texts: Solving a Cournot oligopoly game with N firms

texts:
This is the full question: Find all pure strategy Nash equilibria of the Cournot oligopoly game with $N$ firms facing linear demand $P = a − Q$ when the total cost for each firm is $c_i(q_i) = q_i^2$.

My understanding is that:

$$\pi_i = q_i(a − Q) - q_i^2$$

$$\max_{q_i} \quad q_i(a − Q) - q_i^2$$

Therefore, the FOC:

$a - Q - 2q_i = 0$

This FOC can be derived for each firm.

This is the part that I get stuck at. How do you add all the FOCs of $N$ firms together? Thank you!


texts: If you charge a single (indirect) tax rate, x% on all goods and services in a country, will you get x% back as tax revenues?

texts:
Assuming 100% compliance and no leakages, will charging a single tax rate of, say, 10% give us back 10% of the GDP back as tax revenues?

What could these leakages be in real life that reduce this?


texts: Foreign investment with US equity; typical expected rate of return?

texts:
I have been trying to answer this question but cannot find a suitable dataset or compilation.

When a US investor invests in a non-US project what are typical rates of return he is looking for?

I do realize that these rates will (obviously) vary with the risk of individual projects, sector, project size etc. But is there any dataset that may allow some analysis of this factor?

To provide some context, I was looking at a prospectus for a Asian country manufacturing project that has been pitched to American private investors and offers a 10% post-tax return on investment. Just wanted a ballpark evaluation of whether this would be a reasonable return.

The risk is low to moderate and the sector is specialty chemicals manufacturing.


texts:
In my economics class, we learned that in the short run, there are three stages of marginal returns: increasing, decreasing, and negative.

As a firm adds the first few units of labor, specialization allows for increasing marginal returns (Stage 1).  This makes sense to me.

As one adds more units of labor, marginal returns decrease due to limited capital (Stage 2).  This also makes sense to me.

However, in Stage 3, there are negative marginal returns (total product decreases).  How is this possible?  In practice, the firm would lay off the final worker(s), and the firm would never reach Stage 3 unless management was totally incompetent.  However, by the theory of specialization that causes Stage 1, if, say, a factory could produce 30 items with 6 workers but could only produce 27 items with 7 workers, it seems as though the factory, assuming it kept 7 workers on its payroll, would simply have one worker "specialize" in sitting outside, letting the other 6 workers operate independently of the one sitting outside and thus produce 30 items.  By that argument, if the firm kept hiring more workers, it could have those newly hired workers sit outside, so that total product would remain constant and marginal product would never be negative.  Where am I going wrong?

Thanks!


texts:
I am an undergrad trying to learn the basics of NK models (on my own) and I am having some difficulties understanding the derivation of certain equations.

So we have the representative household seeking to maximize $E_{0}\sum _{0}^{\infty}\beta^{t}U(C_{t}, N_{t}; Z_{t})$ subject to $P_{t}C_{t} + Q_{t}B_{t} \leq B_{t-1} + W_{t}N_{t} + D_{t}$

Where $B_{t}$ is the amount of one-period nominally riskless bonds, maturing in period $t+1$ and $Q_{t}$ is the value of said bond.

I am able to derive the optimal consumption-work hour pair by finding the total derivative of the utility function subject to the budget constraint in $C_{t},N_{t}$ space.

However, next the authors wants to examine the effects of reallocating consumption between period $t$ and $t+1$ on expected utility (holding all else equal). He shows this is;

$U_{c,t}dC_{t} + \beta E_{t}[U_{c,t+1}dC_{t+1}] = 0$  (1)

for any pair $(dC_{t},dC_{t+1}$)

satisfying $P_{t+1}dC_{t+1}= -\frac{P_{t}}{Q_{t}}dC_{t}$ (2)

I kind of understand where equation (1) is coming from (although if someone could derive this mathematically I would be very grateful). But equation (2) I don't understand at all. Is this some sort of budget constraint on consumption?I have tried finding the total differential of the budget while considering changes in $C_{t}$ and  $B_{t}$. $B_{t}$, because I assume since we're considering consumption between two periods, savings is going to matter. However, because it is consumption between two periods and the budget constraint in just for a given period, I am becoming confused.

I was hoping someone could explain how to think about this intuitively and the mathematical derivation behind it.


texts: Where's a good place to find Information on Non-OCED countries?

texts: I'm looking for Private Savings (Sp), Investment (I), Taxes (T), Government Spending (G) for India.


texts:
Setup Blanchard-Diamond (1994) have a model where each unemployed has a single ball (application) that she tosses into urns (vacancies). With probability $a$ the application lands in the urn - the unemployed manages to fill out the form, and his application is "valid".

Vacancies are open for a fixed period and then evaluate their application pool, leading to multiple applications per vacancy. Under some conditions, the distribution of applications per vacancy (denoted as $g(x)$) will be Poisson with expected value $au/v$.

Firm-based job-finding rate The number of matches is hence given by the measure of vacancies that have at least one application, times the number of vacancies

$$M = (1-g(0))v$$

and the job-finding rate is given by

$$ M/u = (1-g(0))v/u$$

Unemployed-based job-finding rate Instead of looking at the firms, one can look at the unemployed. As firms randomly draw from the pool of applicants, the average chance of an unemployed matching is the probability of matching times the inverse of the number of contestants that he will face:

$$ f = a\frac{1}{E[x | x > 0]} \\
= a\frac{1}{\frac{E[x]}{1-g(0)}}\\
= a\frac{1-g(0)}{au/v}\\
= (1-g(0))v/u$$

Which is turns out to be the same job-finding rate as calculated from the firm's perspective. This makes sense, as it needs to be an identity.

Firm-state-based job-finding rate Finally, to the part where I am struggling: An alternative way of computing this job-finding rate should be

$$ \tilde f = a \sum_{x=1}^\infty Prob(\text{applicant matches with firm with $x$ many applications} | \text{ she matched}) \frac{1}{x}$$

Which basically has the same logic, but is more detailed. This is interesting when one wants to analyze the $x$-component to the job-finding rate (i.e.: How relevant are firms with 5 applicants to the job-finding rate). However, the probability appears to be complicated. How do I compute this job-finding rate?


texts: Why would Switzerland, with its export-driven economy, worry about weakening against the dollar?

texts:
I was reading about the SNB's decision to abandon the peg in 2015, and among the various articles I read, one from CNBC quoted the SNB president saying the following

  "The euro has depreciated considerably against the US dollar and this, in turn, has caused the Swiss franc to weaken against the U.S. dollar. In these circumstances, the SNB concluded that enforcing and maintaining the minimum exchange rate for the Swiss franc against the euro is no longer justified," the statement said.

My takeaway from this statement is that part of their justification for removing the peg came from the effect it was having on the franc's value against the dollar.

I know they wanted this peg in the first place to lower the franc's value against the euro as Switzerland's economy was largely reliant on exports to euro zone countries, so having a weaker currency than the euro would help exporters.

But I don't understand why the franc's performance with the dollar would be a concern? Wouldn't that just help Swiss exporters sell to US importers as well as Europeans? Or does falling below the dollar have other consequences?


texts: What drives the Idiosyncratic Volatility puzzle?

texts:
I am currently analyzing the IVOL puzzle and I find in a single sort that the higher the IVOL the lower the return. Additionally I do a double sort, first sorting on skew and then on IVOL. I find that after controlling for slew the IVOL puzzle disappears. After that I do another double sort, first sorting on return of the previous month and then on IVOL. Here also, the IVOL puzzle disappears.

Now I am wondering if it is the lottery preferences (investors seeking highly skewed stocks) that explain the IVOL puzzle or the return reversal?

Would it be now correct to do a Fama macbeth Regression ret ~ IVOL + RET(t-1)? Because this show me that only RET(t-1) has a significantly negative influence on returns.


texts: What would happen if the world switched to a single currency?

texts: What would happen if all countries suddenly stopped using local currencies and adopted a global currency (like the Euro, but for everyone)?


texts: Why are we using exp(.) as the functional form in the household maximization problem inside the RCK model?

texts:
Currently I'm studying the RCK model at my Advanced Macroeconomics I classes.
A question arose almost immediately when I saw the utility function of a household in this model.

The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so.
Thank you really much in advance for your kind responses.


texts: Symmetric Cournot equilibrium: suffciency without second order conditon

texts:
Let $q_i \in Q = \mathbb R_+$ denote the quantity produced by firm $i \in \{1,2\}$. Further let $\pi_i(q_1,q_2)  = (1-q_1-q_2)q_i$ denote the profits of $i$. A Nash equilibrium $(q_1^*,q_2^*) \in Q^2$ satisfies
\begin{align}
&\pi_1(q_1^*,q_2^*) \geq \pi_1(q_1,q_2^*) \quad \forall q_1 \in Q\\
&\pi_2(q_1^*,q_2^*) \geq \pi_2(q_1^*,q_2) \quad \forall q_2 \in Q.
\end{align}
We are considering symmetric equilibria of the form $q^* = q_1^* = q_2^*$ and therefore apply the symmetric opponents form approach.
Define $\pi(q,q^*) = \pi_1(q,q^*)$.
There exists a unique symmetric root to the first order condition $\pi_q(q^*,q^*) = 0$ given by $q^* = \frac{1}{3}$.

Claim The candidate $q = \frac{1}{3}$ is the unique symmetric maximizer of $\pi(q,q^*)$.

Problem: The candidate might be a minimum or saddle.

The idea: In economic settings equilibrium quantities are basically restricted by individual rationality, i.e. $\pi(q^*,q^*) = (1-2q^*)q^*$ implies $q^* \in [0,\frac{1}{2}]$. Since $\pi(\frac{1}{3},\frac{1}{3}) = \frac{1}{9} > 0$, the claim follows.

Edit I edit the question to further clarify the issue. Suppose I don't have any information about concavity of $\pi(q,q^*)$ w.r.t. $q$.

A general argument:
We need to distinguish 4 cases.

$q^*$ is a saddle and $\pi(q^*,q^*) > 0$ and $\pi(\infty,q^*) = \infty$.
$q^*$ is a saddle and $\pi(q^*,q^*) < 0$ and $\pi(\infty,q^*) = -\infty$.
$q^*$ is a minimum and $\pi(q^*,q^*) < 0$ and $\pi(\infty,q^*) = \infty$.
$q^*$ is a maximum and $\pi(q^*,q^*) > 0$ and $\pi(\infty,q^*) = -\infty$.

Since case 4 is considered here $\frac{1}{3} = \arg\max_q\pi(q,q^*)$.


texts: Completeness Axiom in Preference Relation

texts:
My textbook, Microeconomic Theory by Mas-Colell, Whinston, and Green states that given a preference relation $\succsim$ on $X$,

  Strict preference relation $\succ$ is defined by
  $ x \succ y \iff x \succsim y \text{ but not } y \succsim x $

  Indifference relation $\sim$ is defined by
  $ x \sim y \iff x \succsim y \text{ and } y \succsim x $

  Completeness property: For all $x,y \in X$, we have either $x \succsim y$ or $y \succsim x$ or both.

