texts:
If I have a sum utility function like this $U(y) = \sum_{j=1}^J u(y_j)$ where $u$ is convex.

Is there then a way to find walrasian demand for such a function without using calculus or do you need to use lagrange to solve for j,...,J?


texts: How does the government launch of Tomahawk missiles against Syria affect the economy and governmental budget?

texts:
Last night an air strike was launched against Syria of about 60 Tomahawk missiles. At approximately $832,000 apiece, this airstrike cost the US gov't about 49 million dollars. Initially, this sounds like a terrible waste of government funds, but I think I might be missing something here. It seems like the creation of Military hardware as sponsored by the government might be similar to Keynesian spending -- Which is traditionally (At least by Keynesianists) understood to help the economy. The fact that WW2 helped to pull the US out of the great depression certainly supports the principle that war is good for the economy.

That said, is there any reason to believe that governmental use of expendable military hardware won't actually help the economy?

For the purposes of this question, I'm not terribly interested on Moral arguments about why boosting the economy by using military hardware may be a bad thing.


texts: How to the IS curve linearised around the structural equilibrium?, what is the math behind it?


texts: Research community around logistics micro-economic topics?

texts:
Is there the equivalent of a Rand Journal of Economics for the topic of logistics, focusing on the micro-economics of productivity gains via automation or disruptive technologies.

There is the wonderful macroeconomic work by Carlota Perez on effect of technology disruption on financial capital, which helps me think about logistics etc., but in scouring Google, I find a paucity of micro-economic research on the area of logistics and supply chain and manufacturing processes. I am sure I am missing the elephant in the room, any tips for where it is ?


texts: What exactly is the risk Italy's high debt to GDP ratio poses to Eurozone and EU?

texts:
Background
Us laymen read all around that Italy's weak economy and its high government debt/high debt to GDP ratio is threatening the financial stability and health of Eurozone and EU. However, little is being explained by experts what exactly the real risk level is and various mechanisms either already in place or conceivably considerable are not sufficient to mitigate the risk. I am trying to understand this from an expert and non-partisan perspective.
Questions
From my perspective, the main question can be broken down into sub-questions, answers to which could help better understand the bigger picture.

Under current circumstances, what is the level of government debt to GDP at which Italy would likely default on its obligations?
If it comes to such a default, how will we recognise it? I.e., what event/non-event would be an indicator of it happening and what are the timepoints to watch? (I guess scheduled moments of interest installments, or something like that could be such moments)
What options would the Bank of Italy have at that point to mitigate the crisis?
What options would Italian government have at that point to mitigate the crisis?
What options would European Central Bank have at that point to mitigate the crisis?
What options would European Commission and European Council have at that point to mitigate the crisis?
If despite all the doom and gloom Italy's default is unlikely (because for instance the existing policies might as well work, or such), what are exactly the policies/mechanisms/events which would prevent the country to default?

Disclaimer

My background is not in economy, so in the case I posed my question with flaws, I would appreciate help to improve it.
To put a break on speculation, let's assume that Italy leaving EU, or a scenario like that is out of question (barring sub-question 6).
Just to stress: I very well understand this site is not for speculative questions, but since my question is about a possible future scenario (which clearly many serious economists consider realistic and likely), it is by necessity somewhat speculative. Therefore I am asking about current legal/political framework and reality to be considered/executed at some future time point. That is, I am asking about viable options, not some fantastic scenarios.


texts: What are the fundamental theorems of welfare economics?

texts: All of welfare economics is based on some theorems, some of which I can remember, but I am looking for a comprehensive list.


texts:
I'm using the Cobb Douglas production function for a Mathematics investigation into how optimisation works in Economics. The assumption is that the firm require's only one type of capital, that is, a coffee machine. Keeping this in mind, would it be reasonable to take K as the number of coffee machines  used, instead of hours?
Thanks, and cheers!


texts: Interpreting the ratio of two variances in a Bayesian decision problem

texts:
Given a normal prior with mean $\mu_0$ and variance $\sigma_0^2$, and a normal likelihood with known variance $\sigma^2$, the Bayesian posterior, after observing $n$ iid signals $x_1,\dots,x_n$, is also a normal distribution with mean
$$
\left(\frac{\mu_0}{\sigma_0^2}+\frac{\sum_{i=1}^nx_i}{\sigma^2}\right)
\left(\frac{1}{\sigma_0^2}+\frac{n}{\sigma^2}\right)^{-1}
$$
and variance
$$\left(\frac{1}{\sigma_0^2}+\frac{n}{\sigma^2}\right)^{-1}.$$
See https://en.wikipedia.org/wiki/Conjugate_prior#Continuous_distributions.

Pratt, Raiffa, and Schlaifer (2008) suggest that we could define
$$n'=\frac{\sigma^2}{\sigma_0^2}$$
so that the posterior mean and variance can be written as
$$
\frac{n'\mu_0+\sum_{i=1}^nx_i}{n'+n}\quad\text{and}\quad\frac{\sigma^2}{n'+n}.
$$

They say that

  The parameter $n'$ can be interpreted therefore as the "fictitious sample size" or equivalent number of sample observations that describes the amount of information implicit in the prior distribution.

I'm having difficulty understanding the interpretation of $n'$, especially the part after "or". Could anyone help me understand it, by perhaps putting it in a different way, or elaborate it a little?


texts: Optimal control theory: How to maximize Hamiltonian in this case?

texts:
The problem is to maximize $\int_0^1 y(t) + u(t)^2 dt$ where $y$ is state and $u$ is control.

Further we have $y' = u, y(0) = 5$.

I set up the Maximum Principle equations, but, in particular, I need to maximize the Hamiltonian in the $u$-variable.

My nstructor's solutions does this by differentiating and letting it equal zero, i.e. he gets $$2u(t) + \lambda = 0.$$

Then he goes on with the other equations, and sovles for $\lambda$, and then $u$.

However, if we differentiate the Hamiltonian again with respect to $u$, then we get $$2 > 0$$
which is not negative, hence surely the 1st equation is not warranted, as we have found a minimum, not maximum?


texts: How has decreasing quality (or the need to pay more for the same quality) tracked with inflation?

texts:
I'm trying to identity a missing variable that could affect poor and middle class consumers more than more wealthy/resourceful individuals.

Assuming that there are decisions regarding cost reductions that also affects product quality, how does "the need to pay more to obtain the same quality/benefit" align with inflation? ... cost of living?

Simple example, in the 1950's all farms sold (implicitly non-GMO) chickens at a given price. Cost minimization introduced decades later affected quality. No matter what drove the new consumer market for non-GMO/grass fed/humane treatment, these additional "features" now come at a premium.

There is probably a well known marketing/business school of thought about this pattern of getting consumers to pay more for what they are already paying for.

How can I track cost of living with quality of living. Is there any metric that would help identify what I'm referring to "shadow inflation" that affects product quality?
Since it's difficult to get a fiscal correlation over time for this, perhaps the quantity of students enrolled in curriculum X which promotes said business methodology?

...Or the revenue of companies that offer consulting services to enact this change?


texts:
I am curious how I solve this question, I will include an image below. I am not looking to be spoon-fed just informed. If you could answer and provide an expiation for the answer that would be awesome!

The graphs below depict the perfectly competitive market for apples on the left and Farmer Johns perception of the market for apples as an individual farmer on the right. Assume farmer Johns costs are represented by SRATC-1. In the long run will farmer John choose a high, medium, or low level capital for his farm. Indicate the SRATC curve associated with Johns decision. Explain what is going on short term for Johns apple farm. (Drawing a typical MC curve might be helpful)

Is the equilibrium price depicted here a long run equilibrium ? How do you know? If not what will happen to move the market towards the long run? Show the change the move the market towards the long run equilibrium and label the long run equilibrium price, market quantity and johns long run produced quantity?


texts:
In fixed income, the yield on the 10-year US Treasury fell 0.07
  percentage points to 0.56 per cent as investors retreated to the
  safety of core government debt

From : https://www.ft.com/content/26ea5ef9-0619-4e50-b605-58e36d3fc4d9

What is 'core government debt' and how is it raised, since the quoted statement seems to imply it is different from US Treasury bonds.


texts: I would like to ask two questions. What are decent schools to study Economics of Education for a PhD? My second question is if there is anybody who could recommend me a good book or research papers that can be a good introduction to this subject.


texts: Question about deadweight social burden triangle. Error in the test?

texts:
I have been trying to answer the following question for the past two hours. I've looked at textbook examples, online resources and lecture notes. There seem to be two correct answers but I may be wrong. I think both b) and c) are the correct answers to this question. I am assuming that the deadweight social burden triangle is the deadweight loss triangle.
However, only b) is stated as the correct answer.
When does a deadweight social burden triangle occur?
 a) The social marginal benefit equals the social marginal cost.

 b) The social marginal benefit is greater than the social marginal cost.

 c) The social marginal benefit is less than the social marginal cost.

 d) The price is zero.

Can anyone please explain the reasoning behind b) being the correct answer (if it is)? Thank you.


texts: Do rich people on average have the vast majority of their wealth invested or they have lots of liquid cash/no productive properties?

texts: I often read about really rich people with billions of dollars, and I'd like to   know if they have, for example, just a big part of their wealth in shares of their company or they have lots of wealth in not productive activities?


texts: How to deal with a singular Leontiev inverted matrix?

texts:
I am currently studying and experimenting the input-output methodology. It is a 1930's method based on national accountings that allows to measure the interindustry flow of good and services.

Currently, I am experimenting it on the french economy. More precisely, I wish to measure the direct and indirect impact of the state-funded renewable energy funding scheme (the state buys renewable energy at a fixed price to producers since it is not currently competitive on the electricity market, as regards to to nuclear electricity production)

I want to measure the direct growth of the industry and the indirect growth of the associated industries that is created by the investment in the said industries due to this funding scheme.

I know how much production from 4 sectors is needed to install 1Gw of renewable electricity production capacity and I know how many Gw are installed each year since 2006.

Now my question aims directly at the input-output table that is provided by the National Institute of Statistics and Economic Studies. It is an extremely serious state-owned institution and I have no doubt that the information (the table) they provide is accurate.

But I have a problem since my calculator ( the R software) returns the information that the table that I must use to execute the calculs is singular. And since the formula that I have to use is the following :

x = [I-A]^-1 . f

... by definition, if this [I-A] matrix is singular, it has no inverse. And that is exactly my problem : my calculator returns a message error that prevents me from get through the calculus : " objet is exactly singular : the determinant of the matrix (the leontiev inverted matrix) is zero on the last line, which means that the inversion calculs cannot be opérated. Any idea of the cause ?

