texts: Australia and Saudi Arabia - Structural Similarities

texts:
I refer specifically to this article in which Andrew Critchlow paints a pretty dire view of the Australian economy.

The line which challenged my priors was:

Just like Saudi Arabia, which is now burning its foreign reserves to compensate for falling oil prices, Australia faces a collapse in export revenue.

This did not match my perception of the Australian economy at all.

What similarities does the Australian economy have with the Saudi economy? Is the comparison fair? In particular, I am interested in structural issues the economies face.

Secondly, is the quoted line accurate? My understanding was that the extraction cost for oil was very low in the gulf and the lower prices served to make other countries unprofitable before it cost them.


texts: What happened to the national debts after Bretton Woods

texts: When Bretton Woods was created and the world went on to the US Dollar standard, what happened to all the national debt's of all the countries like Japan, Britain, etc?


texts:
From New geopolitics of natural gas:

the policy of assisting friends can include price discounts, [targeted supplies] , or financial or technological support to develop energy resources for partner nations.


texts: Complementary slackness conditions (Kuhn-Tucker)

texts:
Consider the problem of maximising a smooth function subject to the inequality constraint that $g(x) \leq b$. The complementary slackness condition says that

$$ \lambda[g(x) - b] = 0$$

It is often pointed out that, if the constraint is slack at the optimum (i.e. $g(x^*) < b$), then this condition tells us that the multiplier $\lambda = 0$. I agree with this. However, it has also been said that, if the constraint 'binds' (which implies that $g(x^*) - b = 0$), we must have $\lambda > 0$. Is this true? As a logical matter, it is not immediately implied by the complimentary slackness condition: we could have both $g(x^*) - b = 0$ and also $\lambda = 0$.

Edit: it has been demonstrated here why we can have both $\lambda = 0$ and $g(x^*) - b = 0$ (thanks to @markleeds for the pointer). I am wondering, however, whether we can have $\lambda = 0$ while the constraint also binds (i.e. makes a difference to the solution -- note that this is subtly different from the constraint holding with equality). I suspect that the answer is 'no' given that $\lambda$ reflects the effect of slightly relaxing the constraint on the objective function. However, I would appreciate confirmation of this.


texts: Does anybody know what kind of work or where computational economists end up working? It seems most end up in research...


texts: Production Possibility Frontier for 3 goods

texts:
Is it possible to construct a Production Possibility Frontier (PPF)  for 3 goods? Would this require a 3D graph and a part of a sphere, in one quadrant (as opposed to the usual 2D plot, with a part of a circle in one quadrant).

Is this something used in more complex analysis of production?


texts: Decomposing Changes in ROA into Changes in Operating Margin and Asset Turnover via Total Factor Productivity (TFP)

texts:
I am currently reading a paper on the influence of hedge fund activism on plant-level productivity. In the appendix the author describes how he decomposes changes in ROA into changes in operating margin and asset turn-over. I am trying to redo the calculation explained by the author but am unable to do so.

The author is calculating the change in operating margin via a increase in TFP using the following formula:

Operating Margin = 1-1/(TFP x price change ratio)

The author calculates 26,6 percentage as the new operating margin but I cannot replicate the calculation. Any help is appreciated.

Here the part in question:

  In Appendix B, we link formally the magnitude of the change in ROA to
  the change in raw TFP from years  tt  to  t+3t+3 . In particular, we
  use a modified version of the decomposition in Bosch-Badia (2010), in
  which ROA is decomposed into TFP, input and output price changes, and
  asset turnover. Using the “DuPont decomposition” of ROA, we obtain the
  following relation:

  (A2) ROA=Operating margin × Asset turnover,ROA=Operating margin ×
  Asset turnover,  where ROA is the ratio of earnings before interests
  and taxes (“operating profits”) to lagged total assets, operating
  margin is the ratio of operating profits to concurrent sales, and
  asset turnover is the ratio of sales to lagged assets and, as
  Bosch-Badia (2010) shows, operating margin = 1–1/(TFP × price change
  ratio). The price change ratio is the change in output price divided
  by the change in input price. All price changes are relative to the
  benchmark year (i.e., year  tt ). In addition, we further make the
  following two assumptions: (i) The baseline operating margin is 24.7%
  (see Table 2, Column (1)), and (ii) the price change ratio is equal to
  one (i.e., input and output prices change by the same magnitude). With
  these assumptions we can link the change in ROA to the changes in TFP
  and in asset turnover. First, we estimate the change in TFP using the
  specification in Table 4, Column (4). Specifically, we narrow the
  estimation to only manufacturing firms based on Compustat SIC codes
  and find average productivity gains of 2.6% from years  tt  to  t+3t+3
  for plants owned by manufacturing target firms. Second, given the
  baseline operating margin of 24.7%, the increase in TFP of 2.6%
  translates into an expansion in operating margin by 1.9 percentage
  points to 26.6%. Third, the magnitude of the change in ROA also
  depends on the change in firm-level asset turnover, which is driven by
  reductions in capital at the plants that are not sold, and by
  divestitures and/or closures of plants. Using Compustat data, we find
  that for manufacturing target firms asset turnover increases from 1.07
  to 1.20 on average from years  tt  to  t+3t+3 . Taking the two changes
  together, the implied ROA increases by 5.5 percentage points from
  26.4% in year  tt (= 24.7% × 1.07) to 31.9% in year  t+3t+3  (= 26.6% × 1.20).

And here a direct link to the paper.

Go to Appendix B.


texts: If a rational preference relation over simple lotteries $\succsim$ are convex then they satisfy independence?

texts:
Let´s say there is an uncertain situation with $N$ possible consequences $C = \{C_1, . . . C_N\}$. Assume that
there is a rational preference relation $\succsim$  over simple lotteries.
I know that if $\succsim$ satisfies independence, then it is also convex, but is it true if $\succsim$ are convex then they satisfy independence? How can I show this (if the implication is true)


texts: Are there any recommendation for futures market or commodity trading books? I am not interested in trading myself, but would like to have a better understanding of it for my research.


texts: How wealthy are modern day humans compared to preindustrial times?

texts:
I would like to see a quantitative wealth comparison between the average human in a hunter gather or agrarian society to average human in the today's world.

I'm mostly interested in how the discovery of natural energy resources combined with Newtonian physics influence on technology has changed the world in terms of relative worth of a human.

The kind of answer I'm looking for would be something like: We are 10, 100 or 1000 times more wealthy based upon x. X being what ever you use as a basis to create that comparison.


texts: Prediction market based on LMSR: Sell, or buy other side?

texts:
Consider a prediction market with two outcomes (Yes and No) and a scoring rule based on Hansons’s LMSR, i.e. ln(ea+eb), where a and b are the number of Yes resp. No shares sold.

Assume that I have previously bought 10 Yes shares, but now I changed my mind and want to bet on the other side. I have the option to either sell my 10 yes shares, or buy 10 no shares.

When should I choose one or the other option? Is it always the same, or does it depend on, say, the current market?


texts: Asymmetric (in sign) cross-price derivatives in consumer-theory problem

texts:
I'm puzzled why, in the following optimal-choice problem, good $x$ depends on price $p_y$ but the opposite is not true. Should not the sign of $\frac{\partial x}{\partial p_y}$ be the same of $\frac{\partial y}{\partial p_x}$?

Optimal-choice problem: given prices $p_x$ and $p_y$ and income $m$ find the optimal demand function for $x$ and for $y$:
\begin{equation}
\max_{x,y} \{x\cdot(y+6)\} \qquad \text{s.t. } p_x x+p_y y \leq m \tag{1}
\end{equation}
after imposing $MRS_{xy}=p_x/p_y$ and substituting back in the budget constraint I find:
\begin{equation}
x = \frac{m + 6p_y}{2p_x} \qquad\qquad y = \frac{m}{2p_y}-3 \tag{2}
\end{equation}
so that $sign\left(\frac{\partial x}{\partial p_y}\right) = sign\left(  \frac{6}{2p_x}\right)\neq sign\left(\frac{\partial y}{\partial p_x}\right) = 0$.

What I would like to understand better:

How can this happen? I remember having read somewhere in MWG that the  price-derivative matrix should be (even!) symmetric. Can you provide me with some explanation and/or some reference? Alternatively, is there any mistake in the calculations?
Provided the situation described above can happen [i.e. $sign\left(\frac{\partial x}{\partial p_y}\right)\neq sign\left(\frac{\partial y}{\partial p_x}\right)$], I would be very happy if you can come up with some "real world" examples of that.


texts:
Frequently a description that is clear in the mind of its author is not as clear to a reader. It is even worse when the reader finds the description clear but actually misunderstands the intention of the writer.

There are many such descriptions in economics. As social animals, economists learn from each other and copy each others phraseology - if I understood it, it is probably clear. However not all widespread phraseology is clear. A good example is in cooperative game theory, where Lloyd Shapley wrote a note titled 'Let's Block "Block"'. (If you read it be sure to read the footnote as well.) Shapley was among the originators of the phrase 'block' as used in cooperative game theory. But 'blocking' was actually a precisely defined mathematical concept in the science and as events unfolded it became clear that in some cases the popular meaning of the word conflicts with mathematical definition, resulting in Shapley's note.

After this introduction I will state my questions.

Is it correct and/or useful to say that in a market where a per unit tax (or quantity tax) is levied on the good the suppliers push part of the tax onto the consumers?
Is it correct and/or useful to say that in the same situation consumers and suppliers share the tax burden?


texts:
I know that I should optimize production by solving $MR = MC$ with respect to $Q$.

