texts: Clarification on the definition of Bayes Correlated Equilibrium

texts:
I would like your help to understand the definition of Bayes Correlated Equilibrium (BCE) in an incomplete information game at p.7 of this paper.

Let me summarise the definition provided in the paper.

There are $N\in \mathbb{N}$ players, with $i$ denoting a generic player.

There is a finite set of states $\Theta$, with $\theta$ denoting a generic state.

A basic game $G$ consists of

for each player $i$, a finite set of actions $A_i$, where we write $A\equiv A_1\times A_2\times ... \times A_N$, and a utility function $u_i: A\times \Theta \rightarrow \mathbb{R}$.
a full support prior $\psi\in \Delta(\Theta)$.

An information structure $S$ consists of

for each player $i$, a finite set of signals $T_i$, where we write $T\equiv T_1\times T_2\times ... \times T_N$.
a signal distribution $\pi: \Theta \rightarrow \Delta(T)$.

A decision rule of the incomplete information game $(G,S)$ is a mapping
$$
\sigma: T\times \Theta\rightarrow \Delta(A)
$$

Definition of BCE: The decision rule $\sigma$ is a BCE for the game $(G,S)$ if, for each $i=1,...,N$, $t_i\in T_i$, and $a_i\in A_i$, we have
$$
\sum_{a_{-i}, t_{-i}, \theta} \psi(\theta) \pi(t_{-i}|t_i, \theta) \sigma(a_{-i}| a_i,t_i, t_{-i}, \theta) u_i(a_i, a_{-i},\theta)
$$
$$
\geq
\sum_{a_{-i}, t_{-i}, \theta} \psi(\theta) \pi(t_{-i}|t_i, \theta) \sigma(a_{-i}| a_i,t_i, t_{-i}, \theta) u_i(\tilde{a}_i, a_{-i},\theta)
$$
$\forall \tilde{a}_i\in A_i$.

Question:

1) I don't follow how the conditional expectation is computed in the definition. Consider for example the left hand side (LHS) and let me go through each step by using the notation $Pr(\cdot)$ to generically denote any probability distribution.

The LHS is the expected payoff of player $i$ where the expectation is computed wrto anything that is unknown to him conditional on what he knows. Hence,
$$
\sum_{a_{-i}, \theta, t_{-i}} u_i(a_{-i},a_i, \theta) \times Pr(a_{-i}, \theta, t_{-i}| t_i, a_i)=
$$
$$
\sum_{a_{-i}, \theta, t_{-i}} u_i(a_{-i},a_i, \theta) \times Pr(a_{-i}| \theta, t_{-i}, t_i, a_i)\times Pr(\theta, t_{-i}| t_i, a_i)=
$$
$$
\sum_{a_{-i}, \theta, t_{-i}} u_i(a_{-i},a_i, \theta) \times \underbrace{Pr(a_{-i}| \theta, t_{-i}, t_i, a_i)}_{\equiv \sigma(a_{-i}| a_i,t_i, t_{-i}, \theta) \text{ [OK!]}}\times \underbrace{Pr(t_{-i}|\theta, t_i, a_i)}_{\equiv \pi(t_{-i}|t_i, \theta)? \text{ Where is $a_i$?} }\times \underbrace{Pr(\theta| t_i, a_i)}_{\equiv \psi(\theta)?\text{ Where are $t_i, a_i$?}}=
$$

Are we assuming

1) $t_{-i}\perp a_i $, conditional on $\theta, t_i$

2) $\theta \perp t_i, a_i$

?

2) How does the definition of BCE simplify to when $N=1$?

From reading at p.25 of the linked paper, it seems that a BCE is still intended as mapping from state and signal to a probability distribution over actions. From reading at p.26 of the linked paper, the authors then say "[...] In that case, the set of BCE correspond to joint distribution of actions and states [...]". I'm confused.

Also, when $N=1$, how does the definition of BCE differ from the definition of Bayesian Nash Equilibrium?

3) Just as a curiosity, what it is the reason of including the adjective "correlated"?


texts: Markowitz Minimum Variance Line - maximise return with a given variance?

texts:
There are many example online of how to use Lagrange multipliers to solve Markowitz's minimum variance problem (namely  find the weightings for the portfolio which minimises variance for a given return with constraints on the calculated return of said portfolio and the sum of weighting of all assets within the portfolio to 1). However I can't find an example of how to go the other way, find the weighting of the portfolio which maximises return for a given variance. I know they'd both fall on the efficient frontier..

Can anyone help?


texts:
Trickle-down economics, also referred to as trickle-down theory, is an economic theory that advocates reducing taxes on businesses and the wealthy in society as a means to stimulate business investment in the short term and benefit society at large in the long term.

When it works, wealth created by the rich will trickle down to the middle-class and poor. Hence, the name trickle-down economics.

https://en.wikipedia.org/wiki/Trickle-down_economics

Strangely, one of the richest man in U.S, Warren Buffett, does not seem to think so. Why have trickle-down economics failed to trickle down to the middle-class and poor in recent years?

https://www.cnbc.com/2018/01/04/warren-buffett-on-the-failure-of-trickle-down-economics.html

  Buffett says there is a problem with that economic system, which made
  him a king: Many individuals suffer even as those at the top prosper
  wildly.

  He points to the Forbes 400, which lists the wealthiest Americans.
  "Between the first computation in 1982 and today, the wealth of the
  400 increased 29-fold — from $93 billion to $2.7 trillion — while many
  millions of hardworking citizens remained stuck on an economic
  treadmill. During this period, the tsunami of wealth didn't trickle
  down. It surged upward."


texts: Meaning of "Federal Reserve’s various liquidity facilities" and something more

texts:
I've found this link of San Francisco Fed. In it, it's stated that the Federal bank began «paying interest on reserves held against certain types of deposit liabilities.(...) This was important for monetary policy because the Federal Reserve’s various liquidity facilities initiated during the financial crisis caused upward pressure on excess reserves and placed downward pressure on the Federal funds rate. To counteract these pressures, on October 6, 2008, the Federal Reserve Board announced that it would begin paying interest on depository institutions’ reserve balances.»

I need help on clarifying the sentence in bold. Which facilities were those? What's the problem on an upward pressure on excess reserves, and downward pressure on the Federal funds rate?

Any help would be appreciated.


texts: Guess 2/3 of the average with integers - mixed strategy equilibria?

texts:
The "Guess 2/3 of the average" game (Wikipedia) is a game in which n people guess what 2/3 of the average of their guesses will be, and where the numbers are restricted to the integer (in this case) numbers between 0 and 100, inclusive. The winner is the one closest to the 2/3 average.

By iterated deletion of weakly dominated strategies, it is easy to show that all integers but 0 and 1 vanish because it is possible to rule out iteratively those numbers who cannot be 2/3 of the average of the played numbers. For example, the first step is to eliminate all the integers above 66 because even though everybody will play 100, 2/3*100 = 66.67, thus this is the maximum value the right number could reach.

Now, my question is which are the pure and mixed strategy Nash equilibria of this game?

Winning the game gives a payoff of 1, losing a payoff of 0. If there is a tie, the payoff is distributed uniformly among the winners. The pure NE should be playing 0, while I am totally lost about the mixed strategy one.