Suppose $\succsim$ on $X$ is complete. Define $A$ to be the truth set of $x \succsim y$, $B$ to be the truth set of $y \succsim x$.

Since $\succsim$ is complete, $A \cup B$ is the universal set.

First, $x \succ y \iff x \succsim y \land \lnot (y \succsim x)$, hence the truth set of $x \succ y$ is $A \setminus B$.

Next, $y \succ x \iff y \succsim x \land \lnot (x \succsim y)$, hence the truth set of $y \succ x$ is $B \setminus A$.

Finally, $x \sim y \iff x \succsim y \land y \succsim x$, hence the truth set of $x \sim y$ is $A \cap B$.

Using the identity $A \cup B = (A \setminus B) \sqcup (A \cap B) \sqcup (B \setminus A)$, is it safe to say that

  If $\succsim$ is complete, then for any $x,y \in X$ exactly one of $x \succ y$ or $x \sim y$ or $y \succ x$ holds.


texts: How will the UK's economy be affected, if it will be a hard Brexit?

texts: Will the outcome of Brexit have any positive impact on the UK market? Are there any available studies on this topic?


texts:
Romer equation 2.55 on the Diamond model, says:

  Let $s(r)$ being the fraction of income saved, $r$ the interest rate,$\rho$ the discount rate, and $\theta$ the household's willingness to shift consumption between periods, with

  $$ s(r) = \frac{(1+r)^{(1-\theta)/\theta}}{ (1+\rho)^{1/\theta} + (1+r)^{(1-\theta)/\theta} } $$
  implies that saving is increasing in $r \iff (1+r)^{(1 - \theta)/\theta)}$ is increasing in r; equivalently $ds / dr > 0$ if $\theta < 1$

Is the first statement related to monoticity?  Also, how to show this graphically, that is to show, $s(r)$ a function of $\theta$?  Considering this, plotting $(\theta, s(\theta, r=.1))$ I do not see a change at $\theta=1$, but when I graphed $(r, s(r))$ with values $\theta=0.5,$ and $\theta=1.5$ I saw the desired change in orientation.  Which way is right?


texts:
I'm trying to get info on debt service relative to GDP for Morocco. I know these sorts of figures exist for the US, Japan, etc., since a few authors use them, but Trading Economics does not seem to have anything on that and they did a pretty good job of recouping all the available info from the two most reliable sources (central bank and statistics institute).

Are you aware of a good proxy for debt service (i.e interest + amortization) for the public/private sectors?


texts:
A (discrete time) martingale is a stochastic process $\{X_t\}_{t\in\mathbb N}$ that satisfies, for all $t\in\mathbb N$,
$$
E(|X_t|)<\infty
$$
and
$$
E(X_{t+1}|X_1,\dots,X_t）=X_t.
$$
And a submartingale is one with $E(X_{t+1}|X_1,\dots,X_t）\ge X_t$.

I know the classic example of the gambler's payoff in a fair game. But I'm hoping to find other real world examples of martingales and submartingales, particularly those pertaining to economics. Ideally, these examples would have some sort of empirical backing.


texts: Stiglitz: movement capital vs labor, effect on living standars

texts:
Stiglitz argues that increasing free movement of labor would be a much more effective way of increasing living standards, compared to free movement of capital (see for instance this video).

Does someone know which theoretical frameworks have been used to derive such conclusions? (I am looking for papers published in peer reviewed journals or theory books).


texts: What is meant by changes in pattern of production

texts:
I'm doing development in economics and one way economic growth spurts development was accelerating changes in patterns of production.
Does this mean different production methods getting improved so it increases quality of living as it becomes more productive/ efficient?


texts:
Starting position is a principal-agent-model with incomplete information (moral hazard) and the following properties:

Agent utility: $u(z)=-e^{(-r_az)}$
Principal utility: $B(z)=-e^{(-r_pz)}$
Effort levels $e\in \Bbb R  $
Outcomes $x\in \Bbb R, x\sim N(\mu(e), \sigma), \mu'(e)>0, \mu''(e)\le0$
Contract: $w(x)=a+bx$,

where $r_A$ and $r_P$ is the Arrow–Pratt measure of absolute risk-aversion for the agent and the principal respectively.

I am looking for the optimal contract for the principal to offer to the agent when the agent's effort is not visible. The principal's utility can be written as follows:

$$U^P(e,a,b)=\int_{-\infty}^\infty-e^{(-r_P((1-b)x-a))}f(x\mid e) \, dx$$

I want to show that the following equivalence holds, meaning that the maximization of the principal's utility can be written as the RHS of the following equivalence:

$$\max_{\rm e,a,b}\int_{-\infty}^\infty-e^{(-r_P((1-b)x-a))}f(x\mid e) \, dx \Leftrightarrow \max_{\rm e,a,b}(1-b)\mu(e)-a-\frac{r_P}2(1-b)^2\sigma^2$$

where $f(x|e)=\frac{1}{\sigma\sqrt{2\pi}}e^{(-\frac{1}2(\frac{x-\mu(e)}\sigma)^2)}$ is the density function of a normal random variable $x\sim N(\mu(e),\sigma)$, with expected value $\mu(e)$ and variance $\sigma>0$.

I tried to use the explicit form of $f(x|e)$ in the LHS, manipulate it a bit and then itegrate but could not get the equivalence.


texts: Is the consumer surplus on a Giffen/Veblen good negative?

texts: When drawing the demand and supply curves on a quantity/product space for an upwards sloping demand, assuming the two curves intersect, I noticed that the traditional consumer surplus region lies below the equilibrium price, and possibly even under the supply curve. What happens to consumer surplus in this situation? Does it become negative (as an integral definition would suggest), or do we simply say it defaults to zero?


texts: Why was there a sudden rise in trade-weighted US dollar value in 2014-2015?

texts:
I was trawling the web and happened upon this graph: https://fred.stlouisfed.org/series/DTWEXM . The value of the trade-weighted US dollar was going steady until 2014-2015, rose rapidly, then it sort of steadied out again.

I can't recall anything particularly newsworthy in 2014-2015 (though I have a poor track record of paying attention).

What caused the 2014-2015 rise? Which countries did it happen to?

(according to the caption the countries considered in the weighting are the Euro Area, Canada, Japan, United Kingdom, Switzerland, Australia, and Sweden)


texts:
In countries where littering is a problem and the regulations and rules alone cannot give the desired effect due to vary high population,large surface area,etc.. ,will it be effective if the government starts buying garbage on a price per kg basis?
(This money spent can be compensated by reducing the number of sanitary workers and other departments if this method proves effective)


texts: The Economical "justification" of mass killings

texts:
Throughout history people have engaged in wars and mass killings.

I'm sure similar stories exist in all parts of the globe, throughout the world.

So what is the story? If the world revolves around economics, then how does economics profit from mass destruction and killings? If we are to stop this, we must first understand this.

Sorry to ask, but is it that the money made from jobs involved in setting up concentration camps, producing equipment of mass destruction, and all of that, more profitable than what the bastards can earn from the people designated to be killed? Is this why we have all these killings throughout history?

Or are you going to tell me that all the mass killings that happened in history were motivated by something other thanan economical reward optimization problem?

Let us find a solution (or a set of solutions, together) so that this does not happen (again!). So many people spend their time wondering about so many things not realizing their own lives are in danger. TikiI think this is a priority we should be focusing on.


texts: Can you set $C / P^{\eta}$ to be the numeraire in a NK model?

texts:
Consider a static model with CES demand. Real aggregate demand is
$$
C = \left(\sum_j c_j^{(\eta-1)/\eta}\right)^{\eta/(\eta-1)}
$$
and labor supply is inelastic, so the budget constraint is
$
\sum_j p_j c_j = W
$
and the demand function is
$$
c_j^{*} = \frac{C P^{\eta}}{p_j^{\eta}}
$$
where
$$
P = \left(\sum_j p_j^{1-\eta} \right)^{1/(1-\eta)}
$$
is the ideal price index. Can I set $C P^{\eta} = 1$ as my numeraire so that $c_j^{*} = p_j^{-\eta}$? More generally, what is required of a numeraire?


texts: GDP(Expenditure view of GDP): /Why aren't investments categorized as non-final goods?

texts:
My understanding is that consumption = consumption of final goods = whatever consumers buy from companies (with an adjustment for export-import-process + maybe housing is slightly different (not important here). So if you were to buy a fully US-made table it wouldn't really matter that first one company plants and harvests the tree, another then buys the whole tree and transforms it into useable wood (cuts into useable sizes, sorts out bad parts, possibly treats wood etc), and then the last step somebody buys that wood and assembles a table. The only thing that matters is when this table is actually sold to an private customer (for 100\$ or whatever)(assuming its directly sold by the joiner and leaving out dedicated retailer).
So far seems somewhat understandable that only the use of the activity to real persons/consumers would ultimately be relevant and seen as economic productivity (use being measured by $spent). However I don't understand why some expenditures made that are called "investments" still increase GDP (and aren't lumped in with other precursors as non-final goods)?(1)

(1)(Maybe expenditures that are classified as investments, like a new production machine, can be seen as not directly tied to a specific output-product (unlike e.g. a concrete amount of wood bought per output-table to be assembled into a table)? But i would not see why this is directly relevant when measuring the quality/productivity of the whole economy as GDP probably should (just because somebody invests into something doesn't mean that's reasonable, e.g. investing into gold-plated machines etc or just machines not fit for their intended use, while you could somewhat reasonably argue that everythng bought by customers should be defined as a useful product and GDP-increasing because apparently the customer found it useful and satisfying customers is ultimately the purpose of the economy?
Also where would that leave sandpaper and similar things? (Machines detoriating very little with each table produced, wood deterioirating/disappearing completely (into the table), and sandpaper in between depending a bit on luck with the wood and not clear whether its more non-final good or investment))


texts: How to find the maximum profit in a graph?

texts: We know the maximum profit will occur at the quantity where the gap of total revenue over total cost is largest. But how can we find such gap?


texts:
https://www.bis.org/publ/work550.pdf
page 7 extract
"Third, the distinction between external and internal debt is important. External
debt, long seen as a key driver of financial crises in EMEs (Al-Saffar et al (2013)), is more dangerous than internal debt.5 If the assets corresponding to the debt are also internal, then domestic assets rise and this helps to support domestic demand. In addition, there is a fiscal advantage because the holders of such assets can be taxed. Another reason is that domestically-held assets are less likely to “flee”. And the government can also induce regulated financial institutions within their own jurisdiction to hold domestic assets. Nonetheless, foreign currency internal debts – and especially the foreign currency loans of domestic banks to residents – do create risks"
Can you explain why external debt is more dangerous than internal for EM economies and clarify if they mean internal debt in foreign currency?


texts:
In Lecture 20 of MIT's Microeconomics course, a situation is proposed where a 50/50 bet will either result in losing \$100 or gaining \$125 with a starting wealth of \$100. It is stated that a person would be willing to insure themselves for \$43.75 (the difference between \$100 and \$56.25). What is the intuition behind this?