But if $TR > TC$, I am making a profit. Why is not enough to just solve $TR = TC$ with respect to $Q$?


texts: It seems the highest-frequency consumer price index (CPI) data available is monthly. How does one convert weekly or daily price data into real prices?


texts: DSGE models (Dynare) are only based on simulations and approximations? (without data)

texts: I'm beginner in DSGE models. Are they only based on simulations and approximations? Don't we have any real data-sets (for example interest rate, labor force, etc) to estimate the equations? I opened some .Mod files and I can only see equations, variable names and other functions. If yes, why do we have this structure in DSGE models and why can't we use real data-sets in these models?


texts:
Question: An agent who consumes three commodities has a utility function given by:

$u(x_1,x_2,x_3)=x^{1/3}_1+\min\{ x_2,x_3\}$

Given an income $I$, and prices of $p_1,p_2,p_3$. Describe the consumer’s utility maximization problem. Can the weierstrass and the Kuhn-Tucker theorems be used to obtain and characterize a solution? Why or why not?

attempt: I assume $x_i$ represents the quantity and belongs to $\mathbb R_{+}$. You can form the constraints as follows:
$$
x_i \geq0 \quad\forall i \in [3] \\
\sum_{i=1}^3p_ix_i \leq I
$$
You can simplify the objective by noting that for the utility to be the maximum. Hence, the final problem becomes,

$$\
\max_{x_1, x_2, x_3}x_1^{1/3} +x_2 \quad s.t. \\
x_i \geq0 \quad\forall i \in [3] \\
\sum_{i=1}^3p_ix_i \leq I \\
x_2=x_3
$$
Let's eliminate $x_3$ as we know that $x_2=x_3$. The problem simplifies to
$$\
\min_{x_1,\ x_2}\ -x_1^{1/3} -x_2 \quad s.t. \\
x_1 \geq0,\ x_2 \geq 0 \\
p_1x_1 + (p_2 + p_3)x_2 \leq I
$$
$$\
\mathcal L(x_1, x_2)=-x_1^{1/3} -x_2 + \lambda_1(-x_1) + \lambda_2(-x_2) + \lambda(p_1x_1 + (p_2 + p_3)x_2 - I)
$$

Comment: I am unsure how to take this further. I keep messing up the derivatives ( I assume) and when I try to solve for lambda I manage to fail to isolate the lambda variable let alone getting the variables x1,x2,x3. My professor encouraged me to try this complex problem as an “exercise for the reader.” How do I carry this further, or can someone show me a step by step solution from this point onwards?


texts:
The macro-literature insists on a consumption-leisure elasticity of 0 to match the balanced growth fact of constant labor supply.

Is there any paper that tries to evaluate this elasticity using micro-data, for a representative subsample of the population? There are many papers that show that consumption-leisure elasticities are not 0 for most goods, but it can be argued that these studies only use a non-representative sample of the population, and that - with a larger sample - these elasticities are more likely to average out to zero.

What has been done in this respect?


texts:
I've been given a question which I'm struggling with:

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

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

So in the Prisoner's Dilemma:

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

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

Is the question wrong?

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

Is this question wrong or am I misunderstanding these concepts?


texts: Why is a Normal Yield Curve a sign of a healthy economy?

texts: I think the question is pretty self explanatory. I'm just trying to understand the logic behind why an upward sloping yield curve indicates a good economy?


texts: How to approximate stochastic volatility model with finite-state Markov chain?

texts:
A common practice when computing solutions to stochastic dynamic optimization problems is to approximate an exogenous forcing process $z_{t+1} = \rho z_t + \sigma \epsilon_{t+1}$ with a finite-state Markov chain, e.g. by Tauchen's or Rouwenhorst's method. What would be a good way to discretize AR(1) process with stochastic volatility?

That is, if the original AR(1)-SV process looks something like this:
$$
\begin{split}
z_{t+1} &= \rho_z z_t + \mathrm{e}^{v_t} \sigma_z \epsilon_{t+1} \\
v_{t+1} &= \rho_v v_t + \sigma_v \eta_{t+1}
\end{split}
$$
with $\epsilon, \eta$ being independent standard gaussian shocks, my goal is to obtain values $z_i$ and transition probabilities $p_{ij}$ ($i,j=1,\dots,n$) such that the corresponding Markov chain approximates the original continuous-valued process.


texts: Unemployment with Insiders-Outsiders. What is a core employee?

texts:
In Dynamic Macroeconomics book, by Alogoskoufis, on chapter 17, he analyses a model of aggregate ﬂuctuations that is based on periodic nominal wage contracts and can explain involuntary unemployment (a Gray-Fischer-Taylor type of model).
The main distortion is represented as the inability of unemployed/outsiders to influence the determination of nominal wages.
He then describes the objective of insiders as setting the maximum nominal wage, which will minimize expected deviations of employment from the target level of the number of insiders.
The employment target of insiders in period t is determined by $\bar n( j)t= δl( j)_{t−1}+ (1 − δ) \bar n( j)$, where the $j$ index represents firm $j$, and $l_{t-1}(j)$ number of employed in the previous period.
$\bar n( j)$ is the logarithm of the number of core employees of ﬁrm j, assumed exogenous.
What are the core employees? Could it be represented by a union in reality?


texts: On the Ms. Exponential vs Ms. Hyperbolic vignette

texts:
I've come across this little parable purporting to show why exponential discounting is superior to hyperbolic discounting1:

  The greater bowing [of the hyperbolic discount curve] means that if a hyperbolic discounter engaged in trade with someone who used an exponential curve, she'd soon be relieved of her money.  Ms. Exponential could buy Ms. Hyperbolic's winter coat cheaply every spring, for instance, because the distance to the next winter would depress Ms. H's valuation of it more than Ms. E's.  Ms. E could then sell the coat back to Ms. H every fall when the approach of winter sent Ms. H's valuation of it into a high spike.

The figure that the excerpt refers to looks somewhat like the one shown below, the most notable difference being that I've added the legend to indicate which curve is which2, together with the analytical form of the actual discount functions used3.

But it seems to me that the argument, as presented above, is spurious.  It is clear that whose valuation would be more depressed, depends on the time.  Therefore, the exact same argument with the roles of Ms. E and Ms. H reversed, would work for any timepoint between the point at which the curves intersect and the vertical axis.

In fact, for certain choices of coefficients for the hyperbolic and exponential curves, the exponential curve is more depressed than the hyperbolic one for all time points.  For example:

It turns out that the green exponential curve above intersects the hyperbolic curve at only one value of $t$, namely $t = 0$ (i.e. at the time indicated by the vertical axis).  For all $t < 0$, the green exponential curve is strictly below the hyperbolic one.

This means that, if Ms. E's exponential discounting curve were the green one, then Ms. H would be able to quickly immiserate her by applying the strategy described in the excerpt, and this would be true irrespective of the length of the time interval between the buying and the selling back of the winter coat.

In summary, the excerpt's argument for the superiority of exponential discounting over hyperbolic discounting does not hold water, in my opinion.

Now, I realize that the excerpt is not being particularly rigorous, and that there may be a more convincing way to demonstrate the superiority of exponential discounting over hyperbolic discounting.  If so, what is it?  In particular, I want to know the following:

How can someone who uses exponential discounting take financial advantage unilaterally of someone who uses hyperbolic discounting?

(By unilaterally I mean that the strategy is available only to someone who uses exponential discounting vis-à-vis somoneone who uses hyperbolic discounting, and not viceversa.)

1 The reference I have for this passage is to Breakdown of will (2001) by George Ainslie (pp. 30-31).  I don't have the book, though.

2 I have added the labels "hyperbolic" and "exponential", according to my interpretation of what the author means by "greater bowing".  I'm not a native speaker of English, so please correct me if this interpretation is backwards.

3 Note that all these functions have $(-\infty, 0]$ as their domains.  This choice was required in order to match the appearance of the original curves.  Also, I should stress that the functional forms I used for all these curves are my own, chosen so as to approximate the appearance of the original curves.  The text of the excerpt does not give the functional form of the depicted curves.


texts:
In Microeconomics producer surplus is equivalent to profits minus fixed costs.

However getting a tangible definition of consumer surplus has been difficult for me to ponder.

What is the practical use of knowing  consumer surplus and what does it tell us?


texts: Does consumer theory assume that utility functions are consistent overtime?

texts:
I'm interested in how we model a consumer with a changing utility function over time.

  Example: an individual's demand for candy/sweets at 10 years of age will be different when he is 20,30 or 40 years old (based on casual observation).This would seem to indicate the utility derived from this "input" in our utility function has changed.

In basic intertemporal models the general assumption is that the objective utility function does not change. mathematically it makes the model simple to compute, however it does not reflect the changes in preferences over time.

However, if we do allow the individuals utility function to change over time in our model, does this not violate the requirements for a rational consumer ?

How do we model an individual with changing preferences over time and is it economically sound to do so?


texts: Will the market for driverless cars move toward a monopoly?

texts:
There is a short article in The Economist (link below) where the writer makes the claim that because there are firms the exhibit economies of scale - in driverless technology - they will eventually drive out the fierce competition that occupies the current industry. Reasons for this is that falling average cost enables firms to produce more units, which get more testing and data: so, more date includes better safety and technology, resulting in more corporate partners/investment, implying an eventual crowding out of smaller firms.

What I think, is that monopolies - or even 2 or 3 firm oligopolies, although much more possible - don't typically form in this way. Natural monopolies form when markets cannot efficiently contain the introduction of another firm, which means there must be economies of scale and relatively low demand to keep out competitors. At least right now, in this market - which is driven primarily through software development - I don't see a monopoly forming.

Then there are barriers to entry. There aren't any on the books yet, but the article lists a few that could happen in theory, such as regulation and the curtailing of less safe/successful firms being ejected from the market. What are your thoughts? Thanks

https://www.economist.com/finance-and-economics/2018/06/07/the-market-for-driverless-cars-will-head-towards-monopoly


texts:
A consumer with income $m$ has preferences $U(x , y) = x^a y^{1-a} $ where a is between 0 and 1. A paternalistic Government wants to regulate the choices of the consumer to maximize it's own welfare function: $w(x,y) = \min(x,y)$ . The market prices are $p_x$ and $p_y$.

A. Suppose the government can impose a ceiling on the consumption of either good. Under what parameter condition is it necessary to place a ceiling on good $x$?
B. Suppose, instead, government provides a per unit subsidy on good $x$ and charge a lump sum tax $t$. Derive Marshallian demand for any $(s,t)$.
C. A policy $(s,t)$ is budget balanced if total subsidy paid equal tax. Derive relationship between $s$ and $t$ that must be satisfied by any budget balanced policy.
D. From the government's perspective, find optimum s and t values subject to a balanced budget.

Here's how I tried it:
Part A:
Using optimisation methods, from consumer perspective:
$$ X^*= (x^*,y^*) = \left( \frac{ am}{ p_x} , \frac{(1-a)m}{p_y} \right) $$

However, Government's welfare is maximised at :
$$ X^g= (x^g,y^g) = \left( \frac{ m}{ p_x + p_y} , \frac{m}{p_x + p_y} \right) $$

Then, I considered two cases:
$$ 1. X^* > X^g $$
$$  2. X^* < X^g $$

In the first case, ceiling on good 2 would be effective whereas in second case, ceiling on 1 would be effective, the ceiling being the optimal quantity from government's perspective. The parameter condition for second case,by comparing the quantities of good , was:

$$ \frac{p_y}{p_x} > \frac{1}{a} -1$$

Part B:
Simple optimisation problem:

$$ X^*= (x^*,y^*) = \left( \frac{ a(m-t)}{ p_x - s} , \frac{(1-a)(m-t)}{p_y} \right) $$

Part C:
Putting $sx^* = t$ I get
          $$s = \frac{p_x t}{a(m-t)+ t}$$
Part D:
I am not sure if the method I have used is correct or not.