Does anybody know how to proceed?


texts:
I am confused about how individual decision rules are approximated via the Reiter method. In particular, on page 653 of Reiter (2009) (JEDC),  the link is:
https://www.sciencedirect.com/science/article/abs/pii/S0165188908001528
The decision rule $K = (x;\Omega_t)$ is represented by a vector $s_t$ which consists of knot points {$x_{t,i}$}. It seems to me that the method is approximating only along the idiosyncratic dimension, so this vector $s_t$ is different for different aggregate states $\Omega_t$. But then why is this useful when the Euler equation has both $s_t$ and $s_{t-1}$?


texts: Marginal productivity, wages, and profits in neoclassical economics

texts: In neoclassical economics a worker is paid the marginal product of what they produce. If this is true then what is the source of profits?


texts: Expected value of order statistics for uniform distribution

texts:
I have $X$ ~ $U(0,1)$ interval.
Let n=2, i.e. $X_1 < X_2$
I have to calculate the expected value of ${X_2}^{m/(1-m)}$.
Where, $0≤m≤1$
I want to confirm if I have calculated it correctly?
$$\int_0^1 2x^{2m/(1-m)} \,dx = \frac{2(1-m)}{(1+m)}$$
Is the calculation correct?
Thanks!


texts: Does the introduction of credit card affects Money Velocity?

texts: In my macroeconomics class, our professor showed an example of the introduction of the credit card. She says that this will decrease the money people are willing to hold, and thus increase the money velocity. But why is that true? I mean, although it seems like the credit card as a new mean of payment makes us feel we are not holding much money, but the credit card company are actually paying for us them using deposits. So the money people hold didn't actually change because while consumers hold less cash or deposit, banks that offer credit card will need to hold more cash or deposit to pay for it. So I think the claim that money velocity increases is false. Am I right?


texts:
The following exercise is from Wooldrige:

Show that $\hat{\beta} =\frac{1}{N} \sum\limits_{i=1}^{N}\hat{u_i^{2}}x'x $ is a consistent estimator for $E(u^2x'x)$

by showing:

$$\frac{1}{N} \sum\limits_{i=1}^{N}\hat{u_i^{2}}x'x = \frac{1}{N} \sum\limits_{i=1}^{N}{u_i^{2}}x'x + o_p(1) $$

Where $o_p(1)$ is read "little oh p 1"

And we use the hints that:

1.) $\hat{u}_i^2$ = $u_i^2 - 2x_iu_i(\hat{\beta}-\beta) + [x_i(\hat{\beta}-\beta)]^2$

2.) $\hat{\beta} - \beta$ = $o_p(1)$

3.)Sample averages are $O_p(1)$  read as "Big Oh P 1"

4.) we assume all necessary expectations exist and are finite

I'm getting stuck with this. I know I must be missing some simple sort of substitution or there is some gap in my knowledge or understanding preventing me from making the necessary manipulations.

I would love if someone could walk me through this and explain the intuition a bit here.


texts:
My question is the following:

Let's say a person has two career choices. He would be succesful in both, but in one of them he is slightly better and thus he will do better. So let's say career A will bring him a utility of 10 and career B a utility of 9.

So career A will bring him a 1 net utility benefit, due to the opportunity cost of 9 of pursuing career B.

Now suppose that for whatever reason, career B is not a choice anymore for him.

Is he now better off, from the fact that his net utility benefit is 10 and not 1? Why or why not?


texts: Local maximum when Hessian is negative semi-definite?

texts:
If it possible to have a local maximum when the Hessian is only negative semi-definite (i.e., there is one zero eigenvalue and all other eigenvalues are negative).

If not, what it the ultimate recourse to prove that a point is a local maximum is such cases?


texts: Best resource to learn Microeconomics fast?

texts:
I'm going to be honest, I have 2 full days to study for an Introductory Microeconomics exam final, and I am starting from scratch. The course was given online and the assignments were very easy to complete since we had 3 tries and the questions repeated.

I have no background in micro but my math is very good for this type of course (completed Calculus 3 and Combinatorics), and I am looking for a resource to learn the material quickly.

I have looked online and haven't really found one. The book we use in class is full babbling analysis of graphs that I already understand and random examples that don't cover the material efficiently. I am looking for a sort of summary that covers the essentials.

I know that I should have studied earlier, but I still want to try my best to have, at least, a passing grade.

Any recommendation will be appreciated.

Thank you in advance.


texts: Dominated Strategies in an Infinitely vs Finitely Repeated Game

texts:
How does the concept of weak dominance work with infinite games? The abundance of concepts seems to muddy things.

In particular, suppose two players play the following game an infinite number of times.

$$\begin{array}{l*{2}{c}r}
             & A & B  \\
\hline
A & 1,1 & 0,0 \\
B & 0,0 & 0,0
\end{array}$$

In the one shot game, it is clear that playing $A$ weakly dominates the action $B$.

However, what if we consider a bizarre kind of grim trigger:

In the first period, a player plays $B$.
If the other played $A$ in the first period, play $B$ forever.
Otherwise, play $A$ forever.

For a patient enough player, it is weakly best to respond to this strategy with the same one. Any strategy that begins with $B$ and then $A$ afterwards is a best response (the off-path details can be different, so that a best response may not stipulate $B$ forever if the other chooses $A$ at the beginning).

The pareto efficient equilibria involve always playing $A$ on the equilibrium path, and it's tempting to say that playing $A$ no matter what should be weakly dominant, but that doesn't seem to be the case. Has much been written on this kind of thing? What kind of ideas exist to rule out the kind of strategy described above?

Is the strategy in question itself weakly dominated? I would guess that we could concoct an equally sinister trigger strategy $s'$ so that the strategy in question is not dominated by any other $s''$.


texts: Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation

texts:
Why is the partial derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2)$ for $p_1$
$$
\frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2)}{\partial p_1}=\frac{\partial x_1(p_1,p_2,\overline{m})}{\partial p_1} +\frac{\partial x_1(p_1,p_2,\overline{m})}{\partial m}\overline{x}_1
$$
where $(\overline{x}_1,\overline{x}_2)$ is the bundle originally demanded at prices $(\overline{p}_1,\overline{p}_2)$ and income $\overline{m}$ and $x_1^S$ is the Slutsky demand function for good 1 and $x_1$ the Marshallian demand function for good 1?
I understand that $m=p_1\overline{x}_1+p_2\overline{x}_2$ because the pivot ensures that the consumer is still having enough income to purchase his old bundle $(\overline{x}_1,\overline{x}_2)$.
Chapter 8 of Varian shows this to derive the Slutsky equation using calculus. I don't understand the right side of the equation.
I know that $p_1\overline{x}_1+p_2\overline{x}_2=m$ and $\overline{p}_1\overline{x}_1+\overline{p}_2\overline{x}_2=\overline{m}$ where $m$ is the new budget.


texts: Definition of "Structural Equation" In Economics

texts:
The definition of term "Structural Equation" in Economics as defined in  Introductory Econometrics: A Modern. Approach, Fifth Edition. Jeffrey M. Wooldridge. (page 859)

  Structural Equation: An equation derived from economic theory or from less formal economic reasoning

However upon reading earlier works in Studies in Econometric Method I find that structural equations are far from informal.

In this passage of chapter 3 (page 86 in the PDF) by Herbert Simon, he makes a distinction between structural and non-structural equations which I don't fully understand.

How does identifiablity define whether an equation is structural or not? does this mean structural equations assume causality?


texts: I don't understand that the pointed part(with a red circle) is a negative sign. I expect it should be a positive sign since the whole parenthesis was squared. I don't know where I got wrong.


texts: Necessary and sufficient conditions for the existence of a utility function

texts:
I was reading Jehle and Reny, Advanced Microeconomic Theory, where they discuss in detail, the choice problem of a consumer. The Consumption Set (or Choice Set) $X$ is a subset of $R_+^n$, is closed and convex and contains $0\in R_+^n$. They define a preference relation $\succeq$ on $X$ that satisfies completeness, transitivity and continuity. Then they argue that these conditions are sufficient for the existence of a continuous real-valued utility function that represents the preference relation $\succeq$.
I wondered if there are more general results about the existence of utility functions (continuous or not) to represent rational preferences. The theorem in Jehle and Reny has nothing to say about cases where the choice set does not satisfy the conditions assumed or when we simply do not care about the continuity of the utility function. For example, if $C= \{a, b, c\}$ is the choice set and the preference ordering is simply $a, b, c$ (the preference relation is accordingly defined), then $u: C\rightarrow R$, $u(a)=10, u(b)=2.5, u(c)=\frac{\pi}{100}$ is a legitimate utility function, but the theorem in Jehle and Reny does not say anything about these cases. Again, the famous lexicographic preferences (that satisfy rationality but violate continuity) have no utility functions, but Jehle and Reny's theorem does not tell us anything about it. I wanted to know the most general necessary and sufficient conditions for the existence of utility functions, that also cover these and other possible cases.
Formally, let $C$ be the set of all conceivable choices (no conditions on it assumed so far), and let $\succeq$ be a binary relation on $C$ that satisfies completeness and transitivity.
What are the necessary and sufficient conditions that $C$ and $\succeq$ must satisfy, so that a utility function from $C$ to $R$ that represents $\succeq$ exists?
I would appreciate both proofs and/ or reference materials for this, or even partial solutions.


texts:
What is this thing named homebody economy? It seems to be related with the virus
It refers to working at home or maybe at online shopping?


texts: Finding savings in an Overlapping Generations model

texts:
I have not seen this question asked anywhere, so I'm posing it here in case anybody else (hopefully) can help me get to the answer. In a nutshell, my question is: how do we arrive at the saving function in a canonical OLG with Cobb-Douglas utility?

