Term for rapid economic growth when starting over or in a new place Please bear with me as I know little about general Economics, and I'm sure I am massively oversimplifying what I am trying to describe.

I'm looking for a term to describe what happens when an economy starts from a new place with sufficient resources, leading to rapid growth.

I feel like I notice a pattern when I learn about large economic changes:

New place is discovered or old place is destroyed
Things are built/rebuilt, government changes, technology is applied to resources
New place overtakes all of the old, prosperous, stable places around it

I think some factors might be:

Every country fights political, economic, cultural, and regulatory inertia even though it may be relatively advanced or well-off.
When forced to start over or start fresh, people must consider each new piece of the system as it is created intentionally, instead of following or fighting what is already in place.
The rules and policies of a lasting economy were created long ago and may no longer match with the current state of technology, leading to stagnancy.  Whereas after a large change the new rules can be made to fit the times.

Some examples I can think of are:

After World War 2, USA installed democracy in Japan, dismantled monopolies, and built schools.  Japan started over from very little, worked hard, and their economy exploded.
Europe brought technology to the vast natural resources of North America, made a new government, and well, here we are.
The city of Seattle was completely destroyed in a fire.  So they fixed their lasting sewer problem, made the roads wider and properly irrigated, built everything sturdy and fire-resistant, and the economy boomed.
Recent examples might be Singapore, Hong Kong, Shenzhen, Songdo.

Is there a term for this or common way to describe it?

With a bit of humor, you could use the Schumpeterian term "creative destruction" -the humor relates to the fact that Schumpeter used the term to describe an inherent structural feature of capitalism, not historical/natural accidents/disasters.

Apart from that tongue-in-cheek proposal, I am not aware of a compact term to express what you describe. A common way could be a "vintage theory of capital" approach, where it is recognized that "old and new" capital coexists with different levels of technology embodied in it, and so in a sense "averaging" the actual technological/efficiency level used in the economy. Then what you describe amounts to an abrupt loss of "old" capital which may lower the output level but creates a positive discontinuity in the actual average technology level used in the economy, creating abrupt and higer growth rates.

You can broaden the concept of capital to also include "human capital" and maybe also "institutional capital" (and so "technology" will then refer also to "knowhow/experience" and "transactional technology" as well).


Why are prices considered the best information we could have? We often talk about information as pricing being the best information or reflection of different aggregate pieces of information existing on markets. Why do we then also often hear that some prices do not reflect reality or do not compare with the real economy? Thanks.

Concerning austrians and their general attitude towards prices: https://mises.org/library/source-prices.

In short Mises says that

  The ultimate source of the determination of prices is the value judgments of the consumers.

If the value of judgement of consumers  is higher than the cost of production, producers know it is worthwhile to produce that good.

This way producers are informed what to produce and more importantly what not to produce, in order for the produced goods to be useful to people.

Mises even suggested communist central planning would be far less efficient if the planners didn't look at capitalistic prices.
https://en.m.wikipedia.org/wiki/Economic_calculation_problem?wprov=sfla1.

Whenever austrians talk about unrealistic prices, they are referring to price bubbles, an essential element in the ABCT
https://en.wikipedia.org/wiki/Austrian_business_cycle_theory?wprov=sfla1.

In short many austrians believe the primary cause of these bubbles to be the monetary policy of the central bank. The central bank's interest rate is not a market price, and therefore leads producers to believe more goods are wanted right now and less in the future, supposing a lower central bank interest rate. This leads to bubbles, which are then called unrealistic prices by Austrian economists.


Will there be any competition amongst cement retailers? If we consider a cement manufaturer in a given country, say India, then will the cement retailers of that companies' product compete with each other? And if so, then what kind of a competition will it be?

As far as I think, since the prices and the product will be the same the retailers competition will be close the Perfect competition, however consumers in the case of cement do not have perfect knowledge about the product(Considering non-trade consumers). So it might be monopolisitic competition. It will be really helpful if one could give a solid argument regarding the existence and the kind of competition that might occur between cement retailers...

Thank You.

Since they are different retailers, their products are not perfectly homogeneous. The differences might be in delivery times, friendliness of representatives, packaging etc. So, their products are not strictly identical.

For the monopolistic competition, it is mentioned that there are multiple retailers. If we assume they do not collude, there will be a form of competition.

Taking these two characteristics, I would say there is a form of competition, more specifically "Differentiated Bertrand Competition".


An example of endowment effect Suppose a Decision Maker (DM) has willingness to pay (WTP) of 100, and her actual elicited willingness to accept (WTA) is 110, can this DM be a standard rational agent? Why or why not?

My thinking is that if the DM is a standard rational agent, then her WTA should also be 100. Is this correct?

Your reasoning is not entirely rigorous, Even for a rational agent there can be a small gap between WTA and WTP due to the wealth effect. However, empirically this effect accounts for a very small fraction of the WTA/WTP gap, which is why other explanations are generally preferred.


What type of graph can be hepful to explain the type of errors that should be used? I have a regression of wage on several variables, such as education, marriage and so on. I want to explain that it would be a better idea to use cluster errors, since we expect the wage to be correlated with abilities for each person, but I want to do so using a graph, what graph would you recommend me to use and why? When you have one regressor it is obvious, but here how to decide what variables to plot?

Since I am using stata I would appreciate if you could help me with an example of the code for the graph.

You are saying: $y$ is regressed on $x_1$ and $x_2$, say, and you think it would be better to use cluster errors since you expect $y$ is correlated with abilities for each person.

First, $y$ is naturally correlated with the error term $u$ (if you mean the error term by "abilities") because $u$ is a part of $y$. You have no problems with that; $y$ is always strongly correlated with $u$. It also has nothing to do with cluster errors.

If you happen to mean cluster standard errors (SE) by "cluster errors", and if you are saying that you would use cluster SE because $x_1$ is correlated with $u$, I would say that the regressor-error correlation (endogeneity) has nothing to do with cluster SE, what so ever. Cluster SE provides valid inference when the the error term show within-cluster (auto)correlation.

Please enlighten me if I misinterpreted your question.


Unemployment and its relationship with Inflation Can anybody please explain me "Inflation-Unemployment Trade-off under Adaptive Expectation and under Rational Expectation"?

When agents in economy have adaptive expectations they predict future in the basis of what happened in the past. If we consider an inflation adjustment scenario, the expected inflation by the agents is directly dependent on the inflation that prevailed in the immediately previous period and the output gap.

$$Y = Y^0 + b(P - P^e)$$

where $P^e$ is expected price level.

When agents have adaptive expectations there is an inflation inertia.
To reduce unemployment rate the government will try to stimulate the economy and if the economy was at its natural level of unemployment the will be inflationary pressure an inflation will increase. If the agents do not correctly predict the inflation they are likely to produce more. Say for example agents have an expectation that inflation will be 4% based on past experience. And with the government expansion output increases and inflation actually increases to say, 8%. Their nominal wages will adjust according to 4% but the real wage will actually decrease. As a rule of thumb you can remember that if the expected inflation is lower than the actual inflation then output increases and producers hire more workers thereby reducing unemployment. So, there is a trade off here between unemployment rate and inflation level as suggested by the Okun's law and Philips curve.
However this is not the end of story. As soon as the workers realize that their real wages have reduced, they bargain for higher wages and eventually the whole change is reverted as firms' costs increase and they reduce output and fire workers to match the cost. This is also the reason why the long run supply curve is vertical.

With rational expectations ,however, it is a different story altogether. Rational expectations mean that the agents in economy apply all levels of reasoning to the available information to figure out the future scenario. They know the policy of central bank and government, they can correctly predict their actions and hence they know that inflation will be higher and simply ask for more wages. So no effect on output or employment and hence no tradeoff but only an increase in inflation. The policy will not be effective here. This is a concept in neo classical economics and is sometimes called as policy ineffectiveness proposition.


The relationship between structural budget balance and cyclically adjusted budget balance? What is the relationship between structural budget balance and the cyclically adjusted budget(CAB) balance?

I know that $PB=\textit{CAB}+AS$, where $PB$ is primary budget,  and $AS$ are the automatic stabilizers(tax revenues, unemployment benefits, etc. $AS$ term is counter-cyclical, i.e negative in recessions, positive in booms).

My question is, how do I relate, mathematically, the structural budget and the CAB?

Any help would be appreciated.

After searching, I found out that Structural Budget is OECD nomenclature for Cyclically Adjusted Budget.

Here's a link.


German economic growth in the 20th century Regarding this great animation:

Animation: The World’s 10 Largest Economies by GDP (1960-Today)

I have the following questions:

Why did Germany's GDP shrink so much from 1995 to 2000, while the GDP of the US grew very healthily?
What was the factor of US growth in that period and why did other economies did so poorly, especially Germany's?
Is it because the GDP is counted in US dollars which makes other countries' GDP under-counted?

$1.$ My guess is that your videographic's data were simply from the World Bank's GDP (current US\$). This is nominal GDP in US\$ and does not take into account (a) changes in the exchange rate; or (b) inflation.

$\color{red}{\text{2.}}$ And it turns out that the chief culprit here is (a). To correct for (a), we look instead at GDP (current LCU), where Germany's LCU = Local Currency Unit is the euro.

$\color{blue}{\text{3.}}$ We can also further correct for (b) by looking at GDP (constant LCU).

P.S. I would not trust the website VisualCapitalist.com. Here for example, it simply took this videographic from a tweet, which in turn gives no sources.


Railway Mania in England William Quinn et al. in their Boom and Bust (Cambridge University Press) describe the causes of the Railway stock market bust in 1840s England.

The outflow of gold due to problems with the harvest prompted the Bank of England to increase its interest rate from 2.5 to 3 per cent on 16 October and then to 3.5 per cent on 6 November. Some commentators have suggested that the decline in railway share prices was attributable to these rises in the Bank of England rate – the Bank was in essence pricking the bubble.

My question is, how could bad harvest season make the Central bank to increase in key rate? From the description, it seems that the anything but the decrease in economic activity was needed. Also, how the increase in the key rate could could have made a contribution to the declining prices? At least in theory.

how could bad harvest season make the Central bank to increase in key rate?

At the beginning of 1800s Britain still roughly $36\%$ of a employment and $33\%$ of British GDP was generated by agriculture (see Grigg 1992). Hence shock to agricultural output could easily lead to recession and have widespread economic effect.
Given what large role agriculture played in the Britain's economy I do not think it is surprising that central bank decided to act in some way. Hiking interest rate in such situation might seem strange with hindsight and living in current fractional reserve system, but that was part of what Keynes called the 'rules of the game'.  As explained by the oxford reference:

Under the ‘rules of the game’, countries losing gold were supposed to raise their interest rates and cut their money supply; countries gaining gold were supposed to cut interest rates and increase their money supply. These rules were intended to restore equilibrium in the balance of payments fairly quickly.