Government's welfare is maximised at :
$$ X^g= (x^g,y^g) = \left( \frac{ m-t}{ p_x + p_y-s} , \frac{m-t}{p_x + p_y-s} \right) $$

Also,since,budget is balanced, therefore,
  $$ s*\frac{ m-t}{ p_x + p_y-s}= t $$

Now putting the s and t relationship from c part in the above balanced budget identity, I got

$$ t^* = \frac {m(p_x(1-a) -ap_y)}{(p_x +p_y)(1-a)} $$

$$ s^* = p_x - \frac{a p_y}{1-a} $$

Can someone please have a look at my solution and see if I have done it correctly?


texts: How can energy consumption be an indicator of per capita availability of capital?

texts: "An important indicator of low capital per head available in developing countries is the consumption of energy". I could not decipher the concept.


texts: Construct a game with only pure strategy nash equilibrium

texts:
I'm trying to construct a $4 \times4$ Normal-Form Game with two players, where each player has four strategies and it satisfies:

1) The game has exactly 4 Nash Equilibria

2) All equilibria involve only pure strategies (meaning there's no mixed strategy Nash Equilibrium)

Could someone give an example of this kind of game, and explain briefly how you construct it? I'm not sure when a game has no MSNE but only the PSNE. Thanks a lot.


texts: Need help reading early 20th century stock market list

texts:
I have a bit of a problem understanding the stock market price listings for the London stock market. I am mainly concerned with Argentinian government bonds. So far, I have always used the Investor's Monthly Manual for bond prices. That was fine as long as I only needed monthly data. However, I now need daily data.  So I turned to the London Times for bond prices. However, there the bond prices are listed in a somewhat different format. In order to check whether I understand these prices I tried to check the Times prices against the Investor's Monthly Manual (IMM) prices. However, I cannot really make sense of it. For example, if I look up the last day price of the Argentinian 1886-1887 loan for November 1911 in the IMM, I get 104.5. See here:
https://imgur.com/a/6cdMKWs

If I look up the same bond in the "Business Done" section of the Times I get the following prices: 29 Nov 1911: 104 7/8 3/8 and 1 December: 104 7/8 1/2 [the 30 Nov issue does not have any bond price listings]. Here are the pages from the Times:
https://imgur.com/a/vt17mWx
https://imgur.com/a/J2LZbL4

I would be grateful for any advice as to how to read the bond prices with the double fractions in the Times and for any explanation why there is a difference between the IMM and Times.

Thank you!


texts: I'm studying the effect of a law on a sector: how do I select the control group?

texts:
I'm planning on using a regression discontinuity design (RDD) to estimate the impact of a sector-specific law on the firms in that sector. I need to create a control group and I have read somewhere in the literature that you should use "a similar sector". When it comes down the selecting the similar sector, I don't know where to start. Does anyone have any suggestion (readings and such)?
The sectors which would be (separately) analysed are: telecommunication, education, construction, banking, finance.


texts: Why Should Expenditure Equal Income in Computable General Equilibrium (CGE) models?

texts:
I'm reading up on CGE models and one clearing condition that must be met is that Expenditure must equal income.
This seems odd to me because I thought households allocate income to savings and expenditure.


texts: Is weak sustainability (Hartwick's rule) possible on a global scale?

texts:
Hartwick's rule postulates that an economy is sustainable if all rents obtained from the extraction of non-renewable resources are re-invested in produced capital (Source). A typical example would be the Norwegian Sovereign Wealth Fund that invests the resource rents obtained from oil into equity, real estate and fixed income. (Source)
In generic terms the investments that the fund makes will be in capital (e.g. machinery) or land and other rent-generating assets (e.g. land, patents, etc.). However, the produced capital will depreciate over time and the rent-generating assets do not involve the production of a new asset but the purchase of the rent attributable to the rights over an existing asset.
How then would weak sustainability (Hartwick's rule) be possible on a global scale? Presumably this would have to involve investing every cent of resource rent into capital investments with a lifespan that is at least as long as the lifespan of the resource that it substituted?


texts: ICAPM when assets' mean returns and variance-covariance matrix are not constant over time

texts:
The intertemporal capital asset pricing model (ICAPM), under the usual assumptions, produces a multifactor pricing model like the one described in this question.

When and how would it be possible to test this result when the assets' mean returns and variance-covariance matrix of returns are not constant over time?


texts: I need a text book for mathematical economics with real world examples. Currently I'm using A.C Chiang (very good) and Henderson and Quandt ( not the best book for matheco). Can someone recommend any others ?


texts: What will happen to the reserves at the Fed?

texts:
Banks currently have 2.7 trillion Federal Reserves that they hold at their Federal Reserve account. It's part of the monetary base and these reserves were created when the Fed purchased bonds in their QE program.

What will happen to these reserves? How will they get back to the Fed? How will they be retired and won't they have to be used to pay off the treasury bonds the Fed is holding?

http://research.stlouisfed.org/fred2/series/NONBORRES

That's a link to it.


texts: Symmetric Nash Equilibrium in Stahl (1996)

texts:
Let $F(p)$ denote the distribution of prices in a market, $\pi(p, F)$ are profits choosing $p$ given distribution $F$. $E\pi(p,F)$ is defined to be

$$ E \pi(p, F) = R(p) \psi(p, F)$$

where $R(p) = p D(p)$ is the revenue per customer, and $\psi(p, F)$ denotes the expected share of customers that a seller with price $p$, given distribution $F$ will face.

Definition (2.1) in Stahl (1996) (just below eq. 2.3) defines the symmetric Nash equilibrium as:

$$ E \pi(p,F) \leq \max_p p E \pi(p, F) \, \forall p$$

My question is why $(2.1)$ is defined as such? I would have thought that a Nash equilibrium requires choice being optimal, hence no incentive to change profits:

$$ E \pi(p,F) \leq \max_p E \pi(p,F) \, \forall p$$


texts: Fiscal budget: spending in real vs nominal terms

texts:
What does it mean in the context of a budget to “freeze spending in real terms”? And how would this differ from freezing spending in “nominal terms”?

I am looking to understand how this would be implemented and the broader macro relevance


texts:
Suppose that two players play each other for two periods. In the first period they play the
first game below, and in the second period they play the second game below. There is no
discounting between periods. Players observe the action their opponent took in the first
period before choosing their second period actions.
\begin{bmatrix}(2,2)&(-10,x)\\(y,0)&(0,0)\end{bmatrix}
\begin{bmatrix}(8,4)&(0,0)\\(0,0)&(4,8)\end{bmatrix}
(a) For x ≤ 2 and y ≤ 6, find a subgame perfect equilibrium in which player 1 receives a
payoff of 10.
(b) For x = 5 and y = 3 find a subgame perfect equilibrium in which player 2 receives a
payoff of 10.
(c) For x = y = 4, show that there is no subgame perfect equilibrium in which (U,L) is
played in the first period.
I'm totally lost as how to find subgame perfect equilibria. Aren't these games simultaneous games? Why would the players consider the choices made in the first game to play the second game?


texts:
A "no deal" Brexit is presented in negative terms.

In such a scenario the UK would set tariff schedules in line with trade strategy and protect domestic industry/agriculture with tariff rate quotas.

The UK would lose tariff-free exports into the EU and the markets with which the EU currently has free trade agreements (the two main ones being Japan and Canada).

The non-weighted average MFN global tariff is 9%. The weighted average tariff for UK exports into the EU is estimated to be around 4.5% in this scenario. Natural movements in currency value are of this order of magnitude.

There would be increased trade friction for the 44% of our exports that are sent to the EU. British exporters would have to follow the customs rules used by other 3rd-country exporters to the EU like China and the USA.

This would be a major change. Most countries export to the EU under these terms. Our reliance on services mean this change would be economically bounded.

The productive base of the UK would re-orient around the new status-quo with some sectors decreasing in competitiveness and diminishing and some increasing and expanding.

The overall success/failure of the new status quo would be determined by the wider economic strategy rather than tariff changes that are mostly small.

Why is a negative long-term forecast necessitated?


texts:
I asked myself: How is it that the stocks are always rising? How is money generated every year so that the value of a company rises?

I mean, at some point there is a finite amount of money in the system, isn't it? Right now people assume that the stock market is overheated and not many sources are left where money can come from to make it rise even higher.

Now my question is: How and where is money coming from? I know, people invest, but at some point they take money from point A to B and don't create it.

Is there a basic book out there which explains the basics? Not for dummies but also not for experts who assume to know everything. Maybe a pragmatic economics book?


texts: Effects of increased income over short and long run in AD-AS equilibrium model

texts:
I've read in a few places that increased income/wages shifts SRAS to the left, which makes sense because firms' costs are increasing to pay for them. My textbook says that there's no effect on aggregate demand, but this doesn't make sense to me because if people have more income to spend then at each given price level of goods in the economy the amount consumers are are willing to buy will increase, shifting aggregate demand to the right (at least in the long run).

Side note: I'm asking because I'm curious about what this means for the monetarist/neoclassical view of macroeconomic equilibrium; specifically, why aggregate demand does not change between long and short run and why aggregate supply moves to the intersection of LRAS and AD.


texts: Do changes in fixed taxes have a bigger effect on real GDP compared with government spending because they affect consumption

texts: True or False: Changes in fixed taxes have a bigger effect on real GDP compared with government spending because they affect consumption


texts:
I encountered this phrase while reading up on growth models - that is to work with a function in intensive form. What does it mean when a function is in intensive form?

Thanks!


texts: What is a good handbook for behavioral economics?

texts: I recently got interested in behavioral economics because it seems to have a lot of interesting applications in other fields such as macroeconomics. I managed to find a lot of interesting sources on development of behavioral models but I would like to get my hands on some handbook that is a behavioral economics' equivalent of lets say Varian Microeconomic Analysis or something like MWG microeconomic theory. Are there some comparable behavioral handbooks?


texts: Currently studying Intro to Macroeconomics, and faced Expectations augmented PC. In my textbook it is not clear how expected inflation affects unemployment. My view so far, is that expected inflation move the Phillips Curve upwards. For the same rate of Unemployment corresponds greater inflation in the short-run. However, unexpected iflation reduces unemployment in the short-run until labour market and companies absorb the unexpected increase of inflation.


texts: What properties must a utility function have such that we can define level sets and thus indifference curves?

texts:
I asked on Math SE a bit about level sets here.