Thanks in advance!


texts: Does comparative advantage maximize revenue?

texts:
I am reading Lovell's "Economics with calculus", where in Chapter 2, he presents Ricardo's Theory of Comparative Advantage, and states how in a simple model two countries benefit from free trade.
He shows that free trade between two countries $1$ and $2$ producing two commodities $A$ and $B$ equalizes the relative price ratios in those countries via arbitrage, i.e., $\frac{p^1_A}{p^1_B}=\frac{p^2_A}{p^2_B}=\frac{p_A}{p_B}$
. When that happens and goods are produced at maximum revenue in each country (with the marginal rate of transformation $-\frac{dB}{dA}$ in both countries equal to $\frac{p_A}{p_B}$), he then proves that the total production of both goods is maximized, and the allocation of resources is efficient.
My question is whether, although both countries are jointly producing the most total product, the actual revenue $R$ from this production is also maximized. That is, for country $1$, both $A_1$ and $B_1$ are a function of $\frac{p_A}{p_B}$, and each producer in country $1$ obtains
$$ R^1 = p^1_B B_1\left(\frac{p_A}{p_B}\right)+p^1_A A_1\left(\frac{p_A}{p_B}\right)$$
So could there be another price ratio that maximizes revenue for country $1$? Does that always come at a cost for country $2$?


texts: What problems arise when the minimum wage is directly linked to the inflation rate?

texts:
For example if the minimum wage is 10, and the inflation for the year is 3%, then next year the minimum wage is 10*1.03 =10.30. the next year, inflation is 5%, so the minimum wage becomes 10.82.

The idea is that this would be a method of ending the price-hike  where the response to higher wages is to raise prices. Why? It is because raising prices directly raises the CPI, and thus the inflation rate. Companies shoot themselves in the foot if they hike their prices up.

What sort of problems arise when this is the case?


texts: Fractional reserve banking and bank insolvency

texts: I am trying to understand the fractional reserve banking system (with say 10 % reserve ratio). If a bank becomes insolvent because 100 % of the loans of a bank go bust, then who really becomes liable for all that money lent out in excess of the bank's value ? Let us say, the depositors are all FDIC-insured and the stockholders of the bank lose all their money, but isn't the loaned amount still larger than the (stock value + deposit amount) ? So perhaps all that happens is that this money simply gets written off (and adds to inflation) ?


texts:
Field of Economics became mathematical and model based. I can grasp the appeal of the model but fail to understand why do we introduce certain assumptions.

(Actually I am trying to relax the assumptions of the model, Ramsey Cass Kooperman (RCK) model, just as an exercise but before I can relax them I need to know why they were significant in the first place)

So, in the context of RCK model
Why does the assumption of

1.Compactness,

2.twice continuously differentiable function, and

homogeneity (homothetic)  are taken.

Why are the relevant?

I know this that homogeneity produce constant returns to scale with Cobb Douglas production function and lt also implies homothetic. Why do we need homothetic functions?


texts:
I have been trying to figure out conditions on the preferences of traders in an exchange economy such that the equilibrium prices are unique but I cannot be sure since all sources seem to be contradicting each other. On the Arrow-Debreu wikipedia page it says "In general, there may be many equilibria; however, with extra assumptions on consumer preferences, namely that their utility functions be strongly concave and twice continuously differentiable, a unique equilibrium exists." However, the Sonnenschein–Mantel–Debreu theorem does not tells us that the excess demand curve inherits the shape of the utility functions.
I do understand that for utilities satisfying the gross substitutes conditions the equilibrium prices are unique but are prices unique if we assume concave and twice differentiable utility functions?


texts: Socio-Economic Consequences of Nation-Wide Vegan Diet

texts:
An advice I often hear regarding our environmental impact is to 'stop consuming meat and dairy products'. This is stated as the number one way to reduce your ecological footprint, according to multiple sources. Whether this is true or not, obviously much of our economy and society depends on the meat and dairy industry, ranging from farming and transport to butcheries or supermarkets.

If everyone in the United States would stop consuming meat, dairy and eggs within the next twelve months, what would be the economic consequences?
How much of a hit would the economy take?
What percentage of farmers could realistically replace their current products with vegan alternatives?
What other unintended socio-economic consequences would this scenario have?


texts: Central Banks, Large Scale Asset Purchases and Inflation

texts:
First, the overview:

With the fractional reserve system, money/credit is primarily created through loans on deposits but the bank is required to maintain their deposits up to a certain amount (roughly 10% I think).  The other primary avenue of money creation is by the Federal Reserve printing money, but there is severe reservations on printing money given past episodes of hyper inflation, though recent events with quantitative easing and large scale asset purchases, the Fed's balance sheet has reached over 4 trillion dollars.  The Fed has stated that any profits accumulated from these assets will be reinvested into new securities when they mature and any additional profit will be deposited into the treasury.

Here is my question:

If the federal reserve were to regulate the banking industry so that fractional requirements were raised to something like 50% on all future deposits, that would have an appreciating effect on the dollar since the rate of increase in the supply of dollars needs to keep up with the growth of the economy every year.  If the Fed offsets this appreciation with additional asset purchases by printing money, the Fed's revenue/balance sheet would increase... and over time that excess profit could start to make up the overwhelming portion of the fiscal budget (which could take decades or centuries)...  Historical issues with the central bank funding the budget have always resulted in hyper inflation, but with this work around, where the funding of the budget was not coming from the direct printing of money but from the profits from security purchases as they matured, hyper inflation would be avoided, right?

Please explain why this is a bad idea...  In theory the banking system wouldn't have a noticeable impact since, as additional money is created to offset the increased fractional requirements, that money will be deposited into the banking system (where else would it go) increasing holdings and increasing the money available to be lent out...

This is in essence what the Japanese have been doing with paying off Government debt in order to prevent their currency from appreciating naturally (instead of raising reserve requirements), right?

Response (wasn't allowed to respond at length so I'm making an edit to my original post):
Lending would have "some" reductions, but it wouldn't be as severely impacted as it would if it weren't offset by more asset purchases, purchases that are then deposited into banks, expanding the monetary base which then expands the amount to be lent out...  There's also the argument that, by replacing tax's with the profits from maturing assets, there would be a stimulating effect on GDP, which would cause the dollar to appreciate, which would then require more printing or lending to maintain stable prices... though of course it would take a significant amount of time for profits on maturing assets to become a sizable portion of the fiscal budget, but of course the FED isn't purchasing securities with the idea of maximizing revenue so I'd imagine their rate of return could get a little better if they really tried and this where to become a primary mandate...

I'm definitely not saying raising the supply of dollars increases their value, the opposite actually...  My argument says raising reserve requirements would reduce the supply of dollars, but printing would offset this reduction, maintaining the equilibrium.  I suppose an implicit assumption I didn't spell out was that the amount of dollars printed would not equal the number of dollars no longer being lent out since fractional banking has the multiplier effect, i.e. today one dollar created by the FED is equivalent to 9~10 dollars lent out in the banking system.


texts: Multicollinearity in Transformed model: GLS

texts: Hi I am reading Hayashi's econometrics and have got stuck in the review question 1.5.1. The question asks us to prove that the multicollinearity assumption of the CLRM is satisfied by the transformed data matrix CX where C is (n by n) invertible matrix and X is an (n by k) matrix with rank = k. We have to show that the rank of CX = k. I know this is a theorem in matrix algebra and we can prove that rank CX = Rank X = k. But Hayashi suggests in the hint to the question another way to prove it and says that we must show that for all non-zero vectors c it must be that Xc is not equal to zero. Now, I could easily show this from the the fact that X has a full rank. But I get stuck in showing the final result that rank (CX) = rank (X) = k. Any suggestions on how to go about this, will be very helpful. It might something very straightforward that I am missing. Thanks a lot in advance. P.S. In case you are interested in looking at the question it is on page 59 of chapter 1.http://press.princeton.edu/chapters/s6946.pdf


texts: Finding data on (estimated) trade cost elasticities of imports

texts:
I'm an undergrad student of economics, and I need to find estimates of the trade cost elasticity of the UK's imports for some homework. My instructors pointed me to the World Bank's databases, specifically the World Development Indicators, but I've not been able to find those estimates there. Google has not proved helpful either.

I'd be grateful if anyone could point me in the right direction.


texts: Log-normality assumption in consumption based asset pricing

texts:
Consider a very basic discrete time representative consumer maximization problem with CRRA utility. There exist a risky asset with time $t$ price $p_t$ that pays time $t+1$ dividend $d_{t+1}$ , and a riskless asset with price $p_t^f$ that pays a constant payoff 1 at $t+1$. We assume that the dividends are a sequence of random variables that follow a Markov process. Assume further that the consumer has no other income streams (i.e. $y_t = 0 \ \forall t$). At time t consumer invests amount $\pi_t$ in the risky asset and amount $\pi_t^0$ in the riskless asset. Therefore, the maximization problem can be stated as

\begin{align*}
& \underset{\{ c_t, \pi \}_0^\infty}{\text{max}} \ \ E_0 \sum_{t=0}^\infty \ \beta^t \ \frac{c_t^{1-\gamma} -1}{1-\gamma} \\
\\
\
s.t  \ \ \ \ & c_t + \pi_t p_t + \pi_t^0 p_t^0 = (d_t+p_t) \pi_{t-1} + \pi_{t-1}^0  \\
& c_t \geq 0
\end{align*}

Say we want to find the equilibrium riskless rate and expected equity premium. In order to close the model, it is often assumed assumed (see e.g. Claus Munk's book Financial Asset Pricing Theory chapter 8.3) that the log-consumption growth and log-risky gross returns are jointly normally distributed. I.e

\begin{align*}
& ln \ \Big(\dfrac{c_{t+1}}{c_t} \Big) \equiv \bar{g}_{t+1} \sim N(\mu_g, \sigma_g^2) \\
& ln R_{t+1} \equiv \bar{r}_{t+1} \sim N(\mu_r, \sigma_r^2) \ , \\
\end{align*}

where gross returns are defined as
$$R_{t+1} \equiv \frac{p_{t+1} + d_{t+1}}{p_t} \ .$$

What I don't completely understand is where do thelog-normal distribution assumptions "come from". I know that since this is a representative agent economy, consumption of the agent must equal the aggregate dividend in the economy.  But since we assumed that there is no income, $y_t = 0 \ \forall t$, the only exogenous dividend process in the economy is $d_t$ and therefore it should have the same distribution as the consumption growth. However, my impression is that when we say the risky rate has log-normal distribution this actually means the dividend process, since it is the 'random part' in the definition of returns (price $p_{t+1}$ is not exogenous but determined inside the model). To me it seems now that we have made two different assumptions about the same endowment process $d_t$. Where does the assumption for consumption come from or what does it stand for? How would the situation change if the consumer had some income stream $y_t > 0$?


texts: Demand for minimum of $4$ different goods

texts:
The consumer has the utility function with $4$ goods $$U=\min\left \{ \sqrt{x+y},z+w \right \}$$ The prices are $p=(3,2,2,1)$ with wage $m=1$.