Fall in output (in this case agricultural output) would cause gold outflow because suddenly UK would loose production that was meant to be exported which would worsen its balance of trade. Moreover, under gold standard imports create gold outflow and exports gold inflow. So to play according to the 'rules of the game' the central bank had to hike interest rate.
Of course, doing this in our present fractional reserve system would make no sense and hence it feels very counterintuitive. However, under gold standard central bank cannot just let all gold flow out of country as that would lead to balance of payment imbalances as with gold standard all countries are implicitly under the same fixed exchange rate regime. This was also one of the reasons why eventually gold standard broke down and generally it is not very stable and resilient monetary regime (Eichengreen & Temin, 2010).

Also, how the increase in the key rate could could have made a contribution to the declining prices?

Higher interest rate leads to decrease in prices because it incentivizes people to spend less and save more putting less pressure on prices.


Difference between Luxury/Premium/Value fashion segments? What does "value" mean here? I was reading this article on Quartz: https://qz.com/1485141/just-20-fashion-companies-are-making-almost-all-of-the-industrys-profits/

I do not understand the following graph shown:

What does "value" segment mean? Someone please kindly provide the difference and explanation. Thank you.

Consider the ratio
$$
\dfrac{\text{Benefit}}{\text{Price}}.
$$
This is not the same thing as your net benefit, $\text{Benefit}-\text{Price}$.  So a good that might give you a high net benefit might have a low benefit-to-price ratio.  For example, $100-50=50$ and $100/50=2$ versus $1000-900 = 100$ and $1000/900=1.1111...$.

Luxury goods have high gross benefit but low benefit-to-price ratio and possibly a low net benefit.  Affordable luxury is trying to improve on benefit-to-price ratio  and net benefit while still having a high gross benefit.

Value goods are trying to achieve a high benefit-to-price ratio, despite the products having a low gross benefit and a mediocre net benefit.  So you feel like you got a lot for what you paid, even if it's a $\$$20 acrylic sweater instead of a $\$$500 cashmere one.


Determining whether preferences are rational given a utility function Alex's preferences: U(x;y)=x-(1/y). Are his preferences rational?

As long as a preference can be represented by a continuous utility function, it is rational (and continuous). So from the very fact that you're writing down a utility function that is continuous in both $x$ and $y$ (on $(0,\infty)^2$), it follows that the function represents a rational preference (provided that both $x$ and $y$ are positive).

However, if you insist that $y=0$ is part of the feasible choice set, then the preference is not complete. The individual cannot compare a bundle $(1,1)$ with another bundle $(1,0)$ because the utility of the latter bundle is not defined.


How to interpret risk premium I do not understand the notion risk premium. Let us suppose that John goes to the city by car, but he is thinking about not paying for the parking. If he is caught in the act he must pay the fine. How to interpret the risk premium for this game (not paying the parking)?

Let $\pi$ be the fine that needs to be paid besides the parking fee (say, $\phi$) if he gets caught. Further, he may or may not get caught for not paying. So let $p$ be the probability perceived by John about whether he will be caught. Let $u(x)$ be utility function of paying for amount $x$, with $u(0)=0$, $u'(x)<0$.
If he pays the parking fee $\phi$ he has the assured utility of $u(\phi)$. However, if does not pay for parking, his expected utility is $p \cdot u(\phi+\pi)$
Now risk premium is defined as the minimum amount by which the return on risky choice must exceed the risk free choice to make the individual indifferent between the two choices. Let $\pi_m$ be such that: $$u(\phi) = p\cdot u(\phi+\pi_m)$$
So, for John, $\pi_m$ becomes the risk premium for this game. If $\pi>\pi_m$ then $u(\phi) = u(\phi+\pi_m)>u(\phi+\pi)$ and it would be irrational for him to not pay for parking and risk getting caught. If opposite, he takes decides to not pay for parking and risk getting caught.


Explain Basic Supply Demand Graph Can someone please explain these things?  They show up all over the place and it seems people can't be bothered with documenting the labels.  Is this showing f(L) = W?  Is it showing f(W) = L?  If so, what's up with the labels (D) and (S) on the curve?  Is something else going on?  What's the dependent variable?  Are we trying to describe f(x,y) = S with a 2D graph?

Confused.

Assuming that $W$ is wage and $L$ is labor, I would say this is a labor supply-demand graph. TD stand for demand and S for supply.

The graph shows a positive shift in labor supply, i.e. labor offered by workers, leading to an increase in $L$ and a decrease of $W$ due to the excess of supply.

The shift in labor supply can be caused by a variety of shocks as a preference shock which values more labor, a change in non-labor income, etc (look here for explanations)


Will high computing power substitute the certainty-equivalence assumption? Bloom in a recent JEP paper considers that "the increase in computing power has made it possible to include uncertainty shocks directly in a wide range of models, allowing economists to abandon assumptions built on “certainty equivalence,” which refers to the amount of money that would be required as compensation for risk." (2nd paragraph of page 154, third point).

My understanding of Bloom's point is the idea that with computing power we can treat and exploit the heterogeneity of data. We can use high-frequency and/or large-scale data, in combination with computing power, to identify the role of uncertainty shock on economic outcomes.

My guess is that Bloom's point could be an implicit criticism of the expected utility theory given the importance of the certainty equivalent concept, and the related concept of risk premium, in this framework. Is this guess/interpretation right?

This is perhaps a good opportunity to point out that the "certainty equivalence" concept means one thing in microeconomics/choice under uncertainty theory, while it means something different in macroeconomics.

Microeconomics/choice under uncertainty
The Certainty Equivalent of a lottery/gamble, is the amount of wealth which, if given with certainty, provides the same utility as the lottery/gamble. See for example Jehle & Reny's "Advanced Microeconomic Theory" (2011, 3d ed.), p.113.

Macroeconomics
"Certainty Equivalence" is the situation in a stochastic model, where optimal decision rules prove to be identical to those that would have been derived in a deterministic framework (see for example Lungqvist & Sargent's "Recursive Macroeconomic Theory" 2004, 2nd ed, p. 113-115). Informally, this is sometimes described as "agents behave as if the stochastic processes are not stochastic", or "the decision rule is not affected by stochastic variability".

It is a funny coincidence that both references treat the subject in the same page number...

The concepts are evidently linked by the "as if there was no uncertainty" angle, but they are different in essential aspects: the micro-concept is a "buy-out" of uncertainty, providing a certain alternative towards which the agent that faces the gamble is indifferent in terms of utility, while the macro-concept emerges as a property of the solution (and only under restrictive model structures, or linear approximations thereof).


Does non-monotonicity imply non-satiation always? Why or why not? I understand that monotonic preferences imply non-satiation. But I am not sure 100% if non-monotonic functions always have satiation. An intuitive and mathematical explanation would be very helpful.

It depends on the function. A non-monotonic function with satiation:
$$
U(x_1,x_2) = 0.
$$
A non-monotonic function without (global) satiation:
$$
U(x_1,x_2) = \left \lfloor{x_1}\right \rfloor  + \left \lfloor{x_2}\right \rfloor .
$$


Proving AC is minimized when MC=AC I am trying to prove that AC is mininimized when AC=MC

This is how far I am:

FOC:

Showing what I want to prove

SOC:

This has to be positive in order to ensure that AC is minimized, but how can i conclude that?

Hope someone can help :)

You're making this way more complicated than it needs to be.

Edit: Okay it's a little more complicated that I thought but hey! What a cool result!

$AC = \frac{C(q)}{q} \\
MC = C'(q)$

When you minimize $AC$ with respect to $q$,

$$\frac{\partial AC}{\partial q} = \frac{C'(q) \cdot q - C(q)}{q^2} = 0$$
$$\implies C'(q) \cdot q - C(q) = 0$$
$$\implies C'(q) \cdot q = C(q)$$
$$\implies C'(q) = \frac{C(q)}{q}$$

Then marginal cost equals average cost. Which seems to be what you've gotten so far.

So now we check the second order conditions:

$$\frac{\partial AC}{\partial q} = \frac{C'(q)}{q} - \frac{C(q)}{q^2}$$
$$\frac{\partial^2 AC}{\partial q^2} = \frac{C''(q) \cdot q - C'(q)}{q^2} - \frac{C'(q) \cdot q^2 - C(q) \cdot 2q}{q^4}$$

What makes this expression greater than zero?

$$\frac{\partial^2 AC}{\partial q^2} = \frac{C''(q) \cdot q - C'(q)}{q^2} - \frac{C'(q) \cdot q^2 - C(q) \cdot 2q}{q^4} > 0$$
$$\implies \frac{C''(q) \cdot q - C'(q)}{q^2} > \frac{C'(q) \cdot q^2 - C(q) \cdot 2q}{q^4}$$
$$\implies C''(q) \cdot q - C'(q) > \frac{C'(q) \cdot q^2 - C(q) \cdot 2q}{q^2}$$
$$\implies C''(q) \cdot q - C'(q) > C'(q) - \frac{2C(q)}{q}$$
$$\implies C''(q) \cdot q > 2\left(C'(q) - \frac{C(q)}{q}\right)$$
$$\implies C''(q) > 2\left(C'(q) \cdot q - C(q)\right)$$

But recall that given the first derivative,

$$C'(q) = \frac{C(q)}{q}$$
$$\implies C'(q) \cdot q = C(q)$$

So substitute that into the above:

$$\implies C''(q) > 2\left(C(q) - C(q)\right)$$
$$\implies C''(q) > 0$$

And this is true as long as the total cost curve is convex, which is a pretty standard assumption. (I guess also positive production has to be a thing, so basically the firm has to be not shut down.) So we're done.


Proof coefficient in log-log model is equal to coefficient of elasticity I am trying to see how we treat $\varepsilon$ in the following proof:

Suppose we have a log-log single variable regression model

$$ \ln(y) = \alpha + \beta \ln(x) + \varepsilon $$

then take partial derivative with respect to $x$ on both sides

\begin{align}&\implies \frac{\partial}{\partial x} \ln(y) = \frac{\partial}{\partial x} (\alpha + \beta \ln(x) + \varepsilon)\\&\implies\frac{\partial \ln(y)}{\partial y} \frac{\partial y}{\partial x} = 0 + \beta \frac{1}{x} + \frac{\partial \varepsilon}{\partial x}\\&\implies\frac{1}{ y} \frac{\partial y}{\partial x} = \beta \frac{1}{x} + \frac{\partial \varepsilon}{\partial x}\end{align}

We want to show that $\beta$ is equal to the elasticity of $y$ with respect to $x$

$$ \beta = \frac{\partial y}{\partial x} \frac{x}{y} $$

But how do we know the $\dfrac{\partial \varepsilon}{\partial x} $ term is zero?

Because $\Bbb E[\varepsilon \mid x]= 0$ is one of the key assumptions for the estimation.