I'll explain my question in more detail: In Diamond's original OLG model, he describes saving as a function of the wage and the interest rate, so that:

$$
s_t=s_t(w_t,r_{t+1}).
$$

More specifically, when utility is Cobb-Douglas:

$$
U = (1-\beta) \cdot ln (C_{1,t}) + \beta \cdot ln(C_{2,t+1})
$$

Diamond concludes that the saving rate is a fixed ratio of the wage rate, such that:
$$
s_t= \beta \cdot w_t
$$
The same conclusion can found in most online references that cover the canonical OLG (for example, here).

However, I have not been able to find an explanation anywhere of how one arrives at this equation for saving. Most references that are available online, like the one I've just linked to, simply present a formula with no explanation as to its derivation. Meanwhile, in his original paper, Diamond seems to jump to this conclusion (in page 1134) with no step-by-step explanation for how he arrived at this result for the Cobb-Douglas case.

Can anybody perhaps help me understand how this result comes about?

(My motivation for asking is that I want to understand what would happen to consumption in a canonical OLG model if we supplemented the wage with an exogenous source of income "A", so that consumption of the young at time "t" were given by: $C_{1,t} = w_t -s_t + A$).


texts: What type of biases arise from DID estimation using aggregate data?

texts:
I'm considering using difference in difference techniques to write my last two undergraduate papers relating minimum wages and employment/poverty. I've been told issues arise with using aggregate data like you would find on major statistical sources. I have notice most DID papers use survey data, however i do not have access to this or time to get it.

So, my question is: what are the issues with not using micro-level data? how big of a deal is it? and are there possible solutions?

-Thanks


texts: Interior Solution for profit maximisation problem

texts:
A function $c: \mathbb{R}^K_+ \xrightarrow{} \mathbb{R}_+$ is is said to be a cost function if

The value of function $c$ at $y = \textbf{0}$ is $0$: $c(\textbf{0}) = 0$
$c$ is continuous on the domain $\mathbb{R}^K_+$, strictly increasing and strictly convex on $\mathbb{R}^K_{+}$
For any $p \in \mathbb{R}^K_{++}$, the set $B(p) = \{y \in \mathbb{R}^K_+| c(y) \leq p \cdot y\}$ is compact, the interior of $B(p)$ is nonempty.

Suppose a firm has cost function $c(\cdot)$ and $p\in \mathbb{R}^K_{++}$ is the market price. What sort of topological assumption I need to add to guarantee the existence of an interior solution to the profit maximisation problem?
$$
\pi (p) = \max_{y\in\mathbb{R}^K_+} \left\{ p\cdot y - c(y) \right\}
$$
Remark 1: From assumption (2) and (3), the existence of solution is guaranteed. Due to strict convexity, uniqueness is also guaranteed. However, the solution is probably not inside the interior of $\mathbb{R}^K_{+}$. I could not find an example for this at the moment.
Remark 2: My prototype cost function to look at is $c(y) = y_1^2+y_2^2$. However, the cost is not necessarily to be additive separable.


texts: Can State Owned Enterprises compete with each other without a private enterprise in a market? Examples

texts: In a domestic market, there exist multiple (around 5) multi-product state-owned enterprises. In a few products, SOEs compete with private enterprises while in the majority of products, the SOEs share the market among themselves. Economies of scale and scope exist in the industry. What could be the rationale of having multiple State-owned enterprises in the domestic market? I have tried looking at the academic literature but most of them analyze competition between private and  State-owned enterprise. I would like to have examples of competition existing between multiple state-owned enterprises in any country setting.


texts: How to overcome measurement error in variable for immigration year?

texts:
I'm using the Current Population Survey and studying immigration. There's a variable: Year of Entry into the United States for the Foreign Born.

The survey is administered to a representative sample of the United States population, regardless of whether the people are citizens or not. It doesn't ask about whether the person is an illegal immigrant, but still, people probably don't want to share that info or hint at it.

I figure there has to be inherent measurement error in this variable because people might not tell the truth if it hints at anything that reveals that their visas have expired or something.

What can I do to confirm that there is measurement error? Or to account for the error?


texts: Proof of excess community demand function in Sonnenschein (1973)

texts:
Consider the following passage in Sonnenschein (1973; full citation below):

Perhaps because I do not know much about the uniform Lipschitz condition, I do not follow his exposition after the first two sentences of the proof. That is, do the definitions of $g_1^1$ and $g_1^2$ come from some standard result in mathematics? Any intuition here would be appreciated.
Furthermore, what is the source of $(g_1^1, I-pg_1^1)$ and $(g_2^1, I-pg_2^1)$?
Thank you.
Citation:
Sonnenschein, H. 1973. "Do Walras’ identity and Continuity Characterize
the Class of Community Excess Demand Functions?" Journal of Economic Theory 6: 345-354.


texts:
Existence of a subgame perfect Nash-equilibrium

Given is the following game

The game is repeated finitely many times and the total payoff is the sum of the payoff from each repetition.

If we assume that $T=2$, is it then possible to find a subgame perfect Nash-equilibrium such that the strategy $(B,L)$ is played in the first stage (first repetition)?

So far as I can count, it shouldn't be possible to construct any threats for $T=2$ such that the $(B,L)$ strategy is played in the first stage. This is due to the Nash-equilibrium laying in $(T,R)$ and it takes at least $T\geq 3$ to ensure that $(B,L)$ is played in the first stage.

Though, I'm not quite sure how to prove my statement. Can any of you confirm/deny my thoughts and help me with some arguments? Thanks.


texts:
I am reading the Microeconomics Theory book by MWG, and I am having a tough time interpreting what things mean to a real life example, so any help would be appreciated.
For example, it gave this.  Suppose X = {x, y, z} and B, the budget set, = {{x, y}, {x, y, z}}.  It says we can define a choice rule so that C({x, y}) = {x} and C({x, y, z}) = {x, y}.
I am having trouble understanding what C({x, y, z}) = {x, y} means.  Does that mean that when faced with the choice of x, y, and z, the person is indifferent between x and y?  It doesn't mean he chooses both right?  It just means he will choose either or so it's random which one of the two he chooses?
Furthermore, how can we even have a situation where if the consumer is choosing between x and y, he'll always choose x, but then when he is faced between choosing x, y, and z, he will choose either x or y?  Can someone give me a real life example of how this would be possible?  That usually helps me understand better.
Thank you so much!  I appreciate any responses.


texts: How do 'econometric' explanations differ from 'economic' ones?

texts: I am interpreting some coefficients of a regression model and have been asked to, first, give an 'economic' explanation and then an 'econometric' explanation as to why coefficients differ as more variables are added to the regression. I don't quite understand, however, how my answers should differ.


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


texts: Showing that a preference relation admits a utility function representation

texts:
Setting: We have two choices of goods $(x_1,y_1)$ and $(x_2,y_2)$ from the set of choices $[-1,1]^2$. Moreover, we have the following preference relation $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff |x_1|\geq|x_2|\>\>\text{or}\>\> |y_1|\geq|y_2|$$

Question: We have to check if there exists a utility function reprensation of this preference relation.

My attempt: So from what I have learned, we know that a preference relation admits a utility function representation if it is rational (reflexive, complete, transitive) and continuous. I have found that this preference relation is not transitive, but this does not mean that there does not exist a utility function representation, because the aforementioned statement is not an if and only if statement.

Moreover, I thought we could try to derive a contradiction from the fact that if there exists a utility function $u$ representation of the preference relation, then we have $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff u(x_1,y_1)\geq u(x_2,y_2)$$
I tried to use the fact that the relation is not transitive to derive a contradiction by using the statement above, but was unsuccessful.

Sadly, these are the two main theorems/propositions that I've learned to solve these problems.