Find the demand.

So far I have observed that it is perfect complements BUT it must be between the 4 goods. So some combination of $x,y$ to $z,w$. Usually we know that the optimal choice is when $x_2=x_1$ with demand $x_{1,2}=m/(p_1+p_2)$(but with 4 goods, I lose my grib. How do I approach this? Do I just square the right side and let both equal eachother?


texts: Intro to Stokey / Lucas and Sargent / Ljungqvist

texts:
I would like to ask, if you can recommend me some introduction to these 2 macro textbooks: Stokey / Lucas and Sargent / Ljungqvist, which I will be using in the 2nd year MA in Economics.
So something at a lower level (maybe intuitive explanation of the math), but which will help me to progress to these 2 textbooks.
Thank you!


texts:
To me, it seems like gold is the ultimate example of something where the value should go down when the economy, stock market etc go down.

Just like Ferraris, and other frivolous consumer luxury goods, gold has almost no inherent value, beyond what we choose to assign to it. If the economy plummets, people will buy considerably fewer products that are made of gold, much like they will buy considerably fewer Ferraris.

Why does gold's value increase when times are tough? Why do we not see trouble on the stock market lead to increased prices for consumer essentials such as grains, textiles etc - things that have almost no change in demand when there is a change in income because they have real value (stopping people dying).

Note: Answers should be appropriate for countries that have left the gold standard. If there are any countries still on it, answers for those countries aren't what I am looking for.


texts: Finding economy's factor price for perfect complement production function

texts:
Q.Consider an economy producing a single good by a production function
$$Y = min [K, L]$$
where Y is the output of the final good. K and L are input use of capital and labour respectively. Suppose this economy is endowed with 100 units of capital and labour supply is Ls is given by the function

Ls = 50w

where w is the wage rate.
Assuming that all markets are competitive find the equilibrium wage and rental
rate.

Actually I am having doubt in assessing if the economy would use its full capital endowment. Also how we are going to calculate marginal product of labour and capital for finding wage rate and rental rate. I think if we use isoquants and isocost lines, then optimal solution should come where $$K = L = Y$$. But I think I am missing something, please help.


texts:
Talk about Greece leaving the Euro has been reignited by the recent election of Syrzia, with some again talking about how it is practically inevitable.

Why are these people viewing a Greek default as likely triggering an exit from the Euro? Couldn't Greece simply default on its debt and continue to use the Euro? Would this trigger the ECB to freeze the accounts of Greek banks (and if so, why?).

I understand why moving to a local currency, which can be devalued, might make sense for a country that needs economic stimulation. But I don't understand the direct cause-and-effect from a sovereign default to an exit from the Euro.


texts:
I'm given this question. I'm not sure if I'm doing it right. Can any one help?
 Given the following short-run cost function: C=0.04q3 - 0.9q2 + 10q + 5

    And the constant price of the final commodity of $4 for the firm, determine:
a. The best level of output for the firm;
b. The level of profit the firm makes at this level of output;

My answer:
a) Best level of output would be: MR which is 4, since price is 4, perfect competition, MC is the derivative of total cost, which is 0.12q^2-0.18q+10, then equating, 4=0.12q^2-0.18q+10, so q=0.75
b) putting q=0.75 and multiplying price by quantity, level of profit would be 4*0.75


texts: Impact of a reduction of distortions in a flat consumption tax

texts:
I ask about the survey results of some prominent Australian economists shown here (Which is a similar Australian-centric version of the very interesting IGM Forum Surveys). The results of the survey surprised me as it isn't what I was expecting.

“Increasing government revenue collected through the Goods and Services Tax (GST) by removing exemptions (such as food, health and education) is better than achieving the same extra revenue by increasing the GST rate while retaining the existing exemptions.”

My question is, is there any empirical or other research on the impact of transition from a distortionary to a less distortionary tax which could be applied to the Australian case?


texts: What Constitutes The Size Of An Economy?

texts:
My Geography textbook defines the size of an economy as:

  Size of economy is measured in terms of value of goods and services
  and grows over
      time. This is caused by increase in population, improvement in income levels,
      advancement of technology and other associated factors.

I found these statements to be a little iffy. I don't understand how things like advancement of technology could possibly make the economy larger in size. I do get that they could give the secondary or tertiary sector a larger chunk of the economy, but could it make the economy larger as a whole?

The Netherlands, for an example, has just as elaborate an economy as any other country; with possibly the same factors acting on it. However, even with all the advancements in technology and increased income levels, it is no where as gigantic and mammoth (we are talking size, remember?) an economy as India or China when it comes to sheer scale.

I thus concluded that this statement was erroneous. Am I right in propounding that the size of an economy has nothing (absolutely nothing) to do with the intricacies and coming-together of processes, and solely to do with the scale or largeness of it?


texts: An increase in Japan's demand for US goods would cause the value of dollar to appreciate? Why is that? The official answer is "Japan will buy more U.S. dollars." However, my thought was that isn't it usually the case that US companies get paid of Japanese yen rather than U.S. dollars? And hence Japan will not need to buy more U.S. goods. What is the problem in my thought?


texts: What was the US monetary policy like in the 70s?

texts:
Today the US inflation target is roughly 2%.
However in 1974 the inflation rate was 11% and in 1980 it was 13.5%.
What monetary policy did they follow at that time that allowed the inflation to rise to these levels?

Looking at the U.S. National Unemployment Rate:

we see that it had a local minima of 4.6% in october 1973 and another one at 5.7% in June 1979.


texts: Econometrics - Simultaneous Equations and Perfect Inelasticity in the Context of Regression

texts:
Assume a certain market can be described by

Demand Function: $$Q_{d, t} = \alpha_0 + \alpha_1 P_t + \mu_{1, t}$$
Supply Function: $$Q_{s, t} = \beta_0 P_t + \mu_{2, t}$$

The price in this market is determined by the equilibrium point, that is $Q_d$ = $Q_s$ = $Q_t$ . Now let $\alpha_1$ be 0, so that the demand is perfectly inelastic.

Now - is it possible to model the $P_t$ as a linear regression function of $Q_t$ so that: $$ P_t = \gamma_0 + \gamma_1 Q_t + \epsilon_t.$$

The standard simultaneous equation model problem is not present because of the perfectly inelastic demand. Yet I am unsure wether it is possible to model the price like this - several scientific papers I read did exactly that. Yet, Since the Price is still determined by an equilibrium situation and I can determine which $Q_t$ is present by looking at the given value of $P_t$ and the other way around I am of the opinion that there still is some sort of reverse causality present, which in turn implies that I have to replace $Q_t$ by an exogenous regressor so that

$$ P_t = \gamma_0 + \gamma_1 (regressor) + \epsilon_t.$$

Am I right? Or does the assumption of perfect inelasticity "dismantle" the issue of simultaneous equations in the regression context.


texts: Alternative way of deriving OLS coefficients

texts:
In another question of mine, an answerer used the following derivation of OLS coefficient:

  We have a model: $$ Y = X_1 \beta + X_2 \beta_2 + Z \gamma + \varepsilon, $$ where $Z$ is unobserved. Then we have: $$\text{plim}\, \hat \beta_{1} = \beta_1 + \gamma \frac{Cov(X_1^*, Z)}{Var(X_1^*)} = \beta_1, $$ where $X_1^* = M_2 X_1$ and $M_2 = [I - X_2(X_2'X_2)^{-1}X_2']$.

This looks different from the usual $\beta = (X'X)^{-1}X'Y$ that I've seen in Econometrics. Is there a more explicit exposition of this derivation? Is there a name for the $M_2$ matrix?


texts: Why does US equities valuation have the downward pressure on USD?

texts:
While making readings on economics I came across a sentence:
..large valuation gap that has opened up between US equities and the rest of the world. This could help bid up non-US equity valuations and place further downward pressure on the USD.
To my understanding, holding everything else equal, high stock prices of US corporate encourage investors to buy them, thus it should place upward pressure on the dollar. Why would the authors argue that the direction of pressure is down?


texts: Why are New Zealand houses so badly insulated?

texts:
New Zealand is relatively new country.

It essentially was founded in 1840 in a contract between the native Maori people and the British Government.

For some reason a large chunk of the housing stock in New Zealand is badly insulated and drafty and cold, compared to houses in Europe for example.*

I don't understand how a country that was essentially built in the modern era, has built such bad houses.

What economic factors contribute to this?

*Here's a good paper about the subject. PDF.


texts:
EDIT: for future reference, I found out that many businesses price accordingly to the black market rate.

Trading at the official Venezuelan exchange rate is, at time of writing,  about 1:10 USD:VEF.
From what I've understood  black market exchanges offer more than 1:1000 USD:VEF.
They are technically illegal, but its use is widespread to the point of routine.

Now take a look at these numbers from expatisan.com comparing "Monthly rent for 85 m2 (900 Sqft)
 furnished accommodation in NORMAL area" between Los Angeles and Caracas.

  Official exchange rate for VEF:
  LA is 52% cheaper
  Black market rate for VEF: Caracas is 5288% cheaper

I understand Venezuela is in turmoil with inflation after Chavez' version of socialism had its way. Does the rent for one 900Sqft apt. in LA really pay for 52 apartments in Caracas? Naturally, a Venezuelan's income comes in VEF and not in USD by cash,
 so they are not seeing the (assumed) benefit foreigners with USD have.

With that comes my main question, can a foreigner really enter the country with 10,000 USD and turn that into eg. 22 years of rent for the apt. in above example? (assuming steady rate of 37,000 VEF)

There must be something I'm missing here?
Sorry if this Q isn't relevant, but where else to ask than economics stack?


texts: Predicting GDP contribution from market share

texts:
I want to find the GDP share of several companies, but I have their market share.
Now we know that these two are not equal, and the market share to GDP ratio represents general overvaluation or undervaluation of shares.

Is it fair to assume that they are proportional though? That if a company has a high market share, it will also have a high GDP contribution?

What are the general trends regarding this?


texts: What are good books on economic world history?

texts:
I am trying to find a book that covers human history with a special focus on economics. It should answer questions like:

What economic systems prevailed during which eras?
How did these systems work in detail?
How did economic organization evolve (Not just since the industrial revolution)?
Were there civilizations which particularily focused on economic development?

It should NOT be a history of economic thought, like e.g. Niall Kishtainy's "A little history of economics".


texts: Equilibrium price and quantity - consumer and producer surplus

texts:
Inverse function of market demand for certain good is equal to $P=100-0.25Q$, inverse supply function is $P=20+0.55Q$. Calculate equilibrium price and quantity. Furthermore calculate consumer and producer surplus.

