for a country in a solow model including human capital and scarce resources For my thesis I was looking for some help due to the facts of my little knowledge of econometrics. I appreciate any help whether its directly dealing with my question or literature advice.

Basically I would construct the Solow Model with a CES production function including 2 more variables as mentioned human capital and another restricting variable representing a scarce resource such as oil. I would search for Data then for the needed variables and estimate the sigma.

My question here is the technical part on how to actually estimate that parameter given the data. What kind of methods are there to get an approximate value and what kind of programs would be potentially useful to get the solutions?

macro123,

You might want to have a look at MRW (1992) https://academic.oup.com/qje/article-abstract/107/2/407/1838296/A-Contribution-to-the-Empirics-of-Economic-Growth and the literature on growth regressions in the handbook of economic growth and the handbook of macroeconomics. In addition, Acemoglu's textbook on economic growth will provide you with some useful references as well as a clear and concise introduction to the topic. Although, I believe that you'll also be a little bit disappointed as you'll find that something close to what you wish to do has already been done.


Heteroskedasticity assumption in fGLS into linear form? I am following Chapter 8 ("Heteroskedasticity" p. 259) in the 6th edition of Woolridge Introductory Econometrics: A Modern Approach and I don't understand one piece of the transformation of our model.

For fGLS, we assume [1] $Var(u|\boldsymbol{x}) = \sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)$, where $x_i, x_2,...,x_k$ are the independent variables appearing in the regression model and the $\delta_j$ are unknown parameters.

Then, we use the definition of conditional variance to say $Var(u|\boldsymbol{x}) = E(u^2|\boldsymbol{x}$), since our zero conditional mean assumption tells us that $(E(u))^2$ is zero.

Now, here is where I'm stuck: Wooldridge says that our assumption [1] above allows us to write $u^2=\sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)v$, where $v$ has a mean equal to unity, conditional on $\boldsymbol{x}=x_1,x_2, ...,x_k$

Can someone please help me to develop an intuition for this last step that Wooldridge has taken?  Essentially, it seems like we've assumed that $E(u^2|\boldsymbol{x})=\frac{u^2}{v}$ and I don't understand why or the properties that allow us to do this.

I've found this paper https://www.econ.uzh.ch/dam/jcr:e3cddc1b-f89d-4fb4-9474-c2c380355d69/joe_2017.pdf to be useful (specifically, assumption #6 on p. 2), but it doesn't leave me with much intuition for what we're doing and why, especially because I'm fairly new to econometrics.

Thanks-
Maurus

I'm using the 4th edition, but the content should be the same.  It sounds like you are asking how he got from

$$
Var(u|\boldsymbol{x}) = \sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)
$$

to

$$
u^2=\sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)v
$$

As you correctly noted, $Var(u|\boldsymbol{x}) = E(u^2|\boldsymbol{x})$ under the zero conditional mean expectation assumption ($E(u|\boldsymbol{x}) = 0$).  So that allows us to replace the left-hand side of the equation, as Wooldridge did.  $E(u^2|\boldsymbol{x})$ turned into $u^2$ because $u^2 = E(u^2|\boldsymbol{x}) + \epsilon$, where $\epsilon$ is the component of $u^2$ that's uncorrelated with any function of $\boldsymbol{x}$.  That component could have been left in at this stage, but it can be removed because later on it would turn into a part of the error term anyway that does not affect the fitted values from the regression of $log(u^2)$ on $\boldsymbol{x}$ (i.e., part of $e$ in the next equation in the book).

On the right-hand side of the equation, Wooldridge adds $v$, which has a mean equal to unity, conditional on $\boldsymbol{x} = (x_1, x_2, ..., x_k)$.  That means that given some set of values for $\boldsymbol{x}$, $v$ is expected to have a multiplicative factor effect of $1$ on $u^2$ (in other words, no effect).  By introducing this term to the equation (and assuming that it is independent of $\boldsymbol{x}$), we can then convert it into the error term $e$ in the subsequent equation:

$$
log(u^2) = \alpha_0 + \delta_1x_1+\delta_2x_2+...+\delta_kx_k+e
$$

because taking a log of a variable that has a mean of $1$ will give us a variable that has a mean of $0$ plus some constant (equal to the negative of the mean of the log values of the original variable $v$).  That constant is moved to the constant term (that's why this last equation has $\alpha_0$ instead of $\delta_0$) and we are left with an equation that can be estimated using OLS.

P.S. The $v$ in this book is not the same $v$ that you found in Assumption 6 in the linked paper.  There it is a function, not a variable.


Run On The Banks Age of Credit Cards Is the risk of a general run on the banks greatly reduced now that most transactions are done electronically?

If we talk about a run on one bank, I think it's the other way around. Back then, people need to stand in line and wait for their queue to take their money out of the bank (and deposit it to another bank). Now they can transfer their money from anywhere and anytime. So I think the risk of a run is greatly increased.


About marshallian demands Let an agent with utility function $U(x_1,x_2,x_3)=min\{ x_1, x_2 \} +x_3$. We want to maximize $U$ subject to $p_1 x_1+p_2 x_2 +p_3 x_3= I$

First intuitively $x_1^*=x_2^*$ substituting en the budget constraint I have $$x_1^*=x_2^*=\frac{I-p_3 x_3}{p_1+p_2}$$ I don't know how to solve for $x_3$. Then i thought in Kuhn-Tucker but I can't see how to solve it.