NB : to obtain that matrix, I first created an A matrix of technical coefficients by dividing the original input-output table from INSEE by the total production of each branch. This way, each cell of the A matrix of technical coefficients shows how much of any input is needed in euro for the production of one euro of total output.

Hope someone can direct me toward the answer, best regards.


texts: If the players are symmetric and the core is nonempty, then $x_i = v(N)/n$ for all $i$ is a Core element

texts:
Consider a TU game $\langle N,v \rangle$ with $N = \{1,2,\ldots,n\}$ being the set of players and $v : 2^N \to \mathbb R$, $v(\emptyset) = 0$ the characteristic function. The Core of $v$ is defined by undominated allocations $x \in \mathbb R^n$
\begin{align}
\mathcal C(v) = \left\{x \in \mathbb R^n ~ \bigg| ~ \sum_{i \in S}{x_i} \geq v(S) ~ \forall S \subseteq N\right\}.
\end{align}
Let $m_i(S) = v(S \cup \{i\}) - v(S)$ denote the marginal contribution of $i$ to coalition $S$.
We say that the players are symmetric if $m_i(S) = m_j(S)$ for all $i,j \in N$ and $S \subset N$.
The marginal contribution of any agent to any coalition is thus identical.

I am wondering whether the following Proposition is true and how one proves it formally.

  Proposition: If the players are symmetric and the core is nonempty  $\mathcal C(v) \neq \emptyset$, then the equal division of the worth of the grand coalition is an element of the core $(v(N)/n,\ldots,v(N)/n) \in \mathcal C(v)$.


texts: Are stock trade commissions evidence of anti-competitive practice?

texts:
A typical commission on a typical stock trade these days is $8. I don't understood how it can cost this much. It looks like the entire process is happening in software, electronically, and so the actual cost to the parties that supply this service should be near zero.

So I'm wondering, where does that money go? Is someone making a profit? Are they protecting that profit with exclusive dealing, collusion, or some other anti-competitive practice?


texts: Does levying a new tax on production increase GDP?

texts:
Consider a society with no taxes on (e.g) commercial land ownership.
One day the government impose a small tax on land owned by the foresting industries. I would assume that prices on goods produced on these now taxed lands would increase slightly.
Let's ignore dynamic effects from shifting demand (perhaps this tax is levied on goods with very low price elasticity, like toilet paper).
As we know there are three main ways to calculate GDP that all ought to closely match each other:

Production approach
Income approach
Expenditure approach

My thinking is that levying a tax should not raise GDP, as no extra value creation occurs
With the production and income approach its clear to me that the tax will not increase GDP, perhaps falsely. My thinking is that the profit of the producer would not increase, since the price increase on the goods would just offset the cost of the tax.
With the expenditure approach however it would seem like this new tax would in fact increase GDP at a first glance, since the consumption (based on price) would increase. If the government spending also increases with the new tax, we get even more of an increase.
But after thinking more, I came to the conclusion that spending on other inferior goods must decrease with the same amount. For a household that does no saving, spending 5% more on toilet paper would mean that they decreased their spending on other things with the same amount. For households that do save, they either lessen their savings or spend less on other stuff. And savings is just future consumption, meaning that if they save less, they have less consumption in the future.
Is my reasoning sound? Does taxes like this (with these simplifying assumptions) in fact not increase GDP?


texts: Why are allocation and distribution important consequences of the second welfare theorem?

texts:
I'm reading Intermediate Microeconomics: A Modern Approach by Hal Varian.
On page 606, he states:

  The Second Theorem of Welfare Economics states that as long as preferences are convex, then every Pareto efficient allocation can be supported as a competitive equilibrium.

He then states on 604,

  The Second Welfare Theorem implies that the problems of distribution and efficiency can be separated...Prices play two roles in the market system system: an allocative role and a distributive role. The allocative role of prices is to indicate relative scarcity; the distributive role is to determine how much of different goods different agents can purchase. The Second Welfare Theorem says that these two roles can be separated: we can redistribute endowments of goods to determine how much wealth agents have, and then use prices to indicate relative scarcity.

My Question:

How does the second remark follow from the first?


texts: Buy-or-sell deal when there is cash shortage

texts:
A company is owned by two partners: partner $A$ holds a fraction $a$ and partner $B$ holds a fraction $b$ (with $a+b=1$). Partner $A$ wants to break the partnership. A common procedure for this is that $A$ should suggest a price $P$ for the entire company and let $B$ choose either of two options:

Buy $A$'s share for $aP$, or -
Sell his share to $A$ for $bP$.

This procedure incentivizes $A$ to suggest a fair price. Moreover, if $B$ thinks that $A$'s price is unfair, he can profit from this - if he thinks that the price is too low he can opt to buy and if he thinks that the price is too high he can opt to sell. The advantage of this procedure is that it guarantees fairness without requiring for an external arbitrator.

A possible problem with this procedure is that it requires $B$ to have enough cash for buying $A$'s share. If $B$ doesn't have enough cash, and cannot get credit, he might have to select the "sell" option even when the price is low. Moreover, if $A$ knows that $B$ is short in cash, he might exploit this fact and deliberately suggest a low price in order to force $B$ to sell his share.

MY QUESTION IS: is there an improved division mechanism that handles this problem?


texts: Does Progressive Taxation Actually Follow The Decreasing Marginal Value of Wealth?

texts:
From my understanding, the application of a progressive income tax (increasing rate based on income level) follows from the assumptions of: "Equal Sacrifice" - everyone's "sacrifice" should be the same, and the "Decreasing marginal value of wealth" - the actual value inherent in receiving an additional unit of money is less for someone with more money.
My question is, then, to what extent do modern progressive income tax systems match money's "actual" quantity/value curve? Presumably this curve is something that could be estimated/calculated/measured, correct? But as far as I'm aware, no modern taxation system is set with respect to any theoretical or actual quantity/value curve for money.


texts: Has there ever been stock options under hyperinflation?

texts: I believe the most developed example is weimar. I dont think it had any stock options. I dont think there has been any country under hyperinflation with stock options. I wonder how option prices would behave.


texts: Does the concept of Nash-equilibrium conflict with the concept of market equilibrium in the lemon market

texts:
Consider a version of Akerlof's Lemon market with two types of sellers. One type sells Quality cars the other type sells Lemons. Buyers' reservation prices are $r_{B,Q}$ for a Quality car and $r_{B,L}$ for a Lemon. Sellers' reservation prices are $r_{S,Q}$ for a Quality car and $r_{S,L}$ for a Lemon. The buyers cannot differentiate between the types of the sellers but the sellers know their type. Given a market price $p$ sellers decide whether to sell or not by maximizing their surplus $p - r_{S,t}$. (Not selling yields a surplus of zero.) Buyers decide whether to buy or not by maximizing their expected surplus $E(r_{B,t}) - p$. (Not buying yields a surplus of zero.)

Given a number of buyers $n_B$ a number of sellers for both types $n_Q, n_L$ we can reason about the type of equilibrium. Depending on the parameters you can have total market collapse (if no purchase occurs), adverse selection (if only Lemons are bought and sold) and also markets where both types of cars are sold. For some parameter sets you have multiple market equilibria. That is you have a price $p_1$ at which adverse selection occurs and the corresponding demand at $p_1$ is equal to the supply at $p_1$. You also have a price $p_2$ at which adverse selection does not occur and the corresponding demand at $p_2$ is equal to the supply at $p_2$.

If the surplus of a single buyer is larger at $p_2$ and the surplus of sellers is not smaller at $p_2$, can I claim that $p_1$ is an equilibrium? Seems like any buyer would benefit by deviating from $p_1$ and unilateraly setting $p_2$ or $p_2 + \epsilon$. In competitive equilibrium it is assumed that market actors are price takers but if they are sufficiently small (have no bargaining power like a monopoly) then this coincides with their strategic interests. Here even if the buyer is insignificant, this does not hold (probably due to asymmetric information). So is the market in equilibrium with price $p_1$ or not?

Such parameter combinations exist, an example:
$$
n_B = 4, n_Q = 2, n_L = 4
$$
$$
r_{B,Q} = 18, r_{B,L} = 6, r_{S,Q} = 8, r_{S,L} = 5
$$
$$
p_1 = 8, p_2 = 5
$$


texts: Nash Equilibrium and Dominant Pure Strategy when payoffs identical

texts:
What happens if the payoff is the same across strategies? I have some thoughts but I am not sure.

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

Dominant strategy
By definition, a player's strategy X is dominant over his other strategies if strategy X is the best strategy regardless of what the other player chooses as his/her strategy.

For player 1 (Row), is ‘A’ a dominant strategy for player 1? I'm not so sure here. Yes, A is the best response if player 1 plays C, but both A and B are the best responses to player 1 when he plays D. In this case, should strategy A be considered a dominant strategy for player 1?

Same goes for player 2, if player 1 plays A, then player 2 can respond with either C or D. If player 1 plays B, then player 2 respond with C. Can i say C is a dominant strategy for player 2 then?

Nash Equilibirum
Nash Equilibrium is defined such that no other player can do better by unilatarally change his strategy.

Is (A,C) Nash Equilibrium? By definition its Nash Equilibirum since player 1 will not change from A to B since payoff of 0 is not better than 1. player 2 will not change from C to D, since payoff of 1 and not better than 1. (Is this thinking correct?)

Is (A,D) Nash Equilibrium? By definition its Nash Equilibrium since player 1 will not change from A to B since payoff of 1 is not better than 1. player 2 will not change from C to D, since payoff of 1 and not better than 1. (Is this thinking correct?)

Thanks.


texts: Why isn't "long-run aggregate demand (or LRAD)" a thing?

texts:
To give you a sense of where I am in my understanding of economics, I've just learned about long-run aggregate supply in the neoclassical/monetarist view as a vertical curve. It occurred to me why doesn't the same thing that happens to SRAS happen to aggregate demand over the long run - I'm envisioning that prices adjust in the long-run such that prices have no effect on anything; whether supply, demand, or anything else to do with purchasing habits. By the same reasoning as for aggregate supply, it seems like aggregate demand in the long run is also a graphically a vertical line. In the long run, where wages can adjust to match prices, people will continue buying the same quantity demanded as before just with a higher price level, right?

But I'm assuming, from what I've seen, that we don't differentiate between aggregate demand in the long and short run. What knowledge am I missing?