Equlibrium price and quantity i think i know how to calculate:
$$20+0.55Q=100-0.25Q$$
and this will be the quantity whereas the price will be (substituting Q with value calculated above):
20+0.55Q=P
am i correct with this?
I am lost with consumer/producer surplus need more help.
edit: I have and idea about consumer/producer surplus:
consumer:
$0.5 \times 100 \times 25=1250$ and producer $100 \times 55 \times 0.5=2750$
is this correct?


texts: The existence of solution for profit maximization problem

texts:
I'm thinking about the conditions for existence of solution of this profit maximization problem(PMP), i.e.,
$\max_{z \in R_+^{K-1}} pf(z) -wz$,
where $z \geq 0$: input vector, $p>0$: the price of output, $w \gg 0$: an input price vector, and $f:R_+^{K-1} \rightarrow R_+ $: the production function.
Of course, if production set $Y$ is compact, by Weierstrass theorem, we can prove there exists a solution of this PMP. But many cases, $Y$ is closed but not bounded. Then what kind of assumptions on function $f$ are needed to show the existence of a solution, instead of Weierstrass theorem?


texts: CRRA utility function with a scale parameter

texts:
I am wondering if it is possible to write down a following CRRA utility function ;

$$u\left(c(t)\right)=a\frac{c\left(t\right)^{1-\sigma}}{1-\sigma}$$ where $a>0$ is a constant scale parameter. I need this $a$ to have some numerical results but I am not sure if $a$ can be justified.
In a growh model, I am trying to show the existence of Hopf bifurcation and limit cycles. Then, with a scale parameter like that, I can show that it exists.

Normally, it does not change the usual assumptions on a CRRA utility function, (an increasing concave function)

Is there any way to justify it (are there some examples of this kind ?) or are there any types of utility function with constant scale parameters ?


texts: Is the fundamental analysis also a self-fulfilling prophecy?

texts: John J. Murphy in the first chapter of his book "TECHNICAL ANALYSIS OF FINANCIAL MARKETS" says that concerns regarding fundamental analysis being a self-fulfilling prophecy are seldomly raised, as opposed to technical analysis which receives criticism in the form of getting labelled as a self-fulfilling prophecy. So is the fundamental analysis, at-least in a few ways,  a self-fulfilling prophecy?


texts: Why are they raising interest rates in Brazil?

texts:
How does raising interest rates in Brazil (and Russia) help fight inflation and defend their currency?

I understand that the basic model is that raising the rates is meant to encourage banks to lend in brazil to earn on the interest rate differential and it should also reduce local demand for goods and services.

But, both Brazil and Russia are facing recessions and their economies are currently weak. If you raise the interest rates to 14.5 like Brazil has done wont that make the economy even weaker which will make investors flee the country and thus weaken the currency which in turn will increase the price of all imported goods (which for most open economies is a big percentage) and thus make goods more expensive, thereby increasing inflation rather than reducing it.

I would have thought a better way to fight inflation in a recession would be to lower rates to stimulate the economy and thereby stimulate the stock market and attract foreign investment which would strengthen their currency and reduce the price of imported goods. What have I misunderstood?


texts: The Great Depression vs The 2008 Financial Crisis

texts:
So I'm taking this finance course and my professor keeps talking about how the 2008 financial crisis was worse than the great depression.

I have my doubts so my fellow economists, do you think the 2008 financial crisis was worse than the great depression?


texts: What is this economic theory? Cost of investment vs production accounting for time?

texts:
I know there has got to be a standard set of theories or formulas to chart this but I don't know how to search for it. Other than a great place like this. :)

I'm a software developer and not an economist but I need to analyze data of factories that have simple defined expense to set up, each has a specified output and a length of time to build.

While a larger factory might have the lowest cost per unit of production and therefore be the best bang the buck (assuming the setup cost was zero), the actual setup cost might be so large that it would take a long time to actually build the factory. It is actually more economical in the long run to build less costly and lower performing factories because in the long run you will have produced more and aquire the cost of the larger factory faster.

What I am attempting to build is a formula/program that will advise on the next most profitable move and the required time to get there.

If you haven't guessed this is actually to be tested an ran on a game scenario. However, I have many other applications and thought this would be a good start.

I hope that makes sense. The cost of production, the output and such are all intentionally simplistic. There's no need to account for outside/variable factors in this particular scenario.

If you can lead me to a theory/concept, perhaps a link or two or examples of this type of analysis given as set of inputs that would be great!

Thanks!


texts: When is the pegged price equal to the market price

texts:
Suppose the government pegs an exhaustible resource, at a price $P^*$. I found out that the shadow price (initial price of the resource if government didn't peg) would be
$$Q_t = ( \sigma i S_t )^\frac{-1}{\sigma}$$.

Where $S_t$ is the resources left after time $t$. And  $\sigma$ is a parameter, whereas $i$ is the interest rate.

I'm trying to show that if $q(t) = ln Q_t$ and $ \triangle q(t) = i$ (change in q(t)) Then

$$Q_t = P^*$$


texts: What are the factors that drive openness in developed vs developing countries

texts:
My questions are:

What are the factors (both positive and negative) that drive openness in a country?
Do they differ between developed (e.g USA) and developing (e.g China) countries?
Will these factors remain a key factor to drive openness for the respective country in the future?

So far I researched on stage of development, specialisation of each country's skills, degree of trade liberalisation and the geographical size.


texts: How to prove that GDP grows at the same rate as consumption on Lab Equipment Model?

texts:
I'm studying the Lab Equipment Model (Barro-Sala-i-Martin, Chapter 6). I'm having trouble when trying to prove that every variables grows at the same rate as consumption.

I was able to prove that $\dot{C}/C = g_{c}$, which is constant. Also, I have that

$b \dot{N} = Y - X - C$ where $b$ is a parameter,

$Y/N$ is a constant related to the interest rate and

$X = a^{2}Y$, where $a$ is a parameter from the production function.

From the second and third equations above, it's clear that $Y,X$ and $N$ grow at the same rate. However, it's not clear that this rate should be $g_{c}$ or even constant at all. I'm trying to use the first equation to show it, but I couldn't do it.

The book forgoes this proof. It says that it's quite similar to the AK model since there's no transitional dynamics. Is there a simple way to show this result? I think it should follow from a simple manipulation of the first equation. Any ideas? thanks a lot in advance!


texts:
How is a block price decided when there are many products to be sold?
For example the buffet in various restaurants or combos in McDonalds or KFC (like the bucket buddy).
Can somebody point me to research papers or any link or book I can read to get into the logistics and mathematics behind pricing such combos?


texts: What does the sun product of price times quantity divided by average price

texts:
I have a very simple question, what is the meaning, if any, of this?

I.e. Economically what does the following calculation mean?

$$
\left(\frac{(Q1\cdot P1)+(Q2\cdot P2)+(Q3\cdot P3)}{Q1 + Q2 + Q3}\right)
$$

Consider the values being in a table like the one shown below:

$$
\begin{array}{c|lcr}
n & \text{Factory A Generation of good x} & \text{Factory B Generation of good x} & \text{Market price for good x} \\
\hline
1 & Q1 & Q1 & P1 \\
2 & Q2 & Q2 & P2 \\
3 & Q3 & Q3 & P3
\end{array}
$$

Thank you!


texts: With the Federal Reserve set to review interest rates next month, the price of gold may very well drop if they increase it. But with the current prevalence of terrorism and insecurity, is the price of gold likely to be affected (increase/decrease)?


texts: Would be there redistribution of wealth from actors with sticky prices to actors with more flexible prices under stagflation?

texts:
Suppose there is inflation in our country, but we take a short term, thus some prices are sticky and there is non-positive "growth" of the real GDP. In other words, we experience stagflation.
If I understand correctly, non-positive "growth" of the real GDP means that our total wealth does not grow. BUT at the same time I know that stickness of prices allows some people/corporations to make some real short-term profits. They increase their personal wealth while total wealth of the economy does not increase. It seems logical to conclude that they must be increasing their wealth at cost of other actors. But who are these other actors? These people must be ones that experience losses. And who would experience losses under this situation? People who sell goods (including their own labor) and for some reasons (like contracts that take time to renegotiate, menu costs, etc) don't rise prices on their goods fast enough. So there would be redistribution of wealth from actors with sticky prices to actors with more flexible prices.
Is my reasoning correct? Is my conclusion true?


texts:
The following question is based on a hypothetical scenario, in which the goal(s) is/are to identify how system participants may use/abuse the system to their benefit.

You are in the fortunate position to be able to create your own currency, which we will call Galatic Dollar (or GD), which is not tied to any economy or country.

You will act as the "central bank" for your currency by maintaining money supply. You will do this through a set of tools:

Maintaining/Owning at least 99.5% of the money supply
Using a fixed exchange-rate policy by pegging your currency against a basket of other currencies at their lowest denomination

For simplicity sake, there are only 3 foreign exchange providers and >90% of exchanges happen on these providers.

You thus decide to peg your currency against a basket of: USD, EUR and CNY (at their lowest denomination would be 0.01 CNY)

For another simplicity sake, we will assume that the GD (Galatic Dollar) is not a currency with supply in the trillions. Based on this assumption, we (the "central bank") will allow fluctuations of between 0.01-0.05 for normal exchange to flow.

Your mandate is to ensure that the GD meets the standard definition of money: medium of exchange, a unit of accounting, and a store of value.

Scenarios where monetary policy is applied:

Currency pumping : some actors on an exchange decide to create volatility by buying up lots of GD - the "central bank" steps in and quells this by playing market-maker and selling its supplies
Decrease in confidence : some actors decide to spread rumours in order to enable a shorting of the GD - the "central bank" periodically applies measures where money supply from its reserves are destroyed AND by maintaining the peg at the lowest denomination (CNY 0.01), the GD cannot be shorted into oblivion
Arbitrage - the "central bank", as market-maker, ensures no price-arbitrage across the 3 exchanges
Maintaining supply - the "central bank" will occasionally create new currency to maintain its 99.5% supply

Question/s:

How can participants in this model use/abuse the system to profit off of it?
What fundamental flaws exist in this model?


texts: Is there a cost to running the NewYork Stock Exchange? Does it affect the price of stocks sold on the exchange?

texts: Is there a cost to running the New York Stock Exchange? For example electricity costs, management costs,  rents on the building(s).  How do these costs (if any)  affect the price of stocks sold on the exchange?


texts: How the presence of increasing returns to scale lead to market failure

texts: How the presence of a sector with increasing returns to scale in a "perfect" economy may lead to market failure ? Can sb explain for me with the support of charts ?


texts: How a country buy stuff from other countries? and what is its means of exchange?

texts:
I was thinking about this scenario, where a country X wants to buy some toys (worth of 100$) from country Y. both of them have their own currency-- not USD. So, now, how does the exchange happen between X & y?

will the country X print 100$ equivalent of X's currency and convert that into US Dollars? or will country X exchange gold worth of 100$ to buy those toys from Y?

P.s. If I sound too dumb, its OK, I can handle that, am new to economics & trade.


texts: Computation of Different Axiomatic Barganing Solutions

texts:
I need help with the following question.