Any help is appreciated!


texts:
In my OLG model, I have two law of motions for capital and pollution
\begin{align*}
&K_{t+1} = s_t\\
&P_{t+1} = (1-\delta)P_t+\rho K_t
\end{align*}
where $K$ is capital, $s$ is the saving from the last generation and $\rho, \delta$ are exogenous parameters. Pollution in my model is just a by-product of the use of capital. Firms and households do not take it into account when making decisions in each period. I know that $K$ is a predetermined (state) variable, but I am not sure whether pollution ($P$) is a state variable. In my numerical simulation, one of the absolute value of the eigenvalues is greater than one and the other one is smaller than one in my two-dimensional system.
Originally I think both $K,P$ are state variables. Any comments to my misunderstanding will be appreciated.


texts:
Does anyone have a good book on the history of Muni Bonds that focuses on the reasons why they grew in popularity, adoption, and gov policy souring them.

Background on why I need this info

I am writing a paper for my college history class, titled when wall street met main street. We are allowed to self select a topic and I chose to focus on the change in  the bond markets and that relationship with the public.

What I think could be a great topic is the rise lease revenue bonds for funding prisons, and how this has played out.


texts: Is there an economic theory of why people like to hold on to wealth?

texts:
It seems to me that many people work to become wealthy, but not because they want to consume all that wealth. Many people give it away, other's don't, but still they do not spend it. You hear about some rich 40-year old's throwing money away, but you seldom hear of a rich 80-year-old throwing anything away! What is the economic theory for "scrooge"? Are there simple preferences that make this the right strategy?
(I head somebody say that JP Morgan used to say it was a way of keeping score. Is there a theory of this?)


texts:
What is the relationship of the option value and the pay off to an option?
What happens if the option value > pay off? or if it is equal to the pay off?

I read that in a put option , the option value is a solution to $$\sup_\tau E[\max\left\{K-S,0\right \}]$$, where $K$ is the exercise price. Does this imply that the possible option values are just 0 or K-S. How important is the option value?


texts:
Preliminary note: I have nearly zero economical background, I am a physicist and my question is probably very naive, but I would like a clear and simple explanation.

If I am not wrong, the global economy can be seen as an isolated system (ie we do not have any non-Earth economic exchanges). At any given time $t$, there is a given amount of money $M$ in the world. As worldwide economy is an isolated system, $M$ can vary only if it is created or destroyed within the system. To my knowledge, the only way to create money is by creating a debt at $t_{0}$ and when money is reimbursed at $t_{1}$, the money that was created out of thin air is destroyed. I see no problem when the interest rate is $0\%$, because globally the system stays balanced.

Now, if the interest rate is stricly positive, that means that the amount of money $|m_{1}|$ that will need to be reimbursed at $t_{1}$ is higher than the debt $|m_{0}|$ that was created at $t_{0}$. But the thing is that $dm = |m_{1}|-|m_{0}|$ does not exist in the total amount of money available worldwide at $t_{0}$, $M_{0}$. So for the debt to be reimbursed with the interests, $dm$ will need to be created. And the only way to create money... is by creating a debt... with interest. So the system diverges very rapidly with an ever growing debt.

The other way I can see to make the system stable is by inflation/deflation: if $dm$ exactly corresponds to the inflation/deflation rate, then the system can remain at equilibrium without an ever growing debt. The last way I can see to remain at equilibrium, is by crisis so that $dm$ is never reimbursed.

I would like an explanation in simple words about what is wrong about this naive view.


texts: Is the marginal cost the same for every firm in a perfectly competitive market?

texts:
Spin-off from: market equilibrium quantity $\ne$ firm profit maximising quantity?

Consider a perfectly competitive market with equilibrium price $P_{eq}$ and quantity $Q_{eq}$ and firm with profit maximising quantity $Q_f$ as illustrated below:

Is the MC for each firm in the market the same?

Can we deduce such from any of the assumptions listed in the PC Wiki page?


texts: Why is machine built this year but not sold this year included in GDP?

texts: GDP is the sum of market value of all final goods in the current year, so why is is machine built this year but not sold this year included? In addition why is machine not built this year but sold this year not included in GDP?


texts: what can be the proxy variable for measure of product innovation?

texts:
My objective is to prove that international trade leads human capital formation which leads to economic growth. I am regressing GDP on multiple variables among which Human capital is one. According to a paper, I've read, new lines of product provide more learning by doing opportunities for workers and hence accumulation of human capital. Since panel data on product innovation is not available, it uses 'first time export' of a commodity as an indicator of product innovation. The source for the data is https://comtrade.un.org/db/
But I don't understand how to identify first time exported commodities.
i need suggestion for what other variables can be used as a proxy for product innovation.


texts: market equilibrium quantity $\ne$ firm profit maximising quantity?

texts:
Consider a perfectly competitive market with equilibrium price $P_{eq}$ and quantity $Q_{eq}$ and firm with profit maximising quantity $Q_f$ as illustrated below:

I guess any firm in the market would have the same demand, marginal revenue and average revenue (or am I wrong?), but what about profit maximising quantity $Q_f$? It seems to depend on $MC$. Is $MC$ different for each firm?

If so, then $Q_f$ is not necessarily the same for each firm?
If not, why?


texts: What sectors would be most affected positively or negatively by Trump´s trade agreement renegotiations?

texts:
One of Trump´s stated policies is that he will renegotiate the trade agreements with China and the Canada and México (NAFTA). This renegotiation might go well in which maybe the US gets freer access to markets in these countries, or it might just turn into protectionism and tariff increase.
Which industries in the US (manufacturing, industrial, extractive, construction, services, etc) does trade theory suggest would be most affected (either positively or negatively) by an general move towards protectionism and tariffs by the US?


texts: Rosen's unique equilibrium conditions: Multi dimensional strategies?

texts: I was wondering if the uniqueness of equilibrium conditions in n-person games as published in Rosen's 1965 paper (J. B. Rosen. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 1965) are for single-dimensional strategy spaces only? It says in the paper that the strategy of each player can be a vector, but the rest of the conditions seem to be derived for one-dimensional strategy spaces. Can the results be generalized to multi-dimensional spaces as well? Thank you.


texts: State of general equilibrium theories Post Blanchard 2008

texts:
This question arose from a useful comment I received upon answering a question on this site, and a recent question from a doctoral student.

The so-called theory of general equilibrium (including the many variants) is a cornerstone of economic theory, occupying economists' minds since (at least) the 1800s. Although, like other concepts in economics, different schools of economic thought remain polarised about its usefulness (both empirically and theoretically) and its falsifiability, [see Sonnenschein–Mantel–Debreu theorem (1976), positive corner-case results of Brown and Matzkin (1996) and any one of a number of further negative results Nachbar (2004), Kirman (1992), Carvajal (2003),...].

Post Blanchard's now famous 2008 declaration that "the state of macro is....good" and the characterization of DSGEs as state-of-the-art. What is the state of GE theories today?


texts: Could you guys recommend lecture notes or papers that show the step by step of the uzawa-lucas growth model?

texts: I have to study the differences between the model of uzawa-lucas, solow and harrod-domar, so if you guys could reccomend me something to study the uzawa-lucas model, with an easy lecture notes to understand, i would be glad.


texts:
Suppose a consumer whose income is $b$ has a utility function given by $U(x,y) = 2xy+y^2$ with the price of $x$ being $p_x$ and the price of $y$ being $p_y$.

Draw the price-consumption curve assuming $y$ is an inferior good (keep the price of $x$ constant).

If we set up the Lagrangian $$ L = 2xy+y^2 + \lambda \cdot (b - p_xx-p_yy) $$

and solve the maximization problem, we'll end up with

$$x(p_x,p_y,b) = \left( \frac{p_y-p_x}{2p_xp_y - p_x^2} \right) \cdot b, \,\,\,\, y(p_x,p_y,b) = \left( \frac{p_x}{2p_xp_y - p_x^2} \right) \cdot b $$

If $y$ is to be inferior, then we must have (considering income and prices to be strictly positive)

$$ \frac{\partial y(p_x,p_y,b)}{\partial b} < 0 \implies \left( \frac{p_x}{2p_xp_y - p_x^2} \right)  < 0 \Leftrightarrow 2p_xp_y - p_x^2 < 0  $$

However, in order for the amount consumed of $y$ to be non-negative, we must have

$$ \left( \frac{p_x}{2p_xp_y - p_x^2} \right) \cdot b \geq 0 \Leftrightarrow 2p_xp_y - p_x^2 \geq 0  $$

Thus, we can conclude that if the demand for $y$ is to be non-negative at strictly positive prices and income, then $y$ can't be an inferior good.