I'm in SL IB economics and we've just reached macro. I also have a shallow understanding of the Keynesian AS curve.


texts:
In Mian, Sufi and Verner (2017), the authors look at the impact of an increase in household debt on both net exports and the current account, and find a significant negative coefficient in the regression specification employed (see Table V).

Why would you look at both the current account and net exports? Wouldn't net exports be the only item of interest in the current account? Why would one care about the impact on transfers, for instance?
I wonder about this further, because they don't include the current account in their working paper version here.


texts: Why does a company want the value of its stocks to be as high as possible?

texts: My professor claims that a company want the value of its stocks will be as high as possible. Why should the company care? The company "minds its own business" and make its money. Why should it cares if the value of its stocks is \$25 or \$300?


texts: When Does a Shift to the Right Happen in the Demand and Supply Curves Simultaneously?

texts:
If, for example, Health Canada issues a public statement that states eating pizza is good for your overall physical health, would this result in both a shift in the demand curve for pizza to the right, and a shift in the supply curve of pizza to the right?

If not, could you give more information on when this would actually happen?


texts: What happens to the billions in Euros that Greece owes if it leaves the Euro

texts: Greeces owes billions of Euros to the IMF and European Union. What happens to those debts if it leaves the Euro? Do the debts get translated into Drachma or can the government just print Drachma to convert to Euros freely?


texts: Monopoly firm's block pricing strategy making max. profit

texts:
I have question about max. profit condition for monopolist block pricing.

I learned that to maximize profit in block pricing, given a linear demand curve function and constant MC, calculate $Q_2(Q_1)$, and $P_S(Q_1)$ then find $Q_1$ maximizing profit and then find $P_1$ and $Q_2$ the $P_2$.

This is what I read from the textbook (Microeconomic, Besanko).

But I heard somewhere that when in following case,

with right-downward sloping $MC$ and $AC$,

Profit maximizing first block price and quantity is $P_1$ and $Q_1$ where $AC=MR$
and second block price and quantity should be $P_2$ and $Q_2$ where $AC=D$

I've thought about this for 1 day and still couldn't get why maximizing condition is like that.


texts: Is money lent by central banks to private banks counted in MB or M1?

texts:
If a bank borrow money from a central bank but keeps it as a reserve instead of lending it to someone else, is it counted in the monetary base (MB) or money supply measure M1, using US definitions ?
Maybe that case just doesn't happen.

EDIT: A related question: if every debt is paid back (including money lent by central banks), does MB remain constant (which could not be the case according to the answer to the previous question) ?


texts:
Consider a market in which there are three firms, all producing the same good. Firm i's cost of producing qi units of the good is Ci(qi)=0 for qi≥0 for each i∈{1,2,3};  the price at which output is sold when the total output is Q is Pd(Q)=max{16−Q,0}, where Q=q1+q2+q3.

Each firm's strategic variable is output and the firms make their decisions sequentially: initially firm 1 chooses its output, then firm 2 does so, knowing the output chosen by the firm 1, and finally, firm 3 chooses its output, knowing the output chosen by firms 1 and 2. Find the equilibrium and outcome of Stackelberg's oligopoly game. List q1,q2,q3

The answer has been stated as (8,4,2)

I understand that we're supposed to use the Best Response functions of the other firms and then move sequentially by first solving the subgame of length 1.
I was able to find the Best Response of Firm 3 in terms of q1 and q2, but I do not understand how we're supposed to move forward with the question using the given Best Response. For a 2 Firm Stackelberg's oligopoly game, we can simply use the Best Response function of the follower firm and use it in the profit maximization function of leader's firm. However, when I repeat the procedure with a 3 firm Stackelberg's game, the results seem inconclusive. Please help me with this problem!


texts:
As I understand every subject has some goals for example in physics one particular goal is to have a unified field theory. Is there any one or more goals of economics. I was expecting the goals should be like 1) Define laws so that basic human needs are fulfiled. 2) Find out laws so that inequality does not increase only. 3) Define laws such that worth of the world remain in a balance this means does not increase only or decrease only, kind of bounded.
Or is there any other goal of economics?


texts: Are the retirement plans insured in the USA? Or the clients of the pension funds can lose their pensions completely in case the pension funds are going bankrupt?


texts: When first differences contradict a regular regression regarding Investment vs Output relationship

texts:
Im doing some research with  some panel data I have on firm output and investment.

I ran two equations.

$$y=\beta_0+\beta_1x+\beta_2x^2+\mu$$
$$\Delta y=\alpha_0+\Delta\alpha_1x+\epsilon$$

in R these equations were prodouced using these commands

   1) lm(output~investment+I(investment^2))
   2) lm(diff(output)~diff(investment))

The first equation had statistical significance on the 1% level, however with the first differenced data statistical significance was lost, and I ended up with rather high p-values as if there is no relationship between the two variables.

What is the interpretation of such results (i.e is there a relationship between investment and output in this data set) and which regression should I use in my research?


texts: What happens to net assets in case of increasing NPAs(Non-Performing assets)?

texts:
The bank's profit is measured as Return on Assets which is the ratio of Bank’s net profits and Net assets.
In case of increasing NPAs, the bank's net profits will decrease, but what will happen to net assets?


texts: Discount factor and deviating from strategy - Game Theory

texts:
I have an exercise in Steven Tadelis Game theory Introduction book (10.2) :
Grim Trigger: Consider the infinitely repeated game with discount factor
$δ < 1$ of the following variant of the Prisoner’s Dilemma:

a) For which values of the discount factor δ can the players support the
pair of actions (M, C) played in every period?
My attempt is:
First, I find the Nash equilibrium of the game (so we know where the player would deviate if not following the proposed strategy):
For the row player we see that Row T and M are dominated by B, so we leave row B and delete the former 2 rows. Then for the column player, we see that the columns L and C are dominated by R, so we leave R and delete the former 2 rows. So our Nash Equilibrium is (B,R) with payoff $(0,0)$.
By a definition in my textbook:

So the expected value of staying with the strategy $(M,c)=(4,4)$ is :
$4+\delta 4+\delta^2 4+....=4\sum^{\infty}_{t=1}\delta^{t-1}= 4/(1-\delta) = 4+4\delta/(1-\delta)$
Now, if the players deviate to $(0,0)$, then they would get $5$ insted of $4$ in the immediate stafe of the deviation, followed by his continuation payoff:
$v_i'=5+0\delta+0\delta^2_+...=5$
For the player to stay and not deviate, the payoff for the first strategy should be higher than the latter strategy (where they deviate):
$$4+4\delta/(1-\delta)\geq 5 \Leftrightarrow \delta \geq 1/5$$
So, for $\delta \geq 1/5$, the players would not deviate.
Would this reasoning/solution be correct?


texts: What is the exact difference between the $\hat{u}$ in PRF vs SRF?

texts:
I've been confused about the exact difference between PRF and SRF is.

I know that it has to do with other variables that influence the regression that is not accounted for, but what is the difference in the models?

PRF: Population Regression Function
SRF: Sample Regression Function.


texts:
In inner cities in the US there is more poverty (as a proportion of the population) than in mid-sized cities or small towns.

Do we have a definitive answer as to why this is?


texts: How is the matching principle implemented with double entry accounting?

texts:
I understand that the accounting matching principle requires incurring the expense in the same period as the revenue.  But I'm confused how one would go about doing this in double entry accounting.

For example, imagine in 2016 I pay a subcontractor \$50,000; and, in 2017, I finish the work and issue an invoice for \$80,000.  Now, since I didn't invoice for the work in 2016, I can't show the 50k as an expense, but rather an asset; only in 2017 do I move it from an asset to an expense.

Does that mean that every expense in the chart of accounts needs to have a matching asset category? For example, if I have an expense "Subcontractor", I need to have an asset "Accrued Subcontractor"? None of the chart of accounts I've seen have such a repetition, and it seems unwieldy and error prone.

And, if I don't have the same level of detail in my Assets as the Expenses, then, when it becomes time to move them from Assets to Expenses, where will I get that information?

If I invoice based on cost-plus-fee, won't I have a chicken and egg problem? When I look at the cost of a project, there won't be expenses until I invoice? So how will the costs show up?

A great example would be to give the general ledger entries for my exact scenario.


texts: I teach a general equilibrium class in my university and I want to have an exercise that is not too difficult where the Lagrangian multiplier is needed. I was under the impression that with Cobb Douglas and 3 goods I could force them to use it but in the end it turned out that they could easily solve it without it. Is there a rule of thumb or an exercise for what kind of problems force students to use the Lagrangian? To be clear, I want an example with exchange.


texts: What is the purpose of the Treasury issuing bonds?

texts: I have always thought that the US Treasury issues bonds to raise money to allow the US to pay off debts in the short- and long-term. However, recently, I have read in a book on Modern Monetary Theory that that is not the purpose of bond issuance by the Treasury. In fact, the Treasury issuance of bonds serves the purpose of aiding the Fed in conducting monetary policy. May I know if this is the case? If that is the real purpose, then what then does the Treasury do to raise money to pay off US debt?


texts:
When a country make too many of their currencies, it will eventually lower the currencies' value and inflation would occur.

But why won't key currency work like this? If the US is making more and more money, shouldn't the value get lowered at some point? Where did all that amount of money which has been coming out of US go? Is it because the world is still growing even now, and the circulation needs more and more Dollars constantly?


texts:
GDP calculated using expenditure apporach is like this:
GDP=C+I+G+(X-M)
However on this site:
http://www.singstat.gov.sg/statistics/visualising-data/charts/share-of-gdp-by-expenditure

The data is avaialable for C, G and net exports, but there are two variables: Gross Fixed Capital Formation and Changes In Inventories. Since there is no 'I' variable, can I assume that the sum of those two variables are equal I?


texts: Envelope Theorem in Keen and Slemrod (2017)

texts:
This question pertains to the paper "Optimal Tax Administration" by Slemrod and Keen (2017). The IMF working paper is freely available on SSRN, however, it is not necessary to know the paper in order to understand the question.

I am confused on how to arrive at equation (5) in the working paper version.

Suppose there is a welfare function:

$W(t,\alpha)= wl - tz(t,\alpha) -c(e,\alpha) - \psi(l) + v(tz(t,\alpha) -a(\alpha)) $

Here, $v$ is an increasing and concave function, $\psi$ is an incresing and convex function, $t$ is the tax rate, $\alpha$ is tax enforcement, $c$ is evasion/compliance cost and $z$ is declared income, which depends on $t$ and $\alpha$.

