texts: Understanding the Zellener-Revankar Production Function

texts:
I took out a book from my university library called Econometric Modelling with Time Series: Specification Estimation and Testing in an attempt to understand the importance of MLE in Econometrics.

There is a small note mentioning a production function I've never seen before called the Zellener-Revankar Production Function (ZRPF). Its a non-linear production function relating to output, capital and labor defined as:

$$\ln y_t+\alpha y_t=\beta_0+\beta_1 \ln k_t+ \beta_2 \ln l_t + u_t$$

The left hand side makes sense, however the right hand side seems odd. What kind of production it is trying to represent and more fundamentally, how this is mathematically considered a function give that there are two dependents on the left hand side?

Ive looked at the relevant paper work namely:

  Estimation of Zellner-Revankar production function revisited
  SK Mishra,
  Department of Economics,
  North-Eastern Hill University
  Shillong (India)
  ALTERNATIVE FUNCTIONAL FORMS FOR PRODUCTION,
  COST AND RETURNS TO SCALE FUNCTIONS
  by
  Arnold Zenner and Hang Ryu

Any help would be appreciated in terms of understanding what type of process this is coming to represent would be helpful.


texts: Examples of firms having private information about negative event

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as the title says, I am searching for examples where a firm incurs a negative event, for instance, a stockout, a supply chain glitch or investments that went wrong. In the best case the firm was in the aftermath under financial distress or even had to file for bankruptcy as a consequence of that initially privately known event.

If you have a link to an example or just remember firm names, it would be a great help.

Best wishes
Paul


texts: I sometimes play a guessing game with a friend. So fx we might try to guess how many people live in Russia. So person A says 100 milion and then person B says either 'more' or 'less'. If B says 'more' and in fact more than 100 milion live in Russia, then B wins and conversely. Is this game fair? I have an intuition that B probably has an advantage, but I'm not sure how to formally analyse the situation.


texts: Neoclassical Two-Sector Model of Endogenous Growth: Getting the consumption growth rate

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I'm struggling to derive the growth of consumption from a two-sector model with the traditional Cobb-Douglas function. The model I am speaking about incorporates the fractions used by physical and human capital inside the sectors with different elasticities and it is one mentioned in the Book: "Economic Growth" of Barro & Sala I. Martin, page 247.
Starting from the Hamiltonian:
$$
J=u(C) {e^{ -\rho t}}+ \nu [A{(vK)^ \alpha}{(uH)^{1-\alpha}} - \delta K - C]+ \mu [B{[(1-v)K]^ \eta}{[(1-u)H]^{1- \eta }}- \delta H]
$$
Where u(C) is the utility function, rho is the discount rate, $\nu$ and $\mu$ are shadow prices, A and B are the technology for each sector. K and H are the aggregates of physical and human capital respectively with $v$ and $u$ as fractions of each sector employed in the production. And the first-order conditions I calculated are given by:
$$\frac{\partial J}{\partial C}=0 = u'(C) {e^{ -\rho t}} -\nu \; \;  (1)
$$
$$\frac{\partial J}{\partial v}=0 = \nu A \alpha{(vK)^ {\alpha-1}(K)}{(uH)^{1-\alpha}} + \mu B \eta[(1-v)K]^{\eta-1}(1-v)[(1-u)H]^{1-\eta} \; \;  (2)
$$
$$\frac{\partial J}{\partial u}=0= \nu A {(vK)^ \alpha}(1-\alpha){(uH)^{-\alpha}(H)} + \mu B{[(1-v)K]^ \eta}(1-\eta){[(1-u)H]^{- \eta }(1-u)} \; \;  (3)
$$
$$
\frac{\partial J}{\partial K}=-\dot{\nu}=\nu A \alpha (vK)^{\alpha -1}(v){(uH)^{1-\alpha}} + \mu B\eta{[(1-v)K]^{\eta -1}(1-v)}{[(1-u)H]^{1- \eta }} \; \;  (4)
$$
$$
\frac{\partial J}{\partial H}=-\dot{\mu}= \nu A{(vK)^ \alpha}(1-\alpha){(uH)^{-\alpha}}(u) + \mu B{[(1-v)K]^ \eta}(1-\eta){[(1-u)H]^{- \eta}(1-u)} \; \;  (5)
$$
According to Barro & Sala I. Martin, wth Mino (1996) the consumption growth rate can be defined as:
$$\frac{\dot{C} }{ C}={\frac{1}{\sigma }}[A\alpha(vK)^{\alpha -1}{(uH)^{1-\alpha}}-\delta -\rho]
$$
However, I cannot reach this answer, aside that net marginal product of capital is way different, they are missing fraction v in their answer. And manipulation of the differential equations relies on a non-specified result.
By putting as equal (2) and (3) I've found the relationship of elasticities with the fractions. Same answer up to that. However, regarding the growth of consumption, I used logs in (1) and then differentiate with respect to time. And overall consumption growth rate is:
$$\frac{\dot{C} }{ C}={\frac{1}{\sigma }}[-\frac{\dot{\nu}}{\nu}-\delta -\rho]
$$
Using (4) I can just simply divide by $\nu$ and replace it in the general consumption growth rate, however... with (4) the answer implies that the growth rate of consumption also involves the production of the second sector (human capital sector) weighted by the shadow price $\nu$ or $\mu$. And $\mu$ can be cleared out from (2) or (3) or the equity in both.
Here's when I'm starting to get lost because I wasn't able to find a combination between the set of equations (1) to (5) to reach the expression of consumption they show in the book (which I also wrote up here). My closest form to their answer is clearing $\mu$ from (2) and replacing it (4) which leads to the result for me as:
$$\frac{\dot{C} }{ C}={\frac{1}{\sigma }}[Av\alpha(vK)^{\alpha -1}{(uH)^{1-\alpha}}[1+\frac{(1-v)}{v}] -\delta -\rho]
$$
So... any ideas of how to get that consumption growth rate they explicitly define in the book? If anything else is needed to compute the answer, please ask away.


texts: Is it sufficient to conclude by looking the following weekly demand schedule that the good is Perfectly Elastic?

texts:
The following is the demand schedule for cement over a period of one week:-

NOTE: I have written the Price and Quantity demanded in tuples of the following form (Price, Quantity). So in the first case, the price is Rs 275 and the quantity demanded is 80 bags of cement.

Monday-(275,80)

Tuesday-(275,30)

Wednesday-(275,60)

Thursday-(275,70)

Friday-(275,50)

Saturday-(275,80)

Sunday-(275,100)

From the above data, you can see that the price is invariant over one week and that all consumers pay this price. However, after further investigation, I found that the price changes after a period of 15 days. Using this limited sample can one conclude that the demand for cement is perfectly elastic in the short run?

EDIT1: After @Ubiquitos' advice I came up with the following idea, which is partly described in a comment. Nevertheless here is the full argument:

Suppose that the equation of the Demand curve is given by the following equation$$q=\beta_0+\beta_1P+\epsilon_1$$ and the equation for the supply curve is given by$$q=\gamma_0+\gamma_1P+\epsilon_2$$. Notice that there is no other exogenous variable in any of the equations except $P$. I know that this quite a crude assumption as we know that there are non-price determinants such as taste and preferences that affect the quantity demeanded.Thus, it is possible that the error term,  $\epsilon_1$ and $\epsilon_2$ are related to $P$ and thereby create a Selection Bias. Therefore, the parameters in both the equations cannot be determined. But I am still not sure how does this reasoning directly answer my initial question.

PS: If there are loops in my arguments, then please do suggest some rectifications as I am a beginner in econometrics...


texts: Nash equilibrium two players in a joint effortful project

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I have a problem where there are two agents in a joint project,
Each agent $i$ puts in effort $x_i$ $(0 \leq x_i \leq 1)$ which cost each $c(x_i)= x_i^2$. The outcome of the project is
$$
f(x_1, x_2)= 3 x_1 x_2
$$

which is split equally between both, regardless of their effort levels.
I am asked to formulate de situation as a normal form game and find the NE.

What I have done is that I have assumed some values for the efforts to evaluate the game and I have also maximized each player's payoff individually to get best responses and make them intersect to get to the NE.

In this illustration, NE are $(0,0)$; $(0.25, 0.25)$ and $(0.5, 0.5)$

$\max f(x_1, x_2)-c_1$ with respect to $x_1$ ; yields : $x_1 = (3/4)x_2$ and $\max f(x_1, x_2)-c_2$ with respect to $x_2$ ; yields : $x2 = (3/4)x_1$
Both maximization problems intersect when $x_1 = 0 = x_2$

Anyhow, I don't think this is the right way to go...


texts:
While answering this question I was doing some research and found that

the high-income world has Free Markets.

Is it that because they are high-income, they have free markets, Or, is it that their free market made them high-income?

A supplementary question is: if the latter is true, why don't all low-income countries adopt Free Markets?


texts:
Two kids at school are arguing over who owns a cool video game cartridge, and the schoolteacher, a ruthlessly practical social planner who knows that kids can only enforce so much AND that the game is worthless to either kid except in its full cartridge, does not believe in sharing; she demands that the one of them buy the other's share of the game off of the other.

She tells each kid that they will privately submit two values to her, $b_1$ and $s_1$ for the first kid and $b_2$ and $s_2$ for the second. Here $b_i$ is (supposed to be) the maximum willingness to pay for the other agent's share of the game, and $s_i$ denotes the minimum price each agent would be willing to sell their share of the game for.

She starts to propose a mechanism:

If $b_1 > s_2$, and $b_2 < s_1$, then kid 1 buys kid 2's share of the cartridge for $\frac{1}{2}(b_1 + s_2)$.
If $b_2 > s_1$, and $b_1 < s_2$, then kid 2 buys kid 1's share of the cartridge for $\frac{1}{2}(b_2 + s_1)$.
If $b_1 > s_2$, and $b_2 > s_1$, then whoever has the higher valuation of the game $(b_i + s_i)$ buys using the proposals shown above.
She then gets stuck. What if $b_1 < s_2$, and $b_2 < s_1$?

  In the first three cases, can we ensure incentive compatibility (no lying is best), individual rationality, Pareto efficiency, and budget balancing (teacher does not have to subsidize to make a trade)? How would you go about showing these results?

Also, suppose that it is illegal for schoolteachers to give subsidies to ensure trades in the fourth case. The lack of Coasian bargaining is particularly bad for the teacher, whose disutility from listening to little tykes fight would be less than the disutility of just subsidizing the trade.

  What alternative mechanism might you suggest for the fourth case that could satisfy the four conditions above (IC, IR, PE, BB) if possible? It does not have to involve $b_i, s_i$ necessarily.

The first three cases don't seem exceedingly hard to show intuitively, but I'm curious as to how it would be done formally (just do case by case?). As for the other question, I don't think there is an alternative mechanism, since it looks like neither player is willing to trade their share to the other. Maybe the teacher could be authoritarian and simply allocate the good based on chance, weighted based on each person's $n$ or $1-n$ share of the good?


texts: Capital Recovery Factor for Hyperbolic Discounting

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I'm looking for a closed-form capital recovery factor when hyperbolic discounting is used. The Wikipedia article on hyperbolic discounting has this formula for the "present value of a series of equal annual cash flows in arrears discounted hyperbolically":
$$
V = P \frac{\ln(1 + kd)}{k}\ ,
$$
but does not include any references.