Calculate the elasticity of substitution of Epstein-Zin preferences $$
\newcommand{\E}{\mathbb{E}}
$$
Let a consumption
sequence be given $C=(C_0, C_1,...)$ and let
$C_t^+ = (C_t, C_{t+1}, ...)$.
Now, suppose I have Epstein-Zin preferences,
\begin{align*}
U_t(C_t^+) &= f(C_t, q(U_{t+1}(C_{t+1}^+))) \\
U_t  &= \left \{(1-\beta) C_t^{1-\rho}
+ \beta \left(\E_t[U_{t+1}^{1-\gamma}]\right)^{\frac{1-\rho}{1-\gamma}}
\right\}^{\frac{1}{1-\rho}},
\end{align*}
where $f$ is the time aggregator and $q$ is the conditional certainty
equivalent operator. That is,
$$
f(c,q) = ((1-\beta) c^{1-\rho} + \beta q^{1-\rho})^{\frac{1}{1-\rho}}
$$
and
$$
q_t = q(U_{t+1}) = \left(\E_t[U_{t+1}^{1-\gamma}]\right)^{\frac{1}{1-\gamma}}.
$$
How do I show that the intertemporal elasticity of substitution is
$\rho^{-1}$?

$
\newcommand{\dd}{\, \mathrm{d}}
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
$
Here is my solution. Let me know if anybody has a cleaner/clearer approach.

Consider a fixed (non-random)
 consumption sequence $C = (C_0, C_1,...)$.
Then, the elasticity of intertemporal substitution (EIS) is defined
as
$$
\text{EIS} = \left| \frac{\dd \ln(C_s/C_t)}{\dd \ln MRS_{s,t}}\right|
 = \left|\frac{\dd \ln \left(\frac{C_s}{C_t}\right)}
 {\dd \ln \left( \frac{\partial U/\partial C_s}{\partial U/\partial C_{t}}\right)}
 \right |.
$$
To compute this figure, let's start by
computing
\begin{align*}
\pd{U_t}{C_t} &= f_c(C_t, q_t(U_{t+1}(C_{t+1}^+)))  \\
  &= \frac{1}{1-\rho}
  \left( (1-\beta) C_t^{1-\rho} + \beta q^{1-\rho} \right)^{\frac{\rho}{1-\rho}}
  (1-\beta) (1-\rho) C_t^{-\rho} \\
  &= (1-\beta) f_t^{\rho} C_t^{-\rho}.
\end{align*}
Also,
\begin{align*}
\pd{U_t}{C_{t+1}} &=  f_q \cdot \frac{\dd q_t}{\dd U_{t+1}}
  \cdot \pd{U_{t+1}}{C_{t+1}}.
\end{align*}
It will be easier to compute these pieces in parts. First,
$$
f_q = \beta f^{\rho} q_t^{-\rho}.
$$
Next, consider $\frac{\dd q_t}{\dd U_{t+1}}$. This is simplified
by the fact that $C$ is non-random,
$$
\frac{\dd q_t}{\dd U_{t+1}} = q_t^\gamma U_{t+1}^{-\gamma} = 1.
$$
Finally,
$$
\pd{U_{t+1}}{C_{t+1}} = (1-\beta) f_{t+1}^{\rho} C_{t+1}^{-\rho},
$$
which follows from our earlier calculation. Thus,
\begin{align*}
\pd{U_t}{C_{t+1}} &=  f_q \cdot \frac{\dd q_t}{\dd U_{t+1}}
  \cdot \pd{U_{t+1}}{C_{t+1}} \\
  &= \beta f_t^{\rho} q_t^{-\rho}
  (1-\beta) f_{t+1}^{\rho} C_{t+1}^{-\rho},
\end{align*}
where $f_t = f(C_t, q_t)$ and $q_t = q(U_{t+1}(C_{t+1}^+))$.
Now, we can calculate
\begin{align*}
\frac{\partial U_t/\partial C_{t+1}}{\partial U_t/\partial C_t}
  &= \frac
  { \beta f_t^{\rho} q_t^{-\rho}
  (1-\beta) f_{t+1}^{\rho} C_{t+1}^{-\rho}}
  {(1-\beta) f_t^{\rho} C_t^{-\rho}} \\
  &= \beta q_t^{-\rho}
   f_{t+1}^{\rho}
   \left(\frac{C_{t+1}}{C_t}\right)^{-\rho}\\
\end{align*}
Now, let
$$
\frac{p_{t+1}}{p_t} = \frac{\partial U_t/\partial C_{t+1}}{\partial U_t/\partial C_t}.
$$
Then, taking the differentials,
$$
\dd \left(\frac{p_t}{p_0}\right) = \frac{\partial U_t/\partial C_{t+1}}{\partial U_t/\partial C_t}
  \left(\frac{C_{t+1}}{C_t}\right)^{-1} (-\rho) \dd \frac{C_{t+1}}{C_t}.
$$
So,
\begin{align*}
\frac{\dd\left(\frac{ C_{t+1}}{C_t}\right)}{\dd \left(\frac{p_{t+1}}{p_t}\right)}
\cdot \frac{\frac{p_{t+1}}{p_t}}{\frac{C_{t+1}}{C_t}}
  &= \left(
\frac{\partial U_t/\partial C_{t+1}}{\partial U_t/\partial C_t}
  \left(\frac{C_{t+1}}{C_t}\right)^{-1} (-\rho)
  \right)^{-1} \cdot \frac{\frac{p_{t+1}}{p_t}}{\frac{C_{t+1}}{C_t}} \\
  &= -\frac{\frac{C_{t+1}}{C_t} \frac{p_{t+1}}{p_t}}
  {\frac{p_{t+1}}{p_t} \frac{C_{t+1}}{C_t}} \rho^{-1} = -\rho^{-1}.
\end{align*}
Now, plugging this into the definition of the EIS,
\begin{align*}
\text{EIS} &= \left|\frac{\dd \ln \left(\frac{C_s}{C_t}\right)}
 {\dd \ln \left( \frac{\partial U/\partial C_s}{\partial U/\partial C_{t}}\right)}
 \right | \\
  &= \left|
\frac{\dd\left(\frac{ C_{t+1}}{C_t}\right)}{\dd \left(\frac{p_{t+1}}{p_t}\right)}
\cdot \frac{\frac{p_{t+1}}{p_t}}{\frac{C_{t+1}}{C_t}}
  \right| \\
  &= \rho^{-1}.
\end{align*}


Matching problem in continuous time Let's split each period into $n$ intervals. There's a continuum $u$ of unemployed and $v$ of vacancies. During each interval, there is a total of $X/n$ job offers. That means that each unemployed gets a job offer with probability $X/(nu)$ (assuming that $n$ is eventually so small that the chance of multiple job offers to the same person will go to zero).

Single individual Number of job offers - for a single individual - in the interval is distributed $Binomial(k, n, \frac{X}{un})$. Letting $n\to\infty$, the distribution in the continuous-time analog converges to $Poisson(k, \frac{X}{u})$.

I'm interested in the probability of $x$ individuals getting at least one job interval during a whole interval. That is $(1 - Binomial(0, n, \frac{X}{nu}))^x$:

$$ (1 - (1 - \frac{X}{un})^n)^x $$

If I'm not mistaken, the continuous-time analog is

$$ (1 - e^\frac{-X}{u})^x$$

Is that correct? The combination of exponential and power function is making me quite uncomfortable.

An alternative approximating approach you could use as as check might be to say there are $X$ job offers in total and $u$ unemployed.

So the probability that an individual does not get a particular job offer is $\left(1-\dfrac{1}{u}\right)$ and so the probability the individual does not get any job offer is $\left(1-\dfrac{1}{u}\right)^X$ which is $\left(\left(1-\dfrac{1}{u}\right)^u\right)^{x/u} \approx e^{-X/u}$ much as one might expect from a Poisson distribution. You have an error in the sign of $e^{-X/u}$.

That makes the probability the individual does get a job offer about $1-e^{-X/u}$. It makes the expected number of individuals receiving job offers about $u(1-e^{-X/u})$.

The probability that $y$ individuals get job offers (rather than $x$ as you have already used $X$) is then roughly the binomial $\displaystyle {y \choose u}\left(1-e^{-X/u}\right)^y e^{-(u-y)X/u}$ and or if you wanted a Poisson approximation to this then about $\dfrac{e^{-u\left(1-e^{-X/u}\right)}u^y\left(1-e^{-X/u}\right)^y}{y!}$ and you could apply further approximations to this but it would not get much tidier


In a perfectly competitive industry, why is apple considered best example of commodity? Out of these options,

shampoo
apples
ice cream
hotels

Why is apple considered to be the best example of commodity in a perfectly competitive industry? And Why not others?

In a perfectly competitive industry model, out of the examples given, the apple is the commodity with the least differentiation in the market. It is considered to be a homogeneous product.

A person (in this model) is unlikely to care about finding a specific type of apple from a certain company that uses a certain type of advertising. They just want to buy "an apple." All things being equal, they will probably just purchase the apple with the lowest price.

The other examples of shampoo, hotels, and ice cream are heterogeneous  in that these products have many ways of distinguishing their features from competing products. Design, advertising, packaging, utility, and other features stand out in addition to sensory features. Pricing can vary significantly since suppliers can make their products stand out from competing products.

(In reality, apples have a lot of variation, but in the model of perfect competition we just assume apples are of about identical size, taste, texture, weight, shape, etc. Apples are a classic example of a homogenous commodity, but not a perfect one because apples are not identical in the real world. However, they are probably more similar to a consumer comparing products than the other given options.)


Interpreting correlation between fixed effect and explanatory variable I'm dealing with panel data and I chose to do a regression with cross-sectional fixed effects. Some of my explanatory variables (such as $debt_{it}$) do not show very much variation over the time dimension. In fact, the most interesting variation in $debt_{it}$ (but also in some other variables), is probably the cross-sectional variation (i.e. one country having a higher debt over the entire period under investigation) rather than the variation of debt over time within each country.

Therefore, I believe that demeaning the data by using cross-section fixed effects may elimate a lot of interesting information. The $H_{0}$ of redundant fixed effects is strongly rejected, and the Hausman test strongly rejects the consistency of the random effects estimator. Doing a pooled estimation, rather than F.E. estimation, more than doubles the estimated coefficient to debt.

In an attempt to 'retrieve' the valuable cross-sectional information, I plotted each country's fixed effect against each country's average level of debt over the time period. There was a significant correlation $(p<0,01)$ between the averaged debt and the fixed effect. Intuitively, it seems to me that I can conclude that (even though the coefficient to $debt_{it}$ is possibly insignificant, depending on the specification, I'm still working on this) a higher debt does result in higher interest rate spreads (which is the dependent variable).

These are my questions:

Is my intuition correct?
If it is not, which I assume to be the case since I have never come across a similar reasoning, where exactly does my reasoning fail? Can you provide some intuition or an accessible reference dealing with the issue?
Are there any estimators that are better equipped to use cross-sectional variation in the data than the within-estimator?

You have done two different things.

Your fixed-effects model captures the within-group over-time functional relationship between $debt_{it}$ and $y_{it}$ (that is, how much average difference in $y_{it}$ is there between two periods with a 1-unit difference in $debt_{it}$ within a country). In your data, there is limited within-group variability in $debt_{it}$, which probably lead to a large standard error and a resulting insignificance.