Declared income is given by $z=wl(t,w) - e(t,\alpha)$, where $w$ is the wage rate, $l$ is hours worked and $e$ is concealed income. Both $l$ and $e$ are derived optimally.

The first order conditions for $l$ and $e$ are given by:

$(1-t)w - \psi'(l) = 0$

$t - c_e(e,\alpha) = 0$

Here $c_e$ denotes the derivative of $c$ with respect to $e$ and $\psi'$ is the derivative of $\psi$.

I am interested in $\frac{dW}{dt}$.

The author's invoke the envelope property to arrive at:

$\frac{dW}{dt}= -z + v'*(z + tz_t)$

Here $z_t$ is the derivative of $z$ with resprect to t and $v'$ is the derivative of $v$.

How  can I arrive at this expression?


texts: Can someone please explain the concept of absolute advantage with an example? I know it has to do with the fact that a nation should produce a commodity that is cheap relative to other commodities but I don't really understand the concept.


texts: Negative Externality with Tax and Free TRade

texts:
I am unsure of how to think about this negative externality question when there is both tax and free trade.

A country is producing plastic, but it has a negative externality cost of 4 dollars/bottle. The demand is $Q_D=12-P$ and the supply is $Q_S=P$. If a 4 dollars/bottle tax is enacted and the country is opened up to free trade with a world price of 4 dollars, what would the total social surplus be? Based on my calculations, it would be 24 dollars, just the same as when the country has no tax and is open to free trade. Is this correct thinking? Or am I not thinking about the tax and free trade correctly? Thanks.


texts: What does it mean to have a strictly increasing transformation in consumer theory?


texts: Becker Social Pricing and Lack of Smooth Demand

texts:
I was reading an article on Becker Social Pricing, where your demand for a good depends on other people's demand for the good. So basically this paper is meant to be a primer into explaining why some places price in such a way that they have chronic shortages (think of big concerts or popular restaurants). I think the idea is that seeing many people want to attend this event actually is part of what contributes to this high demand for the good, and the demand is not convex.
Since demand is not convex, as in Walrasian smooth demand, (if of course I am interpreting this model correctly), then how do utility maximization problems work here, say, if we had two goods that followed this model? Assuming we still have Kuhn-Tucker sufficiency, would we just set up a Lagrangian as normal, or are there some stronger conditions we need to make sure a maximum exists?


texts:
This is an excerpt from a data source that I am using. According to the authors it has been created from accounting identities such that it matches theoretical variables used in macroeconomics.

For example, they state that the consolidated government constraint is:

$T_t + S_t + \Delta B_t^p = G_t +I_t + i_t B_{t-1}^p$

Where $T_t$ is tax revenue, $S_t$ is seigniorage, $B_t^p$ is government debt owned by the public, $G_t + I_t$ is government spending on consumption and investments and $i_t B_{t-1}^p$ is interest payments to the public. This is inline with government constraints I have seen in textbooks. However, when I use their data, I cannot seem to get correct numbers.

For example, consider $t = 1802$:

$T_t = 9844$,
$S_t =813$, $G_t + I_t = 7096 $, $i_t B_{t-1}^p = 1083$, $\Delta B_{t}^p = 23406 - 22243$ and clearly the number do not add up.

However, when I calculate the consolidated deficit ($G_t +I_t + i_t B_{t-1}^p -(T_t + S_t))$ I get something very similar to $DEF_t^c$.

So I am quite confused as to what I am doing wrong. My only guess is that it has to do with the timing notation. I.e $\Delta B_{t}^p \neq B_{t}^p - B_{t-1}^p$.
Any ideas on what I am doing wrong?


texts: Show that if $\succsim$ is continous on $X$, then the sets $ \precsim (x^0)$ and $\succsim (x^0)$ are closed

texts:
For a set to be continuous, it's contour sets must be closed. Since we can define $$ \succsim x^0 = \{x, x^0 \in X: x \succsim x^0 \} $$ and $$ \precsim x^0 = \{x, x^0 \in X: x \precsim x^0\}$$

it can be seen that $\succsim x^0$ is the upper contour set of $X$ and $\precsim x^0$ is the lower contour set of $X$. Therefore, if $\succsim$ is continuous on $X$, it must the case that both $\succsim x^0$ and $\precsim x^0$ are closed sets.

Is my answer correct?

Edit: definition of continuous preference I'm using:


texts: Using web scraped data for consumer price indices

texts: Is there information and literature regarding comparative consumer price index methods? Specifically, the web scraping method of index construction?


texts: One common definition of recession is "two consecutive quarters of negative GDP growth". GDP growth affects other variables, such as stock prices, interest rates, unemployment, and personal income. Has research found there to be a nonlinearity such that GDP growth falling from 0.5% to -0.5% has a bigger effect on other variables than GDP falling from say 1.5% to 0.5%?


texts: What does it mean when someone says “2 trillion wiped off markets”?

texts:
After a major global event, sometimes the markets move and headlines are written saying something like “2 trillion wiped off markets”. But what does this actually mean? Does it mean the aggregate value of companies on the exchanges has been reduced?

After Brexit similar headlines were generated, has the market recovered its value yet?


texts:
Let $f_1, f_2$ be two smooth strictly-quasiconcave functions.
  Do there always exist monotone transformations $g_1,g_2$ such that the sum
  $g_1\circ f_1 + g_2 \circ  f_2$ is a strictly-quasiconcave function?

While this question is mathematic, its motivation is economic. Given two people with strictly-convex preferences, we would like to represent their common preferences by a social welfare function. One natural way to do this is to represent each person's preferences by some strictly-quasiconcave function and take their sum. However, the sum of strictly-quasiconcave functions is not necessarily quasiconcave. So it is interesting whether we can always find specific representative functions such that the sum is quasiconcave?

I already know that, without the "strictly", the answer is no. Here is an example:

Both functions are weakly-quasiconcave. When one function is increasing, the other is flat, and when the other is decreasing, the first is flat. Therefore, regardless of what transformations we apply to them, the sum will look like a wave and will  not be quasaiconcave.

Note: I asked this question on MathOverflow some time ago. Taneli Huuskonen came up with the negative example for weakly-quasiconcave function, but the question for strictly-quasiconcave function is still open. Due to the economic importance of quasiconcave functions, I thought someone here might have an answer.


texts: Understanding the “Treasury auction results” press release

texts:
This is the press release for a recent 30-Year bond auction results:
https://www.treasurydirect.gov/instit/annceresult/press/preanre/2020/R_20201112_5.pdf
I cannot figure out how the price is calculated. It is not the coupon divided by the yield. So what is it?


texts: Labor theory of value examples and exercises

texts: I'm looking for a working book of Marx's Labor Theory of Value. It would be nice if the book would explain his theory with calculated examples and some exercises with solutions that one can do. Since I'm a German I could read The Capital for myself, but I find it too complicated. Any good books on this?


texts: How are shell companies used for tax evasion?

texts:
The recent release of leaked documents on Mossack Fonseca has information on corporations and individuals using the firm's services for, among other things, tax evasion:

The massive security breach shows how a global industry of law firms and big banks sells financial secrecy to politicians, fraudsters and drug traffickers as well as billionaires, celebrities and sports stars. [...]
Using complex shell company structures and trust accounts Mossack Fonseca services allow its clients to operate behind an often impenetrable wall of secrecy. Mossack Fonseca's success relies on a global network of accountants and prestigious banks that hire the law firm to manage the finances of their wealthy clients.
Panama Papers and Mossack Fonseca explained, Australian Broadcasting Corporation

What are "shell companies" and how can they be used to hide money or avoid paying taxes?


texts: Repositories for working papers in economics and finance

texts:
I would like to post my working paper (broadly defined as theoretical work in finance) on a repository.

Goals

Primary: to get a time stamp for a new idea that I have, such that I could establish the authorship and the date.
Secondary: to get some attention to my new idea, receive comments and discussions, so that I could improve the paper.

Conditions

I would like to be able to post the paper myself and to have good control over updating it when I wish to, provided that a track record is kept (see my primary goal).
(The reason for focusing on easy updates is that the paper is still rather preliminary and changes will be needed. You could say, I should finalize it first and submit only then, and I get the point. But it has been sitting around for too long, and I do not want the idea in it to get stale. Perhaps receiving good comments on the preliminary version will quicken my progress.)

Situation so far

I have considered posting it in my institution's working paper series, but that process goes through a secretary which is always busy and would not normally accommodate requests of updating the paper in a timely manner.
I have considered posting it on my own website, but then I do not get an official time stamp on the idea, and the visibility is low.

What could you recommend?


texts: Why would China and Russia selling the US' debt ruin the economy?

texts: I was listening to an interview with David Harvey and he mentioned that if Russia and China were to sell the debt owed to them by the US, the US economy would take a serious dive. How would they sell the debt and why would that impact the US economy so negatively?


texts:
Consumer 1: $U_1(x_1,y_1)=x_1y_1$
Consumer 2:$ u_2(x_2,y_2)=min\{x_2y_2 , 4\} $
Initial endowments e1=(1,4) and e2=(4,1)
I want to find Pareto optimal allocations and show its edgeworth box
My solution
First I solve utility maximization
For consumer 1,
$MRS=P_x/P_y$ And budget constraint $x_1P_x + y_1P_y= P_x+4P_y$
$x_1^*=(P_x+4P_y)/2P_x$
$y_1^*=(P_x+4P_y)/2P_y$
For consumer 2
At optimum, $x_2y_2=4$
Budget constraint $x_2P_x+y_2P_y= 4P_x+P_y$
Then $x_2[(4P_x+P_y)/P_y -P_x/P_y x_2]=4$
Feasibility constraint
$$x_2=5-x_1$$
$$y_2=5-y_1$$
Then I solve together
$$(5-x_1)(5-y_1)=4$$
When I insert $x_1$ and $y_1$ I will obtain
$$(9P_x-4P_y)(6P_y-P_x)=16P_xP_y$$
From this point I cannot proceed the solution
How can I find the Pareto optimal allocations ?


texts: Can marketing efforts be considered to be a factor of production?

texts: This is a sightly unconventional question, but I want to know whether marketing efforts can be considered as a factor of production. After all, if no one knows about your product, you can't make a profit. Also, marketing efforts may, in some or most cases, show diminishing returns. It is a kind of labor.


texts: I understand the concept of creation of wealth through trade, innovation, labor and capital. New value is being added to the economy. Let's imagine for a second that there are no central banks and the money supply is constant. This would imply that even though one can create wealth and add value to the economy the money would just be changing hands, meaning in order for one individual to get richer another would have to get poorer. We all know that in the real world central banks print money (I am ignoring inflation, nevertheless that's not the point) but that isn't the problem as far as I can tell. The current rebuttal of my example is that even though no new money is being created somehow the pie gets larger so everyone can get a larger slice. But how exactly does this process of expanding the pie happen? I can't grasp my head around the idea that the pie can enlarge while the money supply is fixed. I guess that's the same problem mercantilists had back in the 16th and 17th centuries.


texts: How are real income and utility the same thing?

texts: The textbook I'm using, "Microeconomic Theory: Basic Principles and Extensions", treats utility and real income as the same thing in the chapters on compensated and uncompensated demand. I would like to understand the logic behind it. To me real income always meant "Nominal Income/CPI" but I don't think this can also be translated to utility.


texts: Why do Reserve Banks only move in 0.25 basis point 'leaps'

texts:
It seems to me that a lot of uncertainty is created by Reserve Banks spending 5 months telegraphing "I'm gonna do it, I'm gonna raise rates", as is currently seen in the USA.