If I attempt to sum the series $\sum_{t=1}^n 1/(1 + rt)$ however, WolframAlpha gives me a more complicated formula involving the digamma function.

I would appreciate a reference for this CRF, if one exists. A derivation would be a bonus. Thanks!


texts: Looking for discussion on equilibrium vs dynamic models in econometrics

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I'm a statistician/machine learning scientist more familiar with molecular bio than economics.  Trying to find out if an issue I perceive in bio modeling also occurs in econometric modeling.

A common task in computational biology is to build a model of some biochemical process from data.  These biochemical processes are always dynamic, i.e. something you might model with an ODE or Kalman filter.  However, there is a bias towards modeling such a process from equilibrium data.  This means, you wait until the process has reached some equilibrium (homeostasis), and you take measurements across subjects/replicates.  This is because for many reasons it is much easier and cheaper to acquire equilibrium data relative to time series data.  Training a model only on equilibrium data is a problem of course if you want the model to be predictive when the system is not at equilibrium.

I wonder if the same bias happens with econometric models?  Clearly, in terms of statistical methodology, cross-sectional data is typically cheaper and easier to acquire than time-series data.  And I know economists are concerned with modeling equilibria.
 I'm hoping there is a place someone can point me to that talks about this issue in the econometric context, perhaps with an example?


texts: Why are real interest rates so non-volatile compared to investment?

texts:
Intuitively I would guess that real interest rates are highly related to investment.

But there is a very low interest rate volatility, compared to investment:

log investment is about 20 times more volatile than real interest rates. The standard deviation of interest rates is about 0.15 of that of log gdp, while investment is about 3 times as much.

What explains this massive difference?


texts: National gold reserve vs boosting economy

texts:
In Free to Choose: A Personal Statement (Milton and Rose D. Friedman) I read that when a given country economy is developing well then the national reserve of gold is decreasing, while if that country economy is not developing well then the national reserve of gold is increasing.
I do not understand why is it happening? It is exactly opposite of what I expected.


texts: How to solve a pricing competition for complementary goods

texts:
I am preparing for an exam and I have come across this question in my textbook but I am not quite sure how to solve it so would really appreciate some help!

  Suppose that company L produces left shoes and company R produces right shoes. If L charges $p_L$ for a left shoe, and R charges $p_R$ for the right shoe, then the price for a pair of shoes is $p=p_L + p_R$. The quantity of pairs of shoes purchased is determined by the demand function $q = 100 - p$. The cost of production is $c>0$ per shoe. Both firms choose prices simultaneously and independently of each other. Formulate this situation as a game (specify the players, strategies and payoff functions).

So obviously there are two players in the game, company L and company R. In terms of strategies I am slightly confused but I assume they are the following three:
- $p_R < p_L$
- $p_R = p_L$
- $p_R > p_L$

Please can you tell me is this is correct?
Secondly, I am extremely confused by the payoff. I understand it would be optimal for both firms to price their shoes at the same level. And I know that to calculate the payoff we need to calculate profit.

Profit = $(100-p)\cdot q - c\cdot q$
Where I am stuck is whether it is necessary to sub in the expression that we have for q?

Finally, I believe that the payoff when prices are equal is just half the total profit for each firm. However, I have absolutely no idea what the payoff would be when the prices don't align. Any hint would be really useful! Thank you!


texts:
I'd like to ask a question about  producer surplus. Basically I got the concept and how we calculate when a demand or price changes on a graph, but I cannot figure out how I should apply to real life.

I mean, let's say A = 10, B = 20 and Q = 5.

At first the producers accept to sell at the price $10. Is that right?

And the revenue they get would be  $10 \cdot 5 = 50 $   but the producers managed to sell at the price of 20 and the revenue they get is  $ 20 \cdot 5 = 100$.

And the difference between what the producers get and what the producers would ask for is $100 - 50 = 50$.

But when I calculate producer surplus using graphic (ABC), I get  $\frac{(20 -10 ) \cdot 5} { 2 } = 25 $

So I come to different conclusion in real life than when I calculate using graph. Why? Could anyone explain to me please?


texts:
Show that there is no continuous utility function which represents the
lexicographic preferences $\mathscr{L}$ given by $(x_1, x_2) \succeq  (y_1, y_2)$ if and only if $x_1 > y_1$ or $x_1 = y_1$ and $x_2 > y_2$.


texts: Perfectly competitive firms. Economies of scale

texts:
My textbook says the following:

"Perfectly competitive markets only achieve productive efficiency if you assume that there are no economies of scale in the industry."

Why is this the case? And by "in the industry" does it mean external economies of scale?


texts: Profit Maximization and Returns to Scale

texts:
Assume a labor-intensive production function:

$Q(L)=L^\beta$

Find demand of labor that maximizes profits (unconditional demand $L(p,w,r)$), the demand of labor that minimizes costs (unconditional demand $L(q,w,r))$, the supply function $(Q(L(p,w,r))$), and the benefits $(\pi(L(p,w,r))$ if:

a) $\beta>1$

b) $\beta=1$

For the first case (increasing returns to scale) I am able to Maximize profits by getting the First Order Conditions, etc., and finding $L(p,w,r))$:

$L(p,w,r))=(w/p\beta)^{1/\beta-1}$

Thus, by replacing $L(p,w,r))$ into the benefits:

$\pi(L(p,w,r)=p*(w/p\beta)^{\beta/\beta-1}-w*(w/p\beta)^{1/\beta-1}$ (It can be simplified by doing more algebra).

By replacing $L(p,w,r))$ into the production function:

$Q(L(p,w,r)=(w/p\beta)^{\beta/\beta-1}$

Finally, the conditioned (on a production of "q") labor demand is given by:

$L(q,w,r)=q^{1/\beta}$

However, for the second case (constant returns to scale) I am not able to get the First Order Conditions and so on for obtaining the benefits, the supply function, etc. Thus, I would like to know how to address this problem.

I would appreciate any help,

Thanks in advance


texts:
I'm studying the Dornbusch overshooting model of the exchange rate. Specifically, I'm studying the model presented in a textbook by Copeland (2014).

The economy is represented by the following equations:

$y^d=h(e-p)$

$m_s-p=k\bar{y}-lr$

$\Delta p =\pi(y^d-\bar{y})$

$r=r^*+\Delta e^e$

$\Delta e^e=\theta(\bar{e}-e), \theta>0$

where $e$ is the log nominal exchange rate, $\bar{e}$ is the long-run value of the log nominal exchange rate, (∗) is the log domestic (foreign) price level, $m_s$ stands for log nominal money supply, $\bar{y}$ is potential log output, (∗) is the log domestic (foreign) nominal interest rate, $\Delta e^e$ is the expected change in the log nominal exchange rate, and ∆ is the rate of change for log prices.

You can simplify these equations into 2:

$p=m_s-ky+lr^*-l\theta(e-\bar{e})$

$\Delta p = \pi(h(e-p)-\bar{y})$

You then can find the long-run values of e, p, and q:

$\bar{q}=\frac{\bar{y}}{h}$

$\bar{p}=\bar{m}-k\bar{y}+lr^*$

$\bar{e}=(\frac{1}{h}-k)\bar{y}-k\bar{y}+lr^*$

What I'm confused about is the functioning of fiscal policy. If there is a permanent increase in government spending, $y^d=h(e-p)+g$, correct? From what I can gather, real shocks in the model won't lead to any changes in long-run prices. Indeed, if we plug this equation into the model, only $\bar{q}$ and $\bar{e}$ change.

I have seen an exam question which asks how fiscal policy might be used to bring $q, e, p$ to their equilibrium values after an increase in $r^*$. But surely this would necessitate a decrease in $\bar{p}$ (since $\bar{p}$ has increased with an increase in $r^*$), from which I gather isn't possible in the Dornbusch model?


texts:
What is "Islamic banking," and how is it similar to and different from banking as it occurs in the U.S.?

I have heard Shariah Law prohibits usury, the taking of interest on loans. How do Muslim bankers justify the prohibition of interest? Are there any prominent Muslim economists, contemporary or older, who justify their prohibition of interest not only from a religious perspective?


texts: Why is a 'linear' regression model, with AR(1) error terms, a non-linear model?

texts:
Our model: $y_t=X_t\beta+u_t$

Our error terms: $u_t=\rho u_{t-1}+\epsilon_t$ with $\epsilon_t\sim IID(0,\sigma^2)$, and $|\rho|<1$.

This results in $y_t=\rho y_{t-1}+X_t\beta-\rho X_{t-1}\beta+\epsilon_t$.
Why is this last model not linear in $\beta$ and $\rho$?

Is it because the parameters are multiplied with each other in the 3rd term? or is there something else?

Any help would be appreciated.


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

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

What exactly is a modified IS-LM framework?


texts:
i'm new at this, so i´m really sorry sorry if i do something wrong.
The problem is this:
A choice function satisﬁes condition α if whenever $x = C(A)$ and $x ∈ B ⊂ A$, it follows that $x = C(B)$ as well.
Axiom 1: If $x ≠ C(A)$ then C(A) = C(A\{x})
And i need to show if condition α implies Axiom 1.

C(A) is choice function. Here is a definition of choice function (just in case you need it): "Let X be a ﬁnite set of alternatives. Let P(X) be the set of all nonempty subsets of X. We call the elements of P(X) as menus. A choice function is a map C : P(X) → X such that C(A) ∈ A, for all A ∈ P(X). It selects a single element from each menu. A choice correspondence is a map C : P(X) →P(X) such that C(A) ⊆ A, for all A ∈P(X). From each menu, at least one alternative is chosen"

And i found that Axiom 1 does not implies Condition α. Here is a counter example: We have X = {x, y, z}. Take A = {x, y, z} and y∈C({x, y, z})
y∈C({x, y}), z∈C({x, z}) and {y, z}∈C({ y, z}). Here we have a contradiction because C({x, y, z})≠C({ y, z}).
Thank you.


texts: what is $b(p)$ in the Almost Ideal Demand System?

texts:
In Hal Varian's Microeconomic analysis (page 213) he discusses the Almost Ideal demand system. There he describes the AIDS system as follows:

  The almost ideal demand system (AIDS) has an expenditure function of the following form:
  $$e(\boldsymbol{p},u)=a(p)+b(p)u$$
  where
  $$a(p)=a_0+\sum_ia_i\log p_i+\frac{1}{2}\sum_i\sum_j\gamma^*_{ij}\log p_i\log p_j $$
  $$b(p)=\beta_0\prod p_i^{\beta_i}$$
  $$...$$

So I know $a(p)$ is a second order approximation of $p$ on our expenditure function, however i am having difficulty understanding what exactly $b(p)$ is.