Your reasoning about the correlation between the fixed effects and the explanatory variable is about the cross-sectional functional relationship. You found that countries with higher $debt_{it}$ have higher $y_{it}$ values (as opposed to periods with higher $debt_{it}$ having higher $y_{it}$ within a country). This is not what you originally intended to investigate when you set up your fixed-effects model.

Your Hausman test says that the within-group functional relationship and the cross-sectional functional relationship are different.

That said, yes, it is true that "a higher debt does result in higher interest rate spreads", but it is true only in the specific sense that "countries with higher debts show higher interest rate spreads". You should be careful when saying "result in".

Overcoming the issue of limited over-time variation and having significant results is hard. There is no magic. Abandon the fixed effects model, and try to control for many time-varying and time-invariant regressors, enough for you to argue that you controlled for most country-specific factors. (You can use RE or POLS estimation.) People might still criticize that you didn't control for enough factors, but you will need to defend yourself somehow. You could also move over to dynamic models or others, but that's a different story.


Welfare status when a positive externality is subsidised I was wondering if there is still welfare loss for example there is a positive externality in production of a good and the government decides to subsidise the good?

I think it does still have welfare loss, because the subsidy has to be payed for but I am not sure.

Is it because the government taxes things that have negative externalities and then uses this money to subsidise things that have positive externalities that in the end there is no welfare loss?

Thank you for your help in advance.

Yes. While producer and consumer surplus rise, the total cost to government exceeded the increase, leaving deadweight loss.


Is it possible to have constant marginal cost and decreasing average cost simultaneously? I thought about possibility of occurring such event in the case of presence  of fixed costs, but I would like to know others opinions.

Yes, if there are non-zero fixed costs, and constant marginal cost, then average cost decreases strictly monotonically with quantity, asymptotic to the marginal cost.


How do I begin to approach this dynamic discrete choice model? I'm working through an old problem set (that sadly I don't have solutions for) and I got stuck. It is a dynamic model of entrepreneurship and invention. I'm looking for guidance on this model as well as references or papers that discuss it. Here's the model.

Every period you can choose to start a business. The choice in period $t$ is $b_t \in \{0, 1\}$, where $b_t=1$ is trying to invent something, so it's a discrete choice problem. You have some skill parameter $p$. In every period that you invent, your invention ``succeeds'' with probability $p$ and you get $v=1$. Otherwise it fails and you get $v=0$.

If you don't invent in period $t$ you work and get some wage $w$. The person has linear lifetime utility like this

\begin{equation}
\sum_{t=0}^\infty \beta^t [b_t I\{\text{successful invention}\} + (1 - b_t)w]
\end{equation}

$I$ is the indicator function. The problem is we (and the agent) don't know $p$. They just know its distributed with a beta distribution with parameters $a$ and $b$ and they have to learn about it over time. I know how to update the prior depending on if the invention succeeds or not (if the person chose to invent in period $t$).

The problem set asks me to set up the Bellman equation and use value function iteration to solve the problem numerically, but that's where I got stuck. Can someone give me a push in the right direction for how to start?

The general Bellman equation is something like this

\begin{equation}
V(b) = \max_{b'} (u(b) + \beta E V(b'))
\end{equation}
$b$ is the agent's choice in the current period and $b'$ is the agents choice in the next period. I can't figure out how to incorporate the Bayesian updating of the prior into the expectation, though, since the value of the prior going into period $t$ and thus the value of the posterior at the end of that period depends on the history of successful or failed inventions.

For ex. the person starts out with the prior on $p$ as just the mean of the beta distribution, which is $a/(a+b)$, but if they choose to invent in the next period and are successful, the beta distribution updates to the posterior that has mean $(a+1)/(a+1 + b)$. Etc.

$b_t$ is the decision variable, and the value function is formulated as a function of the state variable of the problem. In your case, the role of the state variable is played by the $p$ parameter, which may change in each period (updated). So your Bellman equation is

$$V(p_t) = \max_{b_t} \{u(b_t) + \beta E [V(p_{t+1})\mid t]\}$$

and I guess now you see where the updating of $p$ enters the picture.

On "Value function iteration", or "iteration on the Bellman equation", the book "Recursive Macroeconomic Theory" of Ljungqvist & Sargent contains clear and practical guidance.


Monetary Policy - How can increasing interest rates cause higher inflation in the short term? My understanding of the interest rates part of monetary policy is the follows:

Borrower's point of view:

An increase in interest rates, increases the cost of borrowing, which may reduce disposable income, causing a reductiong in aggregate demand. The equillibrium between supply and demand will therefore need to be adjusted resulting in a lower average prices (less inflation).

Saver's point of view:

As interest rates rise, the reward for saving increases, therefore people are incentivised to save their money, which may cause a decrease in disposable income and less inflation.

However, I have a question in my textbook which says how can a rise in interest rates cause higher inflation in the short term, and I'm not sure.

If mortgage payments are included in the basket of goods that are used to calculate inflation, then rising interest rates will increase mortgage payments, causing an increase in inflation in the short term. This happens before any of the disinflationary effects show up in the data.


Is a social choice aggregation rule defined for a set of weightings over the set of voters (N)? In Christian List's Stanford Encyclopaedia entry Social Choice Theory (2013, https://plato.stanford.edu/entries/social-choice) he says that:

  "an aggregation rule is defined for a fixed set of individuals N and a fixed decision problem, so that majority rule in a group of two individuals is a different mathematical object from majority rule in a group of three."

I was wondering if, in a similar way, social choice aggregation rules are defined for a set of weightings over N? In other words, does a disagreement regarding how to weight the voters entail a disagreement regarding aggregation rule?

E.g. let's say that N = {voter-1, voter-2}. Furthermore, you and I both favour a lexicographic dictatorship. The only difference is that you favour a lexicographic dictatorship which ranks voter-1 over voter-2, and I favour a lexicographic dictatorship which ranks voter-2 over voter-1. Strictly speaking, do we agree on aggregation rule, or do we disagree?

Any help would be greatly appreciated! :)

First it is important to define our terms.  The concept of "weighted voters" does not necessarily make sense for an arbitrary social choice rule.  So presumably we are interested in social choice rules where, at some point in the aggregation process, we add up a collection of terms, where each term contains information about the preferences or opinion of some voter.  Typically, such rules are "anonymous" in the sense that we can permute the opinions of the voters without changing the answer.  We can easily introduce a "weighted" version of such a rule by computing a weighted sum instead of an unweighted sum.  (Typically, a weighted version of the rule fails to be anonymous.)

Let us say that two social choice rules $F$ and $G$ are different if they sometimes produce different outputs when presented with identical input (e.g. when presented with identical preference profiles).  In that case, it is definitely the case that in general, different voter-weights will yield different social choice rules.

For example, let's consider "weighted majority voting" with three voters, $A$, $B$ and $C$.  One possibility is that each voter receives equal weight (say, 1/3) ---this is effectively the "unweighted" version, which satisfies anonymity.  Another possibility is that voter $A$ receives weight 5, while voters $B$ and $C$ each receive weight 1.  It is easily verified that this "weighted majority rule" is actually a dictatorship for $A$.

Of course, we might say that all the different weighted majority rules belong to the same "family" of voting rules, and therefore they all have certain properties in common.  For example, there are many theorems which are proved for the family of "all weighted majority rules"  (or "for all weighted scoring rules", or whatever).  But that does not mean that they are the "same" rule.

When you ask, "does a disagreement regarding how to weight the voters entail a disagreement regarding aggregation rule?", the answer is "yes and no".  Clearly, we might agree on the type of voting rule to use (say, we agree to use a weighted majority rule because it satisfies certain desirable properties and we all agree these properties are important), while still disagreeing on the exact weights to use in the rule.


What value does one set, in general, for the null hypothesis of $\beta_0$ ("Y-intercept")? Say there is a linear regression model to estimate Y, that is:

$Y_i = B_0 + B_1X_i + u$

When testing the Betas of our sample's regression model for significance the null hypothesis for $B_1$ would naturally be set as zero (assuming X has no impact on Y).

However, what would the null hypothesis for $B_0$ be set as?
If it is set as zero, is that not assuming that a certain value is taken by Y in the absence of X, i.e. zero?
In general is there any non-arbitrary setting for $B_0$ we would test against?

Or does the value of $B_0$ vary from case to case?

I am aware that a sampling test is conducted on $B_0$ and as such am curious as to what the exact purpose of this test would be? Is there any actual null hypothesis $B_0$ is being tested against or is the data presented only to illustrate the confidence intervals and other statistics, such as variance?

If you simply want to estimate the values of Y corresponding to particular values of X, you can calculate the regression to obtain estimates of $\beta_0$ and $\beta_1$, and need not be concerned with hypothesis testing.

If you want to test one or more hypotheses, then the choice of hypotheses should be driven by the purpose of your research. A common aim is to assess the relevance of an independent variable by testing the hypothesis that its parameter equals zero, but that is just one choice.  In this case you might want to test the hypothesis that $\beta_1=0$, and you can do so without testing any hypothesis about $\beta_0$.

Where matters possibly become confusing is that regression software often, by default, generates t-values for all the independent variables and the constant. If you want to test the hypotheses that $\beta_0=0$ or $\beta_1=0$, these t-values are useful.  But you can also ignore them if you are not interested in testing those hypotheses.  The estimated parameters don't depend on these hypotheses or t-values, so you can still use them in estimating values of Y.


Can corporate tax loss carryforward function like a sort of insurance policy? I'm a graduate student in mathematics, with a casual knowledge of economics, so please let me know if this question is a non-sequitur or off base.

Here's the intuition I'm trying to capture: Suppose corporation A has a good year and makes a lot of profit, and corporation B, their competitor, has a bad year wherein they have a net loss. It seems that the following year, corporation B has a relative competitive advantage, in that they have a lower tax burden.

In a system with no corporate tax—and thus no tax loss carryforward—it seems that corporation B wouldn't have this advantage which might give them some time to recover. In a system with a very high corporate tax, this benefit would be even greater.

Value judgments about the utility of a high corporate tax aside, is there anything to the idea that corporate taxes can serve as a sort of "insurance policy" wherein companies with a bad year are more likely to survive?

The structure of the tax ladder is such that the marginal tax rates keep increasing. The upshot is that if you earn more, your net earning (after taxes) will never be lower. So a company with a good year will always be better off compared to a company with a bad year, holding everything else equal. In this sense, tax does not provide advantage to companies with a bad year.

Your idea of "insurance policy" would be most closely related to the concept of automatic stabilizer. But this concept talks about the macro picture of the entire economy, so I'm not sure if it's wise to link the two together.


A decrease in the cost of borrowing (interest rate) will case A decrease in the cost of borrowing (interest rate) will case
a) the demand for loanable funds to increase.
b) the supply of loanable funds to decrease.
c) both A and B.
d) either A or B, but not both.
e) none of the above.