This seems to be the case where everyone knows the rate is wrong, but changing it quickly will cause shocks.

Instead of waiting 5 months and then increasing by 0.25%, why not increase by 0.05% every month for 5 months? Or smaller amounts if that is required.


texts: Predicted recessions that never happened

texts:
It seems generally accepted that recessions are hard to forecast, in both onset and intensity, but the bias seems to be toward rosy outlooks:

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

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

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


texts:
I'm currently trying to solve the following problem:

  Stackelberg with 3 firms Imagine there are three firms on a  monopolistically competitive
  market. The marginal cost of produc- tion in each firm is c. The
  demand is $p(q) = A − Bq$. The leader makes a production decision $q_1$,
  then two followers make a simul- taneous decision about their
  production levels $q_2$ and $q_3$. Calculate the quantity produced by firms
  in this economy, and compare it to Cournot outcome with 3 firms and to
  Stackelberg outcome with 2 firms.

My Workings

I've tried to solve the problem using the following method:

Leader ($q_1$)

$$\begin{align} profit(q_1,q_2,q_3) &= (A - B(q_1+q_2+q_3))q_1 -cq_1 -F \\
& = Aq_1 - B(q_1+q_2+q_3)q_1 -cq_1 -F\\
& = Aq_1 - Bq_1^2 - Bq_2q_1 - Bq_3q_1 - cq_1 -F\end{align}$$

The I took the derivative in regards to $q_1$ leaving me with this:
$$profit(q_1,q_2,q_3)= A - 2Bq_1 - Bq_2 -Bq_3 -c$$

Finally I just tried finding $q_1$:

$$q_1 = \frac{A-C-Bq_2-Bq_3}{2B}$$
To put $q_1$ into the equation and solve it for $q_2$ and then $q_3$

The Problem:

The begining of the solution in the answer sheet looks like this:

  Solution For Stackelberg with two followers, after firm 1 made its
  move, agents 2 and 3 are making their move simultaneously knowing q1.
  So, both firms 2 and 3 maximize

$$profit(q_i) = (A−B(q_1 +q_2 +q_3)−C)q_i ⇒ q_2 = q_3 = \frac{A − C}{3B} − \frac{q_1}{3}$$

Question:
as you can see my workings look nowhere near the answer, I've tried solving the problem using there method but I don't really understand were the $3$ in $3B$ comes from? and why are we using $q_i$? (also I don't quite understand why the method I used is incorrect)

Thank you very much for your help!


texts: How do we define an efficient tax in microeconomics?

texts:
I am currently working through problems to study for an upcoming exam. I am not seeking a solution per se. I am looking at the intertemporal choice model. I am looking at two periods where consumption in each is normal. Let $y_1, y_2>0$ be fixed endowments and $p_1=p_2=1$ be the prices of consumption in periods $1$ and $2$, respectively. Denote consumption by $c_1$ and $c_2$. Using the Slutsky Decomposition
$$\frac{\partial c_t}{\partial r} = \frac{\partial h_t}{\partial r} + \frac{\partial c_t}{\partial W_1}\frac{(y_{1}-c_{1})}{1+r}$$
where $W_1 = y_1 + \frac{y_2}{1+r}$ is the net present value of wealth, $r$ is the interest rate, and $(y_1 - c_1)$ represents savings if positive, and borrowing if negative. The individual has access to capital markets in this respect.

We are given that for a drop in the interest rate, the person's consumption for $t=1$ does not change which (w/o proof) implies that the person is a saver.

The next part of the question states

  suppose the drop in interest rate is due to the introduction of a
  capital gains tax without deductibility of capital losses. Given the
  person's behaviour above, is the tax efficient? Prove your answer
  graphically.

So this gives us a situation where only the portion of the resource constrain such that $c_1<y_1$ (individual is a saver). This gives a piece-wise resource constraint. Since there is no compensation mentioned, I assume the welfare measure to be used is Equivalent Variation (EV). My question is, how would we define whether a tax is efficient?

Would it be efficient if the Deadweight Loss is equal to zero? Or is it related to how large the tax revenue would be relative to EV? The answer to this question will give me enough information to be able to display this graphically.


texts: Why does the nominal interest rate equal 25% in this problem, instead of 16.4%?

texts:
My reasoning: The nominal interest rate = the real interest rate + the expected inflation rate. We need to calculate the nominal interest rate. We know the expected inflation rate, so the only problem is to calculate the real interest rate. In order to calculate the real interest rate we need to see how much money received is more than money given. And due to inflation we need to adjust the initial sum to inflation. 110 - 100*1.03=7, this is inflation-adjusted amount of money by which Daenerys will become richer. In order to calculate the real value we need do following: 7/110=0.0(63), which is about 6.4%. Thus the nominal rate equals 6.4+10=16.4

Here is the offical answer, but I'm afraid it doesn't make sense:


texts:
I am going through some micro concepts and I am confused, is there a difference between deriving preferences through indifference curves and actual preferences of the consumers?

The question I was going through was:

Jim's utility function is $U(x; y) = xy$. Jerry's utility function is $U(x; y) = 1,000xy + 2, 000.$ Tammy's utility function is $U(x; y) = xy(1-xy)$. Oral's utility function is $-1/(10+xy)$. Billy's utility function is $U(x; y) = x/y$. Pat's utility function is $U(x; y) = -xy$.

(a) No two of these people have the same preferences.

(b) They all have the same preferences except for Billy.

(c) Jim, Jerry, and Pat all have the same indifference curves, but Jerry and Oral are the only ones with the same preferences as Jim.

(d) Jim, Tammy, and Oral all have the same preferences.

(e) There is no truth in any of the above statements.

The answer apparently is C, which implies that even though Jim, Jerry and Pat have the same indifference curves, The preferences of Pat and Jim are different, while those of Oral and Jim are the same even though they have different indifference curves. How is that possible?


texts: What is used for calculating equity multiplier between total liabilities and total debts from Datastream?

texts:
Equity multiplier=Total Assets/Total Equity
But I did not download the Total Equity but Total Liabilities and Total Debt from Datastream. Therefore I think of calculating Total Equity by using Total Assets minus Total Debts.
Datastream's definition of these two items:
WC03255 - Total Debt: TOTAL DEBT represents all interest bearing and capitalized lease obligations. It is the sum of long and short-term debt.
WC03351 - Total Liabilities: TOTAL LIABILITIES represent all short and long-term obligations expected to be satisfied by the company.
It seems that Total Debt is the better choice, but whether Total Liabilities is an acceptable alternative for Total Debt in calculating the Equity Multiplier as above?


texts:
I have $P_1 = 24$, $Q_1 = 800000$, $P_2 = 32$ and price elasticity $e = -8$ and need to find the function $P(Q)$.

I guess I need to find $Q_2$ by

$$
\frac{(Q_2-Q_1)/Q_1}{-(P_2-P_1)/P_1} = -8 \Leftrightarrow Q_2 = \frac{8800000}{3}
$$

But does it make sense that the quantity will be so much higher by a price increment and thus not follow the law of demand? I know that $e = -8$ is a high price elasticity but this is quite extreme I think.


texts: What are the best theoretical or empirical defenses of equilibrium analysis in economics?

texts:
An Anarchist FAQ (see Wikipedia page here) focuses its opposition to mainstream economics by criticizing equilibrium analysis. The FAQ notes that,

[Equilibrium analysis] is essentially a static tool used to analyse a dynamic system. It assumes stability where none exists. [...] Thus the whole concept is an unreal rather than valid abstraction of reality. Sadly, the notions of “perfect competition” and (Walrasian) “general equilibrium” are part and parcel of neoclassical economics. It attempts to show, in the words of Paul Ormerod, “that under certain assumptions the free market system would lead to an allocation of a given set of resources which was in a very particular and restricted sense optimal from the point of view of every individual and company in the economy.” [The Death of Economics, p. 45] This was what Walrasian general equilibrium proved. However, the assumptions required prove to be somewhat unrealistic (to understate the point).

[...] Given that general equilibrium theory does not satisfactorily encompass such things as profit, money, growth, instability or even firms, how it can be considered as even an adequate representation of any real capitalist economy is hard to understand. Yet, sadly, this perspective has dominated economics for over 100 years. There is almost no discussion of how scarce means are organised to yield outputs, the whole emphasis is on exchanges of ready made goods. This is unsurprising, as this allows economics to abstract from such key concepts as power, class and hierarchy.

As for the argument about using unrealistic assumptions in economic models, I'm aware that Milton Friedman had written a defense of that practice in his Essays in Positive Economics. However, I am unaware of any work addressing the specific critiques of equilibrium analysis cited in An Anarchist FAQ, or defending equilibrium analysis in economics from a philosophical, or empirical perspective.


texts: what is the optimum level of production?

texts:
The demand function of a monopolist is $q = 12 - p$ where $p$ is the price. Using the total cost and total revenue I was trying to calculate the optimal (short term) level of production.

I tried to solve it using the total revenue $r = p x$. Then I calculated the marginal revenue (the derivative of total revenue) and set it to $0$.
Then I got $p = 6$ and $x = 6$.

However, I never used the cost function, what did I do wrong?


texts: Micro/Macro estimates on Price rigidity(calvo parameter)

texts:
I'm looking for current references on the estimates of price rigidity, and the dichotomy that seems to exist between the micro and macro estimates.

For example, for labour supply elasticities there's a 'recent' review by Chetty, et al, from 2011.