What is $b(p)$?


texts: Can a risk-averse agent's Certainty Equivalent be lower than the lowest possible outcome of a gamble?

texts:
Suppose there is an agent who faces the following gamble g:

50\$ with probability 1/3
100\$ with probability 1/3
150\$ with probability 1/3

Clearly, the E[g] = 100\$. Since agent is risk averse, we would expect that U(E[g]) < U(CE) , where CE is the certainty equivalent. Now, my question is, is it hypothetically possible that the agent's Certainty Equivalent of this gamble will be below 50\$, or is it necessarily true that it will be somewhere between 50\$ and 100\$?


texts:
In a Business Insider piece I read that:

Michael Madowitz, an economist at the Center for American Progress, says he is "unusually unsympathetic to the evergreen skills gap critique."
"First the Econ 101 'pay more for more if you want more' cuts against this well in a period of little wage growth," Madowitz said. "Second, there's fascinating/depressing empirical research showing a 'skills gap' occurs because employers add and remove qualifications for the same job postings depending on the labor market, ensuring there is always a skills gap."

(Emphasis mine.)
Unfortunately, the article has no further details on the latter research/issue to back up this statement that at least some of this "skill gap" is just employer advertisements vagaries, presumably regardless of what the job actually requires. And I'm curious if this is remotely quantifiable, i.e. how much of the "skills gap" in some sector (under study) turned out to be of this ad-based kind.


texts: Fuel trading a market with near-perfect competition

texts:
Can I classify the fuel trading market (wholesalers buying and selling fuel by phone) as a market with near-perfect competition?

It is a market with many sellers and buyers, the product is homogeneous, relatively low barriers to entry, non-increasing returns to scale, rational buyers, etc.

I know they use third degree price discrimination since they are selling the same product to different prices to different buyers, but since they also provide support through phone, they are somehow differentiating their product.


texts:
I am quite new to economics. I was reading about changes in interest rates and its effect on currency value.

The fact is as interest rates increases, the currency value also increases and vice versa. However I want to understand the reason.

At first, I thought following: As interest rate increase, people borrow less, spend less, so cost of goods decreases, value of currency increases.

However when I read in investopedia, it says following:

  Generally, higher interest rates increase the value of a given country's currency. The higher interest rates that can be earned tend to attract foreign investment, increasing the demand for and value of the home country's currency. Conversely, lower interest rates tend to be unattractive for foreign investment and decrease the currency's relative value.

Q1. Now I dont understand what does it mean by increasing the demand for and value of the home country's currency. What is it meant by demand for currency by foreign investors?

In another article it says:

  The rise of interest rates in a country often spurs inflation, and higher inflation tends to decrease the value of a currency.

But on the same page, it says:

  Generally, higher interest rates increase the value of a given country's currency.

Q2. Why these two different statements are there?

If I understand it correct, the word "spurs" here means increases inflation. But this confuses me.

My understanding is:

interest rate increases, people can borrow less, spend less, economy slows, inflation decreases, currency value increases
interest rate decreases, people borrow more, spend more, economy grow, inflation increases, currency value decreases

Q3. Are these understanding correct in general (though I understand the relation is not that straight forward and there are other factors too that affects currency value / inflation)?


texts: Which of Arrow's four desirable properties' is violated in this scenario?

texts:
So the scenario is as follows: there are 3 agents and 4 alternatives, $a,b,c,$ and $d$. Society's ranking of the 4 alternatives is such that

  the highest-ranked alternative is agent 1's highest-ranked
  alternative,

  The alternative that agent 2 ranks highest among the three remaining alternatives is ranked second highest by society

  The alternative that agent 3 ranks highest among the two remaining alternatives is ranked third highest by society.

  Society ranks the 4th alternative lowest.

So my interpretation of the ranking would look something like this:

Which of Arrow's four desirable properties is violated?

I'm guessing that the "Unanimity" preference would be violated, because agent 2 prefers $b$ over $c$, but this is not reflected in society's ranking?

The four desired properties I am referring to are:

1/ Complete and transitive preferences

2/ Respect unanimity

3/ Non-dictatorial outcomes

4/ Independence of irrelevant alternatives


texts:
Assume I have two integrated times-series A and B. I take log differences, that are stationary, and I compute the variance ratios for both time-series for several horizons k=2,...,n.

Now I want to test whether the variance ratio with horizon, say k, for the time-series A is equal to the corresponding variance ratio for the time-series B.

I know that $\sqrt(N)(VR(k)-1)$ is asymptotically normal with asymptotic variance that can be computed under either homoscedasticity or heteroscedasticity.

My goal is the asymptotic distribution of $\sqrt(N)(VR_A(k) - VR_B(k))$. How do I derive it? Any reference or code?


texts:
Suppose the velocity of circulation (V) is constant. Annual growth rate of real GDP is 5%. The money
supply grows by 14% per year. Use the quantity theory of money to calculate the inflation rate.

My solution:
Given M: 14%, V: Constant, Y: 5%, P: ?
M * V = P * Y
14 * V = P * 5
P = 14/5, am I right?

If not, could you please lead me to the right answer..thanks


texts: Intertemporal choice with possibility of death

texts:
Here is the setup:
Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period $1$, and during this period his sub-utility function is given by:
$$u(c_1) = \log c_1.$$
The individual is alive in period $2$ with probability $p$, and if he is alive, his state sub-utility function is given by
$$u(c_2) =\log c_2$$
and if he dies, he receives the fixed utility level $B$. Suppose he has access to a perfect capital market and discounts the future at rate $\beta$. His endowment is given by $(\omega_1, \omega_2)$.

I have a few questions about how to approach this problem. The first question is: do we assume he can die with debt/excess savings at the end of period $1$? If I assume that $p=0$ (dies with certainty), I get that he takes out a loan $s= \frac{\omega_2}{1+r}$ in the first period. Does this make sense, i.e., do we assume that even if he dies he gets an endowment of $\omega_2$ to pay off his debts? This result would correspond to $c_2 =0$.

The second question is about the fixed utility level. Should this be interpreted as, if he dies, he gets utility $u(c_1) + B$? Or $u(c_1) + \beta B$? Or that we assume his total lifetime utility from consumption is $u(c_1) = B$?

Thanks!


texts: Why (neoclassical) economic models have no profits, unlike the real world?

texts:
Consider a simple neoclassical model of an economy populated by firms with a constant returns to scale production function, using homogeneous labour and capital. Firms are equal, and are price takers in all markets. Thus, firms pay factors their value marginal product. In the long run, any economic profit is wiped out by changes in the price of the good, due to the menace of entry of new firms.

In this setting, no income remains after paying out competitive wages to workers (L) and competitive return to the capital hired for production (K). This is, for firm $i$,

$$pY_i = L_iw + K_ir $$

Now, in real markets, even in competitive ones, firms do make profits, even if these profits are not abnormal. Part of these profits might be distributed as dividends.

In the trivial economic model however, the ownership of the firm is not explicitly modeled. Firms do not pay dividends.

Why is this? Why is ownership not relevant? Are profits uninteresting? That is what the capitalistic firms cares about! I'm puzzled.


texts: When treating a relative, normalized utility function as a pmf, what is the interpretation of Shannon entropy or Shannon information?

texts:
Suppose $\Omega$ is a set of mutually exclusive outcomes of a discrete random variable and $f$ is a utility function where $0 < f(\omega) \leq 1$, $\sum_\Omega f(\omega) = 1$, etc.

When $f$ is uniformly distributed over $\Omega$ and $f$ is a probability mass function, the Shannon entropy $H(\Omega) = \sum_{\Omega}f(\omega)log\frac{1}{f(\omega)}$ is maximized ($=log|\Omega|)$, and when one element in $\Omega$ has all of $f$'s mass, the Shannon entropy is minimized ($0$, in fact). This corresponds to intuitions about surprisal (or uncertainty reduction) and outcomes and uncertainty (or expected surprisal) and random variables:

When $f$ is uniformly distributed, uncertainty is maximized, and the more outcomes there are for mass to be uniformly distributed over, the more uncertain we are.
When $f$ has all its mass concentrated in one outcome, we have no uncertainty.
When we assign an outcome a probability of $1$, we gain no information (are "unsurprised") when we actually observe it.
When we assign an outcome a probability closer and closer to $0$, the observation of it actually occurring becomes more and more informative ("surprising").

(This all says nothing about the much more concrete -- but less epistemic -- coding interpretation of Shannon information/entropy, of course.)

However, when $f$ has the interpretation of a utility function, is there a sensical interpretation of $log\frac{1}{f(\omega)}$ or $\sum f(\omega)log\frac{1}{f(\omega)}$?
It seems to me that there might be:

if $f$ as a PMF represents a uniform distribution over $\Omega$, then $f$ as a utility function corresponds to indifference over the outcomes that could not be greater*
a utility function where one outcome has all of the utility and the rest have none (as skewed of a utility as there could be) corresponds to very strong relative preferences -- a lack of indifference.

Is there a reference expanding on this? Have I missed something about the limitations on comparing probability mass functions and normalized, relative utilities over discrete random variables?

*I am aware of indifference curves and do not see how they might be relevant to my question for a variety of reasons, starting with my focus on a categorical sample space and with the fact that I am not interested in 'indifference' per se, but rather how to interpret utilities as probabilities and how to interpret functionals on probabilities when the (discrete) 'probability distribution' in question actually or (additionally) has the interpretation of a utility function.


texts: Continuity of preference relation (iff?)

texts:
I have a question about the following definition of a continuous preference relation. I apologize for not providing a reference and will try to add one as soon as I can find one.

Definition:

A preference relation is continuous if for all sequences x_n, y_n with x_n converges to x and y_n converges to y as n goes to infinity and x_n is at least as good as y_n for all n, then this must also hold for the limits x and y.

My simple question is:
Is the if an iff or only an if? That is, say this condition (or definition?) above is not ful-filled, can I infer that the preference relation is not continuous or might it still be continuous?


texts: (Ricardian model)Is it correct that complete specialization in comparative advantage CAN lead to DECREASE in total production?

texts:
I have the model in my electronic spreadsheet (created by me) and its results quite suprised me. In short, complete specialization (I just call it specialization) in good where a country has comparative advantage CAN lead to inefficiency, to decrease of production of one of the goods (cheese in this case). This result suprised me and I would like it checked in case a mistake (in my reasoning or calculations) was made. (I can also share the spreadsheet if you want)

Suppose there are two countries, USA and France. Each country has industries: cheese production industry and wine production industry. Each industry in each country has exactly 1000 workers(the top is the American workforce, the bottom is the French workforce)

But technologies are different.

From this we conclude that opportunity costs are following:

France has comparative advantage in cheese, while USA hold comparative advantage in wine. So France should concentrate all its laborforce in its chesee industry while USA should concentrate all its labor force in wine industry.

... except it will be bad news for world cheese production.

Production of cheese and wine in both countries before trade and (complete) specialization (the top is the American production, the bottom is the French production):

Production of cheese and wine in both countries after trade and (complete) specialization (the top is the American production, the bottom is the French production):

Now France produces all cheese in the world. But its cheese production technologies are too labor-intensive to produce enough cheese to compensate for fall of cheese production in USA. In order to avoid this USA will have to employ at the least 500 of its workers in cheese production, despite it beign American comparative disadvantage.