The answer is e, but why? Doesn't a decrease in the interest rate will cause people to save less, but it causes firms to invest more? Why is the answer not c?

I believe this is a trick question testing to see if the introductory economics student has overcome the usual confusion over "demand vs quantity demanded" and "supply vs quantity supplied".

When the price of an apple falls, this may cause quantity demanded or quantity supplied (of apples) to change, but cannot cause demand or supply to change.

Similarly, when the interest rate (or the price of loanable funds) changes, this may cause quantity demanded or quantity supplied (of loanable funds) to change, but cannot cause demand or supply to change. Hence, the answer is E.


Maximized tax revenue & foreign labor I'm dealing with a tricky assignment, and I have no idea of where to begin.
Person 1 lives in Denmark and has a utility function given by,
$$(1) \ \ u(c,l)=c-\frac{\eta}{\eta+1}(24-l)^{\frac{\eta+1}{\eta}}$$
Where $\eta>0$, $c$ is consumption and $l$ is leisure.
The danish government imposes a tax on the person, $t, 0<t<1$ such that his 'post-tax' wage is given by $w=\bar{w}(1-t)$. Tax revenue is given by
$$(2) \ \ T=t\cdot \bar{w}\cdot S(w)$$
where $S(w)$ is the supply of labor and $\bar{w}$ is wage.
First I derived the tax that yields the most tax revenue, $t^*=\frac{1}{(1+\eta)}$.
Here comes the problem.
Suppose that a second person (Person 2) with the same utility function is living in Wales. She is only willing to move to Denmark (for example when a big firm want's to import foreign labor because of qualifications) only when she can get a utility (after tax) that is higher than $\bar{u}$. Suppose that:
$$(3) \ \ \bar{u}>\frac{1}{\eta+1}\left(\frac{\eta}{1+\eta}\frac{\bar{w}}{p}\right)^{\eta+1}$$
I have to show that the tax that is maximizing tax-revenue ($t^*$) is 'too high' for Person 2 to move to Denmark.
I get that I have to show that Person 2's utility is higher when she lives in Wales, than if she lived in Denmark - but how?

I give here the procedure but with price $p=1$ you can do it yourself without that simplification.
Set up Lagrange
$$\mathcal L(c,l,\lambda) = u(c,l) - \lambda (c-\bar w(1-t)(24-l)) $$
clearly
$$\frac{\partial \mathcal L }{\partial c} = \frac{\partial u}{\partial c} - \lambda = 1- \lambda$$
so $\lambda=1$ and constraint is binding. Therefore
$$c^\star = \bar w(1-t)(24-l^\star)$$
Furthermore
$$\frac{\partial L}{\partial l} = (24-l)^{1/\eta} - \lambda \bar w (1-t) = 0$$
since $\lambda = 1$ it follows that
$$l^\star = 24 - (\bar w(1-t))^\eta$$
plugging $l^\star$ and $c^\star$ into utility function, starting with $c^\star$ you get
$$\bar w(1-t)(24 - l^\star) - \frac{\eta}{\eta + 1}(24 - l^\star)^{\frac{\eta + 1}{\eta}}$$
then $l^\star$ to get
$$\bar w(1-t)[\bar w(1-t)]^{\eta} -  \frac{\eta}{\eta + 1}(\bar w(1-t))^{\frac{\eta(\eta + 1)}{\eta}},$$
reduce this to get
$$(\bar w (1-t))^{\eta +1}[1/(\eta + 1)]$$
insert optimal tax and get
$$\left(\bar w \frac{\eta}{\eta + 1}\right)^{\eta +1}[1/(\eta + 1)]$$


Why is marginal cost not the cost of producing the last unit? I am slightly confused about this wikipedia article. en.wikipedia.org/wiki/Marginal_cost

It states that marginal cost is not the cost of producing the next or last unit.

Why is this the case? I thought that was precisely the definition of marginal cost.

I also hear marginal cost defined as cost of the last unit. What is meant by this? If quantity is increased by 5, is the marginal cost the cost of the 5th unit only?

The full quote from the cited reference (p. 181) is

  Marginal cost is not the cost of producing the "last" unit of output. The cost of producing the last unit of output is the same as the cost of producing the first or any other unit of output and is, in fact, the average cost of output. Marginal cost (in the finite sense) is the increase (or decrease) in cost resulting from the production of an extra increment of output, which is not the same thing as the "cost of the last unit."

I think the boldfaced part is the important part that the Wikipedia editor left out.

What you have in mind is correct. Suppose we can produce 4 hats for the cost of \$8, and 5 hats for the cost of \$15, then the authors are saying that if you choose to produce 5 hats instead of 4, then it would cost you \$7 more. That's the marginal cost.

They argue that it's not right to say that, having chosen to produce 5 hats, that the cost of producing the 5th hat is \$7.

To me, this is a very minor distinction.


Why so many suppliers of inexpensive ordinary products There are a very large number of suppliers of common, inexpensive products, and I am wondering why a few large companies don't simply provide all the supply? I am not thinking of food or clothing or something where people could meaningfully differ on preferences, I mean things we don't see or can't distinguish anyway, things that I call 'commodities'. The best example I have today is cabin air filters for cars.
I went to buy one at Walmart today, and there were several brands and about 50 different sizes, and all the brands had a different numbering scheme. This was vexing, and I bought one only to discover that it didn't fit. I looked at Amazon.com and found an absolutely staggering number of brand names. Is there some point to this? Are cabin air filters so exciting that everyone needs to get in on the action? Why don't a few companies make them all? Is there a reason that the 'marketplace' can support a huge number of producers for something no one could tell apart or really care much about?
Perhaps this relates to the concept of Indifference in economics. I have seen this dynamic in other products, but this is the best example I know of. Try looking on Amazon and see for yourself.

There can be several reasons or combination of reasons that could be responsible. This is too broad topic to go into every minutiae detail but main well known reasons from industrial organization literature would be (see Peitz and Belleflamme: Industrial Organization: Markets and Strategies):

Small businesses might have cost advantage over large businesses. Not every industry has production function with increasing returns to scale. If returns to scale are decreasing there might be an optimal sweet spot size for a firm beyond which it does not pay to grow output more.
If there are no significant barriers to entry, markets with homogenous products will typically attract a lot of competition.
Government policy might be responsible for that as well. Many countries support small and medium size businesses with various policies. If government positively discriminates towards such businesses with lower corporate taxes, subsidies etc, then this might discourage expansion of these businesses since loosing subsidy is equivalent of facing tax on a margin and thus it would discourage businesses from expanding unless there would be sufficiently large economies of scale that would outweigh this.

Furthermore, note you are likely getting causality in a reverse. It is well established that competition among many suppliers of similar/same product leads to lower prices in most models (see overview of industrial organization literature in the above mentioned Peitz and Belleflamme). Consequently, the reason why common items are cheap is that there are many suppliers in the first place.


Prove that budget constraint is Lower Hemi Continuos (LHC) I need to prove that the following constraint is LHC.
$B=\{x \in R^n : px\leqslant pw)$
But Im not capable of finding and sequence $\{x_n\}$ such that $x_n \in B(p_n,w_n) \forall n$ and that $x_n\longrightarrow x$.
I tried with setting  $x_n=\frac{x}{1+\beta^n}$, $p_n=\frac{p}{1+\beta^n}$ , $w_n=\frac{w}{1+\beta^n}$ because in that case $x_n\longrightarrow x$. and $x_n \in B(p_n,w_n) \forall n$ but I thing I'm not covering the $\forall p_n, w_n$ part.
Help please and thanks in advance.

I don't believe it is lower semicontinous.
Let $w = (0,\dots,0)$, $p \in \mathbb{R}^n_+$ be any vector such that $p_1 = 0$ (the first coordinate being 0).
The allocation $x=(1,0,\dots,0) \in B(p,w)$.
Define the sequence $p_n = p  + (\frac{1}{n},0,\dots,0)$ and $w_n = (\frac{1}{n},0,\dots,0)$. $w_n \rightarrow w$ and $p_n \rightarrow p$.
For any $x^n \in B(p_n,w_n)$, $p_n x^n_1 \leq w_np_n$, so $x_1^n \leq \frac{1}{n}$.
Hence for any sequence such that $x^n \in B(p_n,w_n)$, $x^n \not \rightarrow x$.


Cost function from an easy CES production function How can I find the cost function c(w,p) given that the production is
$f(x) = x_1+x_2$
I did Lagrangien's method but my problem is that I got no $x_1$ and no $x_2$ after taking the derivate.
So I would like to know how can I derive a cost function?
Thanks in advance !