Based on what I learned, it seems like we usually assume a level set $L(f)$ and its function $f$ defined on $\Bbb{R}^n$ have the following properties:

$f$ is continuous
Thus, the curves in the level set are closed curves. (not sure why)
All closed curves are "converging" to a point. (not sure why)
This point will be a maximum for the function: the derivative in the point will be zero, since if it was not then the point would be a 1-manifold, which is absurd.
$\nabla f \neq 0$ on the rest of the points

I don't understand how we know a preference relation on a consumption bundle has a utility function representation such that these properties hold. According to my professor, we use level sets to describe indifference curves.

Therefore, if indifference curves are described by a level set, that level set must have the properties listed above. Note, for economics, we are considering a function $U(\mathbf{x})$, where $\mathbf{x}=(x_1,...,x_n)$, and the level set $L(U)$. Also, note $U: \Bbb{R}^n\rightarrow \Bbb{R}$.

My Question:

In economic terms, what assumption do we have to make to ensure, $U$, $L(U)$ have these properties to create a level set used for indifference curves?

Ideally, it would be great to have an enumerated list of the assumptions (ie 1,2,3).


texts: Derive demand function from utility function with constant elasticity

texts:
Consider a $n$-good industry with a representative consumer with utility function for the differentiated goods given by,

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

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

a. Derive the inverse and direct demands;

My solution: I am writing the lagrange as:

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

FOC:

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

So the inverse demand function is:

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

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


texts: Does the Labor Theory of Value hold in the long term in competitive markets?

texts:
Most criticisms of the Labor Theory of Value I have come across go something like this quote from Carl Menger:

There is no necessary and direct connection between the value of a
good and whether, or in what quantities, labor and other goods of
higher order were applied to its production. A non-economic good (a
quantity of timber in a virgin forest, for example) does not attain
value for men since large quantities of labor or other economic goods
were not applied to its production. Whether a diamond was found
accidentally or was obtained from a diamond pit with the employment of
a thousand days of labor is completely irrelevant for its value.

This is perfectly obvious and Marx even mentions this:

A commodity, such as iron, corn, or a diamond, is therefore, so far as
it is a material thing, a use value, something useful. This property
of a commodity is independent of the amount of labour required to
appropriate its useful qualities.

But putting aside the natural resource example for a moment, in the long term in a competitive market isn't it the case that if there is a situation where someone is able to sell something for more than the cost of the labor that went into it, someone else should be able to step in and sell that thing for a lower price? Eventually prices will go down until they are stopped by another constraint. That constraint being the cost of all the labor required to produce the product.
In situations where this doesn't happen isn't it an indication of some anti-competitive force?
Monopoly of a natural resource, monopoly of a technology through a patent, externalities that result in a small number of large companies, cooperation between large companies to set prices, etc...
So is it fair to say that in the long term in competitive markets the labor theory of value holds?
If the theory is "at any point in time a commodity is worth as much as the cost of labor that went into it" then it is obviously wrong and I can't imagine any classical economist would have believed it.
But if the theory is "over time the cost of a good will tend towards the cost of the amount of labor that went into it assuming the market is competitive" then it still seems plausible.


texts: Why doesn't Nintendo fire up the old factories and re-produce *exact* copies of many of their most popular games, controllers and consoles?

texts:
Let's suppose that Nintendo announce tomorrow that they are going to create exact re-releases of the American and European NES, SNES and Nintendo 64 consoles, exactly the same as when they were originally sold, down to the packaging. As in, not even any new labels such as "Anniversary Edition" or anything. It literally is impossible to tell the difference between the new boxes and its contents from when it was originally sold.
They announce a schedule ahead of time so that they start selling these to match the time difference between each console's original release date. At least 100,000 copies of each console.
They do the same thing with the top-250 titles (in terms of commercial success) for each system, at least 100,000 copies for each game. Again, the games are released to match their relative dates when they were originally released.
Even if only collectors and hardcore nostalgics like myself buy these, wouldn't it very much make economic sense? Am I grossly overestimating the "retro market"?
It's impossible to collect/re-experience the games from my childhood today because they are insanely overpriced, or impossible to get hold of. And of course, Nintendo gets zero profits from somebody buying it second-hand (or more like 20th-hand at this point). To me, it appear as if Nintendo is allowing a lot of free money to go to waste.
Note: We are talking about Nintendo doing this properly, the way I describe it. Not some half-hearted nonsense.
I very much like the idea of buying an original Super Mario All-Stars, with "new manual smell", from Nintendo in the year 2021. They'd earn money and I'd get a copy which is impossible to tell apart from a copy I had kept in perfect condition for all these years. And the greedy auction site sellers would be stuck with worthless items.
I'm convinced that these copies would quickly sell out, and they could create more until the demand is finally met. Unless you have already spent decades paying insane prices to collect all the games, I can't see any reason why anyone would have anything against this. In fact, I wish that many other companies did the same thing with other classic products, but they never seem to.
Why not?


texts: Did William Nordhaus exclude 87% of economic industries from his climate change analysis?

texts:
Economist Steve Keen published in article in 2020 titled, The appallingly bad neoclassical economics of climate change. In it, he alleges that climate economists such as William Nordhaus and Richard Tol have underestimated the impact of climate change by "at least an order of magnitude." Keen primarily responds to two approaches in the economics literature for estimating damages from climate change. The first is the so-called 'Enumeration' approach to estimating damages from climate change. He quotes Tol who said,

In this approach, estimates of the “physical effects” of climate change are obtained one by one from natural science papers, which in turn may be based on some combination of climate models, impact models, and laboratory experiments. The physical impacts must then each be given a price and added up. For agricultural products, an example of a traded good or service, agronomy papers are used to predict the effect of climate on crop yield, and then market prices or economic models are used to value the change in output.

Keen then quotes (Nordhaus 1991) and an FAQ from the IPCC indicating that both Nordhaus and the IPCC explicitly exclude 87% of economic industries from their approach towards estimating damages, since these industries are composed of activities performed indoors. As Keen notes, just because an activity is performed indoors does not mean that it is not affected by climate change. He quotes Nordhaus saying the following,

Table 5 shows a sectoral breakdown of United States national income, where the economy is subdivided by the sectoral sensitivity to greenhouse warming. The most sensitive sectors are likely to be those, such as agriculture and forestry, in which output depends in a significant way upon climatic variables. At the other extreme are activities, such as cardiovascular surgery or microprocessor fabrication in ‘clean rooms’, which are undertaken in carefully controlled environments that will not be directly affected by climate change. Our estimate is that approximately 3% of United States national output is produced in highly sensitive sectors, another 10% in moderately sensitive sectors, and about 87% in sectors that are negligibly affected by climate change.

The IPCC FAQ is quoted as saying,

Economic activities such as agriculture, forestry, fisheries, and mining are exposed to the weather and thus vulnerable to climate change. Other economic activities, such as manufacturing and services, largely take place in controlled environments and are not really exposed to climate change.

Such an obvious blunder on the part of both Nordhaus and the IPCC would be shocking. However, I'm a bit skeptical that Keen fully understands the literature here. In a later section, Keen seemingly admits that he dove into the climate econonomics literature in order to find a flaw, rather than dispassionately reviewing it in order to uncover truth. He says, "While locating the fundamental flaw in the ‘enumeration’ approach took some additional research, the flaw in the statistical approach was obvious in the first reference I read on it." Given my skepticism of his scientific neutrality, I wanted to understand how Nordhaus, Tol and other climate economists would reply to his critique.


texts: How, with complete markets, do we have a representative agent?

texts:
I've read several texts stating that with a complete market assumption, there's always a representative agent lurking. How is it that by assuming complete markets, we're able to prove the existence of a representative agent?

What's the connection between both?

Any help would be appreciated.


texts:
With "trickle-down economics" on the tongue of Americans this year, I wanted to do some research.  The prevailing opinion is "trickle-down economics doesn't work."  I can find many resources which defend this position.  However, I am having trouble finding resources which suggest trickle-down/supply-side economics does indeed work which have not been refuted by history.

Do we have any examples where trickle-down/supply-side economics has been applied, and has been considered a success?  Ideally, I'm looking for examples of events which occurred long enough ago to provide it the opportunity to fail, but in which it is generally agreed it succeeded.


texts:
Say we are in a world described by the consumption CAPM. All investors in this world have quadratic utility. Also, assume that consumption is as follows:
$$c_{t+1} = (1+m_t)c_t + s_t c_t e_t $$
where the shocks $e_t$ are iid with $E_t(e_{t+1})=0$ and $V_t(e_t) = 1$. Now $m_t$ and $s_t$ depend on the business cycle so that in down times $m_t$ and $s_t$ are high, but in boom periods $m_t$ and $s_t$ are low. Assume that the risk-free rate is independent of time.
I have a few questions as follows and was wondering if my answers make sense or if someone can correct me.

Say there is a company (e.g., luxury goods) that is very sensitive to the business
cycle. Will this company have high or low returns?

My answer: Investors don't like uncertainty about consumption. You consume more luxury good in good times and less in bad times. Since it varies positively with consumption, you will require a low price and hence luxury goods will have high returns. Is my explanation right here?

Now consider a security that provides insurance against bad consumption shocks so that in down periods it pays off more. What can we say about the price of this security? Will it have a high/low price when consumption is high? Will it have high/low price during a down period?

My answer: This security would smooth consumption since it varies negatively with consumption. It pays off good in bad times and does not pay off in good times. As a result during a recession/down period, this security would have a high price and during a boom (when consumption is high), it will have a low price. Is my explanation right here?

Using the consumption CAPM, rank the expected returns on the following types of companies: i) computer software; ii) luxury goods; iii) basic consumer products; iv) oil and gas; v) high-growth company.

We need to compare the consumption beta of each company. The higher the consumption beta, the higher the expected return, all else equal. But I'm not quite sure how to roughly compare the betas of the above companies. Could anyone help?

Now for the above ranking, consider other risk factors that could explain expected returns, e.g., Fama-French 3 factors etc. How would the rankings change?