I'm looking for something similar for the new keynesian modelling. I've found the Bils and Klenow (2004), but I would like something more recent.

Any help would be appreciated.


texts: A buyer wants to buy contiguous land plots from three landowners (sellers) who own fixed size plots. Sellers have their private valuation of their plots. The buyer will hold a closed bid procurement auction. The profit for the buyer is greater if he purchases all plots of land as compared to (any) 2 plots(without any specific order), which itself is greater than profit for a single plot. Does someone have an idea of how strategies will be developed for the sellers (in equilibrium)? I will later extend it to multiple rounds reverse auctions.


texts: Is a smartphone app(Non premium or subscribed service like Netflix) a public good?

texts:
A smartphone app that provides users with information on surf conditions at their location. (“Surf conditions” refers to information on wind, waves, and ocean tides that is useful for surfers).
For this I assume the consumption here is strictly the info on the app also assuming the app is free anybody can use it (like google maps). This is a pure public good then. First. they are non-rival in consumption that is my consumption of the app does not in any way affect other people to use the app as well. Even if a million people is using the app, no one will be affected since the consumption here is only the info. It can be opened simultaneously by many user, and adding more users does not affect any of the users on using the app. Second, they are non-excludable, even if I want to deny someone else to use the app there is no way I can do so. Anybody can download the app and it will be really difficult to ban people from downloading the app
That is my answer.
My professor said the app is excludable. Am I correct to say that the app is non-exlucludeable? My logic behind it was a free app is always non-excludeable since there is always a workaround to accessing/downloading the app. For example a certain app that is not available for a specific region, you can always use a VPN to access/download it. If it is a premium service on the other hand, I completely agree that the it is excludable, however the professor has confirmed that the reasoning behind it being excludable doesn't have anything to do with it being a premium service.
Here is the professor's answer
It is, however, excludable because the app provider can limit you from downloading it to your phone.
1)This example is similar to the Netflix option, where Netflix can deny users access to the streaming service.
2)The definition for excludability it “it is possible to deny someone the opportunity to consume it.” It is possible to deny someone the opportunity to consume the app (no matter what they do, like owning the right smartphone) because it is possible for the app designer to restrict your ability to download the app. As for paying for it, that is a resultof the app being excludable. If it were a public good, the app design could not get people to pay for it.


texts: Difference between merchandise trade and trade in goods?

texts: What is the difference between merchandise trade and trade in goods? Are they the same? If so, would total trade be just trade in goods + trade in services, aka merchandise trade + trade in services?


texts:
Which of the following best explains how an economy can experience stagflation.

Women and teenagers stayed out of the labor force.
Negative supply shock cause the factor prices to increase.

Official answer : 2.

My thoughts: While 2 is correct, I think 1 is also correct. the fact the  women and teens stay out of the labor force will increase the wage and thus cause the supply curve to shift to the left and thus cause stagflation. Am I wrong?


texts: Defining a Competitive Equilibrium for a two Period Model

texts:
Consider an economy that lasts for two periods populated by a representative consumer/worker, a representative firm, and a government. After these two periods, the economy ends.

The question asks me to
- Define a competitive equilibrium for this economy.
- Show the demand and supply curve in a diagram with variables (r, Y ).
- Show the effect of an increase in the current capital stock K.
- Compare the equilibrium path with the case in which workers have a preference shock that reduces the disutility from work h − l in period one. Preferences are back to normal in period 2.

My Problems I am so confused: what are the steps to defining a competitive equilibrium? Do I just rewrite what competitive equilibrium is from the lecture notes, or do I have to define one from the problem above?

Also, there are a lot of variables with no numbers. I am very confused to how to approach a question with no numbers.


texts:
You probably are familiar with Malthus' Theory of Population Growth.

If you are not, Malthusian model has the following mathematically form:

$$P(t) = P_0e^{rt}$$

A basic graphic representation is:

Note that population is growing in a exponential form where as the resources are growing only linearly. By resources, I do not only mean food resources, but they also include water, energy, land and anything else that support the continuation of expansion of human societies.

Malthusian theory of population growth has been subjected to criticism, mostly, IMHO,  a reaction for the theory being too pessimistic.

But let's have a look at the real population growth for the past couple of thousand years:

Now, let's smooth the graph out:

Do you see what I see?

Still not convinced? Let's zoom in for the more recent times (vertical axis is in billions):

Those are the figures from wikipedia, on which I have calculated percentage change per five years:

Note that even at the current stage, we are still at an above the average trend for over the past 211 years (since 1804 when the world population hit 1 billion):

$$1.0095^{211} = 7.35$$

There are, currently 7.35 billion people on earth.

The average of annual population increase is 0.95% per year, but we are increasing at a rate of more than 1% per year.

Is Malthusian theory of population growth being realized? If this is true, are we going to hit the point of crisis soon because of the limited resources?

If not, why not?

Please support it with number and figures, I would appreciate a more scientific than opinion based discussion.


texts: When do workers versus capital owners share of income increase?

texts:
The share of total income obtained by workers rather than capital owners is for obvious reasons of interest. Assuming that the economy can be desribed by an aggregate production function
$$Y = F(K,L)$$
where $K$ is capital input and $L$ is labor input the total expenditure on labor and capital is given as
$$pY = rK + wL,$$
where $p$ is output price, $r$ is user cost of capital and $w$ is the wage (perfect competition is assumed on all markets). Labors share of total revenue or expenditure is therefore given as
$$s_L := \frac{wL}{pY} = \frac{wL}{rK + wL},$$
depending only on $w,r,L,K$.
The elasticity of substitution is defined as
$$\sigma := - \frac{d\log(K/L)}{d\log(r/w)},$$
describing how the capital to labor ratio changes given a change in the ratio of user cost of capital to wage.
Since both labor share of expenditure and elasticity of substitution depend on the variables $w,r,L,K$ this suggest the question:
How does changes in labors share of income $s_L$ as a result of changes in relative price $(r/w)$ relate to the elasticity of substitution $\sigma$?


texts: Constant Elasticity of Substitution (non-special cases)

texts:
I am trying to better understand the CES function:

$$Y_{t}=C\left[\pi\left(A_{t}^{K} K_{t}\right)^{\frac{\sigma-1}{\sigma}}+(1-\pi)\left(A_{t}^{L} L_{t}\right)^{\frac{\sigma-1}{\sigma}}\right]^{\frac{\sigma}{\sigma-1}}$$

I understand the special cases where $\sigma=1$, where $\sigma=0$ and where $\sigma\rightarrow0$.

I am, for some reason, having a really hard time developing intuition for other cases. Don't the exponents cancel for all other values of $\sigma$ and the expression reduces to:

$$Y_{t}=C(\pi(A_{t}^{K} K_{t}) +(1-\pi)(A_{t}^{L} L_{t}))$$

This, of course, can't be right as $Y_t$ should vary for different values of $\sigma$, no?


texts: Why are Canadian provinces' debt-to-GDP so much higher than the US?

texts: By the current account, the highest debt-to-GDP state in the US is NY, which is around 23%, with most states around 18%. By comparison, Canadian provinces tend to have much higher ratio, with Ontario at around 37% and Quebec over 40%. What accounts for this? Are the Canadian provinces responsible for distributing social benefits that would be under the federal jurisdiction in the US which skews up their %? Or are they just spending more irresponsibly than the US?


texts: Permanent Income Hypothesis - Changes in r

texts:
I want to analyze the changes in the interest rate $r$ when dealing with the permanent income hypothesis. First of all,

$r$ is the interest rate $0<\beta<1$ is the discount factor, $Y_t$ is the labor income for period $t$, $A_t$ is the net asset wealth, $C_t$ is the consumption in the period $t$.

Now the Euler equation comes up :

$$u'(C_t)=\beta(1+r)u'(C_{t+1}) \ \  (*)$$

And If we assume $\beta(1+r)=1$ (We are going to be assuming this all the time when we are doing our analysis (closed economy)). Then:

Consumption in each period equals to each other (derived from the Euler equation) and it is equal to :

$$C = \frac{r}{1+r}(A_0+\sum_{t=0}^{\infty} (\frac{1}{1+r})^t Y_t )  \ \ (**)$$

I'm not gonna go through the details of how the equation $(**)$ is derived, since it will distort the scope of my question here.

Now Clearly It could be observed that when the interest rate $r$ increases, we use the $eq(*)$ to identify the substation effect and $eq(**)$ to identify the income effect. Substitution effect could be identified easily by using the fact that $u''()<0$

However when identifying the income effect there are two cases :

$(1)$ Consumer is saving
$(2)$ Consumer is borrowing

When looking at the case $(2)$ I could easily show that consumers that are borrowing will decrease their consumption for all periods if the interest rates increase (Intuition = formula)

However if Consumer is saving:

Then $A_0 >0$ So $$ A_0 \frac{r_2}{1+r_2} > A_0 \frac{r_1}{1+r_1}$$

Where $r_2$ is the new interest rate. However, We need to look at the change that occurs for $\sum_{t=0}^{\infty} (\frac{1}{1+r})^t Y_t$ when the interest rate increases. However this decreases with a higher $r$. Since the change in $A_0 \frac{r}{1+r}$ and $\sum_{t=0}^{\infty} (\frac{1}{1+r})^t Y_t$ act in opposite directions, I couldn't show whether $C$ would decrease or increase. (i.e I couldn't show that $intuition = formula$)

Any help?


texts: What is the relation among "welfare economics", "institutional economics", "environmental economics" and "neoclassical economics"

texts:
I'm doing research about environmental economics, being myself a beginner in the subject.

I got confused with the branches and subdivisions of the schools of thought.

Is environmental economics a branch of welfare economics or institutional economics, and how is this related to the neoclassical school?


texts:
In The Wind of Change: Maritime Technology, Trade and
Economic Development (2015), Pascali estimates various effects on freight rates (i.e. the cost of transport) on outcomes such as trade volumes and economic development. To do this, he exploits a kind of natural experiment that results from the fact that different shipping routes benefit in different ways due to the preexisting wind patterns (i.e. those with wind flows against the route direction).

I guess this controls for demand for shipping, so that freight rates are exogenously affected by transport times. But I don't understand why this is needed to estimate the effects of shipping technology. Isn't the invention of the steamship itself an experiment that allows you to see the effects of shipping technology on trade volume? Why is this additional variation due to asymmetric benefits needed?