Thus we can conclude that in this case full specialization in cheese is a bad idea.


texts: Amazon vs Netflix, closely resembles which type of competition?

texts:
So we all know Amazon is following the path of Netflix regarding tv shows and movies. Both firms are increasing production of film, and now have their own productions.

If we were to categorize this type of competition, would it more closely resemble Hotelling's Model or Cournot?


texts: Anyone care to explain how exactly decreasing returns to scale (DRS) can lead to specialization? Having come across a few studies showing how large farm enterprises tend to experience DRS, I came to think about this but never really understood the logic behind it. How does specializing increase efficiency in such a case?


texts: Positive effects of a Tunisia-EU free trade agreement?

texts:
Tunisia might be signing a free trade agreement with the EU very soon. It's called ALECA or DCFTA.

Many activists and labor unions are opposing such an agreement because it would result in losing jobs and shutting down local businesses, according to them.

Would an FTA between Tunisia and EU be beneficial for the Tunisian economy? How?


texts: Conversion of GDP PPP International \$ 2005 into GDP PPP International \$ 2011

texts:
Essentially I have two different datasets that I'm trying to consolidate. One set of data comes from the World Bank Databank, and is a set of historical GDP PPP values for all countries expressed in 2011 international \$. The other dataset is a set of forecasted GDP values for all countries, and is expressed in GDP PPP expressed in 2005 international $. I would like to convert one of these sets into the same units as the other.

Is this possible? If so, how would I do this?

The latter dataset has some historical values, so I've tried dividing the 2011\$ by the 2005$ for different countries, but have found that the ratio is different in all cases.

Eg.

China - GDP 2008 in \$2005: 7,566.755billion;  GDP 2005 in \$2011: 10,437.906billion - Ratio: 1.38

Canada - GDP 2008 in \$2005: 1,197.757billion;  GDP 2005 in $2011: 1,383.398billion - Ratio: 1.15


texts:
Expectations are model consistent, on average, in a RE framework, so errors are made, but on average they are zero.

thus

In a rational expectation framework, do all agents know the true law of motion of the economy? But they make errors, only on average, they are correct, right? So, the average agent does know the law of motion then? But this agent does not exist... . Well actually the average agents equals the individual agent, because all agents are the same, representative agents? But how then do you explain the random errors with zero mean?


texts: Microeconomic Model of Knowledge and Technology

texts:
Can you point me to any microeconomic models of knowledge and technology?

It is intended to be used for simulation.

The problem that arises is that you need to simulate the effects of technology on the economy without knowing anything concrete about the technology and knowledge.
But the technological breakthroughs are not random. They have a pattern that needs to be modeled.

I made my own model but there are too many magic numbers and distributions that I will be using.

Please note that it is still in development, so it is internally inconsistent. So treat it as a series of thoughts at the moment.


texts: How to calculate semi elasticity in fixed effect model with interaction

texts:
Given the model specification
$$Y_{it} = \beta_1 X_{it} + \beta_2 D*X_{it} + FE_{i} + e_{it}$$
The above model specification is a Fixed effect model with interaction term ($X_{it}$ interacting with D- i.e binary dummy variable[1,0])
Question
1.) If $Y_{it}$ is in log form and $X_{it}$ is (in percentages) unlogged, do I need to apply $100*(exp(\beta)-1)$ to both $\beta_1$ and $\beta_2$ to get the actual effect of $X_{it}$ on $Y_{it}$ when $D=1$?
2.) how do I interpret the effect?


texts: Debt accumulation equation derivation: valid given that it rests on calculus and the time period is a year? (nowhere near infinitesimal?)

texts:
Above is an image of what I’m referring to. The top ‘rule of thumb’ is derived using calculus, and hence is only valid for infinitesimal changes in t. However, this equation is considered over the period of a year, which is a large unit of time. How can this equation be justified?

I've put a derivation of the 'rule of thumb' below (in case you weren't sure how it was derived). I've derived the product case, but it can be used to show the quotient case, which is what I put at the very bottom. Please excuse my naff handwriting!!


texts:
I want to model TFP series using an econometric model, be it AR(1) process, unit root with drift drift process etc. I was wondering if anyone knows of published papers discussing various methods of modelling technical progress. Alternatively, type in your model of TFP.

Thank you


texts: Unions and their effect on salary with tenure

texts: I'm wondering if labor unions cause a steeper salary over experience(or tenure) graph. I.e. low salaries in entry positions and very high salaries in tenure positions for union workers vs. similar workers non-unionized.


texts: What does it mean if a question asks me to find the set of "rationalizable actions" for a given game?


texts: What is the difference between gross, operating, net profit and EBIT(DA)?

texts:
What is the difference between the following accounting measures, if any?

Gross profit
Operating profit
Net profit/income
EBIT
EBITDA


texts: What's the next largest company after Facebook of which the majority of the votes is controlled by a single person?

texts:
Mark Zuckerberg controls 57.9% of all votes among Facebook shareholders [1]. Currently, Facebook's market capitalization is more than $650B. It has been among the global top 10 public corporations by this measure for a long time.
Which company is currently the next largest by means of market capitalization in which a single person controls the majority of the shareholder votes? Also of interest: in which a single entity (possibly institutional) takes that position.
PS: please help me out with the tags


texts: Cholesky Decomposition in R package "vars"

texts: I'd like to know if, when running a VAR model in R (package "vars"), the cholesky decomposition matrix is upper triangular (so I should order my variables from more endogenous to less endogenous), or lower triangular (so I should order my variables from less endogenous to more endogenous).


texts: Post Brexit Referendum employment theory

texts:
According to Chuka Umunna, Labour MP for Streatham and prominent pro-EU campaigner:

  People were told: "if immigration levels fall, it will be easier to
  get a job, and easier to get a job that's paid well." Since 2016, net
  immigration from the EU has fallen. Yet this indicator has gotten
  worse.

He did not cite which study the numbers came from, but let's just assume it's true. From a purely supply / demand perspective it does seem counter-intuitive, but it could be more nuanced and complicated than that.

My personal best guess was: this result could be from a lagged effect of all the previous immigration up until then. With the red tape and time needed to immigrate, settle down, get a sponsored visa, find a job, it may take months or years for immigration levels to have a measurable influence on jobs. I first envisioned conducting a lag / lead regression analysis to test my hypothesis, but have since redirected my interest in theory.

Question: Is there anything in existing economic theory that could explain a fall in immigration correlating and/or causing higher difficulty in finding employment? (note I use and/or for causality) And related, what other empirical findings outside the UK support Umunna's claim?

Further Clarification:

"easier to get a job": I am not quite sure how to quantify this section of Umunna's claim, I'm guessing he meant: average number of months unemployed before finding a job, or perhaps he meant: average availability of jobs in said sector. In your answer, explain which interpretation you use.


texts: Can inflation show up in assets without necessarily being reflected in classic inflation indexes?

texts: I have been having an argument with a friend of mine who obtained an economics degree in college. I have been arguing that increased money supply from the fed has led to inflation in asset prices, despite 'inflation' not really showing up in things like CPI. He argues that since Fed economists use CPI, I am wrong to even consider any other metric since I am not smarter or more knowledgeable than the fed. Is he right? Does inflating asset prices not really count as inflation?


texts: Who is Butler in Marx' footnote in Das Kapital?

texts:
In footnote [7] of Marx's Capital, T.I, Ch. 1, Sec 1, after ...contradictio in adjecto, there are these quotes: «Nothing can have an intrinsick value.» (N. Barbon, t. c., p. 6); or as Butler says - «The value of a thing is just as much as it will bring.».

Does somebody knows who is this Butler and where is that quote?


texts: How can the bond market be overvalued when the value of a bond is a function of interest rates?

texts:
I seem to have a major misconception in my understanding of the bond market and how interest rates and demand and supply influence valuation levels. I hope someone will be able to clarify.

My thinking is as follows. If the fair value of a bond is the present value of the cash flows resulting from coupons and principal repayment, discounted at an interest rate that depends on a policy interest rates, how can the bond market be overvalued, given a specific set of interest rate levels?

I understand the idea of overvaluation in equity markets, where demand and supply freely determine prices, and demand may be artificially high in expectation of fiscal stimulus or because investors buy into unrealistic success narratives of specific companies. But in bond markets, the situation is a little more complex because both the policy interest rate and demand and supply feature in the valuation mechanism.

So my questions are the following:

How to interest rate levels on the one hand and demand and supply on the other hand interact to determine the market price of bonds?
Can the bond market be overvalued or can bond market valuations be inferred perfectly from policy interest rates?
How can it be that bond markets are referred to in the media as overvalued when valuations depend on interest rates? Do they mean that market participants are assuming inappropriately low spreads to discount bond-related cashflows in valuation?

Thank you in advance for any clarifications you may be able to provide!


texts:
I believe the following is the multiplicative property of bilinearity:

$$ Y=F(K,AL) $$
$$ c_1 F(K,AL) = F(c_1 K, AL) $$
$$ c_2 F(K,AL) = F(K, c_2 AL) $$

But when we have multiplied through the production function with a constant we have done so through each term as below

$$ c_3 F(K,AL) = F(c_3 K, c_3 AL) $$

e.g.

$$ \frac{1}{AL} F(K,AL) = F\left( \frac{K}{AL} , \frac{AL}{AL} \right) = F(k,1) = f(k) $$

What is the name of this property?


texts: In my understanding, the seminal contribution of Easterlin (1974) showed that within a single cross section, both within and across countries, happiness correlates positively with income. However, growth in income over time  within a country is not met with similar increases in happiness. Is my understanding correct?


texts: Can monetary union work without fiscal union?

texts:
If I understand correctly, when a state joins a monetary union it relinquishes its ability to competitively devalue/increase the money supply during downturns.

Another mechanism Governments use to work their way out of downturns is to participate in the economy themselves, for example by undertaking infrastructure projects. Does monetary union somehow limit the ability to use this lever too?


texts: Optimal pricing for Crypto-Currency Exchanges

texts:
I have a general understanding of game theory, and want to try to apply it to crypto-currency exchanges, which are completely decentralised systems. I come from a finance background so I will define some key terms.

BID Price: Price at which the exchange is willing to buy an asset from you.

ASK Price: Price at which the exchange is willing to sell an asset from you.

ASK>BID, so as a trader, you will always pay the higher ASK price when buying and will get the lower BID price when selling.

The BID-ASK spread is ASK price minus BID price.

Consider the following autonomous Bitcoin exchanges with the following prices on a certain date:

As you can see each exchange quotes its own price and spread.

In a frictionless world, a trader can buy Bitcoins at the cheapest ASK price (in this case exchange B at 1477) and sell the coins on the exchange with the highest BID price (exchange A at a BID price of 1603). This arbitrage opportunity is also
found on the other exchanges as long as the ASK price paid by the trader is less than the BID price on the other exchange.