Imagine that you are a dictator in Sausageland. Your legitimicay depends on you delevering sausages to the inhabitants. Each inhabitant must be given 1 sausage and there are $y$ inhabitants. To produce sausages you command two factories: One factory produces $x_1$ vegan sausages using $x_1$ cabbage heads the other factory produces $x_2$ pork sausages using $x_2$ units of pork meat. Which factory do you use?
Well since the factories are equally productive transforming one unit of input into one unit of output independent of the level of production $y$ you simple follow the rule of cost minimizing and use the factory for which the input is the cheapest.
Vegan sausage case:
So in the case where $w_1<w_2$ it follows that $\min(w_1,w_2) = w_1$ and $y=x_1$ so costs are $w_1x_1$ which is $\min(w_1,w_2)y$.
Pork sausage case:
So in the case where $w_2<w_1$ it follows that $\min(w_1,w_2) = w_2$ and $y=x_2$ so costs are $w_2x_2$ which is $\min(w_1,w_2)y$.
In the knife edge case where $w_1=w_2$ it does not matter whether you produce pork
sausages or cabbage sausages they are equally costly to produce so the only requirement is that the total number of sausages  add up to $y$ hence $x_1+x_2=y$ with the solution set $\{(x_1,x_2) \lvert x_1+x_2=y,x_1\geq0,x_2\geq 0\}$.
Combined sausage case:
So in the case where $w_2=w_1$ it follows that $\min(w_1,w_2) = w_2=w_1$ and $y=x_2+x_1$ so costs are $w_1x_1+w_2x_2 = w_1(x_1+x_2) = w_1 y$ which is $\min(w_1,w_2)y$.
So in all three cases the cost function can be written as
$$C(w_1,w_2,y) = \min(w_1,w_2)y$$
Cost minimizing program
Another approach is to set up the cost minimizing program. The costs are given as $w_1x_1 + w_2x_2$ which is the objective function to be minimized. The constraints are that $f(x_1,x_2) = x_1 + x_2 \geq y$ and $x_1\geq 0$ and $x_2\geq 0$.
The cost function is derived by solving the problem
$$\min_{x_1,x_2} \ \ w_1x_1 + w_2x_2 \\ s.t. \ \ x_1 + x_2 \geq y \\ \ \ x_1 \geq 0 \\ \ \ x_2 \geq 0$$
The costs are given as $w_1x_1 + w_2x_2$ and they are to be minimized subject to the constraint that at least $y$ is produced as output.
One potential first step could be to check if some of the inequality constraints must be binding in optimum. So consider the case where $f(x_1,x_2) = x_1 + x_2 > y$ for which a numerical example could be that you are supposed to produce at least $y=4$ and you produce $f(x_1,x_2)=4.1$ using inputs $x_1=2.1$ and $x_2=2$. Clearly you could reduce costs by using less $x_1$ and still respecting the constraint $x_1 + x_2 \geq y$ (I am assuming that $w_1$ and $w_2$ are both strictly positive so reducing $x_1$ decrease costs $w_1x_1 + w_2x_2$). Hopefully you can convince yourself that it would always be a waste of money to produce more output $f(x_1,x_2) = x_1 + x_2$ than required $y$. And you can therefore conclude that any solution $(x_1^\star,x_2^\star)$  must satisfy
$$(1) \ \ x_1 + x_2 = y.$$
You now have one equation in two unknowns which is great progress but not enough.
Again you follow the procedure of considering the three cases $w_1>w_2$, $w_2>w_1$ and $w_1=w_2$. For the cases $w_1\not =w_2$ you should be able to convince yourself that you produce with the cheapest production factor and therefore for the other factor you have $x_i = 0$. In either case you have two equations with two unknowns and by similar arguments as above $\min(w_1,w_2) y$ are the costs.
In the knife edge case where $w_1=w_2$ non of the constraints $x_1\geq 0$ and $x_2\geq 0$ are binding. You therefore do not end up with two equation in two unknowns and but simly have the inequalities $x_1\geq 0$ and $x_2 \geq 0$ and the equality $x_1+x_2=y$ and infinitely many solutions $\{(x_1,x_2) \lvert x_1\geq 0, x_2 \geq 0,x_1+x_2=y\}$. Obviously, this can seem annoying when hoping for a unique solution. However, you should be familiar with this case from utility maximization for perfect substitutes.
Lagrange
You can perfectly well use Lagrange for this problem. However, imagine that you forget the positivity constraints on $x_1$ and $x_2$ then your Lagrangian function becomes
$$L(x_1,x_2) = w_1x_1 + w_2x_2 - \lambda(x_1 + x_2 - y),$$
with first order conditions
$$w_1 - \lambda = 0 \\ w_2 - \lambda = 0$$
using the assumption that $w_1>0$ it follows by the complementarity condition $\lambda(x_1 + x_2 - y)=0$ that $x_1 + x_2 - y=0$ so $x_1+x_2=y$. That is not a problem.
However, you also have the implication that $\lambda = w_1 = w_2$ which is a problem because it excludes the real possibilities that $w_1\not = w_2$. Nevertheless, let us assume that $w_1=w_2$ then the FOC do not tell us anything about $(x_1,x_2)$ and are trivially satisfied by any $(x_1,x_2)$. Again you are left with the solution being all $(x_1,x_2)$ where $x_1+x_2=y$ for the case where $w_1=w_2$. In this case it is not wrong bu it is incomplete.
So including the positivity constraints in the Lagrangian you get
$$L(x_1,x_2) = w_1x_1 + w_2x_2 - \lambda(x_1 + x_2 - y) - \delta_1x_1 - \delta_2 x_2$$
with FOC's
$$w_1 - \lambda - \delta_1 = 0$$
$$w_2 - \lambda - \delta_2 = 0$$
Here you should use the complemetarity conditions to consider which inequalitites are binding in optimum.
So first assume that $x_1>0$ then by complementarity $\delta_1 x_1=0$ it follows that $\delta_1=0$. Using the first order condition you then get that $w_1 = \lambda$ and since $w_1>0$ it follows that $\lambda>0$. Using that $\lambda>0$ in combination with the complementarity condition $\lambda(x_1+x_2-y)=0$ you get $x_1+x_2=y$.
Combining $w_1=\lambda$ with the second FOC $w_2 - \lambda - \delta_2=0$ implies that $w_2 - w_1 = \delta_2$. It is known from KKT-theorem that $\delta_2\geq 0$. If we assume $\delta_2 = 0$ we are back in the solution $w_1=w_2$ so we instead let $\delta_2>0$ but by complementarity this then implies that $x_2=0$ and by the identity $w_2 - w_1 = \delta_2$ this is the case where $w_2>w_1$.
A completely symmetrical arguments is used to solve for $w_1>w_2$. But as you can see using Lagrange is tedious in this simple case. For a statement of the KKT-theorem you can see Nocedal and Wright page 328.


What might happen if the Fed stopped paying interest on excess reserves? I am curious to hear what economists think might happen if the Fed stopped paying interest on reserves held in excess of the penalty free upper bound. I am also curious to know how economists think this practice might be fazed out gradually in such a way that the Fed could mitigate the negative effects that might accompany a sudden and complete cessation of the practice.

For example - If banks stop earning risk-free profit on these reserves (current at .25 percent, I think) would they feel compelled to channel these excess funds into profitable loans? Perhaps this is a way the Fed could keep interest rates low after ending QE practices? Would ending the interest payments overnight cause banks to start lending such that we would experience significant inflation?

Any feedback, papers, etc. much appreciated!

If the Fed paid paid 0% on excess reserves, banks holding excess reserves would immediately try to buy Treasury bills that paid more than the 0% paid by excess reserves. This would drive Treasury bill (and other short-term risk-free rates) to 0%.

The Fed pays interest on excess reserves to allow short-term market rates to be near their target (which is now above 0%).


Clarification about demand elasticity and monopoly I am having a difficulty understanding certain things about elasticity and would like to clarify them.

What I understand.
Elasticity is the percent change in quantity due to a percent change in price, that is, how does output change due to a change in price.
A good is inelastic, if there is only 1(or few) producers of this firm, since, there are no perfect substitutes for this good. Which implies that if the price where to increase quantity would not decrease as consumers have no other options.
On the other hand, a good is elastic, when there are various other firms selling this same good. Thus if there is an increase in price of a good, consumers will chose to purchase from other firms who offer the same product.

Now, this is where I get really confused.
The sentence that "monopolists always operate on the elastic portion of their demand curve." The reason this confuses me, is that I thought if you are a monopoly then your good is inelastic as mentioned above.

The only explanation that I can provide to myself is that there are two levels of elasticity going on here. That is 1. elasticity between monopoly and perfect competition and 2. depending on which one there is another elasticity inside. To further explain what I mean, is if for instance we are dealing with a monopolist, we know that his demand will be inelastic. But not within this inelastic demand there is an elastic and inelastic portion. Am I completely incorrect? Please help me understand this concept.

If the assumption that there is one elasticity within the other is incorrect, this is my ultimate question.

If monopolists have inelastic demand (since they are the only producer of this good) how can they operate on an elastic portion?

You are correct in saying that there is an elastic portion within the inelastic demand. The concept is much easier explained when using a simple demand curve diagram. From the diagram given below, we can clearly see the varying elasticities in different parts of the curve. You can even try it yourself, using 2 points on each part and comparing the elasticity.


Is this Cost function concave or convex? Given the following cost function, where t is the quantity of some product.

$$C(t) = 1/3t^3 - 7t^2 +11t + 50$$

here is a graph between $t= 0$ and $t = 25$

We are asked if this function is convex or concave?

Technically it is neither, but I am asking, in the context of economics, do we have to define intervals and say, between $0$ and $4.11$, it is concave, and for $t>4.12$ we have a convex function?

"In the context of economics", it is neither - because convexity in economics means the same it does in math. If you redefine its domain, such that it's only computed for any $t > 4.12$, this function's image is clearly convex: no line between two vectors inside it isn't entirely contained in the set.

P.S: Although convexity has the same definition in both fields, it has an important economic interpretation and is a very important hypothesis in many classical general equilibrium models.


Unemployment and the Frisch-Elasticity There is the long debate on the Frisch-Elasticity being the driver of unemployment over the business cycle.

One argument against the voluntary-unemployment mechanism of RBC models is that if we distinguish two subgroups of the population with different Frisch-elasticities, the one with the higher elasticity should respond stronger to wage fluctuations.

Women have a bigger elasticity than men, yet their employment fluctuates less over the business cycle.

Is there a counterargument to this that salvages the neoclassical model of voluntary unemployment? I'm specifically referring to this argument that builds on heterogeneity in the elasticity, not on the Micro vs Macro estimation discussion.

There are a couple of good papers on this that I know of.

Keane, Michael and Richard Rogerson, “Micro and Macro Labor Sup-
ply Elasticities: A Reassessment of Conventional Wisdom,” Journal of
Economic Literature, 2012, 50, 464-476.

"The response of aggregate labor supply to various changes in the economic environment
is central to many economic issues, especially the optimal design of tax policies.
Conventional wisdom based on studies in the 1980s and 1990s has long held that the
analysis of micro data leads one to conclude that aggregate labor supply elasticities
are quite small. In this paper we argue that this conventional wisdom does not hold
up to empirically reasonable and relevant extensions of simple life cycle models that
served as the basis for these conclusions. In particular, we show that several pieces
of conventional wisdom fail in the presence of human capital accumulation or labor
supply decisions that allow for adjustment along both the extensive and intensive
margin. We conclude that previous estimates of small labor supply elasticities based
on micro data are fully consistent with large aggregate labor supply elasticities."

Peterman, William B, “Reconciling Micro and Macro Estimates of the
Frisch Labor Supply Elasticity: A Sensitivity Analysis,” Technical Report,
Federal Reserve Board of Governors 2014.

"Microeconometric estimates of the Frisch labor supply (0 to 0.5) tend to be much lower than the values used by macroeconomists to calibrate general equilibrium models (2-4). This paper explores whether the gap in these ranges can be explained by two restrictions present in the micro Frisch elasticity that are implicitly relaxed in these values of the macro Frisch elasticity. First, the micro estimates focuses only on prime-aged married males who are the head of their household, while the macro values incorporates the whole population. Second, the micro estimates only include fluctuations in hours on the intensive margin, while the macro values also incorporate fluctuations on the extensive margin. Within a consistent microeconometric estimation strategy, this paper estimates a micro Frisch elasticity of 0.2, and, upon relaxing the two restrictions, a macro Frisch elasticity of about 3. The increase in the estimates suggests that these two restrictions can explain the gap. However, given that this paper demonstrates that the estimates of the macro Frisch elasticity are fairly sensitive to the estimation procedure, the sample of agents, and also the margins of fluctuations that are used for estimation one must careful choose the appropriate value for calibration purposes."


Pareto efficient quantity of public good (quasi-linear preferences) I am doing a question on finding the Pareto efficient quantity of a public good. Instead of using the condition $\sum MRS_i = c'(G)$ where $c(G)$ denotes the cost of the public good, it asks you to find the efficient quantity by maximising the sum of the agents' utilities. Apparently this is only valid if preferences are quasi-linear so whilst I can do the question I do not understand why this is a valid approach. Any help on this matter would be appreciated.