Again, I know I need to think about the covariance between the returns of the companies and how they co-vary with the risk factors, but I am unsure of the direction of the covariance. Could someone help here?


texts: Showing the Utility Possibilities Frontier is downward sloping

texts: The slope of the UPF must be equal to the slope of the MRT and the MRS. Is it therefore enough to show that the slope of the MRS is negative?


texts: Do minimum wage laws bring more bad than good?

texts:
Let me begin by saying I know nothing about economics.

In the past couple of days I've been listening to some lectures by Milton Friedman. They are of non-technical nature. In one of them he makes an argument which I have understood approximately as follows:

  Having a minimum wage law is harmful to workers who compete for low paying jobs and are relatively less skillful because it deprives them of their "only weapon" - working for less.

Do minimum wage laws increase unemployment? Is there any information enabling this comparison?
Are there purely economic arguments, or empirical evidence, favoring minimum wage laws? Have they in any sense improved the economy?


texts: Lagrangian multiplier and optimal bundle

texts:
I would like to know where I am wrong (if I am) and why I am wrong here please:
If a consumer has an income of 600 euros to spend for good x (Px = 10 euros) and good y (Py = 5 euros).
What is the optimal bundle considering that U(x,y) = y + 100 ln(x)?
Here is how I did it (but I'm not confident):
Data:
$$
U(x,y)=y+100ln(x)
$$
$$
M=600 , p_{x}=10 , p_{y}=5
$$
Applied Lagrange equation:
$$
\mathcal{L}= U(x,y) - \lambda (p_{x}x+p_{y}y-M)
$$
$$
\mathcal{L}= y+100ln(x) - \lambda (10x+5y-600)
$$
Condition 1:
$$\partial U/\partial x-10\lambda = 0$$
$$100/x -10\lambda = 0$$
Condition 2:
$$\partial U/\partial y -5\lambda = 0$$
$$1 -5\lambda = 0$$
$$(\lambda = 1/5)$$
Using a system of equations I get:
$$ 100/x - 10\lambda = 2-10\lambda$$
$$ x  = 50$$
Now, plugging this into Condition 3:
$$M-p_{x}x-p_{y}y=0$$
$$600-500-5y=0$$
$$y=20$$
Therfore xMax = 50 and yMax = 20
The optimal bundle is (50,20)
Comment:
I'm so not sure about this...
I'm skeptical because condition 2 doesn't seem to show the y variable, which seems to indicate that y should be equal to 0 at that point (so we should expect a corner solution).
But then, as I found x after equating the two first conditions and plugged it in the third condition, it gave me y=20 after all.
So I'm kind of confused.
If both lambda in cond1 and cond2 are indeed equal to 1/5, my answer (y=20) should be ok but if it's not the case, it might very well be that y=0.
I don't know how to check my answer to be sure I'm right...or wrong.
And, if by chance, I got it right, can we rule out corner/boundary solutions anyway?
Thank you for your help.


texts: Homothetic function versus straight Engle curve

texts:
Homothetic functions can be defined as follow (Green, 1964, p.49):

  If two figures A and B are "homothetic", or "similarly placed" with reference to a point P [for example, the origin], then for any two straight lines PQR and PQ'R' through P, cutting A in Q and Q' and B in R and R', the ratios PQ/PR and PQ'/PR' are equal.

Additionally, consider the case where "each set of points, in output of commodity space, at which marginal rates of substitution are constant, is a straight line". This is, a straight Engel curve.

Are these two definitions equivalent, in the sense that each implies the other?

Or to put it differently, can we define:

an homothetic function as a function which yields straight Engle curves? and
a function with straight Engle curve as an homothetic function?

I am a bit confused, because in a text I'm reading both are used at different times, without mention their direct relation.

The answer to me seems to be yes. However, Maybe in special cases like when an homothetic function does not start in the origin, or where Engel lines are horizontal, the relation might break. If so, would these be the only exceptions, such that we could conclude that, for most of our purposes, they are indeed equivalent?


texts:
Does anyone know of some papers that look at how risk preferences affect demand for information (or related topics about the connection between risk and Information)? I took an information economics class a while ago and misplaced the syllabus.

I can remember that some classical models predicted that higher risk aversion leads to lower consumption for information. My professor remarked that this seemed pretty counter-intuitive, and might be a result of a fundamental mis-specification in modeling information. Thoughts? I'd also be interested in experiments that look at this problem empirically. Thanks!


texts: Preparation for the rigors of an economics graduate programme

texts:
I realize now that my undergraduate program is not nearly as rigorous as it should be - it required almost no math to complete. This is concerning because I've been accepted into a decent (top 30) PhD program. However, I (luckily) am also completing a degree in mathematics.

My question:

Can anyone recommend a good textbook(s) to help me bridge the gap between my non-rigorous program and a PhD program (level of rigor is whatever might be typical of a top 30 school??). I would also love any online resources such as video lectures, problem sets with solutions etc.

I looked at MIT's OCW but most of the courses beyond the principles do not include lectures, which was really disappointing.


texts: Changing the base year of Real GDP from 2001 Euros to 1990 Geary–Khamis dollars

texts:
Estimating regional Gdp in Italy (1871-2001):
sources, methodology, and results (Felice, E)

This article has Italian historical regional GDP figures, but they are in constant 2001 euros not in 1990 Geary–Khamis dollars where I can compare them more easily with other GDP figures. Would someone show me how you go about converting 2001 euros to 1990 Geary–Khamis dollars?


texts:
I am a little confused about the statement of 1.D.5 in MWG, which I will reproduce here for convenience. I have "solved" the problem, I just don't understand something particular.
$\textbf{(1.D.5)}$ Let $X = \{x,y,z\}$ and $\mathscr{B} = \{ \{x,y\},\{y,z\},\{z,x\} \}$. Suppose that choice is now stochastic in the sense that, for every $B \in \mathscr{B}$, $C(B)$ is a frequency distribution over alternatives in $B$. For example, if $B = \{x,y\}$, we write $C(B) = (C_x(B), C_y(B))...$
So, my issue is that it seems that $C : \mathscr{B} \to \mathbb{R}_+^2$ is not well-defined, and would be more appropriately defined as a function $A (\subseteq X^2) \to \mathbb{R}_+^2$. What am I missing?


texts: Bayesian Mechanism vs Prior-free Mechanism

texts:
I have a double auction mechanism in which the valuations of the agents for the items are drawn from a known random distribution. To be precise, the valuations are the probability of each agent utilizing the items, i.e. in the range [0,1]. So I guess this is a Bayesian mechanism!

First: Why is it necessary to show that the mechanism is prior free?
Second: How could I prove that?


texts: Insignificant Interaction effect in applied econometrics (multinomial logit regression)

texts:
I'm currently writing my master's thesis where I'm applying a multinomial logit regression with interactions effect.

The model I'm using is
$$
P(y=j) = exp(xb_j)/(1+∑exp(xb_h))
$$
where
$$
xb_j =x_1b_{ij} + x_2b_{2j} + x_1x_2b_{3j} + XB + \epsilon
$$
  $x_1$ and $x_2$ are dummy variables ($x_1$ is coded 0/1 for man/woman).

I use marginal (or incremental) effects to report my results, since I'm interested in the effect of a unit change on the probability of af given outcome of my y-variable.

My question is regarding my results, where I get an insignificant marginal effect of the interaction term, which I guess indicates that there is no difference between how men and women are affected by a unit change in $x_2$. But when I look separately at men and women, I get that the marginal effect of $x_2$ is significant for men ($\frac { \partial P(y=j) } {\partial x_2 }$ when $x_1=0$) and insignificant for women ($\frac { \partial P(y=j) } {\partial x_2 }$ when $x_1=1$). (I use three different significance levels (0.1, 0.05 and 0.01))

How do I interpret an insignificant effect from the interaction, but significant in a subgroup (men)?


texts:
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.


texts: Are there empirical studies that quantify shoe-leather or menu costs?

texts:
Two theoretical arguments why a high level of inflation is bad (e.g. for growth) are:

shoe-leather cost: keeping lower money balances when inflation is high (implying more frequent trips to the bank/ATM).
menu cost: time and effort to change price lists in an inflationary environment

Are there any empirical studies that measured these two costs? (And I mean measure them separately from the slower growth due to inflation, which in itself is somewhat controversial, e.g. Barro (1995) vs Emara (2012).)


texts: An agent's expected utility depends only on mean and variance

texts:
Consider an agent with the expected utility function $U(L) = \sum_{s=1}^{S}\pi_s U(Y_s)$ over the lottery $L = (Y_s, \pi_s)$ where $\pi_s$ is the probability of state $s$, $Y_s$ are state $s$ payoffs, and $U(y_s) = -\frac{1}{2}(\alpha - Y_s)^2$ for $Y_s < \alpha$ is the utility index
  over payoffs. Show that this agent's expected utility depends upon only
  the mean and variance of the state-contingent payoffs.

I do not really understand what the question is asking of me to show. Any suggestions or comments are greatly appreciated. Specifically, is the question asking me to find $$E[U(s_s)]$$ and $$Var[U(Y_s)]$$ if so how do we do that when we don't really have any defined distribution for $Y_s$? Also what does even mean that the mean the agent's expected utility depends upon only the mean and variance of the state-contingent payoffs. Does not make sense to me, I do not have much of an economics background as a graduate student in Applied Mathematics.


texts:
What are translog preferences? The wikipedia article only clears up that it stands for transcendental logarithmic preferences, and that they are a generalization of Cobb-Douglas preferences.

Do they have special features that make it more appealing? I have never seen these being used in Macroeconomics.


texts: What is the economic sense in multiplying standard deviation by the root of the sample size?

texts:
I found an example when a so-called volatility index is calculated by multiplication of a sample standard deviation by the square root of the sample size, see here

Does it make a good sense, and why? If it does, why not SQRT(N-1)?


texts: Monetary policy: increasing interest rate

texts:
What happens to the quantity of treasury bonds when central bank sells short-term bonds?

The overall question for the assignment is: Suppose that the central bank of a country decides to increase the short-term interest rate. Discuss the transmission of this decision via financial markets. Your discussion should include the transmission to the money market, longer bond markets, wider borrowing rates, common stock prices, and the exchange rate.

However, I already got stuck at the first part...

I would highly appreciate any help with this assignment as I am very lost and I do not know if I can just apply the opposite results as when the central bank would lower the interest rate.


texts: Proof of Proposition 1.4 from Microfoundations I by Kreps

texts:
Regardless of the size of X (set of all possible objects), if a preference relation which is complete and transitive is defined on it, then the corresponding choice function generated by it will satisfy the property of finite nonemptiness.