Now let's say I want to create my own exchange. If I want to eliminate all arbitrage opportunities, I would quote a BID price equal to the lowest BID (exchange B: 1475) and an ASK price equal to the highest ASK (exchange A: 1604). While this eliminates arbitrage on my exchange, it also makes me very uncompetitive given that my spread will equal 129. As such, no one will trade on my exchange.

Given that I want to keep my spread competitive, with a goal of minimising arbitrage opportunities. What is the best course of action to take for quoting Bitcoin prices?

This is a real case, and the figures in the table are actual Bitcoin\USD prices taken on a particular date for these anonymised exchanges.


texts: Modeling Asymmetric price adjustment (downward price inflexibility)

texts: There is any way to model downward price inflexibility? Because the different models of sticky prices, don´t have more downward inflexibility than upward.


texts:
The USA is issuing a lot of treasury bonds and investors are buying it.
But does China issue such bonds too?
If yes, then how many such bonds did they issued and who are the largest owners of those debts?


texts: What are the pro's and cons of GST (goods and service tax) ? And what influence it can make in the Indian economy?

texts:
As government is planning to introduce GST in India, what change it will make in India's economy?

GST is introduced in many countries except American, so why American has not introduce GST yet?


texts:
What is the common definition for economic richness of a person?
When can you say John Doe (hypothetical name) is rich (objectively)?

Strictly economically speaking, no philosophical debate.


texts: Quantity theory of money: microfoundations

texts:
The quantity theory of money states the price level is proportional to the amount of money in circulation. That is, if the quantity of money increases by some factor $k$, the price level will increase by the same factor $k$. My question is simple: in which economic models should one expect such a claim to hold true?

To be clear, I am asking about 'microfounded' models which contain full descriptions of the preferences and constraints of the underlying agents (including but not restricted to general equilibrium models). I am not interested in equations like $MV = PY$ unless you can show that they arise from such a model.


texts: General equilibrium regarding on U= max(ax,ay) + min(x,y)

texts:
Please kindly instruct me on solving the following in a general equilibrium framework with standard budget constraint,
$$ u^{1}\left ( x  \right )= max\left [ \frac{x_{1}}{10}, \frac{x_{2}}{10}\right ]+ min\left [ x_{1},x_{2} \right ] $$
, with $e^{1} = (10,10)$

What would this consumer demand at prices $p = (\frac{3}{4}; \frac{1}{4})$?

Given the other two consumer utilities

$$u^{2}\left ( x  \right )= x_{1}^{\frac{2}{5}}x_{2}^{\frac{3}{5}} $$

$$u^{3}\left ( x  \right )= x_{1}^{\frac{3}{5}}x_{2}^{\frac{2}{5}}$$
, with $e^{2} = (4,6)$ , $e^{3} = (4,4)$

Find one Walrasian equilibrium (and determine both equilibrium prices and the equilibrium allocation).

I have completely no idea how to start with it...

Thank you!


texts: How is Aggregate Supply(Willing) equal to National Income(Actual)?

texts:
Acc. to definition of Aggregate Supply

It is the total value of final goods and services that the producers are willing to supply in country .

Definition of National Income

It is the value of total output produced by normal residents of a country in given period of time .

AS is what producers are wanting/willing to supply i.e it is not the actual output produced

Whereas National Income is the value of output produced i.e it is the actual value of output that has been produced.

Then how can we say that Aggregate Supply (Willing) = National Income (Actual) ?


texts: CES First order Condition with two labour types

texts:
I am struggling to derive a first order in this model with Cobb-Douglas production function and CES labour aggregator with two types labour (here male and female, but could be equally low and high skill).
Setup: Cobb-Douglas production function
$$
Y = A K^{\alpha}L^{(1-\alpha)} \tag{1}\label{1}
$$
where $K$ is capital and $L$ is labor, and $A$ the TFP. There are two types of labor $i \in \{F,M\}$ that are aggregated with constant elasticity of substitution
$$
L = \left[(1-\lambda) (a_M M)^{\frac{\sigma-1}{\sigma}} +\lambda(a_F F)^{\frac{\sigma-1}{\sigma}} \right]^{\frac{\sigma}{\sigma-1}} \tag{2}\label{2}
$$
where $\sigma$ represents elasticity of substitution between $M$ and $F$, $a_M$ and $a_F$ are productivity terms, and $\lambda$ is the share parameter. Combining these two equations gives
$$
Y = A K^{\alpha} \left[(1-\lambda) (a_M M)^{\frac{\sigma-1}{\sigma}} +\lambda(a_F F)^{\frac{\sigma-1}{\sigma}} \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}} \tag{3}\label{3}
$$
Solution: Setting marginal products of labour equal to wage should give
$$
W^{F} = (1-\alpha)\lambda a_F A K^{\alpha} (a_FF)^{-\alpha} \times \left[ (1-\lambda) \left( \frac{A_MM}{a_FF}\right)^{\frac{\sigma-1}{\sigma}}+\lambda \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1} \tag{4.1}\label{4.1}
$$
$$
W^{M} = (1-\alpha)(1-\lambda) a_M A K^{\alpha} (a_MM)^{-\alpha} \times \left[ (1-\lambda) \left( \frac{A_FF}{a_MM}\right)^{\frac{\sigma-1}{\sigma}} \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1} \tag{4.2}\label{4.2}
$$
Steps: So, I wanted to get the foc of equation $ \eqref{3} $ to get the marginal product of each type of labor and doing double chain rule for each powered bracket, but my result seems not to simplify to what it should.
$$
\frac{\partial Y}{\partial F} = (1-\alpha) \lambda a_F  A K^{\alpha} (a_FF)^{\frac{-1}{\sigma}} \times  \left[(1-\lambda) (a_MM)^{\frac{(\sigma-1)}{\sigma}} + \lambda(a_FF)^{\frac{(\sigma-1)}{\sigma}} \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1}
$$
Edit: Edited the FoC for the mistake. And to close this, I am putting here the simplification as suggested in the answer (hopefully without typos):
$$
 = (1-\alpha) \lambda a_F  A K^{\alpha} (a_FF)^{\frac{-1}{\sigma}} \times  \left[\left((1-\lambda) (a_MM)^{\frac{(\sigma-1)}{\sigma}} + \lambda(a_FF)^{\frac{(\sigma-1)}{\sigma}}\right) \times \frac{(a_FF)^{\frac{(\sigma-1)}{\sigma}}}{(a_FF)^{\frac{(\sigma-1)}{\sigma}}} \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1}
$$
$$
= (1-\alpha) \lambda a_F  A K^{\alpha} (a_FF)^{\frac{-1}{\sigma}} \times  \left[(1-\lambda) \left(\frac{A_MM}{a_FF}\right)^{\frac{\sigma-1}{\sigma}}+ \lambda \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1} \times (a_FF)^{\frac{1-\alpha \sigma}{\sigma}}
$$
$$
 = (1-\alpha)\lambda a_F A K^{\alpha} (a_FF)^{-\alpha} \times \left[ (1-\lambda) \left( \frac{A_MM}{a_FF}\right)^{\frac{\sigma-1}{\sigma}}+\lambda \right]^{\frac{(1-\alpha)\sigma}{\sigma-1}-1}
$$
Sources:
Cahuc, P., Carcillo, S., & Zylberberg, A. (2014). Labor economics. MIT press. Chapter 3
Acemoglu, D., Autor, D. H., & Lyle, D. (2004). Women, war, and wages: The effect of female labor supply on the wage structure at midcentury. Journal of political Economy, 112(3), 497-551.


texts: Why is the term structure curve of agricultural commodities often downward sloping?

texts:
I have retrieved the below term structure curve for livestock (lean hogs) from Bloomberg and noticed that it is inverted. I have a vague intuition that this has to do with the storage costs and perishability of agricultural underlyings, but I lack a rigorous explanation. Searching for the solution online has yielded publications and PhD theses on term structure models which slightly exceed my understanding as an undergraduate student.

I would thus greatly appreciate any suggestions for economic explanations.


texts:
Suppose I have a series of debt as % of GDP.

By computing returns on this serie e.g.

debt as % of GDP in year 1 is 50% in year 2 is 60%

I compute $(60\%-50\%)/50\%$ can I interpret this measure as a sort of deficit for year 1-2? Hence, deficit for this period is 20%. Or shall it rather be the difference $10\%$?


texts: What changes the structural rate of output/unemployment?

texts:
To me the structural rate of unemployment was defined by $$\frac{1}{1+m} = F(u_n,z)$$ where $m$ is the markup and $z$ a catch-all variable. We could equivalenty get this in terms of $Y_n$ by letting $u_n = 1 - \frac{Y_n}{L}$, $L$ being the labor force.

Let $L$ now rise. What happens to $u_n$ and $Y_n$? From the equation, if $L$ rises but everything else must remain constant, then $Y_n$ must rise in order to still satisfy the equation, by the same amount. But then $u_n = 1 - Y_n/L$ is unchanged? Does this make sense? Why is the natural rate of unemployment unchanged when we just increased the amount of people willing to supply labor?

EDIT: The markup is the one that firms use to set prices, with respect to wages, $\text{prices} = \text{wages} \cdot (1+m)$, F is a function which is negative in $u_n$ (more $u_n$ means smaller $F$-value given constant $z$) and positive in $z$, and $Y_n$ is the structural rate of output.


texts: Why do lump sum transfers affect prices?

texts:
Let's suppose that I want to maximize total welfare (Social Planner Problem) using lump sum transfers to individuals.

It's known then that the price ratio changes relative to when there are no lump sum transfers. Total income and total endowments are fixed in the model, only distribution of initial endowments is changed between the individuals by planner.

My Question is :

Why do lump sum transfers affect the price ratio in the social planners problem?


texts: In using CES production functions of the form $f(x_1,x_2)=(x_1^\rho+x_2^\rho)^{1/\rho} $, we always assume that $\rho\leq1$. Why do we make that assumption? I understand that if $\rho>1$, the production function won't be concave anymore (and hence production set will not be convex), but what does that imply about profit and cost functions?


texts: Is it possible to give, in economics, an example of a relation ( set of ordered pairs) that is not a function?

texts:
In mathematics, some relations ( sets of ordered pairs) are not functions.

I know economists make use of functions.

But do they also consider relations that are not functions.

In which branch of economics could "non-functional" relations be useful?


texts: What is the A in the Accumulation and Amount functions for the value of investments?

texts: A number of interest functions, such as the accumulation function and the amount functions include an A (sometimes capitalized, sometimes not).  Could someone tell me what the A represents?  Here's an example:


texts: How does a stock market work under a command economy

texts: If a central government owns the means of production and controls business, what ramifications does that have on a stock market? Under such an economy are shares still traded as they are in a mixed/market economy? What about securities?


texts: Monetary Policy - How can increasing interest rates cause higher inflation in the short term?

texts:
My understanding of the interest rates part of monetary policy is the follows:

Borrower's point of view:

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

Saver's point of view:

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

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


texts: Prove all cost functions are concave in input prices and demand for inputs is downward

texts:
I've seen proofs that cost functions are concave of the form

$C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$

although this neither feels convincing nor does it seem like a path towards also proving that input demands are downward sloping.

To be more concise in my question, it is two parts.