Take a two-agent bargaining problem. d=(0,0). Pick a strictly concave function for the bargaining frontier. Fix the intersection of the frontier with the y-axis to be at 1. Vary the intersection of the frontier with the x-axis between 0.1 and 10 with increments of 0.1. Graph the points proposed by the following solution concepts.

So y^2=1-x^2/0.1 can be the function. Does anyone know how can it be computed in matlab or a similar program?


texts: What are some good graduate-level econometrics books for someone with a strong mathematics background?

texts:
Related: Book recommendations on empirical methods in economic research and econometrics?

I would like to focus mainly on graduate texts in Econometrics. From the question above, I gather that Wooldridge's text is nice.

In terms of "strong math background," I did my undergrad in Statistics, consisting of two semesters each of linear algebra, real analysis, and abstract algebra, along with a measure-theoretic probability course.

What are some econometrics texts that you would recommend for me? I learned some intro econometrics in a course which taught from Studenmund but was extremely bored.


texts: What does the Leontief Inverse represent? (Intuitive Meaning or Real World Concept)

texts:
I encountered that nobody, even my profs and lecturers so far, has an intuitive way to explain what the Leontief inverse represents. Does somebody here?

As most people here would know, it goes:

$\ x=Ax+y $ where $x$ is the output and $y$ the final demand. So

$\ x - Ax =y $

$\ x (1 - A) =y $ or

$\ x = (1-A)^{-1}  y  $ or

$\ x = Ly $

While $A$ is clearly the proportion of total output that comes from intermediate value exchanges and not from transactions to final demand $1 - A$ should be the proportion of total output caused by final demand. However $L = (1-A)^{-1}$. So what would this be? The inverse proportion of what in total output is related to final demand? You can also just say of course $L$ represents the multiplier or scaling factor of how $x$ responds to changes in $y$, but that is not what I am asking for. I wonder if there is any real world interpretation possible on what L represents. Or is it an entirely abstract multiplier?


texts: model design - fixed effects model for paired differences

texts:
I have two panels. One panel that consists of an economic indicator variable across firms and years. The second panel consists of the same economic indicator variable across the same firms and years. However, the indicator variable in the second panel is calculated on the basis of different data than the one in the first panel, I call that data "adjusted". Hence, the values of the variable in the second panel data differ from that in the first panel. Put differently, I have two panels of paired observations of a single variable.

I now want to assess wether the indicators based on the adjusted data are significantly larger than the ones based on the unadjusted data.

Or simply: Are the values in one panel larger than the values in the other panel that describes an alternative set of values of the same variable for the same firms and years.

One issue to keep in mind is that the indicator variables are autocorrelated by construction, since they are computed on a rolling (overlapping) window basis. What I have come up with is as follows:

Step 1: I calculate the paired differences, i.e. $\delta_{i,t} = x_{i,t} - y_{i,t}$, where $x_{i,t}$ is the economic indicator based on adjusted data and $y_{i,t}$ is the economic indicator based on unadjusted data.

Step 2: I estimate a fixed effects model on a constant only, i.e. $\delta_{i,t} = \alpha + \gamma_{i} + \epsilon_{i,t}$, where $\alpha$ is the constant and $\gamma_{i}$ is a firm fixed effect.

I test the hypothesis that $\alpha > 0$ against the null hypothesis $\alpha = 0$ using the usual t-test. I employ robust standard errors to account for the autocorrelation that I expect in the $\delta_{i,t}$.

If the $\alpha$ is significantly larger than $0$, I assume that the $x_{i,t}$ is, on average, larger than $y_{i,t}$.

I am not an expert in panel regression, so my question is: Is this model design reasonable or flawed? Moreover, are there "better" ways to assess my question of interest?

--------------------------------------------------------------------------------

EDIT 1: What I mean by paired samples is that the observations are paired, i.e. they are somewhat linked because they refer to the same {i,t}. That is why I compute the differences of each "pair" (paired t-test).

EDIT 2: I actually analyse the quality of reported earnings. The one panel consists of quality metrics that are calculated based on actual reported earnings ($y_{i,t}$). The other panel consists of quality metrics that are based on "alternative" earnings values ($x_{i,t}$). What I mean by that is: For example, one could hypothetically imagine a firm in the US applying different accounting standards (e.g. German accounting standards), which leads to different values of reported earnings of the same firm in the same period. Now simply imagine that the second panel are earnings quality metrics that are based on earnings quantities reported under a set of different accounting regulations than the one in the first panel, but for the same years and firms!

EDIT 3: The panels consists of around 500 firms and 10 years each. I want to conduct the test for the entire sample. That is, I have 500 $\delta_{i,t}$ (500 firm-year differences).


texts:
I have the following optimal control problem

$$\max_{c_t,l_t} \int_0^{\infty} [ln(c_t)+\theta ln(1-l_t)]e^{-pt}dt$$
st. $$\dot{k_t}=k_t^{1/2}l_t^{1/2}-c_t-\beta l_t$$ $$k_0>0$$

I do big part of its solution. But I'm stack at a part. Please share your ideas about that part with me.

Now, I typed my solution:

Firstly, $c_t, l_t$ are control variables, $q_t$ is co-state variable and $k_t$ is state variable (according to me, I hope it is correct)

current value Hamiltonian function is

$$H= ln(c_t)+\theta ln(1-l_t) + q_t[k_t^{1/2}l_t^{1/2}-c_t-\beta l_t]$$

FONCs:

(1) $${\partial H \over \partial c_t}= \frac{1}{c_t}-q_t \le 0$$, $$c_t [\frac{1}{c_t}-q_t]=0 ; c_t>0$$

(2) $${\partial H \over \partial l_t}= \frac{-\theta}{1-l_t}+q_t [k_t^{1/2}l_t^{-1/2}- \beta] \le 0 ,  $$

$$l_t[\frac{-\theta}{1-l_t}+q_t [k_t^{1/2}l_t^{-1/2}- \beta]=0; l_t>0$$

(3)$${\partial H \over \partial k_t}= q_t l_t^{1/2}k_t^{-1/2}=- \dot{q_t}+pq_t $$

(4) $${\partial H \over \partial q_t}=k_t^{1/2}l_t^{1/2}-c_t-\beta l_t=\dot{k_t}$$

(5) TVC: as $t$ goes to $\infty$ $$\lim q_t e^{-pt}k_t=0$$

I think that $c_t=0$ and $l_t=0$ are not optimal. so I have $c_t, l_t>0$

Since $c_t>0$, $q_t=\frac{1}{c_t}$ by (1).
so, $\frac{\dot{q_t}}{q_t}=-\frac{\dot{c_t}}{c_t}$

By(3),  $$\frac{\dot{q_t}}{q_t}=k_t^{-1/2}l_t^{1/2}-p$$

Form here, I have $$\frac{\dot{c_t}}{c_t}=k_t^{-1/2}l_t^{1/2}-p$$

Now, I have put the equation (1) into the equation(2) as follows:

Since $l_t>0$, I have $$\frac{\theta}{1-l_t}=q_t [k_t^{1/2}l_t^{-1/2}- \beta]$$

And I know that $q_t=\frac{1}{c_t}$ by (1).

So I have $$\frac{\theta}{1-l_t}=\frac{1}{c_t} [k_t^{1/2}l_t^{-1/2}- \beta]$$

$$c_t= {[k_t^{1/2}l_t^{-1/2}- \beta]\over \frac{\theta}{1-l_t} }$$

If I take its derivative,

$$\dot{c_t}= (-1/\theta)\dot{l_t}[k_t^{1/2}l_t^{-1/2}- \beta]+\frac{1-l_t}{2\theta} [\frac{l_t\dot{k_t}-k_t\dot{l_t}}{l_t\sqrt{k_tl_t}}]$$

And so what?

I am stack here.I try to find $\frac{\dot{l_t}}{l_t} $

I need to find all differential equations that the dynamic system requires in order to find optimal path.

This is a bit difficult question for me. What all I can do is that. I will be happy if you teach me and show me the true way. Thanks a lot

(The existence of two control variables makes solving it difficult according to me. Therefore, I am asking for.)


texts:
$$U(q_1,q_2)=4{q_1}^{0.5}+q_2$$ $$P_1=1$$ and $$P_2=2$$ Initially $$Income=40$$ Then the question asks :how do I know what income I can get a corner solution?

Anyone can help me with this?

Thank you


texts: Are there any measures of U-6 Unemployment that take into account ageing out of the work force explicitly?

texts: Labor Force Participation has been steadily decreasing over the last 20 years or so. The Fed says that this has been the case mostly due to the demographic shifts, and to an extent the data backs that up. But I can't find anything specifically showing this effect. Is the data set used to create this information publicly available and/or is there information on U-6 measured  specifically for ages 25-54?


texts: Alternative to Intermediate-macroeconomics book by Mankiw

texts: Please suggest a good alternative to intermediate macroeconomics by Mankiw. A book with better teaching and which develops better understanding but at a similar level in terms of difficulty. I personally do not like mankiw's book. I can understand concepts at superficial level but do not get in depth understanding.


texts: How would consolidation in the brokerage space make things better for banks?

texts:
There is a bit from an article I don't quite understand:

China has been eager to whip its brokers into shape. Officials want
capital markets to lessen the burden on banks, which last year
provided two-thirds of all new credit. The ten biggest Chinese banks
have roughly 30 times more assets than the ten biggest securities
firms, and are also far more profitable.

Part of the issue is the excessive use of phrasal verbs: "whip into shape" and "lessen the burden." Perhaps using more precise domain-specific terms would have helped here. Regardless, I don't understand the connection between the consolidation of brokers and new credit. To my knowledge, brokers can "lend" for buying and shorting securities, but not "lend" in the general sense like a bank might. So, to me, having big conglomerate brokers won't help the credit extension burden of banks since the business scope is still narrowly limited to the financial nexus (i.e. fund custody, market making, ect).
Question
What theoretical or empirical findings could support the notion that consolidation in the securities services space could lead to a potential positive externality for banks?
For reference:
https://www.economist.com/finance-and-economics/2020/07/04/as-foreign-banks-circle-china-plots-an-aircraft-carrier-defence


texts:
We have a principal-agent model with hidden actions in which the principal is risk averse and the agent is risk neutral; Assume also there are two levels of output, $x$ and $x'$ (with $x'>x$) and two actions $a,a'$. Define $p(a),p(a')$ the probabilities of $x'$ under actions $a,a'$ respectively. Also, the agent disutility from action $a'$ is $-1$. The wages associated to $x,x'$ are $w,w'$ respectively.

My problem is that I am not sure how to show that the optimal contract requires $x'-w' =x-w$, i.e. that the agent, being risk neutral, takes on all the variability associated with the project.