I don't think it is true in a standard public good economy the question is referring to. Consider the following counterexample:

Suppose $I  = \{1,2\}$ and utility of the individual $i$ depends on his consumption of public good $(G)$ and private good $x_i$: $u_1(G, x_1) = 2\sqrt{G} + x_1$ and $u_2(G, x_2) = 2\sqrt{G} + x_2$,

Also, the CRS technology used for production of public good uses private good as input:
$G = f(x_0) = x_0$.

If the society has only 4 units of private good in the beginning, then the set of feasible allocations can be written as

$\{(G, x_1, x_2)\in\mathbb{R}^3_+: G+x_1+x_2 = 4\}$.

Notice that the allocation $a_1 = (G, x_1, x_2) = (1,3,0)$ is Pareto efficient, but does not maximize the sum of utilities. The reason is that allocation $a_2 = (G, x_1, x_2) = (4,0,0)$ yields the higher sum.

$\color{blue}{u_1(1,3) + u_2(1,0)} = 5+2 =7 \color{blue}{<} 8 = 4 + 4 = \color{blue}{u_1(4,0) + u_2(4,0)}$.


What's a singular model in economics? What's a singular model in economics? I've tried google, but I didn't find a definition...

In an article by Ingram et al (1994), they state:

  This linear model is singular because it predicts that the current value of consumption is an exact(non-stochastic) function of current output and lagged consumption.

Also, the paper says that any model (RBC and extensions) with a number of shocks smaller than the number of observable endogenous variables, has this particular behaviour. So, the models are not 'singular' as a dictionary definition.

From this I get that any stochastic model, which determines some observable endogenous variable to follown a non-stochastic path, then I can call it singular. Is this correct?

Also, does this definition have any relation to bifurcation? In ODE we have a 'bifurcation' of solutions, when

$\dot x = F(x,\mu)$, and at $\mu=\mu^*$, $DF(x,\mu^*)$ is singular, but non-singular at every other value of $\mu$. The equilibrium will depend continuously on $\mu$ and 'after' stability is lost, new stable equilibria will appear. (this lacks mathematical precision, but I think it suits the purpose of stating the intuition of bifurcation)

Any help would be appreciated.

I have tried to grab the article to read it, but my library apparently doesn't subscribe to JME as full text.  However, when I have seen the word singular used in economics it is usually in the framework of a singular matrix.  As this article appears to be a criticism of another model, it would appear they are arguing the other model would not give rise to an invertible matrix.  In the above set of comments, it is implying that the stochastic component is vanishing and that the model is deterministic, despite the fact, there are no actual deterministic models in economics if you have to measure things.

My guess is that they are criticizing the other model by showing it can't work.


Understanding Classical Rationality at a Basic Level I am a high school student in an intro Microeconomics class (note that we have not covered utility functions) and I'm utterly confused about the classical concept of rationality. I certainly understand that that conception does not accurately describe a good chunk of real-world behavior (hence behavioral economics).

Nevertheless, my concern which I ask about here is more basic: Classical rationality as described in my textbook (Krugman/Wells' Economics) doesn't even seem coherent. It's essentially just defined as "people act to make themselves better off," but then the book (and online sources) go on to conclude that, under this definition, it is irrational to, say, honor sunk costs.

But why need this be so? (again, I'm not even talking about behavioral economics, I'm just trying to understand the justification within the traditional paradigm) After all,suppose person A knows they will derive satisfaction from honoring sunk costs. Then doesn't honoring sunk costs make them better off (it fulfills their desire for happiness), and therefore becomes rational for person A?

I feel like there may be some restrictions to the traditional definition of rationality that my book and teacher have glossed over. Because right now I am utterly at a loss for how my book can draw such specific conclusions about what is rational and irrational when the definition of rational behavior given seems malleable enough to make virtually any action rational for at least some people.

After all,suppose person A knows they will derive satisfaction from honoring sunk costs. Then doesn't honoring sunk costs make them better off (it fulfills their desire for happiness), and therefore becomes rational for person A?

Utility experienced from honouring sunk costs is treated separately from honouring sunk costs themselves. ( section 2 of http://www.princeton.edu/~tkelly/papers/Sunk%20Costs,%20Rationality,%20and%20Acting%20For%20the%20Sake%20of%20the%20Past.htm )

If I feel good for rescuing my phone from a toilet, or feel bad, that’s separate from the phone being in the toilet.


Should mean wages increase with inflation? Should mean wages increase with inflation?
If not, why? Has this profound consequences in the redistribution of wealth?
(not an expert in economics...I apologise is the question is too naif)

Should mean wages increase with inflation? If not, why?

No. Inflation is not the only factor that determines wages. Inflation has to do with the nominal value of wages, but these also entail components pertaining to the real value of work.

Here are three examples that tend to push mean wages down,

(1) technology, to the extent that it replaces human labor;

(2) foreign markets may lure high skilled workers (or, for what matters, workers with the highest salaries) to emigrate, causing -caeteris paribus- mean wages to decrease;

(3) public policy (whether it stems from unions or from policies aimed at reducing the number of unemployed) might prompt -otherwise unneeded- entry of more people in the labor market.

Other factors would have the effect of pushing mean wages up. For instance, the converse of (2) (that is, emigration only of workers earning the lowest salaries), unavailability of workers with high productivity, and so forth.

  Has this profound consequences in the redistribution of wealth?

That depends on the particularities of the economy being analyzed: what fiscal policy is implemented; whether households own significant portions of capital; the sensitivity and preponderance of different sectors in the economy; etc.


On what basis, is currency created? This is more like a homework question. I am quite a beginner. I would appreciate any help, preferably with less technical terms, that guides me in the right direction.
I went through the Wikipedia articles on Money, Debt, Government debt, Internal debt. And somehow I understood these lines from these articles.

Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context.
Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor.
Governments create debt by issuing government bonds and bills. Government debt can be categorized as internal debt (owed to lenders within the country) and external debt (owed to foreign lenders).
Internal debt or domestic debt is the part of the total government debt in a country that is owed to lenders within the country.

Perhaps, I came across hints but could not understand

How does any government "create" the currency in the first place?

Do the central banks just print some notes and offer it as a service? Say, Use our notes as an exchange medium

Or, is it something like we own the land and other assets, we put it at a value of some X amount

Is it something else?

How does any government "create" the currency in the first place?
Do the central banks just print some notes and offer it as a service? Say, Use our notes as an exchange medium

Currency in economics is just the notes and coins in circulation. These are minted and printed by government. In every country the institutional arrangement will be bit different. In some places central banks do the printing/minting of the currency in some others its done by mints or treasury departments. In US the printing of paper money is done by The Bureau of Engraving and Printing (BEP) and minting is done by the US Mint (see explainer in Investopedia). These agencies are nominally under the treasury department but in practice they create new currency when Fed orders it.
If you are interested in money more general not just currency (i.e. notes and coins) then in general money is created by Fed with help of private banks. The money is created whenever bank makes a loan as whenever a loan is issued a matching deposit is created with the money in it. This is done for a most part all electronically. The amount of loans private banks can issue depends on monetary policy of Fed, its regulations and how much reserves/base money it creates (if you are interesting in reading more on this you can have look at this BoE paper McLeay,  Radia, and Thomas; 2014). Money is also created when Fed directly purchases some assets, for example when Fed purchases treasuries it is done with newly created money.
It is not enough to just say: "Use our notes as an exchange medium" in fact there are many examples of countries where people decided simply not to use official government issued money but decided to switch to some other money (this is known as currency substitution). For example, in Zimbabwe people substituted their local currency for dollar (such currency substitution is called dollarization) and in fact between years 2009-2015 even government of Zimbabwe decided to give up and declare dollar official legal tender.
In order for money to be used there must be some demand for it. The demand for money can be created by government requiring that all taxes be payed with its issued currency. Furthermore, in order for people to keep using the issued money they must also be able to perform the function of money reasonably well (i.e. be medium of exchange, unit of account and store of value). In Zimbabwe the problem was that due to hyperinflation money completely lost its store of value function and hence people decided to use dollar - but that's just one example.

Or, is it something like we own the land and other assets, we put it at a value of some X amount

Not anymore. Modern fiat money are not backed by anything of intrinsic value. In the past under gold standard money was backed by gold and ever further in past money was literary some commodity (it could be gold or other precious metals, but also shells, stones, coca, cigarettes, livestock etc.). In such systems money derived their value also from the intrinsic value of the asset (or more precisely commodity).
If you want to know about history of money then a good non-technical account is provided by Ferguson in Ascent of Money and more technical account can be found in Davies (2010). History of money.


How do you keep up to date and find the most relevant papers? What tools or methods you use to keep up with the frontier of the field? I follow some specific papers and  authors. I was wondering what's the best way to keep up to date with relevant things with so much information there's available.

Seminars and conferences are the best ways to get exposure to working papers, in addition to following specific authors. (Some of my colleagues also follow economists on Twitter, where they sometimes post new working papers.)

In addition, subscribe to the email alerts from the journals in your field/interest. This will get you up to date with what comes out in the latest issues. The AEA journals (as well as Econometrica) will also send you the titles and abstracts of the articles; the Elsevier journals will only send you the TOC with the article titles only.


exchange rate and domestic money supply part II This question is related to the answer to the question
exchange rate and domestic money supply

It is said that the 'CB purchases foreign currency on currency market'.

Is it possible that some of this purchasing is even done within the domestic market (I would guess not but don't really know)? Or are we assuming that in circulation means within the domestic market and foreign market (again I would guess not)? Or is maybe that we assume/know that when in circulation, our currency will find its way back to our market and this will obviously result in more money in circulation. Maybe I am really thinking about it in the wrong way, and in circulation simply means that there are lenders out there now (foreign or domestic) that have more of our currency and will lend at a low interest rate.

@Toby comments noted, I will attempt an answer.  First, the FX market is international so you cannot tell whether the foreign currency seller is domestic or foreign. However, if it is a foreign buyer, they will typically reinvest the dollars in either a commercial or financial asset such as a Treasury bond, which could result in the remittance of the dollars back to a domestic holder.   What you know for sure is that the dollars will be deposited in a bank somewhere and will add to the pile of excess reserves currently held by the US banking system.  Hence technically the money supply goes up.

Perhaps the greater question is whether raising the money supply in this way has any effect on the economy.  I would suggest not, since banks already have excess reserves.   Rather, the transmission mechanism for FX intervention is via changes in the exchange rate.   But that could be debatable.


Ranked choice preference with ties - Arrow's Impossibility Theorem My question relates to my understanding of Arrow's Impossibility Theorem and ranked choice.  It seems to me that the requirements on social choice functions are too strict. A social choice function cannot result in ties. This sounds unreasonable to me.
Let two voters with preferences $a > b > c > d$ and $a > c > b > d$. It seems that any "reasonable" choice function would choose $a > b = c > d$. Any other output would be making an arbitrary distinction between $b$ and $c$. So my question is: if we relax the output of our social choice functions to allow for ties, is there a social choice function that satisfies Arrow's criteria? Is there proof that no such function exists?
As an addendum, I tried a "trivial" such function but it doesn't seem to work.
Let $f$ a social choice function which if every voter prefers $c_1 > c_2$ then in the final output $c_1 > c_2$; otherwise $c_1 = c_2$.
This seems to fail by the transitivity of ties. So, for two preferences $a > b > c$ and $c > a > b$ then $a > b$ but $c = a$ and $c = b$ which is a contradiction. If we were to choose, $a > b = c$ we would be violating the independence of irrelevant alternatives. As, if we were to delete $b$ the result "should" be $a = c$. Is there a way to work around this?