First, prove that all cost functions, regardless of the production function, are concave.

Second, using the first step, also show that input demands are downward sloping.


texts: Effect of default risk on the interest rate of bonds

texts:
So I want to calculate the effect of default risk on the required interest of bonds (not on the price of bonds as that is normalized to one).

I thought of using the consumption capital asset model and calculating the following.

$$ U = u(C_1) + \beta (1-p)E_tu(C_2) + \beta p u(C_2) $$

Where the following applies:

$$ p = no \; default ,\; (1-p) = default $$

and the following budget constraints apply:

$$C_1 = Y_1 - T_1 - S_1$$
$$C_2 = Y_2 - T_2 + (1+r)S_1$$

I got to the following result using Lagrange, such that the consumer maximizes utility by deciding on how much to invest:

$$1 = \frac{\beta E_t[U'(C_2)p(1+r)]}{(u'(C_2)}$$

However, I want to get it ultimately in an equation that uses covariances but I do not know how.


texts: What's wrong with the "airline marginal cost pricing" argument?

texts:
This is a very common argument found in introductory classes and texts. Here's Mankiw's version:

Thinking at the margin works for business decisions as well. Consider an airline deciding how much to charge passengers who fly standby. Suppose that flying a 200-seat plane across the United States costs the airline \$100,000. In this case, the average cost of each seat is \$100,000/200, which is \$500. One might be tempted to conclude that the airline should never sell a ticket for less than \$500. But a rational airline can increase its profits by thinking at the margin. Imagine that a plane is about to take off with 10 empty seats and a standby passenger waiting at the gate is willing to pay $300 for a seat. Should the airline sell the ticket? Of course, it should. If the plane has empty seats, the cost of adding one more passenger is tiny. The average cost of flying a passenger is \$500, but the marginal cost is merely the cost of the bag of peanuts and can of soda that the extra passenger will consume. As long as the standby passenger pays more than the marginal cost, selling the ticket is profitable.

Do airlines actually do anything like the above? I think they don't as I have frequently been on planes with mostly empty seats (even before the current pandemic).
Mankiw says the marginal cost of another passenger is "tiny". Let's say it's \$30. Then if a flight has some empty seats 24 hours before scheduled take-off, why doesn't it offer the seats for say \$50 each and fill them all up? Why is it that, in practice and contrary to the above argument, the airline will usually prefer to leave the seats empty?
What, if anything, is flawed or incomplete about the above argument?


texts: Why does Bimetallism require international cooperation to have a chance at succeeding?

texts: I was reading the Britannica encylopedia's article about Bimetallism and under the arguments put forth against it, they cite that bimetallism doesn't work without international cooperation. Could anyone explain to me why this is? I can't seem to find a succinct answer to my question.


texts: Why do some researchers include oil price in a VAR model?

texts:
Why do some researchers include international oil prices in a VAR model for small open economies? My intuition is that international oil prices cannot be a endogenous variable in the context of a small open economy. For example, I don't see how one would justify a two-variable VAR model (say, for international oil price and GDP) for a country like Ghana. Because oil prices are not endogenous for small open economies, right? I mean, Ghana's GDP or its lags do not affect the international price of oil. However, I see in the literature that people still use a VAR model with oil prices as one of the endogenous variables in the model. I am finding it hard to understand how they can do that, and these papers do not state how.
Any help is appreciated.


texts: What are the pros and cons of a "long stock, short call" position compared to a "short put"?

texts: The profit-loss diagram for the "long stock, short call" position and the "short put" position are almost exactly the same, except that for the former, you may be able to profit more when the stock goes up as, in addition to the premium collected from selling the option, you also get to profit from capital gains and dividends from ownership of the stock. Additionally, you are able to allow for a greater decrease in the stock price before you start incurring a loss. However, to take two positions, there may be more transaction costs compared to just taking a "short put" alone. Are there any other pros and cons that I have not considered?


texts: Find the optimal labor supply when labor utility is linear

texts:
I have been working the afternoon on an intertemporal exercise where I'm blocking on something very basic. Have been looking on previous posts but didn't find a similar question.

We have the utility function of the household : $ U(C_1,C_2,n_2)= \log(c_1) + \beta \log(c_2) - \beta n_2 $

We have an allocation $ \bar y $ for period 1 and none for period 2, the household can only work in period two.

Here is the budget constraint : $ c_1 p_1 + c_2 p_2 = p_1 ( \bar y - x ) + qx + wn_2 + \pi  $

And the production function of the firm : $ f(k) = k^\alpha n_2^{1-\alpha} $

What I did until now is replacing $ c_2 $ in the utility function to have it depending on $c_1$,$ n_2$ and $ x $ only. Then I derive it for each variable and I can get the optimal condition for consumption :
$ \frac{c_2}{c_1} = \beta \frac{p_1}{p_2} $, the other derivatives gives me : $ w = p_2 c_2 $ and $ q = p_1 $ .
By replacing $c_2$ in the budget constraint, I can determine $ c_1$ and then $c_2$, and x is given by the market clearing condition $ \bar y = c_1 + x $.

But I can't find anyway to determine $n_2$, it's usually in a logarithm so we can find it in our First Order Conditions...

Edit :
$ x $ is the amount of capital given to the firm by the household, so we sould have $ x=k $ on capital market

$ q $ is the price of capital per unit

$ \pi $ is the profit of the firm , i.e. $ \pi(k,n_2) = p_2 k^\alpha n_2^{1-\alpha} - kq - wn_2 $

Edit 2 :
Rereading my question, I realize I should precise :
The household can only consume the firm production in period 2, which is why he contributes to the capital and labor of the firm, earning wages and profits.
Therefore, we should also have $ f(k,n_2) = c_2 $ I believe

Edit 3 :
My profit maximisation gives me :
$ \frac{\alpha}{1-\alpha} n_2 w = k q $

Edit 4 after @X recommendation :
So I do the lagrangian and derivatives, which gets me :

$ \frac{1}{c_1} = \lambda p_1 $

$ \frac{\beta}{c_2} = \lambda p_2 $

$ \beta = \lambda w $

$ p_1 = q $

After computing, I find : $ c_1 = \frac{p_1 \bar y + w n_2 - \pi}{p_1(1+\beta)} $ and $ x = k = \bar y - c_1 = \frac{\beta p_1 \bar y - w n_2 + \pi}{p_1(1+\beta)} $

But still having trouble regarding my original issue, $ n_2 $ : I did , according to your advices :
$ \frac{\alpha}{1-\alpha} n_2 w = k q $

$ \frac{\alpha}{1-\alpha} n_2 \frac{\beta}{\lambda} = \frac{\beta p_1 \bar y - w n_2 + \pi}{p_1(1+\beta)} p_1 $

$ \frac{\alpha}{1-\alpha} n_2 \beta p_1 c_1 = \frac{\beta p_1 \bar y - w n_2 + \pi}{(1+\beta)} $

$ \frac{\alpha}{1-\alpha} n_2 \frac{\beta}{1+\beta}(p_1 \bar y + w n_2 - \pi) = \frac{\beta p_1 \bar y - w n_2 + \pi}{(1+\beta)} $

$ \frac{\alpha}{1-\alpha} n_2 \beta(p_1 \bar y + w n_2 - \pi) = \beta p_1 \bar y - w n_2 + \pi $

$  n_2 \beta(p_1 \bar y + w n_2 - \pi) = \frac{1-\alpha}{\alpha} \frac{\beta p_1 \bar y - w n_2 + \pi}{\beta(p_1 \bar y + w n_2 - \pi)} $

Still pretty stupid as results ... I also used the central planner way and found $ n_2 = 1 - \alpha $ , which is weird..
I'd still like to go at the end of this way if someone has an idea.

Any idea ?
Thanks.


texts: Without knowing the Slutsky equation and income/substitution effect, how can I show a certain good is inferior or Giffen?

texts:
Say I've got a function $x_1(p_1,p_2,m)$ where $p_1, p_2$ are the prices for good 1, good 2 respectively and m is the income.
Now, I haven't heard of the Slutsky equation yet nor the income/substitution effect.
How do I show for this function that it is an inferior/normal and ordinary/Giffen good?
My initial thought was to simply use the partial derivate and to check whether it's greater or less than zero, since
$\frac{\partial x_1(...)}{\partial m} \gt 0$ should be true for normal goods, $\frac{\partial x_1(...)}{\partial m} \lt 0$ for inferior goods, $\frac{\partial x_1(...)}{\partial p_1} \gt 0$ for Giffen goods and $\frac{\partial x_1(...)}{\partial p_1} \lt 0$ for ordinary goods.
Is this correct?
Is this all I can do to formally show that the good is normal/ordinary? Is this sufficient?
Also, if I can show that the same function for $x_1(m)$ is homogeneous of degree 1 (i.e. homothetic), i.e. $tx_1(m)=x_1(tm)$, this means that the partial derivative $\frac{\partial x_1(...)}{\partial m}$ is homogeneous of degree 0, so it would be a constant. Could I thus conclude that the good is strictly normal/inferior (is that a term?), i.e. it doesn't change if the income changes?


texts: Relationship between government expenditure and exchange rate?

texts:
I've read an increase in government expenditure can lead to increase the chances of currency crisis but shouldn't it lead to the opposite?
Fiscal deficit ----> Govt will undertake borrowings ---> crowding out -----> interest rates will rise ----> capital inflows -----> rise in forex/international reserves
what is wrong with my reasoning/logic?


texts: Rentier capitalism vs investment capitalism?

texts: A company has backers who put in money seeking a return from either share-price growth through company growth, and yearly rent in the form of dividend payments. Debt is clearly the case where share price growth is 0 and only the yearly rent is paid, (Socialism is 1/population for both + a wage). Why do stockholders get both the right to make money from the investment, and the right to extract rent at the same time? How does having both rights at the same time impact the economy? Is there any economic thinker that considers banning dividend payments on shares from a legal perspective?


texts:
I am slightly confused about the requirements necessary to conduct a cointegration test with structural breaks such as the Gregory-Hansen test.
Suppose I have two I(1) variables.
Variable 1 follows a trend, then the trend slopes up and drops back down.
Variable 2 follows a similar trend, the trend similarly slopes back up and then similarly drops back down.
In other words, the variables behave very similarly even though their trend isn't constant over time. Does the behavior described above imply that one has to test for cointegration in the presence of a structural break or does that mean that you want to test whether the variables cointegrate if there is a structural break in only one of the variables?
Also given the above description of the variables is it possible to model cointegration between these variables given their behavior? If it is does a standard Granger 2 step cointegration test or Johansen Test still apply or is a Gregory-Hansen test necessary to be performed?


texts: Arrow-Debreu Theorem of Existence: Non satiation

texts:
Let $n$ be the number of consumers and $m$ be the number of commodities.
The Arrow-Debreu theorem requires closed and convex consumption sets $X_i \subset \mathbb{R}^m$ for all buyers $i \in [n]$. Additionally, it requires the utility function of any consumer $i$, $u_i: \mathbb{R}^m \to \mathbb{R}$ to be continuous, quasi-concave and non-satiated over the consumption set $X_i$, where non satitation is defined as $\forall \mathbf{x} \in X_i, \exists \mathbf{y} \in X_i$ such that $u_i(\mathbf{y}) > u_i(\mathbf{x})$ (pages 268-269).
It seems to me like these assumptions are contradictory. How can the utility function be non-satiated if the consumption set is closed, i.e., compact since it is a closed subset in $R^m$. Doesn't compactness and continuity of the utility function guarantee that there exists a bundle within the consumption set that maximizes utility which implies that non-satiation cannot hold?


texts: What textbook can I use to understand engineering economics?

texts: I'm an Engineering Physics student and this semester I took the course "Engineering Economics" as a requirement to complete the management sciences credits in my program, I need a good textbook to understand engineering economics, thanks.


texts: Industries that thrive in crisis like COVID 19

texts:
I am aware that some industries thrive during crisis times like COVID 19...Food supplies, medical, counselling, funeral services, liquor etc.