I will give a hint. To increase/decrease utility by 1 unit, you can do two things. Increase $x_1$ and $x_2$ by $\frac{1}{2}$ units and this would cost you $\frac{p_1+p_2}{2}$. The second option is changing $x_3$ by one unit that would cost $p_3$. One other option is of course using a linear combination of the above changes. If you remember from well behaved utility functions, you would like to buy things for which utility per price is higher. Now you would go for a similar reasoning here and would try to buy extra utility at a cheapest price.


How to calculate price function from demand curve when marginal cost is given? This example is in a oligopoly market with two firms. The demand curve is given and also two firms' MC is given. How would one calculate price function in this scenario?

I found the slope using the demand curve and then found the y intercept to the get the price function. However, I also know that MC is the derivative of the price function. If I take the derivative of the price function I got, it's not the same as the MC.. Any thoughts on this?

Let $y_1$ and $y_2$ denote the output of firms $1$ and $2$. I suspect by price function you mean the inverse demand function. So if
$$
y_1 + y_2 = Y = D(p)
$$
then
$$
D^{-1}(Y) = p(Y) = p(y_1 + y_2).
$$
Let us introduce the notation
$$
MR_i(y_1,y_2) = \frac{\partial p(y_1 + y_2)}{\partial y_i}.
$$
Generally
$$
MR_i(y_1,y_2) \neq MC_i(y_i),
$$
that is the functions are not the same. But if the outputs $y_1^*,y_2^*$ constitute an equilibrium, the functions take the same value.
$$
\forall i: \ MR_i(y_1^*,y_2^*) = MC_i(y_i^*)
$$

Another example:
 The function $x^2$ is not the same as the constant function 4. But if $x=2$ they take the same value.


Academic paper which justifies why companies are run better privately A few years ago I was reading The Economist and I remember it stated a particular academic paper that underpinned the rationale for the existence of private equity firms. I have tried to find this article but have had no success. I believe this paper justified why companies are run better privately. Does anyone know what this paper is/might of been?

I think this is what you are looking for.

It is a quite interesting paper. I hope it helps.


Profit maximization, when $MC = P$, in a simple supply table and curve Our economics school book states that the profits of a company are maximized when MC = P.
However, I am having some trouble wrapping my head around that.
For example, I have the following exercise:

The question is: If the equilibrium p is $P_E = 72$, (in which the product is sold), what quantity $Q$ will the company have to produce and sell in order to maximize its profit?

So, we get that the supply table is:

The answer is: it will have to produce and sell quantity of $Q_E = 450$.
My questions are:

Is this because of the equilibrium p, which is $P_E=72$ equals the $MC = 72$?
If the equilibrium price was set as $P_E = 36$, then would the answer be $Q_E=400$?
If the equilibrium price was, for example, $P_E=71$, then would I be able to answer just with this data?

Thanks for your time!!

What your school economics textbook must say is that :

"In a Perfectly Competitive Market (PC), firms maximize profits when MC= P ". This equality applies only to firms in a perfectly competitive market.

This is because, in a Perfectly Competitive Market there is an infinite number of buyers and sellers and the prices are set by the overall market forces, and the firms and the consumers take that price to be given.

Using Calculus, it can easily be shown that MC=P is the condition for Profit Maximization in PC markets.

We can further see other conditions of maxima using second-order conditions (which relate the slope of the MC curve in relation to the slope of MR curve ) but we can ignore those for now.

Intuitively, a producer earns P on each unit sold. If the MC < P, they earn more on each marginal unit than they spend on its production, and hence they would keep producing more. If MC > P, then the cost of producing each marginal unit is more than the revenue it fetches and hence they would cut down on production. Neither of these is a position of equilibrium for the firm. Hence MC=P is the position of equilibrium and the First Order Condition for profit maximization.

Yes
Yes
Yes, you can't answer this question, because the data set given to you is made up of discrete points.


Who paid the bill for cheap Chinese exports? We have all enjoyed the flow of cheap Chinese imported goods, whether in the shops, or online.
The shipping costs from China have always seemed very low.
Now I see this note:

Got notification today that all USPS international GEPS contracts will be terminated September 31st.
This is all related to the Universal Postal Union agreement that allows Chinese sellers to ship products to the U.S. for less than it costs us to ship to the same state.
The administration has given the UPU an ultimatum, that they: either allow the USPS to set rates for China mail that arrives in the U.S., or the U.S. will officially leave the UPU on October 17th.
Either way, this means as of October 17, no more cheap Chinese shipping. They will have to pay the same domestic rates as us once their e-packets arrive here.
This is great news for U.S. sellers, especially eBay sellers.

My question is: Who paid the bill for cheap Chinese export shipping?

The United States was paying the bill. (This has now changed).


Where can I find the statistics of import crude oil to China? Is there any website that shows statistics of import crude oil and commodities to China daily or monthly?

I'm not sure how helpful this is but the way the information is displayed is really nice. https://oec.world/en/profile/country/chn/