Allowing indifference will not solve the problem of the effect of the independence of irrelevant alternatives (combined with the unanimity and transitivity requirements).
You have said $b >_1 c$ and $c >_2 b$ should lead to $b =_s c$
Now consider  $a >_1 b$ and $a >_2 b$, which should lead to  $a >_s b$ by unanimity

so $a >_1 b >_1 c$ and $c >_2 a >_2 b$ should lead to  $a >_s b =_s c$ by transitivity
and thus $a >_1  c$ and $c >_2 a $ should lead to   $a >_s c$ by the independence of irrelevant alternatives

And also consider  $c >_1 a$ and $c >_2 a$, which should lead to  $c >_s a$

so $b >_1 c >_1 a$ and $c >_2 a >_2 b$ should lead to   $b =_s c >_s a$
and thus $b >_1  a$ and $a >_2 b $ should lead to   $b >_s a$

Combining these means $b >_1 a >_1 c$ and $c >_2 a >_2 b$ should lead to $b >_s a >_s c$

but that implies $b >_1 c$ and $c >_2  b$ should lead to $b >_s  c$

inconsistent with your $b >_1 c$ and $c >_2 b$ leading to $b =_s c$


Does comparative advantage sustain over long periods of time? Let's say that given the same resources,

company A can produce 40 pens or 50 pencils,

company B can produce 30 pens or 30 pencils.

Since A has a comparative advantage in pencils, A decides to produce 50 pencils while B agrees to produce 30 pens. They trade 10 of A's pencils for 9 of B's pens.

Over time, A forgets how to make pens and B forgets how to make pencils. Does it still make sense for them to trade? Would it have made sense for them to trade if A never knew how to make pens and B how to make pencils? Since the situations of 'forgetting' and 'never knowing' are essentially the same.

The theory of comparative advantage, like Ricardo/Rybczynski/Stolper-Samuleson, is classically a static theory, but you seem to be worried about dynamics.

You seem to think specialization and "unlearning by not doing" might be bad bad.  The question is why?

Specialization is almost a necessary condition for trade: if we are all equally good at all tasks, what is the point of trading?  We could just produce whatever we wanted in autarky. Specialization is about learning and seems to take place over time. This goes in the direction of innovation, perhaps like Schumpeter: the country that makes pens might innovate a new writing tool that makes pencils and pens obsolete, and then A will regret specializing. Similarly, in the theory of firms, there is an idea of Absorptive Capacity of ideas.  If no one at Tesla knows anything about combustion engines, they might miss out on breakthroughs in that technology that would benefit Tesla. Maybe it's because the breakthroughs are valuable in themselves, or maybe it's because having an open mind means you can have more creative ideas.  So perhaps firms should keep some capacity to do things in which they do not have a comparative advantage in order to expand their R&D capacity.

But you talk about countries.  The US subsidizes food production because it wants to have its own food supply for national security reasons; look at the medical mask shortage right now.  So perhaps it makes sense to subsidize production of things in which a country does not have a comparative advantage in order to avoid becoming completely dependent on other countries.

So, given the information provided, perhaps you are mixing together the short-run classical theory with concerns about innovation, uncertainty, or long-run fitness?


How to find opportunity cost if each choice has more than one important effect? Let me start with an example where I DO understand how to find opportunity cost.
Suppose I have choice to either work for firm A (\$1000 wage) or for firm B(\$2000 wage) or for firm C(\$500 wage). If I choose frim B, then I will forgo my best out of remaining alternatives, namely wage that I would get working for firm A.

Now let's add another aspect:traveling time. Working for different firms will imply different time needed to spend on traveling back and forth between my home and work. Suppose I can't monetize saved time, but I prefer to have more free time nonetheless.

I have three choices, between firm A(\$2000 wage, 2 hours traveling time), firm B(\$1500 wage, 1 hour traveling time) and firm C(\$1200 wage, 0.5 hour traveling time). Suppose I chose to work for firm B, what will be the opportunity cost of such decision? Two things confuse me in this case. There seems no clear way to pick the best alternative and then declare its effects (i.e. wage and traveling time) to be opportunity cost. Firm A offers better wage than firm C, but firm C offers lower traveling time than firm A.On ther other hand, our choice has two effects (wage and traveling time), is it really correct to take them both and declare as ONE opportunity cost, rather than two separate opportunity costs?

Note that as a rational agent you will have preferences on the set of (wage, free time) bundles. Your own answer suggests that these two "goods" are perfect substitutes, but this is not the general case. If your preferences are given by a utility function you can calculate the utilities for the three bundles in your choice set and then proceed in the way you indicated, measuring opportunity costs by utils foregone.

Alternatively, you can for each of the three bundles find a respective indifferent point at the maximal-free-time line in the space of bundles (corresponding to zero traveling time) and compare the wage levels of these points to get a monetary measure of opportunity costs. This corresponds to converting the traveling time contained in each bundle to some wage loss which you would be prepared to face if traveling time could be eliminated from the respective bundle. (If your preferences happen to be quasi-linear in money, this amounts to calculating your willingness-to-pay (WTP) to avoid traveling time, but in the general case this WTP need not be independent of the wage level.)


If Trump's economic policies are destructive, why is the US economy so healthy? One doesn't have to look very hard to find suggestions that Trump's economic policies are damaging to the US economy. Example, example, example, example. In fact I barely recall reading any articles in the mainstream media that said that Trump's policies are beneficial.

However all indications are (example from just earlier this month) that the US economy is extremely healthy.

Why is there a disconnect? Are the economics theories wrong? Is this a case of the economy being too complicated to model, and the results in this case turned out to be incorrect? Are the economists who made those predictions politically biased? Are the indicators imperfect and conceal hidden weakness? I notice that economists also predicted that Erdogan's policies will be destructive for the Turkish economy, and that panned out; I'm wondering why the predictions evidently aren't working for the US economy.

I'm not an economist and know little about the topic, so would prefer an elementary explanation.

(1) Most of Trump's proposed policies have been implemented only to a limited extent or not at all.

He promised dramatic tax cuts. Examples from the June 2016 Moody's analysis you cited:

Replacing the current seven personal income tax brackets with three and reducing the top marginal rate from 39.6% to 25%.

The Tax Cuts and Jobs Act 2017 (TCJA) cut the top rate, but only from 39.6% to 37%. Also, the seven brackets have remained.

Increasing the standard deduction to \$25,000 for single filers and \$50,000 for joint filers, and indexing to inflation thereafter.

The TCJA increased the standard deductions from \$6,500/\$13,000 to \$12,000/\$24,000 — an impressive increase, but still less than half of what Trump had proposed. (Note also that these increases in the standard deductions were partly offset by the elimination/restriction of many deductions.)

Trump promised to immediately repeal and replace Obamacare. As of May 2019, this has not happened.

Trump also promised to deport over 11M illegal immigrants. This has also not happened. In fact, under Trump, there have been fewer deportations than under Obama (e.g. in FY2018, there were 256,085 deportations, well below the Obama 2013 peak of 438,421).

The above proposals would have severely damaged the US economy. But none have been fully implemented.

(2) The trade war.

Again it is the case that Trump falls far short of some of the wilder "promises" he made during his campaign (e.g. in Jan 2016, he proposed imposing 45% tariffs on China).

Nonetheless, to the extent that he has been "successful" at waging this trade war, there has been damage to the US economy.

Fajgelbaum et al. (2019) estimate that:

  the trade war lowered aggregate U.S. welfare in the short-run by \$7.8 billion, or 0.04% of GDP.

Amiti, Redding, & Weinstein (2019) estimate that:

  by the end of 2018, import tariffs were costing U.S. consumers and the firms that import foreign goods an additional \$3 billion per month in added tax costs and another \$1.4 billion dollars per month in deadweight welfare (efficiency) losses.

(3) It may be too soon to tell.

Or in economists' jargon, there is usually a policy lag of months or years.

For example, the TCJA just came into effect in the most recent tax season (whose deadline just passed a few weeks ago in April 2019). Even if the TCJA has any effects, it will be a little while before economists are able to measure them.

Also, as the Dec 2018 piece by Nouriel Roubini suggests, it was really only in 2018 and in particular the last few months of 2018 that Trump began to impose his economic policies:

  many trusted that at the end of the day, the “adults in the room” would restrain Trump and ensure that the administration’s policies didn’t jump the guardrails of orthodoxy. // These assumptions were more or less vindicated during Trump’s first year in office ... But things changed radically in 2018, and especially in the last few months.

(4) That the US economy is healthy is not evidence that Trump's policies are sensible.

It could be that absent Trump's policies, the US economy might be doing even better. We can't just look at things as they are; instead, we need some sort of a counterfactual analysis.


How does the stock market correlate with the economy? What's the Correlation Coefficient between the Canadian and US stock  and economy?  Don't hesitate to discuss other stock exchanges.

On Apr 30 2020, Paul Krugman wrote Opinion | Crashing Economy, Rising Stocks: What’s Going On?

  Yet stock prices, which fell in the first few weeks of the Covid-19 crisis, have made up much of those losses. They’re currently more or less back to where they were last fall, when all the talk was about how well the economy was doing. What’s going on?

  Well, whenever you consider the economic implications of stock prices, you want to remember three rules. First, the stock market is not the economy. Second, the stock market is not the economy. Third, the stock market is not the economy.

  That is, the relationship between stock performance — largely driven by the oscillation between greed and fear — and real economic growth has always been somewhere between loose and nonexistent. Back in the 1960s the great economist Paul Samuelson famously quipped that the market had predicted nine of the past five recessions.

I know it's $< +1$, because

The stock market only consists of publicly traded companies, which is a subset of the economy (generally large businesses). Economic activity can also come from private companies (most small businesses are private), government activity, and not-for-profit organizations. A US stock index can also track companies that have a lot of foreign production, so the value of a company can increase from production that's not measured in US GDP.
The current economy can mismatch what investors expect the economy to be in the future. Stock prices don't only reflect current wealth but also future payoffs. After all, people invest to transfer wealth from one time period to another. That is one of the tasks (if not the most important task) of financial markets.

This study, "Is There a Link between GDP Growth and Equity Returns?", compares a number of advanced economies over the period 1969-2009. On average, the growth in stock prices was just 0.3% higher than the growth in GDP. However this ratio varies considerably between individual countries. Stock price growth was 4.5% higher than GDP growth in Spain, but -3.5% in Sweden. Here's the relevant data table.