However, if we respect the condition given by the non-negativity of $y$, we can still plot the price-consumption curve. Taking the following pairs of prices

$$ (p_x,p_y) = \{ (1,1),(1,3),(1,5) \}$$

and letting $b = 48$, we'll have:

$$\begin{cases}
x(1,1,48) = 0, y(1,1,48) = 48 \\ x(1,3,48) = 9.60, y(1,3,48) = 9.60 \\ x(1,5,48) \approx 21.34, y(1,5,48) \approx 5.34
\end{cases}$$

Plotting these values on a graph, we have:

Is my answer correct?

Thanks!


texts:
Consider a game of delegation. An uninformed principal must delegate some task to an informed agent with preferences imperfectly aligned.

I'm aware of plenty of literature that studies these kinds of problems when there is a continuous action space, Alonso and Matouschek (2008) for example. Their lit review also seems to feature papers with continuous spaces. Quadratic loss utilities are very popular.

Are there any papers featuring delegation of a decision which is constrained to some discrete space? Do qualitative results change?


texts: What are the economic perspectives regarding the game of salary negotiations?

texts:
Apologies if I use non-economic language to explain what I suspect is a practical application of economics. I have no formal education in economics whatsoever but hoping you guys/girls might be able to help. :)

I'm the managing director of a company in which we run appraisals every 6 months. Each time we negotiate salary I have in my mind's eye this picture...

Assuming the 'correct' salary for an employee is 70k, there's an incentive to offer slightly more. 'Slightly more' because there's some error in estimating the market rate and the costs of getting this wrong are high. I've added a staff churn costs of £20k/yr for getting this wrong based on loss of knowledge, morale, recruitment costs and what I refer to as a 'change incentive' for the replacement employee. The change incentive is the amount you must offer a new employee beyond their current rate (market rate?) to discount the loss of familiarity and to take on the risk of joining a new employee.

Belief 1 - Underpaying employees is much more costly over the long term once staff churn is taken into account.

Belief 2 - the employee has better information about their value - based on them being nearer the information about their skills, positive contributions and self interest in the literal sense.

Belief 3 - salary expectation in job adverts are positively skewed to discount against the risk and transaction costs to the employee of change. Nobody switches to an identical salary unless it's a sideways move. Anecdotally, I've heard advice to change jobs every few years in order to raise your salary faster. Humans tend to be unnecessarily risk adverse and you can give yourself a competitive edge by overcoming this bias.

Belief 4 - primary information source for market value are job adverts and job offers. These overvalue for the reasons in belief 3.

Belief 5 - Protracted and/or aggressive salary negotiation is costly in itself. If there's a big discrepancy it can create feelings of being undervalued.

Belief 6 - Employees will be content and thus likely to remain with the company if they feel they are receiving the market rate.

Assumptions: the company is otherwise a pleasant place to work.

In my particular industry, I'd consider low staff churn rates and high staff morale as being a distinct and powerful competitive advantage. The figure of 20k churn cost is probably conservative.

In England, where I live, the cultural norm is for the company to either start the negotiation or more commonly simply state what the pay rise is going to be. This is followed by a period of watching how much they squeak squirm with dissatisfaction. Given the beliefs above and an industry where staff churn is costly, I'm inclined to lean in the other direction and either let them begin the negotiation or even more radically, simply request what their salary should be; as is common for sellers of other types of good. Salary negotiation seems to me to be unique in that the buyer of the good (their labour) dictates the price and then watches to see if the supply vanishes (resigns).

Is it an optimal strategy in salary negotiations to let the employee decide?


texts: Can anyone recommend a resource for monthly trade data for Mexico from before 2010?

texts:
Can anyone point me to a resource where I can find monthly series data (specifically for 2003-2013) on Mexico's imports and exports in nominal (current) Mexican Pesos (MEP) including broken down by major industry?

I've found UN data and OECD, but am having trouble navigating the INEGI site (since my grasp of Spanish is limited to the colloquial).


texts:
Why do we assume convex transaction costs in theoretic models? What is the intuition and the strict definition of this assumption?

Well, I have in mind the Glosten model in 1994. Neither he provides some details, nor it is obvious why he defines convex transaction costs. He only claims that the quasi-concavity of the utility function, ismplied by the concavity of some function $U(\cdot)$ and the convexity of the transaction costs function $TC(\cdot)$. This is a link of the Glosten 1994 article, you can see in page $1132$. I wonder does he assumes convexity because this comes from any micro foundation assumption, or it is just for solving the problem, because he can not solve it differently. Why not assuming that the function of transaction costs is a linear function which in fact is a convex and a concave function simultaneousely.


texts: How to find interest rates with fractional reserve banking?

texts:
As I understand it, interest rates are set by supply and demand, like any price. Money can be thought of like any other finite commodity. Lenders are willing to supply a certain amount of money at each interest rate, and borrowers are willing to borrow a certain amount at each interest rate. The rate can be calculated by setting supply equal to demand.

However, with fractional reserve banking, this picture seems to fall apart. While the demand curve can still be found, the supply of money is not so easy to quantify. If the reserve requirement were low enough, banks could loan out an arbitrarily large finite amount of money. The only limit to the money supply is the reserve requirement. It doesn't make as much sense to say here that the interest rate is set by supply and demand.

I see a two possibilities:
1) There is a supply curve that depends on the reserve requirement. This means that the interest rate would be a function of the reserve requirement.

2) There is no supply curve. As far as I know, no one sets interest rates (the Fed included, since they only influence rates via open market operations: if they didn't do anything there would still be an interest rate). How can interest rates be calculated in this case?


texts: What was the Rogoff & Reinhart spreadsheet mistake?

texts: In class our professor said that the Rogoff and Reinhart research on growth and debt was discredited due to spreadsheet mistake. What was this mistake? Also did they perform their research in excel instead of R, stata or some other advanced program?


texts: Why did Germany use hyperinflation to free itself from an external debt?

texts:
Im reading about how Germany used almost any solution To free itself from its WWI debt: hyperinflation, calculating payments on the basis of the economy's potential, rescheduling annuities and finally cancellation outright. But i didn’t understood why they used hyperinflation. I understand it neutralized the domestic debt, but did they had that much ? Why did they did so if they had to reimburse the external debt that was imposed after Versailles congress?

Hyperinflation certainly neutralizes the domestic debt, but the collapse of the mark makes the external public debt unbearable.


texts: Where did Adam Smith write the following and in what context?

texts:
Contra the a certain fetishisation of Adam Smiths thought he wrote:

  The vile maxim of the masters of mankind: all for ourselves and nothing for other people.

I'm assuming that this is from his Magnus Opus, The Wealth of Nations. Is this correct? What is the context in which he felt he had to make such an observation?


texts: Ruling out boundary solutions in Utility Maximization

texts:
Solving the basic Utility Maximization Problem, i.e.

\begin{align}
max_{x\geq 0} u(x) \\
s.t. \,\,\, p^Tx\leq w
\end{align}

we get the Kuhn-Tucker first order condition

\begin{gather}
\frac{\partial u(x)}{\partial x_l}\leq \lambda p_l
\end{gather}

which holds with equality when $x_l > 0$, i.e. when solutions are interior.

Is it enough to say that since preferences are assumed to be monotonous, we can rule out the possibility of boundary solutions and thus we are safe in setting the FOC with the equal sign?


texts: I've seen a derivation of MRS, but it's not immediately obvious to me why letting MRS equal to the price ratio of two goods will give you the solution to an optimization problem. Can anyone link me to a paper that explains this (or explain it themselves)? It would be great to get both the intuition and mathematical derivation! Thanks in advance!


texts: What economics theory explains changes in purchasing different types of goods?

texts:
I am thinking about the first of the month. I spend more of my money on superior goods and, because of that decision, less on normal and inferior goods. Are income and substitution effects enough to explain this or not?