I formalize the problem (assume the principal wants to induce $a'$, otherwise my question is trivial)

$\max\limits_{\{w,w'\}} u(x'-w')p(a') + u(x-w)(1-p(a'))$

st

$w'p(a') + w(1-p(a')) - 1 \geq 0 $

$w'p(a') + w(1-p(a')) - 1 \geq w'p(a) + w(1-p(a))$

In particular, when I try to solve the problem by maximizing the principal expected payoff subject to the "standard" Individual rationality (with $\lambda$ multiplier) and incentive compatibility (with $\mu$ multiplier) constraints (I assume the principal is interested in the more costly action $a'$) I end up with two equations which are not consistent with the aforementioned result. In particular:

$ u'(x-w) = \lambda + \mu [1- \frac{(1-p(a))}{(1-p(a'))}]$

$ u'(x'-w') = \lambda + \mu [1- \frac{p(a)}{p(a')}]$

It is evident that $x-w = x'-w'$ holds iff $p(a) =p(a')$ which is not the case in this problem (here we have that $p(a') >p(a)$). Another possibility would be to assume that the Incentive compatibility constraint is slack (hence $\mu = 0$); however I cannot understand why that should hold, when the principal wants to induce the most costly action $a'$ (help here)

I have read online that another approach would be to assume that the principal "sells" the project to the agent and the agent, after having chosen which level of effort maximizes its expected utility, pays back a fixed amount to the principal (call it $\beta_{a}, \beta_{a'}$)

So we would have something like:

$w'p(a') + w(1-p(a')) - 1 -\beta_{a'} \geq 0 $
if the agent chose to undertake high effort and
$w'p(a) + w(1-p(a)) -\beta_a \geq 0 $ otherwise.

But then how to go from there? How to insure that the agent is going to choose the action $a'$? How are the fixed amounts determined? Why are they optimal?


texts: What are the main drivers of insolvency at a macro level?

texts:
In July, Euler Hermes published a report that claimed that insolvency will explode due to covid by late 2020, the first half of 2021.
To support their statement, they show the evolution of what they call the "global insolvency index". I want to further understand how they compute this index. Unfortunately, they give very few details on this, probably because this index is a proprietary tool and they want to protect their IP.
I was nevertheless wondering what are the main factors that can explain insolvency at the macro level. I can think about:

global debt
interest rate
corporate profitability

Am I missing some important factors here?
Any references or links to online resources that can help me to better understand the dynamics of insolvency at a macro level will be highly appreciated.


texts: What is the difference between monopoly profit and monopoly rent?

texts:
I understand that monopoly profit is the return on capital (=profit) of the monopolist, which is larger than the normal profit in a competitive market.
As monopoly rent I understand the income in excess of the factor cost (=rent) of the monopolist.
In this sense both would refer to the same thing.
Is this correct?


texts:
I understand that you measure inflation by first measuring what the average person buys. Then you compare the total cost of these goods in year x with year y to get the inflation (from x to y).

The problem: Not only the cost of goods, but also the quantity that people buy changes all the time. Things go out of fashion or are replaced by different (better?) things. When you calculate inflation, you implicitly assume that the amount of goods people buy is constant (during the measurement period, say one year).

I do not doubt that this is reasonable from the practical perspective. But I doubt that today's inflation measurement approximates a well-defined concept.

Assume you know for every day/month/year how much people buy from each product and what it costs, what would be the formula for inflation? How do you incorporate the fact that people might by apples at 1\$ in May and oranges at 2\$ in June, i.e. that costs and quantities change all the time?


texts: Finding distributions of wealth from utility functions

texts:
Maximize
$$\begin{align}
U_1(x) \qquad & (1)\\
\text{s.t.} \quad U_2(a-x) = c \qquad & (2)\\
\end{align}$$

where we have bundles $x = (x_1, x_2), \quad a = (3,5)$, and want to split our resources between the two users.

$$\begin{align}
U_1(x_1, x_2) & = (x_1 + 1)x_2 \\
U_2(x_1, x_2) & =  36 - (x_1 - 4)^2 - (x_2 - 6)^2
\end{align}$$

The question is

In equations $(1)–(2)$, choosing different $c$ would lead to different $x$. Find all those $x$ with $x_1 ∈ [0, 3]$ and $x_2 ∈ [0, 5]$. Those set of points will comprise those distributions of wealth which are reasonable in the sense that no person’s utility can be improved without hurting someone else.

I don't understand how one can solve $(1)-(2)$, since I think this gives

$(x_1 + 1)x_2 - 36 − (x_1 − 4)^2 − (x_2 − 6)^2 = c$

I can plot this as $c = f(x_1,x_2)$, but I feel this isn't what the question is asking for, since it doesn't define a set of points.  If anyone can give me the direction in which to pursue this question, or let me know if I need to provide more information.  Thanks.


texts: Is the labor force participation rate related more to labour supply or to labour demand? Or both?

texts:
I have read several Labor Economics books, but I am stuck. Is the labor force participation rate related more to the labour supply or to the labour demand?

If the labor force participation rate decreases in a year (with respect to the previous year), should we worry that employers are not hiring (i.e., labor demand)? Or, is it due to workers that are not currently interested in work (i.e., homemakers)?

Furthermore, from this and this online documents it seems that the LFPR (labor force participation rate) is strongly dependent on labor demand from employers (i.e., positive/negative business cycles) rather than from labor supply. For instance, the LFPR dropped strongly during the Great Recession as employers were not willing to hire workers. Any opinion on these problems?


texts: How monetary policy affects bank reserves

texts: In discussions of the "credit channel" in the transmission of monetary policy, I've read that increasing the policy rate reduces bank reserves. Can someone explain how this happens?


texts: Do governments issue debt at low r to pay debt with high r?

texts:
I have a question. I know governments do debt rollover from time to time. But, to me it seems logical that governments do this when the interest rate of bonds they have issued in the past is higher than the one they could get now. This way, they pay more expensive debt with cheaper debt. To me this seems like a no-brainer. But is this what they do?

With current QE and low interest rates, are governments doing this? I think they are not. Why?


texts: Income Elasticity of Demand vs. shift in demand curve

texts:
I've just read an econ textbook and want to verify a statement/definition about income elasticity of demand.

Changes in income shift the demand curve, and we can measure the responsiveness of demand to income changes by calculating income elasticity of demand as follows:

Question: Where does this change in quantity demanded come from? Is it from a movement along demand curve, or from a shift of demand curve?


texts:
Let $\delta\in(0,1)$ be the discount factor. Consider the stage game in the infinitely repeated prisoner's dilemma game:

The goal is to derive conditions on $\delta$ such that the symmetric tit-for-tat strategy profile is a Nash equilibrium.

To recall, tit-for-tat is when a player cooperates (here plays Yield, $Y$) the first round and then every round after copies the action of their opponent the second round.

I am told that if A is playing tit-for-that then B's best possible replies would be to alternate between $N$ and $Y$ (playing $N$ first), to always play $N$, or to play tit-for-tat himself resulting in both players always playing $Y$.

We compute the expected payoffs of each depending on $\delta$ and then figure conditions on $\delta$ so that $B$ should play tit-for-tat. As the payoffs are symmetric, these conditions provide $A$ should also play tit-for-tat given $B$ is and we have a Nash.

My only question is why it must be that these are the only best possible replies. Why might not $B$ have some periods where he plays $N$ for a while then switches to only cooperating? Or vice versa. Or anything outside of these three.


texts: The title says it all.  Why did the Swiss National Bank end the currency peg?  The issue obviously has many aspects, so I'm looking for a concise summary with references to explanations for each of those crucial aspects.


texts: How does the Federal Reserve reduce "excess reserves"?

texts:
Over the last few years, the amount of currency is circulation (and the corresponding liability on the Fed's balance sheet) has been growing; however, the asset side of the BS hasn't increased. By basic accounting, that means one of the other liabilities (either required reserves or excess reserves) has been shrinking.

I'm guessing the growth in currency volume has been offset by declining excess reserves, but I don't understand the mechanics of that. Does the fed send $100 bill to a bank and then reduce that banks' excess reserves by 100 dollars? If so, how does the Fed decide which banks' account will be reduced by how much?


texts: The Fed has a $4.5 trillion balance sheet: where did they get that money?

texts:
Who paid for that $4.5 trillion balance sheet?

https://www.cnbc.com/2017/09/19/hedge-fund-titan-ray-dalio-says-to-succeed-in-markets-you-need-to-bet-against-the-consensus--and-be-right.html


texts: Do you know any paper that discuss the effect of the deterrence of fines of individuals' behaviours? What is the difference between a fine a fee?

texts:
According to Gneezy and Rustichini the presence of an extrinsic reward in activities with a level of intrinsic motivation (e.g. volunteering) reduces intrinsic motivation, thus it may determine opposite results from the expected.

I wonder whether there is any research about the effect a price may have in crowding out intrinsic motivation compared to a fine. Michael Sandel faces this topic in "the moral limits of market", however he does not provide any empirical evidence. Do you know any research that can be used to support this thesis?


texts: How to get the effect of one dummy variable against many others?

texts:
I have the following regression:

wage = constant + (beta1)*michigan+ (beta2)*california+...+(beta49)florida+(beta50)education + u

where michigan is equal to one if the person is from michigan and zero otherwise, and so on for all of the next state variables.
education is equal to the number of years of education of the person.
The base case is South Dakota, which is the state that does not appear in the regression, that is why the coefficient for florida is 49 and not 50.

I want to get the effect of being from south dakota against any other state in wage. My idea is to run this regression, and then add up betas for all other states (beta1 to beta49). If the sum is positive that would mean that people from any other state earn on average more, and the opposite if the sum is negative. Is this correct? if so , why? if not, why not? and what would be the right way to do it?


texts: Example production function with increasing returns to scale but diminishing marginal product

texts: I know that diminishing marginal returns even to all factors of production doesn't imply decreasing returns to scale. But could you please give me just an example of such production function?


texts: How were unit labor costs estimated by Gali and Gertler (1999)?

texts:
I am trying to estimate a NKPC like the one
Gali & Gerter, 1999 and Gali &Gerter, 2001 estimated. I am having trouble with understangind how they calculated the marginal cost, i.e., which time series they actually used. I tried consulting '''Sbordone, 2002, who estimates the same model using the same (or at the very least a similar) proxy for the marginal costs. As far as I could understand MC = C/Y where MC is the marginal cost, Y is GDP and C are the total compensations given to workers, i.e., the sum of all real wages paid to workers. I would like to know if that is correct and, if it isnt, how Gali & Gertler calculated the marginal costs. In the specific interpretation I have described I dont know if one must use real or nominal GDP. If I use real GDP, it seems to me, that when dividing real salaries by the real GDP the deflators dividing both nominal salaries and nominal GDP will "cancel" each other and I would only get the ratio between nominal salaries and nominal GDP, which does not seem useful given the fact that in the price formation model firms are considered not to suffer money ilussion. I apologize in advance in case my words have not been precise enough and thank you all for your answers. Any help and references to articles or textbooks is greatly appreciated.


texts: How to have same utility function for two persons?

texts:
I have a question regarding utility functions:

Utility can be defined as follows:

$U=1+e^{\frac{x}{RT}}$

U:Utility

x: What we want to find the utility for (Certain equivalent)

RT: Risk tolerance

My question is what conditions must be upheld in order for two persons to create the same utility functions for a bet?