Are there any other industries that may do well during these testing times?


texts: Statistics on which businesses use flyering the most for advertising

texts:
Flyering is a well-known method of advertising. In my country (Russia) flyering is a very common practice and there is a fair amount of demand for flyer designers.
I am interested in businesses of which size are mostly behind flyering. On one hand, small businesses which wield single premises would probably not benefit from flyering as they could do with one in-street promoter or even a banner near the premises. On the other hand, I have never come across Google or Amazon flyers.
So, have any statistics of such kind been gathered and/or analyzed?


texts: Principles of Economic Reasoning: How Are Expected Costs and Benefits Distinct from Ethical and Moral Judgments?

texts:
This question relates to principles of economic reasoning in a non-financial context:
How are economic principles applied to non-financial models, such as a democratic election?
One may reverse the assumption and ask how benefits and costs in a financial context would be evaluated without recourse to making ethical and moral judgments?
For brevity one may describe an ethical philosopher as a person who makes an effort to answer two questions:

What is good?
How should one act to cause the good?

Terse principles of economic reasoning might be stated as follows:

Maximum benefits are good.
One should act to maximize benefits and minimize costs in the social context.

Public good would be an effort to maximize benefits and minimize costs for a group of individuals. Private good would be an effort to maximize benefits and minimize costs for each individual while interacting with members of the social group. Edit: Pareto efficient outcomes occur when no one is worse off.
How then is economic reasoning distinct from more general efforts to determine what is good and how one should act to cause the good? If people demand government solutions to social problems and economists debate the costs and benefits of different types of government institutions then is this not a political, ethical, and moral debate which cannot be resolved via recourse to an independent economic reasoning skill?


texts: What is the correct way of calculating the "average" price based on the "Open,High,Low,Close" daily trade fields?

texts:
Open,High,Low,Close

I have these fields, representing the "opening" amount, the highest for the day, the lowest for the day, and what it closed at.
I'm trying to determine the "average" price for the day.
I currently do this:
(Open + High + Low + Close) / 4

Is this correct? I get slightly different numbers if I do:
(High + Low) / 2

Which one is correct? Or, most common/used?


texts: Computational economics and global market simulation

texts: What is the largest - by number of agents - reported known global market simulation as of summer 2017?


texts: Identification of a "modified" wage equation with firm-worker fixed effects

texts:
Consider the traditional AKM model
where
$$
Y_{it}=\alpha_i+\psi_{j(i,t)}+\epsilon_{it}
$$
for $i=1,...,N$ (individual index), $t=1,...,T$ (time index), $j=1,...,J$ (firm index), and $j(i,t)$ is the firm employing worker $i$ at time $t$. $\alpha_i$ is called worker $i$'s fixed effect. $\psi_{j(i,t)}$ is called firm $j(i,t)$'s fixed effect.
By stacking observations over individuals, the equation above can be rewritten as
$$
\underbrace{Y_i}_{T\times 1}=\underbrace{D_i}_{T\times N}\underbrace{\alpha}_{N\times 1} +\underbrace{F_i}_{T\times J} \underbrace{\psi}_{J\times 1}+\underbrace{\epsilon_i}_{T\times 1}
$$
Assume that:
[A1] We have a sample of observations $\{Y_i, F_i\}_{i=1}^N$ i.i.d., for $N$ large and $T$ small.
[A2] $E(\epsilon_i| D_i, F_i)=0$ for each $i=1,...,N$.

As shown here, the identification of $\alpha$ and $\psi$ passes through dividing the sample into connected groups. In turn, under A1-A2 and for each of these groups $g=1,...,G$, $\alpha_g$ and $\psi_g$ are identified if and only if

One element of the vector $(\alpha_g, \psi_g)$ is set equal to a known constant.

$N_g>1$ and/or $J_g>1$, where $N_g$ (resp. $J_g$) are the numbers of individuals (resp. firms) in group $g$.

My question:
Consider the following "modified" AKM model
$$
Y_{it}=\alpha_i+X_{j(i),t}\psi_{j(i,t)}+\epsilon_{it}
$$
where $X_{j(i),t}$ is an observed covariate with support in $(0,1)$, indexed by the time period $t$ and the entire history of employing firms $j(i)\equiv \{j(i,t)\}_{t=1}^T$. In other words, at a given time $t$, two workers are endowed with the same realisation of such covariate if and only if they face the same entire history of employing firms.
Note the purposely different subscripts of $X_{j(i),t}$ and $\psi_{j(i,t)}$.
My question is: does the presence of $X_{j(i),t}$ change the identification result of the traditional AKM model?
My intuition is that identification of the firm and worker fixed effects is still guaranteed only within connected groups. However,
(1) the normalisation of one among the firm-worker fixed effects within each group may not be needed anymore. Therefore, we can be able to make comparisons across groups.
(2) we may be able to identify firm-worker fixed effects also when $N_g=J_g=1$.
What are your thoughts?


texts:
There is company A, which has Assets = \$100, Equity = \$50, Debt = \$50.

I, Ant, found a new company, company B. I personally invest 10 in this company, and I find people who lend me \$50. Assets = \$60, Equity = \$10, Debt = \$50.

With this \$60 cash I buy company A (I apply a \$10 premium because I can't expect to buy it at the current market price. Also I assume that the book value of equity is equal to the market value of equity)

The shareholder of the company A are happy as they got away with a 10 premium.

The balance sheet of B now looks like

Assets = \$100 Debt = \$150 (?) Equity = (?)

I don't know exactly how debt and equity would be in this case.
Also, I believe that the market value of the debt held by debtholder of the first company should go down, because now they have that their debt is alongside another 50 million dollars of debt against company assets that are still fixed at 100.

Can somebody help me clear up this point?

(Also, help me find the correct tags.. It seems like there are very few!)


texts: Why does the answer not include increased negative unplanned stock investment?

texts:
I will focus on the event "c":

The answer for "c" is following:

  A sharp increase in the rate of real GDP growth leads to
  a higher level of planned investment spending by producers, according to the accelerator principle, as they increase production capacity to meet higher demand.

I agree with the answer, but it seems to be incomplete. It was already established that growing negative change in unplanned inventory investment is a sign of a booming economy:

  In fact, economists who study
  macroeconomic variables in an attempt to determine the future path of the economy pay careful attention to changes in inventory levels. Rising inventories typically indicate positive unplanned inventory investment and a slowing economy, as sales are less than had been forecast. Falling inventories typically indicate negative unplanned inventory investment and a growing economy, as sales are greater than forecast.

So it would seem to be logical to expect that "A sharp increase in the economy's growth rate of real GDP" will cause increased negative unplanned inventory investments, AKA decreased inventory stocks. Does the answer omit this part without a good reason or do I misunderstand/miss something?


texts: What condition is exactly used to solve forward New Keynesian IS equation?

texts:
In http://www.uni-hamburg.de/fachbereiche-einrichtungen/fb03/iwwt/makro/slides3.pdf, you can see New Keynesian IS equation being solved forward to yield a formula for output gap (page 40 of the pdf slides). I do get that it is based on output gap becoming zero at infinity. But exactly what condition is this justification based on? Is it $\lim_{T \to \infty}E_t[\tilde{y_T}] = 0$? Or $E_t[\lim_{T \to \infty}\tilde{y_T}] = 0$ Or other conditions?

Also when getting the solution for new keyneisan models as done in later pages of the pdf (especially Blanchard-Kahn in page 44), if it is true that the above output gap formula depends on $\lim_{T \to \infty}E_t[\tilde{y_T}] = 0$ or $E_t[\lim_{T \to \infty}\tilde{y_T}] = 0$, does the solution mechanism also depend on these?


texts: In my last subject of studies I am analyzing trade costs in a gravity model, e.g. multilateral trade resistance and bilateral trade resistance terms. The gravity model assumes world trade. However, I want to analyse the effect of these trade resistance terms only on a subset of countries, , e.g. trade costs of war on LDC's. I therefore would drop all developed countries as exporters and would only analyse LDC's as exporters. Developed countries would be included as importers though. Would it be statistically misleading or would that regression work ?


texts: Theoretical models of copyright infringement and efficiency implications

texts:
I wanted to know if there are theoretical models of copyright infringement and what are their implications for efficiency in the market and also, if possible, any empirical support they have.
When I think about it, firstly it seems that there can be loss of efficiency due to under-supply, as the actual number demanding the commodity would be higher than those who buy it legally, thus the legal producers perceiving it as less demand. What exactly does this inefficiency depend on, however? What would be the effect of the marginal cost of the unauthorized copy? Or maybe this common sense explanation is not true at all and the models reveal something totally different.
So I wanted to read some formal models to gain more insight, and also if possible the empirical support such models have.


texts: Are there fundamental reasons why (exponential) economic growth is highly desirable?

texts:
One of the most widely published measures of the economy is the economic growth as a % of the GDP; i.e. the degree to which an economy grows exponentially.  In my understanding, when the rate of economic growth is declining or close to 0%, this is considered undesirable and acts are undertaken to avert recession.

In a situation where population is not growing, why do we want the economy to grow?  In other words, is there something inherently wrong with a steady state economy?

See also: Why is economic growth measured exponentially rather than linearly?


texts: How much precious metals prices come from their use as investement vs practical use

texts:
Some precious metal price come almost exclusively from their value as an investement, as gold, while some others like palladium or osmium have important uses in industries. But lately those metals also gained attention as a location of capital. Are there some estimations of how much of the price come from use as ivestement vs use in industry and others?

https://en.wikipedia.org/wiki/Precious_metal


texts: What is the "bequest condition" in a finite-horizon discrete optimization problem?

texts: For a finite-horizon discrete time optimization problem, my textbook provides a condition called the "bequest condition", which I'm not familiar with. Specifically, where the state at time $t$ is denoted $x_t$, the bequest condition states that at the final state, $x_T$, it must hold that $x_T\geq \bar x$. What does this mean?


texts: Difference between automated and living labor pertaining to surplus value

texts: In the Marxist concept, animals, machines and slaves are incapable of producing surplus value. They only produce as much as they have to in order to function, and no more. Doesn't this also describe the condition of "wage-slaves"? I have heard that the difference is that the wage-slave sells his labor. But I fail to see how a machine that sells its labor for fuel and spare parts would suddenly be able to produce surplus value. Explain please.


texts: What did the Swiss National Bank use to purchase EUR while pegging the Franc to the Euro?

texts:
To peg its currency (CHF) to the Euro (EUR), the Swiss National Bank (SNB) made purchases of EUR to the tune of several hundred billion.  By reducing the supply of EUR, the SNB made the EUR relatively valuable, achieving the peg.