I am thinking about a hypothesis for why people change their types of goods given that budgets change according to pre-decisions.

I will not misguide you: this is not only a goods decision or money constraint; it is also related to the time constraint and time-involved work.

For example, an agent has a given time constraint, T, to work on his given projects over a time period, t, which requires only T-r amounts of time for the period t+1. Hence he spends the time r to do other things according to opportunity cost theory. Therefore, he spends his time working on this project only at amounts equivalent to T-r and the opportunity cost of this project decreases as time approaches t+1.

So at this point, if he is an expert at this job, everything will go smoothly but, if not, this is a false prediction and the agent has to face his false decision and survive on his present condition. The hypothesis starts here: 1. Will he increase his purchasing power (i.e., sleep less to increase the time constraint)? 2. Will he bargain with his boss to increase his time constraint? Why?


texts:
Majority of countries (if not all) use tax brackets to define how much tax should the earning workforce pay. So we could have something like this.

Pay | Tax
0 - 10,000 | 10%
10,001 - 20,000 | 20%
20,001 - 30,000 | 30%
etc.

The breakpoints are what I am going to ask about. It has been proven in other schemes, such as the UK's Stamp Duty Land Tax that separating tax into categories like this leads to clusters on the lower bound of the breakpoints. My understanding is that this is not a desired effect and the distribution on the scale should be more fluid.

I come more from the software engineering side as opposed to the economic side, so I assume that in the past it was easier to calculate tax using this system and that's why it was chosen. Humans would not be able or willing to do complex tax calculations had we used rules that can be charted for example as S curves.

However, I wonder if we could have a better system today? (Assuming the current system is not sufficient.) Are there any proposals or significant movements that are not satisfied with the current tax system?

Note: I am not making assumptions about how the collected money is being spent, or how much is being collected. This is purely about the curves behind the tax brackets and clustering.


texts:
I am not an economist, so my question could be stupid for you.
However, I need to understand how market order works and which variables plays in a trade.
For example: let us suppose I am a trader and I have at the time t=0 a sum of cash and stocks.
How do they change?
Do I need consider intraday and daily trades?
And what about the spread between bids and asks?


texts:
I will be conducting a research about the market structure of an outdoor farmers market. I wanted to know what kind of survey questions could help me for example to determine the PES of the market or anything else that I could use in order to determine the market structure.
I already will survey people about how do they choose the shop, how much time they spend finding a shop, if they have the information of the cheapest shop and how often do they return to the same store. In addition to that, I will be observing the price changes for about a month, and also use the Herfindahl-Hirschman Index (HHI).


texts: How do we calculate Beta in a OLS regression of the mean of y on the mean of lag of y?

texts:
In a simple OLS regression we calculate the estimator Beta by dividing the covariance of x and y by the variance of x.

How do we calculate the estimator Beta if we regress the mean of a variable (at time t) on the mean of its lagged variable (at time t-1) ?:


texts: In what country outside of the EU is the public sector the highest percentage of GDP?

texts:
The article Railway strikes test Macron’s reforms - French strikes states that "Mr Macron’s reform of SNCF is only part of a bigger effort to reshape the welfare state in a country where the public sector consumes 56% of GDP, the highest in the EU."

What country outside of the EU has the highest percentage of GDP in the public sector?


texts: Do countries with centrally-planned economy have Entrepreneurship as a factor of production?

texts:
Let's don't count self-employed people without other employees (like "lone wolf" craftsmen) and people who have an illegal business as entrepreneurs. By centrally-planed economy I mean an economy without legal private sector (or where its contribution to GDP is so small, that it can safely be ignored).
If the answer is "yes", then how? For an example, can we count a state-owned factory director as an entrepreneur?


texts: How do different Indifference Curves relate to each other?

texts:
We note the following graph

There are three different Indifference Curves on this graph.

  An indifference curve shows a combination of two goods that give a
  consumer equal satisfaction and utility thereby making the consumer
  indifferent.

The goods on the axes are x1 and x2. Assuming they all represent the points at which our economic actor is indifferent to the bundles. How can the person be indifferent to the bundles of goods on each indifference curve, when the lowest indifference curve has less goods in each bundle, than any of the higher ones?

edit: I answered my own question, but would still love it if someone take a look at it, and told me if it makes sense


texts: Competition and welfare - empirical evidence

texts:
Consider the following claims:

less competitive markets deliver worse outcomes for consumers,
less competitive markets deliver lower social welfare,
less competitive markets deliver higher prices/lower quality.

These might be considered fairly canonical claims in the sense that they emerge naturally from many 'textbook' models from introductory economics or industrial organization. That means that many students of economics are exposed to such claims through the lens of theory. I would like to supplement this with empirical evidence.

I am looking for references to empirical work that supports or refutes one or more of the abovee claims (or close variants of them). Particularly welcome would be survey articles covering literatures that address them.


texts: Does comparative advantage sustain over long periods of time?

texts:
Let's say that given the same resources,

company A can produce 40 pens or 50 pencils,

company B can produce 30 pens or 30 pencils.

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

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


texts: Derivation of demand for intermediate goods in DSGE model

texts:
I'm self-studying Herbst-Schorfheide book on DSGE estimation and having troubles replicating their steps in the derivation of demand for final goods firms (Ungated model is here, page 3: http://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=1361&context=soe_research). Their final goods producers maximize profit function:

$\Pi_t = P_t (\int_0^1 Y_t(j)^{1-\nu} dj)^\frac{1}{1-\nu} - \int_0^1 P_t (j)  Y_t(j) dj$

and get the demand:

$Y_t(j) = (\frac{P_t(j)}{P_t})^{-\frac{1}{\nu}} Y_t$

My trouble is that I cannot understand derivation steps: how FOC looks like and why? Help is much appreciated!


texts: What are macro-economics simulations horizons and limits possible with exascale computing?

texts: What are typical examples in literature of large scale simulations of macro-economies of our time as of 2019 and what will change with the introduction of exascale computing? In terms, are there problems which might become feasible to assess then?


texts: What does it mean when a discount lender "rediscount[s] reserves"?

texts:
I was reading a wikipedia article about the evolution of global financial system: https://en.wikipedia.org/wiki/Global_financial_system#Interwar_period:_1915%E2%80%931944.

In the passage about the pre-WWI financial system, it is written that

  [Immediately before the outbreak of WWI,] European tensions and
  increasing political uncertainty motivated investors to chase
  liquidity, prompting commercial banks to borrow heavily from London's
  discount market. As the money market tightened, discount lenders began
  rediscounting their reserves at the Bank of England rather than
  discounting new pounds sterling.

What do "rediscounting reserves" and "discounting new pounds sterling" mean?


texts: Fraction of labour force providing income redistribution services

texts: What % of the labour force for an OECD country like the UK (mostly civil service I'm guessing) deals primarily with income redistribution, rather than income generation? Would a simple flat income tax at 40% and a universal basic income have the extra benefit of letting more people enter the value adding economy?


texts:
I am working on a paper for university about the car industry in Argentina.
I found a lot of data, but I cannot find any data about the turnover, profits and part of the GDP of this industry (Neither for each one one the companies) between 2014 and at least 2000 maybe more if possible.

The national office of statistics (INDEC) does not seems to have it, neither the ADEFA (Association of car constructors).

Does anyone have a good data website about this industry in Argentina?


texts: Differentiating under integral sign, capital accumulation

texts:
I am reading a paper, the author takes the derivative of the following equation with respect to $t$:
$$ q(t) = \int_t^\infty e^{-r(s-t)}c(s)e^{-\delta(s-t)}ds $$

$q$ price of capital goods
$r$ discount rate
$c$ cost of goods
$\delta$ rate of replacement
$t$ time of acquisition of goods
$s$ time of supply of goods

I have the answer, but I was hoping someone would explain the intermediate points. Here, is the process similar to differentiating the functions with summation operators in discrete cases?


texts:
In Mas-Colell microeconomics textbook I have found that profit maximization problem (as well as many further optimization tasks) could be represented with application of some transformation function (p.135):

$\begin{cases}Max\text{ }p*y\\s.t.\text{ }F(y)\leq0\end{cases}$

Where y is production vector and F(.) is a transformation function.