Example:

Person A bet \$5 that horse number 1 wins. Person B bet \$20 that horse number 2 do not win. Is it then possible that their utility functions is the same given that their probabilities for horse 1 winning is the same and that they have the same risk tolerance?


texts: Certainty equivalence when the utility is semi-continuous instead of continuous

texts:
Let $U:\mathbb R^2\to\mathbb R$ be a utility function.
If $U$ is strictly increasing and continuous, then it is well known that for any $(x_1,x_2)$ there exists a certainty $(c,c)$ such that $$U(x_1,x_2)=U(c,c).$$
If we assume that $U$ is strictly increasing and upper semi continuous, can we still find a certainty equivalence $(c,c)$ or not?

Clarification:
$U(x_1,x_2)$ is not necessarily expected utility (EU). It could be other utility models under uncertainty, such as the max-min expected utility, choquet expected utility, and others.
For example, see: http://www.columbia.edu/~md3405/BE_Risk_4_17.pdf

My try:
Of course one important example of $U$ is the additive representation (subjective expected utility): $U=\sum_ip_iu(x_i)$.
Consider a special case: let $p_1=p_2=0.5$; let $u$ be upper-semi continuous, for example $u(a)=a$ when $a<1$ and $u(a)=a+3$ when $a\geq 1$.
In this case, $U(0,1)=2$.
$U(c,c)=c$ when $c<1$; $U(c,c)=c+3$ when $c\geq 1$. None of the certainty has a utility of 2.
So the answer seems to be "NO"?


texts: Application of Poisson process in economic modelling

texts:
To understand the emergence of constitution, Myerson (2008) models a scernario that a political leader gathers supports from captains in order to defeat challengers whose arrival is modelled by a Poisson process.

I found using Poisson process seems to be simple and reasonable, but it is the only model I know that utilizes Poisson process.Are there any other well-known models utilizing Poisson process in a similar way? If not, what's drawback of Poisson process?


texts: Does this explanation pertaining to the Supply Curve and Law of Supply make sense?

texts:
I was having some trouble understanding the Law of Supply, and I now understand that I was looking at it from the wrong perspective.

Now, I'm confused with shifts in the Supply Curve. After reading through the answers in the thread, I think I'm on the right track.

However, some of the material I'm studying doesn't make sense. Take a look at my study material below. If you were to shift the image 45 degrees counter clock-wise, yes the curve would shift left, but that doesn't indicate "a smaller quantity at any given price".

It's the same quantity, isn't it? I hope I'm not missing something completely obvious. My apologies if I am, and thank you for your input.

I googled "shift in supply", and below is what I was expecting:


texts: Is there an index, parameter, ecuation, or anything to compare the tax pressure exercised by a country in relation to others countries?

texts:
In my country we are told often that the tax pressure over the companies and people is huge, making it unbearable and being a reason bankrupting the Economy, and one of the largests in the world. We are told that each product price is more than 50% of taxes and each company has to pay more than 50% in taxes for each employee they have. But when I take a look at the overall amount of money collected by taxes in a year, this seems to be over 100 times smaller than United States, a supposed very capitalist country which opposes heavy taxation. Of course we have to take in consideration other parameters, such how large are the economies of each country, but if I compare the amount of money collected with taxes in relation with the GDP of each country, it would seem my country pays half of the taxes of United States (100 times less taxes with 50 times less GDP than US) . I thought that may be I should compare people's wages with the amount of taxes divided the amount of people, but it still seems that United States is paying over twice the taxes that we pay here.

Then, because of all of this, my question is,

Is there an index, parameter, ecuation, or anything to compare the tax pressure exercised by a country to its own Economy in relation to the pressure exercised by others countries?


texts: Uniqueness of utilities in competitive equilibrium

texts:
Suppose several traders are given some initial endowment of goods. Then, a free market opens and they trade until the market is at a competitive equilibrium. Each trader now has a final utility which is at least as high as his initial utility.

MY QUESTION: Is the vector of final utilities unique? I.e, is this possible that, with the same initial endowments and the same utility functions, there will be two different equilibria in which the final utilities are different?

EXAMPLE: Suppose there are two goods and two traders, Alice and Bob, with the same utility function: $u(x,y)=x+y$. The initial endowment is $(10,0)$ for Alice and $(0,10)$ for Bob. In competitive equilibrium, the price vector has $p_x=p_y$. There are many different equilibrium allocations, for example: $(10,0),(0,10)$, $(9,1),(1,9)$ and $(5,5),(5,5)$ are all equilibrium allocations. But, in all these allocations, the utilities of both traders are the same: $(10,10)$. I would like to know in what cases this uniqueness happens.


texts: Why teach Arrow's impossibility theorem?

texts:
As part of a Macro class on social welfare, I am about to teach a very brief introduction to Arrow's impossibility theorem.

The classic demonstration of this involves three voters choosing between three alternatives, whose preferences are as follows:

  A B C
1 x y z
2 y z x
3 z x y

We are then shown the supposedly interesting result that, given these obviously incompatible preferences, no possible voting system can pick a favoured option in a non-arbitrary way.

More generally, any voting system risks ending up in this kind of three-way tie situation.

But this seems impossibly theoretical a concern. Clearly if voters' preferences split n alternatives precisely n ways, as in this example, there's no outcome that satisfies a majority. But in an electorate, the probability of this is vanishingly small. Also, if each alternative is joint first in preference, we surely don't care which one is selected.

Why do we teach this mysterious theorem at all? Is it just because it's got a cool name? Has it ever been usefully applied to a real-world problem?


texts: Is the economic behaviour of a competitive market as a whole the same as a monopoly market?

texts:
We know that the price-setting mechanics and individual firm's behaviour in a competitive market are different with those of monopoly powers'.

However, the demand curves of both competitive market(as a whole)and monopoly market slope down.

So here's the question: can we view the competitive market as a whole as some kind of monopoly power?

PS: What I'm talking about is purely theoretical. Hence pure theory is ok for my question.


texts: Is $y$ always output per person in DSGE/RBC models?

texts:
As title says, is $y$ output per person in DSGE/RBC model? If so, why did macroeconomics decide not using Solow/Cobb-Douglas style of using full labor to characterize economy?

Model reference: http://crei.cat/people/gali/pdf_files/monograph/slides-ch3.pdf

For Gali's model, would $y$ represent output per worker? Or the whole output of the economy represented by representative household?

Reference: why is labor $h_t$ often average working time percentage of non-sleeping time in RBC?

this for me seems to say that full maximum working time is assumed to be 1 with $h_t$ representing working time per labor unit. Thus it seems to be that $y$ is output per person..


texts:
In time series analysis, it is often important to determine the optimum number of lags in order to remove serial correlation. For example, in VAR, Dickey-Fuller unit-root test or Granger causality test, and many other models. This is usually done using information criteria such as Akaike, Bayesian or Hannan-Quinn information criterion.
Are there any rules about which criterion should be applied to a series based on how the series looks and the properties it has or based on what we can assume about variables from the economic theory? Or should all be used and decisions be made based on results from most of them? Are there some situations where some criteria are biased while others are not?


texts: Is there any evidence on the effect of China's investment in African countries on their economic development?

texts:
Apparently, China made substancial investments in infrastructure and commodity extraction in several African countries over the last couple of decades. Is there some econometrically sound evidence of the effects on growth or other economic variables?

See this, for example: CNN posting on Kenyan Railway


texts: Intermediate demand vs. Intermediate consumption

texts:
I am trying to understand what's the difference between intermediate consumption and intermediate demand. The context is the European System of Accounts, which says that intermediate demand is the same as intermediate consumption for the total economy, but not whithin sectors. I think the difference may be related to trade margins or transport, but I can't find it.
Thank you so much


texts:
Suppose I have a function of a varying values represented by randomness. A stock or price of a commodity would be a good example.

What is the average return for that stock on any given interval of prices?

Let average return be defined as the most likely return achieved given two bounds.

I've come up with an initial hypothesis for my average value function.

Let $A$ be the average value.

Let $x_i \in [0,M]$
Where $M$ is the most recent index for a price.

$$A = \sum_{x=0}^M \frac{1}{M} \sum_{y=x}^M \frac{1}{M -y+x} f(x,y)
$$

Let $f(x,y)$ be the return using an arbitrary strategy between the intervals $[x,y]$

Is this a good indicator for any return? Does this say more about the stock or commodity or the strategy itself?


texts: Fixed-Effects on individual level with explanatory variable on state level

texts: I am planing a panel data analysis evaluating a continuous policy intervention. I do have individual level data. I would like to account for individual fixed-effects. However, the explanatory variable does not vary on individual level, but only on state level. The response variable is on individual level. Is that a problem?


texts: OLS, Frisch-Waugh-Lovell Theorem and few observations

texts:
I was talking to a colleague a few days ago and the following question came up:

Why can't we just use projection matrices and the FWL Theorem to "gain" a few degrees of freedom in case of very few observations?

Imagine a case where you want to estimate

$$y_t = \beta_0 + z\beta_1 + x_2\beta_2 + x_3\beta_3 + u_t$$

but unfortunately, you just have 5 observations (extreme example). Luckily, you are just interested in $\beta_1$. Now you could just create some projection matrices in the form

$$ M_x = I - x'(x'x)^{-1}x'$$

and project off your "unwanted" $x_2$ and $x_3$ (following Davidson and MacKinnon). You would be left with the regression

$$M_x y = M_x  z  \beta_1 + residuals$$

where $\beta_1$ is numerically the same as in the regression above. But now you are able to estimate just one (beta-)parameter with 5 observations compared to three parameters before. So, obviously, the estimates improve, don't they?

Where is our mistake?


texts: How can the HKMA peg the Hong Kong dollar at 7.8 HKD/USD for so long?

texts:
A lot of pegged exchange rate systems don't stay pegged for so long (e.g. because the central bank run out of reserves to maintain their values)

So far I understand that the HKD is 100% backed by the USD. How does this become a really good peg?


texts: Are risk-costs a form of external costs?

texts: An example to make to question more clear: With the use of nuclear power plants come several risk-costs (the risk of a nuclear disaster). These costs aren't included in the energy price and there is nobody who pays for it. So are they considered as external costs?


texts: Cross derivatives of payoff functions in potential games

texts:
In Monderer and Shapley (1996) (pdf) there is the following theorem.

  The next theorem is well-known (and very useful).

  THEOREM 4.5

  Let $\Gamma$ be a game in which the strategy sets are intervals of
  real numbers. Suppose the payoff functions are twice continuously
  differentiable. Then $\Gamma$ is a potential game iff
  $\frac{\partial^2{u^i}}{\partial{y^i}{y^j}}=\frac{\partial^2{u^j}}{\partial{y^i}{y^j}}$
  for every $i,j \in \mathbb{N}$.

Where was this from? I might be missing something but I don't see a reference. Thank you in advance for your help.