The proof in the text is by induction on the set A which in turn is an element of the collection of all possible subsets of X.
But the proof assumes finiteness of A. I am not very sure about this assumption. Can anyone please help me understand this?


texts: Difference-inDifference model with Discontinued Treatment

texts:
I have a situation where I observe two groups A and B for three years. Group A never received any treatment. Whereas group B received treatment in year 2 only. I can estimate the impact of the treatment by using only years 1 and 2 data with standard difference-in-difference approach. I am also interested in estimating the impact of discontinuation of treatment.
If I use year 2 and 3 data only, the treatment happens in period 2 and the treatment and control groups are not comparable. Would it be okay to use all three years of data and treat the "discontinuation of treatment" as second treatment?


texts: How can I build a fixed point theorem argument in pure strategies?

texts:
To begin with, I am recalling the Banach Fixed Point Theorem.
Let $(X,d)$ be a non-empty complete metric space with a contraction mapping $T:X\to X$. Then $T$ admits a unique fixed-point $x^*$ in $X$ i.e. $T(x^*) = x^*$.
In order to prove that the combinantion of the best response strategies of $N \geqslant 2$ agents consitutes a Nash Equilibrium, we need to use a fixed point theorem argument. Is this necessary only in cases where the agents employ mixed strategies or this holds in the case where they also follow pure strategies? I am searcing for some guidance to use the Banch fixed point theorem in guadratic utility functions when agents act by submitting pure strategies. How can I build this argument? What confuses me the most is that the mapping $T:X\to X$ is about the strategies isn't it?
I can provide more details of my problem if you wish so. I would also be glad if you could answer with great details, since I do not have any idea about the topic


texts: Question Regarding Equilibrium Price & Surplus

texts:
So here's an example of a standard Supply & Demand Relationship for an Individual Supplier:

As a supplier, for 1 dollar, I'll produce 1 unit of something. For 2 dollars, I'll produce 2 units, for 3 dollars, I'll produce 3 units, and so on and so forth up until 10 dollars for 10 units.

At 1 dollar, I'll have 10 buyers, at 2 dollars, I'll have 9 buyers, at 3 dollars, I'll have 8 buyers...all the way up to having 1 buyer at 10 dollars.

As you can see, there's an inverse relationship with the equilibrium price being right in the middle: Producing 5 units with 5 buyers buying each of them at 5 dollars per unit. Simple...

But now I'm wondering what would happen if there was a surplus. Ideally I should've made 5 units at 5 dollars each and sold them all to 5 buyers. But let's say I make 6 units, thinking I'll be able to sell all of them for 6 dollars each, but I only end up selling 4 of them to 4 buyers. If I wanted to sell all 6, I would have to sell them at 4 dollars each to reach equilibrium. The problem is if I sell 6 of them for 4 dollars each, I'll make less money than I would selling only 5 of them for 5 dollars each.

So do I reduce the price to 4 dollars so I can sell all 6 of them, making 24 dollars? Or do I sell 5 of them at 5 dollars each, making 25 dollars, and then sell the remaining one for less money?

Thanks in advance for answers.


texts:
On the website https://www.core-econ.org/ in the book provided, there is an exercise 19.10. It asks whether poll tax is progressive, regressive or distributionally neutral. To answer this question of course we need to know first what is regressive, progressive and distributionally neutral tax.
First of all a poll tax is a tax levied as a fixed sum on every liable individual.

Progressive tax is a tax in which the tax rate increases as the taxable income increases.
Regressive tax is the opposite, it takes larger percent from low-income earners and  lower percentage from higher income earners.

However I could not find the definition of distributionally neutral tax.

My question: What is the definition of distributionally neutral tax?


texts: Purchasing Power Parity (PPP) and Law of One Price (LOP)

texts: If PPP were to be satisfied in reality, does that mean the Law Of Price is satisfied for all goods in a basket of goods used to generate the price levels of the country? Or, since PPP uses only average price of basket, is there possibility of "accidentally" PPP is satisfied without holding LOP for each good?


texts: Has Germany’s migrant policy improved the economy?

texts: What causal relationship is there, if any, between the country’s 2015-17 migrant policy and its economic growth?


texts: Why Is Cointegration Important In Practice?

texts:
In one of my econometrics classes. I'm nearly finished a problem set and assigned readings on an introduction to cointegration. I've essentially finished the assignment, run dickey fuller tests on some data, estimated cointegration relationships, and estimated an error correction model. But I'm often surprised at how textbooks in econometrics tend to drive right away into the details without first explaining the big picture and how various concepts are applied in practice. I was wondering:

Could anyone offer an intuitive explanation on how cointegration is important in practice. For example, if you are building models for policy analysis, or finance, or macroeconomic analysis, could you talk about some practical instances where cointegration comes into play and why it is important in these instances?

Thanks very much everyone for the help!


texts: Derivative of definite integrals - how did MWG arrived at this result? Microeconomics

texts:
For a wage as a function of profit: $w(\pi)$ and profit $\pi \in [\pi_{min},\pi_{max}]$, the owner of a company sets the minimum wage to satisfy the following condition:
obs $e = \{e_l, e_h\}$ but in this case effort is observable and contractible, and $f(\pi|e)$ is the pdf of $\pi$, thus:
$$\min_{w(\pi)}  \int^{\pi_{max}}_{\pi_{min}}w(\pi)f(\pi|e)d\pi$$
subject to manager's participation condition:
$$\int^{\pi_{max}}_{\pi_{min}}v(w(\pi))f(\pi|e)d\pi-g(e) = \bar{u}$$
after doing a lagrange optimization F.O.C
$$-f(\pi|e) + \gamma v'(w(\pi))f(\pi|e)=0$$
What exactly I do not understand is how the author took the derivative of the integrand and disappeared with the integral signs... why does it work?
edit: Just in case, you can find this situation in MWG page 480-481, but it happens often in microeconomics.


texts: Business cycle stylized facts are not country specific?

texts: Business cycle and macroeconomic stylized facts are country-specific, right? But in my macro classes, they teach it as something universally true whiles using US data...:). For example, after an RBC model, we only check for US data where $\frac{C_t}{Y_t} < 1$, end of story...:). How about other countries where $\frac{C_t}{Y_t} > 1$? The model is not good for that country?


texts: Why does a currency devaluation make a country more attractive for foreign direct investment?

texts:
The author of this article says "[the devaluation of the yuan] may also have impact on [foreign direct investment (FDI)] if China becomes a more attractive destination vis-a-vis India". Why is this?

I understand that the following sentence then says "investors would go there where with the exchange rate he will get more kick for his dollar", but what makes China a more attractive destination for FDI than India following the devaluation of the yuan?


texts: Other option to compute regions wages in real term in the UK (Urgent!)

texts: Is there any good indicator that can replace region CPI in order to deflate workers income. I have tried to get the data from the ONS in the UK but they only contain the data for England as a whole rather than per region


texts: Existence of market sharing equilibrium in hotelling model

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I'm reading a paper on Competition in Two-Sided Markets. The model is a Hotelling-type model, with consumers on some interval, choosing their preferred firm based on price and 'distance' to the different firms (see below). In it, there's an assumption made that guarantees that there's no single monopoly that serves all consumers, which amounts to the condition:

$$4t_1t_2>(\alpha_1\alpha_2)^2$$

But I'm not sure how this is derived. Annoyingly, the paper says: "it turns out that the necessary and sufficient condition for a market sharing equilibrium is $4t_1t_2>(\alpha_1\alpha_2)^2$", without providing the derivation. I'd appreciate a hint on how to derive this, or an actual derivation of this condition.

These screenshots are from page 8 from Competition in Two-Sided Markets.


texts:
I think everyone know this Friedman's quote nowadays:

  Inflation is always and everywhere a monetary phenomenon in the sense
  that it is and can be produced only by a more rapid increase in the
  quantity of money than in output

However, things are not that simple. The US had emitted lots of money and has very little inflation. In some cases there's also a spiral effect. Some heterodox economists talk about lack of supply of goods too. And emission still applies only to the mid & long term.

To sum up, the questions would be:

Can businesses be an important cause of inflation, or is it a pure monetary effect?
In not-so-developed countries, there might not be much competition.  Can that generate inflation?

Edited. Original question: Can anyone help me understand when that quote is true and when other factors should be considered too?


texts: Is it possible to peg a cryptocurrency to a stock or bond index?

texts:
What if the creators of a new cryptocurrency gave out new units of the cryptocurrency in exchange for shares of a stock or bond index fund, held these shares in reserves, and allowed owners of the cryptocurrency to redeem them back for shares in the index fund? Wouldn't this effectively peg the cryptocurrency to such a fund?
Wouldn't such a system offer a lot of stability, desperately needed in today's most popular cryptocurrencies?
What kind of issues would the creators or the consumers of the cryptocurrency run into with such a system?


texts: separable utility function and cross price effect

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Suppose that consumer's utility function for three goods is separable, that is,

$U(x_1, x_2, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ ...(i)

where $f_i$ is increasing and strictly concave, i=1,2,3. Show that

$ df_i/dP_1 $ for i = 2,3 can be either positive or negative, but they must be of the same sign where $f_i$ is the demand function for good i and $P_1$ is price of good 1.

i reasoned using the equimarginal principle where at optimum we must have

$ MU_1/P1 = MU_2/P2 = MU_3/P3 $.

suppose good 1 is normal, if $P_1$ rises demand for good 1 falls, that is $df_1/dP_1$ < 0. Due to law of diminishing marginal utility $MU_1$ rises, however to maintain equilibrium $ MU_2,  MU_3$ must also rise. So, $df_2/dp_1 < 0$ and $ df_3/dP_1 < 0$. But i couldn't do it more mathematically, taking the derivative of (i) w.r.t $P_1$ isn't of much use, please help.


texts: Restrictions proving quasiconcavity of utility function

texts: I have the utility function given as $u(x)=x_1+x_2^\gamma$. The answer says that for a utility function to exhibit strict quasi-concavity, $\gamma$ needs to be between 0 and 1; but I don't understand why this is true. I know strict quasi-concavity means that if $f(x) ≥ f(x')$, then $f((1−λ)x + λx') > f(x')$ but I don't know how this can be shown in this example...


texts: Consider the utility function U(x,y) = y√x

texts:
Draw the indifference curve for U= 10, U=15, U=20.

My knowledge of algebra has deteriorated over the last few years of being out of school and I am really unsure of how to answer this.