A typical regression equation used by him is the following:


texts: Stationarity of log industrial index and log CPI

texts: I'm looking to estimate a VAR, one of the variables in this VAR is the log of industrial production, and another is the log of the consumer price index. Will I need to difference these to get consistent estimates? Or will leaving them as is be fine?


texts:
If a country's central bank prints money, it causes inflation. However, apparently, small amounts of inflation is a good thing.

Why is the case? What would happen if central banks stopped printing money altogether (except to replace destroyed bills)?


texts: Heuristics with time series measured in dollars

texts: Suppose the price indexes are adequately measured and there are no problems regarding the data in itself. By my experience, using a sector price index -- for the industry sector that you might be analyzing -- is more adequate than a more general price index for deflating the series. But there could be a situation in which it is more adequate to use a more general price index than a sectoral price index for deflating the variables?


texts: What is the effect of currency depreciation on import prices?

texts:
In Macroeconomics: A European Perspective (3rd ed., Blanchard, Amighini and Giavazzi), when discussing the reason for differences in the GDP deflator and the HICP for the EU, it states the following on p. 32:

In 2005 and 2006, the increase in HICP was significantly smaller than the increase in the GDP deflator. The reason is not hard to find. Recall that the GDP deflator is the price of goods produced in Europe, whereas the HICP is the price of goods consumed in Europe. This means that when the price of imported goods decreases or increases less relative to the price of goods produced in Europe, the HICP increases less than the GDP deflator. This is precisely what happened in 2005 and 2006. The euro depreciated by about 10% vis-à-vis the dollar. This made imports by the EU cheaper than before. The result was a large increase in the GDP deflator compared with the HICP.

My question: is the bold section correct?
My reasoning to the contrary is a follows. If the euro depreciates, then it can purchase less dollars than before, and so imports become more expensive. Suppose yesterday, €10 = \$20, but today, €10 = \$15 (so depreciation has occurred). Then, I needed €30 yesterday to buy \$60 worth of goods, but today I need €40 to buy \$60 worth of goods, and so imports by the EU are more expensive than before. I have no background in economics and am trying to learn introductory macroeconomics, so I have no idea if my interpretation of depreciation is even right. Otherwise though, I think there are a lot of errors in this textbook - incorrect regression equations, incorrect references etc. Has anyone else used the book and found this?


texts:
I took statistics class years ago in my college and I don't remember much of it now. I am into public policy research now and I am bit confused about about what conclusion to make from available evidence.

Poverty is the 'root cause' of child labour is what is claimed by International Labour organization (ILO) and thus by lot of other countries. Evidence often cited for this is: most of the child labourers are from poor backgrounds in most of the countries where child labour is prevalent. So there is a correlation and for causality, if we think about it, no money => to earn money => all healthy individuals must work including children => child labourers.

Now I've read few research studies which claim that Poverty is not the root cause of child labour and the evidence they cite is,

There are poor countries where there is hardly any child labourers.
There are children studying in schools who are lot more impoverished than those who are working.
There doesn't exist a poverty line below which a parent is compelled to send their child to school.

So people on this end say, if poverty is the root cause then could we explain this. But this argument could be reversed too. Either way, I'm confused.

How should I go about interpreting and understanding this?

What data is required, and what analysis has to be carried out to settle the question, whether poverty is the cause or not? In other words, I want to set my hypothesis to be "Poverty is not the root cause of child labour", what should I do to either prove or disprove it?

I want to see this to the end. So feel free suggest some readings if you need to.


texts:
I am considering a regression discontinuity design (RD) where the "treatment" has a definite sorting rule (below the threshold, you are not fined - above the threshold, you are fined). The outcome I am considering is how much you are fined the FOLLOWING year. There are 4 options: 1) remain without a fine, 2) go from no fine to fined, 3) fined less than you were the previous year, or 4) fined more than you were the previous. While I have listed these as categorical, I have the continuous amount of the fine as well.

Here are my questions:
1.) I have never seen a "longitudinal" RD design where the treatment is at a time period before the outcome. Are there any methodological issues with this approach?
2.) Assuming this approach is valid, how best should I model the outcome given the multiple possibilities?

Thanks in advance for any advice!


texts: Does PPP measure conversion taken into account government service and taxes?

texts:
Apology in advance if this question seems too elementary. I am intrigued by this article I came across,Do We Care About Income Inequality, or Absolute Well-Being?

And in the article the author was trying to make a percentile by percentile comparison, which is very interesting, but I am slightly skeptical about the conclusion the author was trying to drive at. The concept of PPP is conceptually pretty straight forward, but unfotrunately I can't find the detailed construction methodology on World Bank. What I am trying to figure out is this: in the price level calculation, how did the economists taken into account the almost zero education and healthcare cost of some wellfare states.  The charts cited states that tax and transfer was taken into account, but I am not sure if it means only direct transfer or if it includes service provided like education and healthcare. I think to most people, a tin of coke cost twice as much in Europe for example,  probably won't affect their living standard significantly; But say the off-the-chart private school tuition fees would significantly influence one's living standard, assuming one has children. I wonder if the PPP income level taken that into account? Please note I just want to know the facts, not political ramble.  I also would appreciate if someone could provide some additional resources on this topic.


texts: Lagrangian: when to discount budget constraint?

texts:
I am getting a bit confused about setting up the Lagrangian in intertemporal constrained optimization problems. The confusion is as to when is the one-period budget constraint multiplied by the discount factor Beta and/or when is it included in the summation? Here is what I mean. In this first example:

the constraint is not multiplied by Beta, nor part of the summation. Now, in example 2:

the constraint is multiplied by the discount factor Beta and part of the intertemporal summation. Why this difference? Aren't the two cases pretty much equal, both maximizing subject to one-period constraints? The only difference I see is when the interest rate on the assets is realized, but that should not matter I believe(?)
I also found a third case (will upload an image later if I find it) in which the one-period constraint is summed up intertemporally, but not discounted by Beta.
So to conclude: what is the rule here? What am I missing?

EDIT:

By looking at the FOCs that follow example 1, it becomes clear that the author means the Lagrange Multiplier to be part of the summation, but not discounted by Beta. This is clear from the following:

So this really looks to me like a different formulation to the second example. The "funny" thing, however, is that in both cases you get the same result (i.e. the same Euler Equation).


texts: Are white collar workers the blue collar workers of the future?

texts:
Edward Luttwak published an essay in 1994, titled Why Facism is the Wave of the Future; he wrote in this essay:

  Partly because with generational change even senior managers can now themselves work those machines if they want to, thereby allowing them to understand their uses, abuses and non-uses; partly because more junior managers are increasingly compelled to use those machines in place of clerical help and clerical companionship;

then

  and partly because computer networks allow managers at the next level up literally to oversee, right on their own screens, the work that their underlings are doing or not doing, thereby giving it the same transparency as assembly-line work, with the same immediate visibility of inefficient procedures, inefficient habits and inefficient employees – for all these reasons the long-awaited, long-delayed increase in the efficiency of office-work has finally arrived, exposing hitherto more secure white-collar workers to the work-place dislocations, mass firings or at least diminishing employment prospects that have long been the lot of blue-collar industrial workers in mature economies.

I've heard the term 'precariat' banded about a bit in the UK for the past few years, which sort of tallies with this projection; but can firmer figures be put on this phenomenon?


texts:
Consider a game in which, simultaneously, player $1$ selects any real number $x$ and player $2$ selects any real number $y$. The payoffs are given by:

$u_1 (x, y) = 2x − x^2 + 2xy$

$u_2 (x, y) = 10y − 2xy − y^2.$

(a) Calculate each player’s best-response function as a function of the opposing player’s pure strategy.

(b) Find and report the Nash equilibria of the game.

(c) Determine the rationalizable strategy profiles for this game.

I got the first two part

$\partial u_1 / \partial X = 0 \implies 2 – 2X + 2Y = 0$ $\implies$ Best Response of Player $1 = 1 + Y$

$\partial u_2/ \partial Y = 0 \implies 10 – 2Y – 2X = 0$ $\implies$ Best Response of Player $2 = 5 – X$

Nash Equilibrium

$BR_2 = 5-(1+Y)$

so that

$Y^* = 2$ and $X^* = 3$.

The Nash equilibrium is $(3,2)$.

I am unsure abut rationalizable strategy. I think it is rationalizable strategy for both players are all real numbers because there is no single number that is strictly dominated by another number. For example, if player 2 chooses 10, 11 is the best strategy for player 1 and dominated other number. But, if player 2 chooses 11, 12 is the best strategy for player 1 and 12 dominated 11 in this case. This logic then applies to all real numbers. I am unsure if this logic is correct. Any help is greatly appreciated.


texts: How to create a Budget line in excel or R

texts:
Im interested in programming a budget line or PPF which is responsive to changes in relative prices, and income effect.

I know the equation for the budget line is $$m\geq p_1x_1+p_2x_2$$
Lets say we have an Income of $m=100$ and prices $p_1=1$ and $p_2=2$.

How would I go about programming this into an excel spreadsheet or R?


texts: Is there really an "efficient equilibrium *price*" with externalities?

texts:
In the "Intro to Micro" approach to externalities, I've always felt uneasy as a teacher with the idea that there is something like an "efficient equilibrium" with a single "efficient price".

To keep things simple, I will focus on external costs, but everything applies symmetrically to external benefits.

The graphs you often see are similar to those in the Wikipedia article on externalities. These graphs use the term "ideal equilibrium" instead of "efficient equilibrium", but the rest is standard (I include the captions from Wikipedia):

 "Demand curve with external costs; if social costs are not accounted for price is too low to cover all costs and hence quantity produced is unnecessarily high (because the producers of the good and their customers are essentially underpaying the total, real factors of production.)" (https://en.wikipedia.org/wiki/Externality)

I have of course no problem with recognizing and explaining that there is a unique efficient quantity.

My main issue is with the idea that there is a unique "ideal price" above the actual equilibrium price, and secondarily with the fact that this price is dubbed an "equilibrium" price (however "ideal" or "efficient").

At first sight, it seems ok to explain that, in the presence of an external cost, the good is under-priced because the actual equilibrium price only takes private costs into account (as opposed to social cost).

However, this only makes sense if we are talking about the price for consumers. For producers, a higher price would mean a higher quantity supplied. So in the presence of an external cost, the good is actually overpriced for producers, and underpriced for consumers only.

This is, in fact, the reason why a Pigouvian tax is a good instrument to solve the external cost problem: Because it increases the price for consumers and decreases the price for producers. Under a Pigouvian tax, the efficient quantity is indeed the equilibrium quantity. However, we now have two equilibrium prices (these are real equilibrium prices this time), one for consumers --- higher than the old equilibrium price --- and one for producers --- lower than the old equilibrium price.