But how did the SNB fund its EUR purchases?  My original assumption was that the SNB simply printed CHF to buy EUR.  Is this correct?

The reason I ask is (a) I have not been able to find explicit documentation of this and (b) a colleague suggested that the SNB may have been using other means to purchase EUR, such as tapping into gold reserves or other kinds of reserves.


texts: Prove that if a bond trades at a discount, its yield to maturity will exceed its coupon rate

texts:
Can someone give me a mathematical proof of this statement?

  If a bond trades at a discount, its yield to maturity will exceed its
  coupon rate.


texts:
Suppose we are using GMM to estimate the model $y=m(x;\theta_0)+u$ (for some function $m$ and $\theta_0 \in\mathbb{R^p}$)  and we are using the moment condition: $\mathbb{E}[g(\theta_0)]=0$ where $g:\mathbb{R^p}\rightarrow\mathbb{R^p}$ so the model is just identified. My question is how do we know that our estimator $\hat\theta$ is not dependent on the weight matrix?

Thanks!


texts: How do I convert (this OECD data of) median disposable income to pre-tax income?

texts:
I want to convert the "Median disposable income (current prices)" found in the link below to Median pre-tax income (current prices).
How do I do so? Are there for example any appropriate OECD data-tables for taxes that I could use?
Median disposable income (current prices): https://stats.oecd.org/Index.aspx?DataSetCode=IDD
Thanks in advance!

EDIT:
Could these tax data be of any use?

https://data.oecd.org/tax/tax-on-personal-income.htm

https://stats.oecd.org/index.aspx?DataSetCode=TABLE_I5


texts: What will happen to property prices if local currency weakens against USD?

texts:
Say that the conversion rate of a local currency changes so that the currency is now relatively weaker against foreign currencies and as a result the inflation rate increases and as a result of that the central bank raises the interest rates.

On the one hand more locals will be forced to sell their properties because they cannot afford the increased interest rates on their home loans. With the over supply of properties and the shortage of buyers who can still afford properties, I would suspect the property prices should drop.

On the other hand, only the currency weakens not the property. So if the conversion rate was 1:10 against the USD and now the conversion rate is 1:20, shouldn't the prices of the properties double as well?

What could be expected to happen to the property prices in such a country?


texts: Why division of labor or specialization boosts productivity

texts:
The three reasons given by Adam Smith were:

Increased dexterity.
Saving of the time which is commonly lost in passing from one species of work to another.
The invention of a great number of machines which facilitate and abridge labour, and enable one man to do the work of many.

What other reasons are there?


texts: Distance transported used to price goods in Marxism

texts:
A friend mentioned that in Marxism, the distance a good was transported was used to determine the price of said good.

I can't find anything on the Internet to support this claim, although I might be misremembering his statement.

Can anyone think to what he was referring?


texts: Can Quasi-Linear functions be monotonic?

texts: I want to ask that Can Quasi-Linear utility functions satisfy the more is better (monotonicity) assumption?


texts:
I'm looking to see if someone can help improve my understanding of sterilized intervention in FX markets.

My intuition/understanding is:

Assume that the domestic currency is depreciating, perhaps due to a trade deficit (let's say temporary for now) - if the domestic central bank wants to avoid depreciation, they use some of their foreign reserves (of the foreign currency) to buy domestic currency.
This would increase supply of the foreign currency, decrease supply of the domestic and therefore help prop up the domestic currency.
However, this would reduce the monetary base of the domestic currency (as some of it has now disappeared into the central bank which doesn't participate in the economy, and hence doesn't count towards supply).
Therefore, a sterilized intervention occurs when the central bank uses its newly acquired domestic currency to buy domestic bonds, which re-injects the domestic currency back into the money supply.
This leaves

the foreign currency supply higher than when we started and
the domestic supply unchanged from the start.

Therefore, this increased supply of the foreign currency devalues the foreign currency and hence helps prevent the domestic currency from depreciating.
To have the same level of effect on exchange rate as an unsterilized intervention, one may have to intervene to a greater extent (since only the foreign supply is increasing).

Is the above roughly correct? Is there some other reason / mechanism via which the exchange rate is being maintained? The main thing I'd like to understand is whether it is really this increased supply of foreign currency that is causing the effect or whether this is some other mechanism.


texts: In a positive externality, can government just set the price to the socially efficient price instead of a subsidy to correct an externality?


texts: What did "18/9", "25/", and "30/" mean in this 1800 British document?

texts:
In "The Petition of the Master Taylors of London and its Vicinity, December 1800" (reproduced in Galton, 1896), it is stated

the wages and allowances ... were accordingly settled at the rate of 18/9 per week ...
the wages the journeymen now receive is 25/ per week ...
have refused to work unless their respective masters will raise the wages they now receive to 30/ per week

I'm guessing that "18/9" means 18s9d, while "25/" and "30/" mean 25s and 30s?


texts: Consumer Econometrics: Identifying nature of goods

texts:
I have some data on household income and goods purchased. The first three columns and rows are:

Income    Good1    Good2  Price1  Price2
  100       4        12      1.5    2
  140       18       12      1.5    2
  200       9        3       1.5    2

I'm interested in understanding how I would use regression analysis/econometrics to understand the nature of the goods in question (i.e are they normal, ordinary, inferior, etc).


texts: Integral solution (or a simpler) to consumer surplus - What is wrong?

texts:
Problem
Given demand $D(p)=A-ap$, and $A,a>0$ and a fixed price $0<p_1<A/a$ by some company.
Calculate the consumer surplus and its derivative with respect to $p$. What is this number?
My solution so far
I could not find a simple way to do it since quantity is not known, $q_0$. I calculated the consumer surplus as
$CS=\int_{p}^{A/a}D(p)dp=\int_{p}^{A/a}(A-ap)dp=\frac{1}{2a}(A-ap)^2=\frac{(A-ap)^2}{2a}$
and its derivative as
$\frac{\partial CS}{\partial p}=\left ( \frac{(A-ap)^2}{2a} \right )=2(A-ap) \left ( \frac{\partial }{\partial p} (A-ap) \right )\frac{1}{2a}=-(A-ap)\left ( \frac{\partial }{\partial p} p \right )=-A+ap$
Which I am almost certain is incorrect. I am not sure on how to approach this without a equalibrium or am I missing it?


texts: Microeconomics - Expected Utility Theory - Piecewise utility index, certainty equivalence, etc.

texts:
I am solving old problems from various qualifiers from different universities to prepare myself for an upcoming test. I came across this and wanted to ask if anyone can confirm my answers?

My answers:

** I use $\succeq$ to denote "at least as good as".

(a) A certainty equivalence, in general, is the amount of money $c(F,u)$ so that:

$F \in \Delta(\mathbb{R})$, $\delta_{C(F,u)} \backsim F$ $\equiv u[C(F,u)] = U(F)$

Here, I've never seen something like this and so it is my best guess:

$ \forall$  $x<M $ , $C(F,\sqrt(x))= u^{-1}[\int\sqrt(x)dF$]
$ \forall$ $x\geq M$, $u[C(F,\sqrt(M))]= [\sqrt(M)] \implies C(F,u)=x$

Since $u()$ isn't 1-1, thus not invertible, over $x\geq M$ I eventually just decided my result above was true?

Or should it be something more like:

$u[C(F,u)] = F(M)\sqrt(x) + [1-F(M)]*\sqrt(M)$

(b) I know that the certainty equivalent is less than or equal to the expected value of $F$ iff an agent is risk averse.

I think that is the same as saying $u[C(F,u)] \leq u(\int x dF)$ , $\forall F \in \Delta(\mathbb{R})$

(c) An agent is risk averse if and only the agent's preferences are represented by a concave utility index $u(.)$  and so this agent is risk averse since:

$x < M$ $\implies u(x)=\sqrt(x)$, which is clearly concave.
$x\geq M$ let ${x_1,x_2} \subset [M,\infty)$ and let $\alpha \in [0,1]$ Then $\alpha*x_1 + (1-\alpha)*x_2 \in [M,\infty)$

Now, note that $u(x_i)=\sqrt(M)$, for $ i=1,2,3$

and so $$u(x_3) \geq \alpha u(x_1) + (1-\alpha)u(x_2)$$

$$\to u(\alpha x_1 + (1-\alpha)x_2) \geq  \alpha u(x_1) + (1-\alpha)u(x_2)$$

(D) Again, I am not sure about this. All i know about F.O.S.D is that for two lotteries F,G, then for all EU money monotone preference:
 $$F \geq_{FOSD} G \iff F \succeq G $$

Any and all help is appreciated.


texts:
We constantly assume convexity in economics. Convexity of production sets, convexity of preferences etc.

Is there literature that addresses when convexities fail? For example, is there any literature that addresses the existence of equilibria when agents have non-convex preferences? What are the problems associated with non-convex production sets?

It just seems like GE theorem relies heavily on convexity assumptions and I have yet to hear anyone reasonably addresses how to approach situations in which these assumptions fail.

I would appreciate any good references or any general discussion of non-convexity from both a consumer and a producer perspective.


texts: Nominal GDP versus PPP in comparing military spending of different countries?

texts: Military spending as percentage of GDP is the most used measure of the economic capability of a certain country/military. But Some countries like India for example, have a huge difference between their nominal and PPP GDP (2 billion vs 7.7 billion). So which number is more meaningful to express the economic capability of a certain military ?


texts:
We know from the balance of payments identity that:
$$
BOP=CA+KA+FA=0
$$
 where $CA$ is current account, $FA$ is financial account, and $KA$
is capital account. The BOP is an identity that always balances. Although
in some cases, the intuition is quite clear how this happens, it is
not always transparent. Specifically, there are a few types of external
financing that take place: bond finance, FDI, portfolio investment
and government foreign bank borrowing. Note that these will show up
as a + in the Financial Account. Imagine then that these funds are
used to fund domestic purchases (building a damn, building an office
etc). These are technically inflows of external capital that are funding
domestic purchases, and hence not imports. I wonder then, how do these
activities balance out mechanically in the BOP? In other words, how
are capital inflows that go towards financing domestic consumption
balanced out in the BOP? Thanks!


texts:
Where can I learn about market value of specific sector? What keywords should I be looking to being understand which reserch facilities publish relevant reports?

I'll put it simple: I'm building a startup, and I need to answer how much my market is worth. Where do I being this research? I believe this is a question every aspiring entrepreneur has to deal with, and I'm sure answers by knowledgeable people on this forum will become invaluable resource to the general community.

In my specific case, I'm looking at the b2d market where companies such as Twilio, Stripe, Github, Zencoder and StatHat operate.