The X value is going up in the standard 1 to 10.


texts: Euclidean spaces,vector spaces,metric spaces,commodity spaces,Cartesian spaces

texts:
What exactly is the difference between Euclidean space,vector space ,metric space ,commodity space,Cartesian space?

I am reading about consumer choice and I came across this line:

"A commodity vector (or commodity bundle ) is a list of amounts of the different commodities and can be viewed as a point in Rl,the commodity space.
We can use commodity vectors to represent an individual's consumption levels.The lth entry of the commodity vector stands for the amount of commodity l consumed."

When I googled the meaning of commodity space ,it says - commodity space is Euclidean space and here,as we have taken l entries ,it is l-dimensional Euclidean space.

By l dimensions ,do we mean l directions?

Because when we consider only two commodities in a simple Cartesian plane,we can show them as perpendicular distance from two axis (moving in two perpendicular directions).

Is an l dimensional Cartesian plane similar to l dimensional Euclidean plane?

Since we are taking consumption bundles as commodity vectors,commodity space should be same as vector space.

We are now left with metric space ,the Google search engine defines it as " a set for which distances between all members of the set are defined"

We read about various consumption sets defined as a subset of the commodity space Rl.These consumption sets can be open as well as closed..

This shows that all the spaces listed above are interconnected..or similar to each other.


texts: The coming US interest rates rise by the Fed. Will it affect the european bonds?

texts:
Recently, or maybe not so recently, there has been talk of the Fed going to enter in cycle of raising the interest rates. When interest rates are expected to be risen in the future, bonds with long-term maturity(>1year) will suffer the most since their price is expected to drop to have the same increasing interest rate.
But will this put pressure on the long-term European bonds of countries like Portugal, Greece, etc? (I'm new to this, hence the lack of specificity in my question. Sorry ;). Also feel free to correct me any time. I'm learning.) I would expect them to be obliged to follow the current, and also have a decrease in price(increase in rates), unless the ECB is willing to allow devaluation of the Euro against Dollar. Is this a strong hypothesis?

Also, I've heard that since this talk of increasing the rates has been going for sometime now, and if the markets are at least semi-strong, then there really should be no change, since they have already incorporated this public information. I'm not expecting no change whatsoever if the Fed increases the rates, but should we give some weight to this perspective, and expect little changes?

Any help would be appreciated.


texts:
This question is related to References for particular definitions of risk and uncertainty, which offers an excellent description of risk and uncertainty.
Just as a recap: Knight (1921) described risk and uncertainty as two different beasts.

"Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all."

Keynes (1921) similarily discussed the term probability.
Now I am looking for a term that encompasses all three types (risk, uncertainty, probability) of "uncertainty" without being tautological. Is there something better and more concrete than saying "situations that involve risk or uncertainty"?


texts: Topological intuition to continuous preference relation

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For a Microeconomics Course, we are going through MWG, and in the lecture we discussed the notion of a continuous preference relation.
A preference relation $\succsim$ on a set $X$ is called continuous if
$\forall x,y\in X$, for all sequences $\{x_k\}\to x,\{y_k\}\to y$ for which we $x_k \succsim y_k,\forall k$, we have that $x \succsim y$. I am trying to understand the choice of words for continuity of the preference relation here: by some steps, using a theorem from Debreu, we can get from a rational and continuous preference relation to a continuous utility function that represents it. However, can we phrase the above definition in such a way that it corresponds to the usual topological notion of continuity? (A function is continuous if every pre-image of an open set is open.)
What spaces and what function should we consider, to find an equivalent topological definition of continuity of a preference relation? I got as far that it must be either some map $f: X\times X \to X$, or a map $f: X\times X\to \{0,1\}$, with X in the topology induced by $\succsim$ and $\{0,1\}$ in the discrete topology. But where to from here?


texts: I do Industrial Organization course, and I've seen the phrase "market is covered" several times in my lecture slides, however, I'm struggling to find the formal definition of "covered market" and the condition when it's true. Can you please help me with that?


texts:
I am trying to answer this past paper question on microeconomics and a rather complicated utility function question. The question is below as well as my answer.
In my answer, I use the fact that the marginal rate of technical substitution (MRS) is equal to their price ratio. I think that I derive both demand functions for pizza and apple. I am not sure if they are right and I don't know how to answer:
How James responds to an increase in the price of Pizza?
Just looking at the price of pizza (p1) in the demand functions would mean that an increase in p1 would result in a decrease in demand for apples.
I feel like I have done something wrong and that I would have to consider substitution and/or income effects? I'm terribly confused.


texts: Show mathematically that in a competitive market, a price-taking firm has a zero profit. Also, justify the assumption that there is only one firm

texts:
Consider a firm that has a production function given by $F(x)$, where $x \in \mathbb{R}^n_+$. Assume that the function $F$ is strictly increasing in each argument, concave, twice continuously differentiable and homogeneous of degree one. Let the price of the good produced be given and equal to $p$ and let the vector of input prices be $w \in \mathbb{R}^n_+$.

(i) Show that if the firm acts as a price taker profits are zero.

The firm's maximization problem is $\max_x pF(x) -wx $. The first order condition tells us that $p \frac{\partial F}{\partial x_j}(x^*) = w$ for $j = 1,2, ... , n$. So, $\pi^* = p F(x^*) - p\frac{\partial F}{\partial x_j}(x^*)x^* =p [F(x^*) - \frac{\partial F}{\partial x_j}(x^*)x^*]$. For the right most side to be equal to zero, the average product should be equal to the marginal product of $x_j$ for all $j$. But why should it be true?

(ii) Show that if there are $N$ firms with the same production function, that are at an interior point in the input space and facing the same input prices, then given the total amount of all inputs used, the total output of the industry is independent of $N$, regardless of whether they behave as price takes. In what sense does this result justify the usual assumption that there is only one firm, i.e. $N=1$.

I know that this problem has to do with the derivative of a homogeneous of degree one function has a homogeneous of degree zero, but I don't know where I should use it in the proof. I think that there are $N$ identical firms, and these $N$ firms produces outputs until marginal product is equal to marginal cost. Therefore, the total output is not affected by $N$. How can I mathematically present this result? Why does my first statement has to do with this problem?


texts: What fraction of new businesses die out within a year?

texts:
Is there a simple way to figure out how many new businesses appear and disappear each year in the US economy?
It seems a key question to figure out how the economy is changing over time, although I suppose the data is potentially messy...


texts:
Consider a game with $N$ players, each indexed by $i=1,...,N$. Every player $i$ has to choose a $J\times 1$ vector of actions $a_i\equiv (a_{i,1},...,a_{i,J})$ where each $a_{i,j}$ can be zero or one. The payoff of each player $i$ is $u_i(a_i, a_{-i})$, where $a_{-i}$ denotes the actions of the other players.
As a first best, I would like to show that this game has a pure strategy Nash equilibrium (PSNE). I'm unable to do so and I also don't want to allow for mixed strategies. As a second best, I would be happy to consider a weaker notion of equilibrium (still, in pure strategy) and show its existence.
In particular, by revealed preference, if $(a_1,...,a_N)$ is a PSNE, then the following holds:
$$
\forall i=1,...N \quad \forall j=1,...,J: \quad \text{if } a_{i,j}=1\text{, then } u_i(a_i, a_{-i})\geq  u_i(a_{i, \{-j\}}, a_{-i})\\
\hspace{6.5cm} \text{if } a_{i,j}=0\text{, then } u_i(a_{i}, a_{-i})\geq  u_i(a_{i,\{+j\}}, a_{-i})$$
where $a_{i, \{-j\}}$ denotes $a_i$ where $a_{i,j}=1$ is replaced by $a_{i,j}=0$; $a_{i, \{+j\}}$ denotes $a_i$ where $a_{i,j}=0$ is replaced by $a_{i,j}=1$.
Question: Is there any equilibrium notion in pure strategy such that:

it is weaker than PSNE

it implies the revealed preference inequalities reported above

its existence is typically easier to be shown (and, if you could give references on this)


texts:
Who is the first person/paper to introduce "mixed strategy"? The PNAS by Nash used this notion without citing anyone.
Does the earlier book: Von Neumann, J., and Morgenstern, O., The Theory of Games and Economic Behavior
include the introduction of mix strategy?


texts: I have a 2 consumer 2 goods economy. Both the goods produce an externality for the other consumer, therefore, they are a part of the other's utility function. How do I show that despite the externality, the equilibrium is efficient?


texts:
A woman pays her gardener £60 per year and later married him. The gardener continues to work in the garden but unpaid. The woman earns £1000 before and after the marriage. Statement: the marriage decreases GDP by £60.

My question is why the decrease? The economy still has £1000 regardless of whether it's consumed separately or combined (herself and her husband)?


texts: The law of supply and demand - How does it work?

texts:
I've learned what the principle of supply and demand says, and would paraphrase it like this:

The price of a good is at equilibrium when supply and demand are
equal.

Or with other words:

The price of a good is dictated by the principle of supply and
demand when supply and demand are equal.

My question is:

How does the principle (or even law) of supply and demand work in practice? Which
forces force the price to be at equilibrium?

That's what I came up with (a very raw model):

The producer or seller of a product notices that the product sells better than before.
From this he draws the conclusion that there is a bigger need for the product: consumers want to have it more urgently than before.
That means, consumers will probably be willing to pay a higher price for it than the current one.

Now there are different cases:

The producer can produce as much of the good as he could sell. He does so and sells it for the old price (making people happy). Or he takes a higher price (because he can, but not too high).

The producer can not produce as much of the good as he could sell. a) He doesn't want to grow, so he produces as much as he can and
sells it for the old price ("first come first serve"). Or he takes a higher price (but not too high).
b) He grows (taking credits) and raises the price to compensate the interests to be paid. Or he raises the price even more (because he can, but not too high).

Which of these scenarios is mainly responsible for rising prices
in case a good is demanded more strongly?
And what is responsible for rising prices of goods with no rise of demand? (Is this only a collateral effect?)


texts:
This is an example taken from Krugman's book:

Consider the case where the international relative price (of cloth in terms of wine) is

$\frac{p_{c}}{p_{w}} = \frac{a_{lc}}{a_{lw}}$. Where $a_{lc}$ and $a_{lw}$ are the unit labor requirements for the production of cloth and wine respectively (think of these as being the inverse of productivity in each sector). These prices are below $\frac{a_{lc}^*}{a_{lw}^*}$. The Home country has a lower opportunity cost in the production of cloth.