This issue becomes even more salient if, after discussing external costs in the context of the above graph, you attempt to make sense of external benefit in the context of the symmetric graph (https://en.wikipedia.org/wiki/File:Positive_externality.svg) which again suggests that the good is underpriced at the actual equilibrium (whereas it is really underpriced for producers, and overpriced for consumers).

My questions are:

Am I missing something? Is there really a sense in which the price $P_S$ in the above graph is the "correct efficient price" across the board, both for producers and consumers?
Presentations of externalities that rely on graphs like the one above are typically agnostic about the "source" of the externality (whether it is a consumption or production externality) and only care about its sign (i.e., whether it is an external benefit or an external cost). I guess if we assumed that the external costs came from a consumption externality, then $P_S$ would indeed an efficient price (because it would reduce consumption to the efficient quantity, which is all we would care about). But then again, isn't it a stretch to call $P_S$ an "equilibrium" price when, clearly, imposing $P_S$ across the board for both consumers and producers would induce a shortage?
If you were teaching externalities out of a textbook using similar graphs and terminology, how would you try to make sense of all this for your students? Depart from the textbook and explain you don't agree with the idea of an "efficient equilibrium" with a single "efficient price"? Or try to work around the issue without opposing the textbook?


texts: Gale's version of the Rubinstein-Wolinsky (1985) model

texts:
Likely to be a very stupid doubt.
I am reading Douglas Gale's book "The Strategic Foundations of General Equilibrium", which presents a brief version of "Equilibrium in a Market with Sequential Bargaining" (pg 15). I am not sure how the model is being set up in the book. Maybe it is a typo, or maybe I am missing something which is extremely obvious.
The book says, "There is continuum of traders, M buyers, and N sellers of a N indivisible good".
I am not sure what this means:

Is there a continuum of indivisible goods, each of which has M buyers and N sellers?

Is there only one indivisible good, with a continuum of buyers and a continuum of sellers, with M and N being their measures, respectively?

I tried referring to the original paper and the latter seems to be the case, but I am not very confident.
Is the author referring to something I am completely missing?


texts:
How to prove that if $f$ is strictly quasi-concave and homogeneous of degree 1, then $f$ is concave? It was left as an exercise by Silberberg & Suen (2001), p.140.

I simply could not elaborate any sketches to leave here as a starting point.


texts:
I'm interested in technologies that are directed towards improving productivity of workers with high human capital.

What kind of data could one use to look at directed technical change, as in Howard-Howitt-Aghion, or Acemoglu (2002)?


texts: Seminal papers that later were proven to contain errors

texts:
I was reading on institutions, and I came across Acemoglu, Johnson and Robinson (AJR) paper on The Colonial Origins of comparative development: An Empirical Investigation, and this paper seemed so 'perfect' that spawned a lot of other papers based on the data of ancient settler mortality rate and how it was used by AJR as an IV for the current quality of Institutions in former colonies.

However, as I began searching more on this paper, I found out that the paper is in fact ridden with errors, specially on data treatment. (Albouy's 2012 comment on the same paper, published by The American Economic Review)

I would like to know, if, besides this paper on development economics, are there any other seminal papers, in any area of economics, that later on were proven to have crucial mistakes/errors that invalidated the paper conclusions?


texts: Thesis-advisor/student pairs that won the nobel prize

texts:
I am trying to compile a list of winners of the Nobel memorial prize in economics whose thesis advisor also won the prize.

So far I have

Eric Maskin (advisor) / Jean Tirole (student)

Are there other pairs?


texts: Is monetary expansion the same as quantitative easing

texts: Is monetary expansion policy the same as quantitative easing (i.e the buying of US treasuries by Federal reserve which injects more USD into the economy)?


texts:
I tried to summarize my thoughts about oil price changes, and try to understand the next weeks.

Will decrease price:

OPEC output is higher every month, increasing supply.
interest rates goes up, will reduce demand, less cars, less depending, less companies.

Will increase price:

Canada production outage
inflation, causing goods price to be increased
fracking extracting is costly, which is sensitive to interest rates, higher rates will cause less fracking, less supply.

I'm trying to understand to increasing factors, that released the price from 50-60\$ area into above 70\$ area.

Does anyone have ideas for why we are at high levels right now (and it looks like we will get higher)?

Thanks


texts: What analysis has been done to predict the next big financial crash?

texts:
There has been a lot of talk about a big pending financial crash due to the slowing global economy, low interest rates, rising debt levels, etc.  Now I'm wondering:

Has anyone done any analysis to predict exactly when the next big crash / credit crunch will be?

Specifically, what indicators have analysts been tracking to predict when the next crash will happen?  Has anyone agreed or suggested what will be the critical thresholds, and/or likely trigger(s)?

Ideally I am looking for some measure of systemic risk which effectively gauges how unsustainable a system is, or rather, how long an economic system can be sustained before it is likely to collapse.

I have made my own analysis and prediction based on long-term trends in slowing growth vs rising debt, but has anyone done this kind of analysis before?

Slowing growth: http://bit.ly/1IbPZam

Rising debt: http://bit.ly/1N94886


texts: How to find an optimal strategy in an auction?

texts:
I have asked this question in mathematics forum as well but since I have not recieved an appropriate answer yet, I ask it here as well.
Consider an auction of sculptures by four artists: A, B, C and D. The auctioneer introduces each item to be sold in the auction room, and all bidders write their bids on a secretly sealed note that is given to the auctioneer. At the end of each round, the auctioneer announces the highest bidder as the winner, collects payment, and moves on to the next item. There are two different scenarios in this game:

If there is a target set of sculptures to be purchased, the auction is won by the first bidder who purchases this set of items, and in each round, the highest bidder pays their own bid. The target set's essential requirement is 3 sculptures by any artist, 2 by another artist, and 1 by another artist. For instance, 3 by artist B, 2 by artist A and 1 by artist D. Or another example, 4 by C, 1 by D and 3 by B (the order is irrelevant).
But if there is no target set, the bidding will run until no further items are available to bid on. In this case, in each round, the highest bidder pays the second-highest bid, and the winning bidder is the one who has the largest net worth of sculptures—the sculpture of artist A is worth \$3, artist B is worth \$10, artist C is worth \$21, and artist D is worth \$50.

In both cases, the number of rounds (which is also equal to the number of sculptures) is 200, and the starting budget for every bidder is \$1000. Also, at the end of each round, the previous round's information is revealed so the bidders can use it for their benefit. The game each bot plays in each round is a one-shot game against the other bots. Each game a bot plays in each round is dependent on the games it has already played.
The information includes:

Details of all bidders, including their names, what they have won, and their remaining budgets.
A list of the full sculptures order.
A list of the winners' names of each round till now.
List of amounts paid for items in the rounds played till now.

I should find an optimal strategy for my bot to beat other bidders (bots). My field is neither mathematics nor economics, and this problem is new to me, so I need help with the theory part based on which I will do the coding implementation. I have searched about the relevant concepts and think that the second case above must be Vickrey auction; however, I am not sure if in the Vickrey auction the remaining budget of each bidder is revealed and if the other information (above bullet points) provided for the bidders in each round, is associated with the Vickrey auction conditions. Also, in the Vickrey auction, it is always optimal for bidders to place a bid that reflects their own valuation of the good. But in this game, the bidders (bots) are provided with more information, so does the truthful bidding idea still apply? Is Nash equilibrium applicable here? Sorry to ask several questions. To encapsulate all, I would appreciate it if someone suggests the correct type of auction in each scenario explained above and helps me with some formulas/tips/references to find the optimal strategy.
Any help is much appreciated.


texts:
Suppose there is a number of identical firms producing diamonds. Let the total cost function for each firm be given by  $C(q, w)$, where q is the firm’s output level and w is the wage rate of diamond cutters.

I'm supposed to solve for a firm's (short-run) supply curve, given a wage rate $w$, and the industry's (total) supply curve).

I'm very confused with the relationship between the cost function and the supply curve. For part a this question, I get the marginal cost from taking the derivative of the cost function -- is the marginal cost also the supply curve? We know the cost function of the firm, but how can I arrive at the industry's supply curve?


texts: Weak axiom of Revealed Preference application

texts:
The following is a problem I am dealing with related to Weak Axiom of Revealed Preference. I have given my solution below to the situation. What I am not getting is how is WARP not violated?

A law firm looking to hire to fill three positions gets applications from Andrew, Barbara and Celia.

The law firm's set of alternatives is the set of possible hiring decisions:

$ X = \{ \phi, \{a\}, \{b\}, \{c\}, \{a,b\}, \{b,c\}, \{a,c\}, \{a,b,c\}  \} $

For any $Y \subset \{a,b,c\}$, define the power set of Y as

$ 2^{Y} \equiv \{Z | Z \subset Y \}$.

$ 2^{Y}$ is the set of hiring decisions that the firm can make when it receives applications from the lawyers in Y.

The law firm's budget sets $ B \in \mathcal{B} $ are the sets of hiring decisions it can make after receiving applications from some combination of Andrew, Barbara and Celia :

$\mathcal{B} = \{2^{Y} |Y \subset \{a, b, c \} \}$

1) When it receives applications from Andrew and Barbara, it will choose to hire Barbara (and not Andrew):-

$ C(2^{\{a,b\}}) = \{b\} $

2) When it receives applications from Barbara and Celia, it will choose to hire Celia (and not Barbara):

$ C(2^{\{b,c\}}) = \{c\} $

The following is the problem I am confused in :
Q) What restrictions does the weak axiom place on the firm's hiring
decision $C(2^{\{a,b,c\}})$ when it receives applications from Andrew, Barbara and Celia?

My Solution:

According to Mas-Colell et al (Definition 1.C.1) , the Weak Axiom of Revealed Preference says that if x is ever chosen when y is available then there can be no budget set containing both alternatives for which y is chosen and x is not.

So based on my understanding of WARP, in my situation above, when Andrew and Barbara apply the firm chooses Barbara , i.e.
$ Barbara \succsim_R Andrew$
and when Barbara and Celia apply, the firm chooses Celia i.e. :
$ Celia \succsim_R Barbara $

Here we see that since Barbara is not chosen over Celia , WARP is violated. Because WARP would imply that Barbara is chosen everywhere when Barbara is a choice in the set. So when Andrew , Barbara and Celia apply, and WARP violates the above relation given , the firm would hire only Andrew.

What I am not getting is how is WARP not violated?