The only information I have found about this function states that $F:R^L\to R$ and that production set of a firm could be represented as $Y=\{y\in R^L:F(y)\leq0\}$. Also if $F(y)=0$ it is named transformation frontier (p.562)

So I am interested in what concrete are these transformation function and transformation frontier. Intuitively it must be related to some feasibility restrictions but I whant to have some full and strickt explanation.

Will be very greatfull for help!


texts: Is marginal cost different from extra cost?

texts:
I have been reading this resource which talks about why derivatives can be used to find the marginal cost.

https://www.dummies.com/education/math/calculus/how-to-determine-marginal-cost-marginal-revenue-and-marginal-profit-in-economics/

I am slightly confused about a statement referring to marginal cost and extra cost. They write "If you look very closely at the right side of the above figure, you can see that the extra cost goes up to the curve, but that the marginal cost goes up a tiny amount more to the tangent line, and thus the marginal cost is a bit more than the extra cost".

Are they stating that the marginal cost is different from the extra cost? Isn't that incorrect as the marginal cost is the extra cost from producing one more unit of a good? Or is marginal cost separate from the extra cost?

is it saying that marginal cost is different from extra cost?


texts: Best method for extracting cycle component of time series

texts:
I have macroeconomic time series data, including both quantity and proportion variables (i.e. aggregate consumption, unemployment rate, etc.). I want to work with the rawest version of the data, meaning that they all are likely to have a very present seasonal and trend components.
After performing appropriate removing of the seasonal component, and only being left with trend, cycle and irregular component, since my research is focused on business cycle I'm only interested in this component. Then, I want to use the best possible method for that end, the most common option would be Hodrick-Prescott filter, Christiano-Fitzgerald, and other that yield very similar results.
Then, I'd like some recommendations of other methods that might be well accepted, and as statistically rigorous for extracting the cyclical component of time series of this nature. An alternative that comes to my mind is from the known HP's critic Hamilton (2018), but is this approximation really better?
The final aim of my research is to get good estimates of main macroeconomic variables' second moments in the business-cycle, in order to be compared with a theoretical BC model.
You comments would really help me.
Thanks!
PD: By "best" I mean that the method meets good econometric standards in terms of statistical rigorousness.


texts:
I was wondering if it is possible to run a country based only on domestic economy and not to enter the world economy. Basically, if certain economy of a certain country fails and poses threat to world economy, can other countries seal off their economies and still function with sustained growth and flourishing markets based on domestic economy itself?

I know this a naive question, but I tried to find an answer on on the internet and didn't get a satisfactory answer.


texts: How does one prove the convergence of a trajectory in the Ramsey model?

texts:
Consider the Ramsey-Cass-Koopmans model in discrete time. Specifically, consider the following phase diagram.

For simplicity, let's consider the trajectory marked A which is in the northwest corner of this diagram.

In this location, supposedly $K_{t+1}<K_t$ and $C_{t+1}>C_t$. But how does one show this? Up to this point, all I have seen is that "supposedly" this trajectory veers off, but I don't see how it necessarily does so.

Let $$C_t = K_t^\alpha + (1-\delta)K_t - K_{t+1}$$

My Quesiton

Can someone explain why A veers off towards the NW direction? Specifically, why must $K_{t+1}<K_t$ and $C_{t+1}>C_t$?


texts: Profit Function: Just revenue maximization subject to constraint? if so where is $\lambda$?

texts:
Disclaimer: I dont know i'm getting confused with basic microeconomic prodoucer theory (note: Ive been watching some Hak Choi Videos on youtube),but this is my overall thought process.

We know that the standard profit maximization problem can be described as:
$$\max\pi=py(x)-wx$$

let $y(x)=x^\alpha$

it follows that the optimal $x^*$ from such a formula is:

$$\frac{\partial\pi}{\partial x}=p\alpha x^{\alpha-1}-w=0$$
$$x^*=\left(\frac{w}{p\alpha}\right)^{\frac{1}{\alpha-1}}$$

it follows that the optimal $y^*$

$$y^*=\left(\frac{w}{p\alpha}\right)^{\frac{\alpha}{\alpha-1}}$$

however, isn't the profit maximization problem also just a revenue maximization problem subject to a constraint?
$$\max py(x) $$
$$s.t.\bar{C}(x)=wx $$

let
$y(x)=x^\alpha$

It follows that our Lagrangian for this problem is:

$$L=py(x)+\lambda(\bar{C(x)}-wx)$$

taking the derivative of our Lagrangian With respect to $x$ we find
$$\frac{\partial L}{\partial x}=p\alpha x^{\alpha-1}-\lambda w=0$$

$$x^*=\left(\frac{\lambda w}{p\alpha}\right)^{\frac{1}{\alpha-1}}$$

it follows:
$$y^*=\left(\frac{\lambda w}{p\alpha}\right)^{\frac{\alpha}{\alpha-1}}$$

I find that there is a great deal of similarity between these two problems and their solutions are also very similar. based on this reason I ask, is this an appropriate way to solve for the input and out of a profit maximizing firm? if so what happens to $\lambda$ in the profit function?


texts: When the ECB does QE, does it print new money?

texts:
I knew that when the Fed in the US buys bonds through Quantitative Easing, it does so using money it has from previous profits and that it doesn't print new money.

However, I was reading this article about QE, which states that the European Central Bank prints new money when doing QE.

So the ECB, unlike the Fed, does print new money when doing QE?


texts: Why don't governments ban businesses from passing tax costs onto their customers?

texts:
So, after a bit of discussion in the comments of this question on the Politics SE, I figured I'd post it here:
One of the arguments against taxing large businesses is that they'll just pass the costs on to their customers, effectively raising inflation and harming the working class, or cut costs by making employees redundant.
Why don't countries pass laws imposing taxes and legally mandating that companies are forbidden from doing either of these things, and that it must be paid directly out of their profit and/or owners' equity? This might possibly take the form of the government mandating that all businesses over a certain size must issue X% of their shares to the government without granting the government voting rights, so that the government owns X% of all of their profits.
Are there any countries who have done anything like this? How did it work for them, if so?


texts: I have a producer price index which is the composite of 9 various commodity prices including that of coal. I want to remove the effects of coal price changes from the original index. I have data on coal prices. Does anyone know of a method that I could use to filter out the effects of coal price changes from the original index?


texts: Demand curve:log Quantity, logprice,logprice of N substitute goods,log income, need something else?

texts:
Imagine the following situation: a seller of a company has the price and quantity sold for a certain good, that seller can simply make a regression like:
ln(Quantity) = ln(Price) ~ ln(price of substitute good1)+ ln(price of substitute good2)+ ln(price of substitute good N)+ ln(income)
thinking only in terms of the demand curve, would this type of model explain reasonably well what would be the demand quantity at a price lower than what he sells at the company he works for?


texts:
I am confused about how to proceed about testing for cointegration. I am interested in testing for cointegration between 3 stock indices.

I was instructed to use returns and not prices. So my question is how do I proceed about identifying a cointegrating relationship since the definition is finding a combination of I(1) variables that is I(0). Since returns are I(0) because they are the first differences, can I still use the Johansen test?


texts: Extension on the suspension of national debt ceiling

texts:
So I just want to make sure i got this right,

The national debt ceiling was suspended, i.e. the government can now freely spend until Dec.8, which they "say" was for providing $15bn in hurricane relief.

But lets face it, the treasury was running out of "extraordinary measures" to keep the debt below the ceiling, thus the extension. Source -> http://www.businessinsider.sg/us-debt-20-trillion-how-much-2017-9/?r=US&IR=T

The debt increased by 317 billion. But that aside, I want to get into the economics fundamentals. What does this mean for the dollar?

So foreign debt is increased, I am assuming the USD is going to plummet if expectations of quantitative easing to pay off the debt increases?


texts: What were the effects of the 2016 Indian banknote demonetisation?

texts:
On 2016-11-08, the Government of India announced that it had:

  decided to cancel the legal tender character of the High Denomination bank notes of Rs.500 and Rs.1000 denominations issued by RBI till now.

What were the effects of this demonetisation? Have there been any estimates of its net benefits or costs? And all things considered, was it a good idea?