So given these prices, i.e., $\frac{p_{c}}{p_{w}} = \frac{a_{lc}}{a_{lw}}$ and $\frac{p_{c}}{p_{w}} < \frac{a_{lc}^*}{a_{lw}^*}$, I understand that Home will produce both goods (i.e., not specialise) while Foreign finds better to specialise in wine (since the relative price of wine is higher than the opportunity cost). But how does Foreign obtain cloth? Since Home is not exporting any cloth and there are only two countries, how can one of them be an autarky while the other specialises in one of the goods?


texts: Does non-binding price ceiling effect the market?

texts:
If the Price of a commodity is 1 dollar and this price is the equilibrium price. At this price, the quantity demanded & supplied is 100(KGs). If government sets the price ceiling of 10 dollars, What would be the effects on the market?

My curve for this question is:


texts: Have there been any attempts to turn free-trade agreements into Pareto improvements?

texts:
The textbook economic case for free trade agreements is that they constitute a Kaldor-Hicks improvement, which that in any given country the winners win more than the losers lose, when the benefits and losses are measured in dollars.  (See this blog post by Steve Landsburg for a proof.)  The reason that it matters that something is a Kaldor-Hicks improvement is that any Kaldor-Hicks improvement can be turned into a Pareto improvement, i.e. a policy that benefits some people and hurts no one, by having the winners pay the losers to compensate for the losses.
But the thing is, even though free-trade agreements are often argued for on the basis of this textbook case, once the agreement is passed the Kaldor-Hicks agreement is not actually turned into a Pareto improvement.  This is illustrated well in this dialogue by Gene Callahan:

Joe: An unemployed steel worker.
Thaddeus: An economist holding a chair at Free Market U.
Joe: Boy, free trade sure hasn't worked out as promised. Just look at the devastation it has created in the Rust Belt.
Thaddeus: I can't imagine what you are talking about: why, I have a very sophisticated model in which it is clear there are always net gains from free trade.
Joe: What you mean by "model"?
Thaddeus: It is a mathematical abstraction, that leaves out large parts of the real world in order to reach a determinate result.
Joe: So if your model leaves out large parts of the real world, how do we know its results apply to the real world?
Thaddeus: I did mention that it is a very sophisticated model, didn't I?
Joe: OK, let's say I grant that the results of your model do apply to the real world. You said it shows that there are always "net gains" from free trade. That implies that some people gain while others lose. How do you decide that the gains of the gainers are greater the losses of the losers?
Thaddeus: We use a compensation principle: if those who gained from some free trade agreement could, in principle, compensate those who lost, so that both sides would now prefer the free trade outcome, then we can conclude that free trade creates net gains.
Joe: Can you give me a concrete example of how this works in practice, for instance, in terms of the steel industry?
Thaddeus: I am glad you asked, because of course I can! Free trade allowed the steel company you used to work for to shut the plant at which you worked and move that production to China. Certainly, this move devastated the lives of workers in your town, and essentially left the town for dead. But other people benefited, for instance the consumers of goods that contain steel, but especially people like the upper management of the steel company that endows my chair at Free Market University. Let me tell you, those executives are doing really, really well as a result of that plant moving! I've been to a party at the CEO's house, and the upgrades he's been able to commission are just fantastic. I've never seen an infinite pool so sweet. Plus, they have been able to double my speaking fees at their summer seminar series.
Joe: I see. So, per your compensation principle, you will be recommending that those executives give up a portion of their gains to help out the town they left in ruins?
Thaddeus: I'm sorry, did you miss the part about "the company that endows my chair"? Jeez, do we really have to wonder why low-IQ workers like you are suffering in the great, global economy?

So my question is, have there been any attempts to turn a free-trade agreement from a Kaldor-Hicks improvement to a Pareto improvement? That is, a policy that taxes the winners in order to compensate the losers.


texts: Is it true that $\frac{dL}{dq}=1/\frac{\partial q}{\partial L}$?

texts:
Marginal costs MC is defined as $MC=\frac{dC}{dq}$. Taking into account that $C=wL+rK$,

$$MC=\frac{dC}{dq}=w\frac{dL}{dq}+r\frac{dK}{dq}$$

Recall that marginal product of labor $MP_{L}=\frac{\partial q}{\partial L}$ and marginal product of capital $MP_{K}=\frac{\partial q}{\partial K}$.

Question: is the following correct

$$\frac{dL}{dq}=1/\frac{\partial q}{\partial L},\;\frac{dK}{dq}=1/\frac{\partial q}{\partial K}$$

which implies

$$MC=w\frac{1}{MP_{L}}+r\frac{1}{MP_{K}}$$

If no, then no need to read further.

If yes, then, consider profit maximization of a firm.

$$\max_{L,K}pq\left(L,K\right)-wL-rK$$

FOC:

$$\begin{cases}pMP_{L}=w\\pMP_{K}=r\end{cases}\Rightarrow\begin{cases}MP_{L}=\frac{w}{p}\\MP_{K}=\frac{r}{p}\end{cases}$$

Therefore,

$$MC=w\frac{1}{MP_{L}}+r\frac{1}{MP_{K}}=w\frac{1}{w/p}+r\frac{1}{r/p}=p+p=2p$$

The result is wrong for sure. I wonder, at what step of derivation I made a mistake?


texts: Can the Income Consumption Curve have a non smooth shape?

texts: Can the Income Consumption Curve have a shape that is kinked?


texts: how to calculate the average annualized return?

texts: I can do average return, I don't know what is annualized thou. can somebody say where (in a textbook hopefully) can I read about this? thanks!


texts: Does analysis at two points in time count as 'longitudinal'?

texts: According to whatever norms and expectations exist in the econometrics literature - if an analysis looks at two points in time can this be described as longitudinal, or would more time slices generally be expected for work that describes itself as such?


texts: What's holding the U.S. from decreasing unemployment by cutting H1B limits?

texts:
I don't understand why doesn't the U.S. decrease the number of H1B visa holders (foreign workers) during the current economic crisis? The unemployment is skyrocketing, wouldn't this measure decrease unemployment? I'm sure there are many other economic implications, but I don't see any harm in opening up jobs to the U.S. citizens.
Recently there was a suspension of H1B applications, but I'm talking about cancelling all currently active H1B visas. Is this possible?
Or maybe this is wrong. Decreasing the number H1B workers will impact other economic factors?


texts: What are some currencies that are not pegged and fixed?

texts: Are there any currencies that are not pegged to the dollar or euro and are purely fixed exchange rates?


texts: Why are trade deficits considered unfair?

texts:
President Trump has accused Germany and China of unfair trading practices over trade deficits.

What is unfair about trade deficits?

This may be economics 101, but in my naive eyes every time a trade is done it is done deliberately because both sides believe there is a profit to be made. Hence, each time American companies give money to Chinese companies in exchange for goods and thus enhance the trade deficit,  this would presumably be to the advantage of both the USA and China.

You don't see Apple accusing Samsung of unfair trading practices because Apple bought Samsung screens but Samsung didn't buy Apple batteries in return.

Note that I am not asking why trade deficits are considered bad. Though I don't understand that either, my question how deliberate trade can be considered unfair stands even if trade deficits are bad as a whole for one country.


texts: Dynamic contract theory: Demarzo, Fishman(2007) optimal long term financial contracting

texts:
I am reading Demarzo, Fishman(RFS,2007). Any suggestion will be appreciated. My questions are the following:

(a)
\begin{equation*}
    b_T^e(a) = \left\{\begin{array}{lll}
             -e^{(\gamma-r)(T^{+}-T)}a & for & a \ge 0\\
             -\infty & for & a < 0
            \end{array}\right.
\end{equation*}

Paying the agent amount $a$ at time $T$ is the same as paying $e^{\gamma (T^{+}-T)}a$ at time $T^{+}$. We discount $e^{\gamma (T^{+}-T)}a$ back to time $T$ and get $e^{(\gamma-r)(T^{+}-T)}a$. Since $e^{(\gamma-r)(T^{+}-T)}a>a$, why don't we just pay the agent amount $a$ at time $T$?

(b)
    On page 2090, the paper says"the most efficient way ... is to pay the agent $e^{\gamma(T^{+}-T)}a$ in the following period $T^{+}$". In the same paragraph, it says"... while it is feasible to pay the agent after period T,..., such payments are (weakly) inefficient." Whether we should pay the agent before T, or at $T^{+}$?

(c)
    How does $b_t^{e}$ is plotted in figure 2? What is the intuition of $b_t^{e}$ when $a<a_t^L$ and $a>a_t^l$?


texts: Terminology for separability in price and value

texts:
Take an agent with mean-variance utility over something that is uncertain:
$$
U(x) = \mu_x^\theta - \sigma_x^\lambda
$$

$A\in \{0,1\}$ happens if $U(x)>0$, and $x$ is a random variable

$$
A = \mathbf{1}\left(\mu_x^\theta - \sigma_x^\lambda >0\right)
$$

Saha (1997) has shown that $\theta$ different from 1 corresponds to DARA or IARA preferences.  If an agent isn't necessarily CARA, and $\mu = value - cost$, then the first term is
$$
\mu_x^\theta = \left(E[value] - cost\right)^\theta
$$
This assumes that cost isn't separable from value.  In reality however, agents may not operate this way.  The simplest example is a cash/credit constraint.  You'd thus have
$$
A = \mathbf{1}\left(\left(E[value] - cost\right)^\theta - \sigma_x^\lambda >0\right) s.t. cost < c
$$

Alternatively, maybe cash expenditures are psychically painful.  Like, even if I value something at \$5, the thought of not having that \$5 just bothers me.  Maybe because of loss of option value, for example.

$$
A = \mathbf{1}\left(\left(E[value] - cost\right)^\theta - \sigma_x^\lambda  - f(cost) >0\right) s.t. cost < c
$$
where $f$ is weakly positive and monotonic.

My questions:

Is there a specific term for this sort of separability in cost and value?
Would it go away entirely if there were no credit constraint?
And if I simply model $\left(value - cost\right)^\theta$ with a nonparametric $g(cost, value)$, would economists know what I am talking about if I justify it as represeting "non-classical behavior" or "deviations from the classical behavioral model?"


texts: Confusion about multiple information Sets

texts:
I'm confronted with the following situation:

First of all nature decides which of two games is played. Then each of two players make a simultaneous move, but only player I knows which game is played.

How can I display this information in extensive form?

The root will be the nature, which decides whether Game I or Game II is played. Now we have two additional layers for each game. Now I would use an information set to display that the moves are taken simultaneously, but how can I display that only player I knows about which game is played?