(Wikipedia article, related question.)


texts: Relation between demands of $x, y$ and $z$

texts:
Question: Consider a consumer with utility function $U(x,y,z)=y\min\{x,z\}$. The prices of all three goods are the same. The consumer has $100 to spend on these three goods.The demands will be such that:
(a) $y<x=z$
(b) $y>x=z$
(c) $x=y=z$
(d) None of the above
My attempt: The consumer will consume equal amounts of $x$ and $z$ because otherwise the allocation would be inefficient, that is, he can obtain the same level of utility by spending less. So $x=z$. I cannot figure out how is $y$ related to $x$ and $z$. I think the answer would be (d) None of the above because it does not matter if $y$ is less than or greater than or equal to $x$ and $z$.


texts: Research at the county-level: Macro or Micro?

texts:
Is research at the county-level considered applied micro or applied micro?

The standard undergrad definitions ("micro" = "individual", "macro" = "nation") are of no help with units of measurement that lie in between.

Any help is appreciated.


texts: How is it economically responsible to destroy proprty which has value?

texts:
precursor: bitcoin.stackexchange.com/q/1851

How can it be economically responsible to destroy property which has value?

If a property is destroyed (which is the right of the property holder in most cases, I do not dispute that) then, the holder robs themselves of the economic benefit of otherwise disposing of the property which has value and that they no longer want, rob the economy also of that passed on benefit or, at least their heirs and the future economy are robbed of the benefit.

How can this be economically responsible dominion over property?

I take it that under most jurisdictions a company would be prevented from doing the same as it is not in the best interests of the company, a principle which the directors must uphold.

I wish to gain an economic view of flaw/benefit this practice.

Can this even be justified in such extreme circumstance as; I possess the only ten copy Picasso's, they are validated and dated and, there is no surviving original. I destroy nine of the ten copies.


texts: Is it possible to establish macro-effects of low code platforms?

texts:
Low code platform means, you can implement there complex business processes with less or even no code, just by interacting with a user interface.
Historically, for example Visual Basic for Applications and SAS have been usual business tools going into this direction in a limited sense (in many cases more feasible that develop your own solutions using C++/FORTRAN).
Nowadays where cost of IT is often required to develop towards zero, and with higher degrees as information technology becomes more and more ubiquitous, so it has become possible to build whole businesses using this platforms and advanced integrated solutions, now cloud based:

Google business services and Salesforce for marketing and sales, also Facebook;
Microsoft either Google for your whole documentation workflow
One or more cloud solutions from same above either Amazon in case you want to process raw data either have virtual infrastructure

Now what are macro long term effects if any of these developments?


texts: Is there a theory about investors' behaviour during bubbles?

texts:
As far as I can see there are two senses in which it's 'rational' for an investor to buy during a bubble.

The investor has erroneously overvalued the value of the stock/commodity.
The investor is aware that it's a bubble and is overvalued, but believes he can make a profit by selling before the bubble bursts.

There are also 'irrational' explanations, such as the investor being caught up in the hype, or fearing missing out.

The question is, is investor behaviour during bubbles well studied, and are there models explaining it?


texts: Risk neutral probability for each of 3 states

texts:
I need help to find the risk-neutral probability for states 1,2 and 3

I have two stocks: A and B.

The price of A today is 180 and in a year it will be worth 288 (S1), 180 (S2) or 120 (S3);

The price of B today is 100 and in a year it will be worth 94(S1), 134(2) or 54(S3)

The annual rf rate is 2%

I did the following for stock A:
up : 288/180-1= 0,6
down :120/180-1 =-0,3333

Finding prob for s1: (2- (-33,33))/ 60- (-33,33)) = 0,3785

Then tried to solve for p2 and then p3:
PV= (0,3785* 288 + p2*180+ (0,6215 -p2 )* 120)/1,02= 180

These probabilities don't add up when I try to find the price of stock B, so they are clearly wrong. Can you tell me how to find the right probabilities?


texts: Do banks pay each other from their reserves?

texts:
Suppose Alice wants to buy Bob's house but they use different banks. Alice gets a loan from bank A and needs to transfer her new deposits to Bob at bank B to pay for the house. Obviously Alice's deposits at bank A will decrease by the same amount that Bob's increases at bank B, but now bank B's liabilities have increased (more deposits) while bank A's have decreased (less deposits). How is this imbalance settled between the two banks?

I'm guessing bank A sends money to bank B through the central bank (since both banks have an account there), which means A is sending B some of its reserves. But it also seems possible to me that bank B could have an account at bank A that gets credited new deposits.

Similarly, when banks loan to each other to meet reserve requirements, do they loan money that the central bank credited to them or do they credit each other with the reserves they need?


texts: Why are the concepts of short-run and long-run equilibrium exclusive to aggregate supply and demand and macroeconomics?

texts:
Shouldn’t there also be a concept of short vs. long-run equilibrium in microeconomics? After all, short-run equilibrium describes the state of the economy when wages and prices are still adjusting and when worker misperceptions are affecting quantity-supplied of labor; and long-run equilibrium is the state of the economy when worker misperceptions have been corrected, and wages and prices have adjusted to their final levels.

Doesn’t this happen in microeconomic situations? If not, why not?


texts: Intermediate macroeconomics: optimal bundle for quasilinear utility?

texts:
How would I go about solving this question:

Assuming consumer's utility function is $U(C,L)=c+2l^{0.5}$, consumer earns a wage of 0.5/hour, $h=24$ and there is no real dividend and tax is $T=11$. find:

a. The maximum amount of leisure the house hold can have and still pay taxes
b. find the optimal bundle of consumption and leisure.

For part (a), I took the derivative of $U$ with respect to $L$ and set it to 0, giving me $l^{0.5}=0$ and $l=0$. Is this part correct? Intuitively, this feels very wrong to me.

I'm also stuck on part (b). I took the derivative of the utility with respect to $C$. From my understanding, MRS is the derivative of $U$ with respect to $L$ over the derivative of $U$ with respect to $C$. I ended up getting $1/(L^{0.5})$.

I know the optimal bundle is when the budget line is tangent to the indifference curve and I also know that the slope of the budget line would be $-W$. However, when I solve for $1/(L^{0.5})=0.5$, I end up getting $L=4$ and $C=-1$. It doesn't make sense to me that a consumer will be able to have negative consumption.

Would greatly appreciate it if someone could point out where I went wrong!


texts:
I'm working on a game theory problem.I'm having trouble understanding what the mixed strategy nash equilibrium is exactly in this game.

The game is :Two players have to choose how distribute a piece of land ($size = 1$). Each player (1, 2) send his decision $x_i \in{[0, 1]}$ to an external agent.

If $x_1 +x_2 \leq 1$, each player gain a land portion equal to $x_i +\frac{1-x_1-x_2}{2}$

If $x_1+x_2 > 1$, they end up with nothing.

The first part of the problem is to solve the game in pure strategies. I figured out that the answer of this part is:

Player 1 should pick $1- x_2$, any higher and he gets 0. The game is symmetric so the same hold from player2's perspective. The optimal strategy is the intersection of these two functions.

The second part is to solve the game in mixed strategies (if exist). But I don't know how to aproach this part.


texts:
I'm new to auction theory and only started reading it a few days ago.
My question is this: Is it possible to design efficient auctions of multiple non-identical items? By efficient I mean maximize the social welfare.
Also, let's say there is only one seller who owns all items and seeks to sell them to multiple bidders who can get at most one item.
I'm a little discouraged as I haven't found a lot of theory papers on this problem. Is it because what I described above is a special of bundling (where bundle sets are singletons)?
I'd appreciate it immensely if you could direct me to a source (paper or book). Thank you.


texts: Getting a market supply curve from firm supply curve

texts:
PFA the image below.

As there are n firms in the market, and a tax of t moves up the cost curves of an individual firm by t units, shouldn't the cost curve of the market move up by n*t units? If yes, why does the book move the curves up only by t units. If no, could you please explain where my reasoning is going wrong?

Thanks


texts: Why hipothesis of perfect competition market implies fixed price of a product in every transaction?

texts: My book says that from the axioms of perfect competition follows that the price is fixed in every transaction but it doesn't specify in which way it is possible to prove it. Besides, are all the axioms necessary to prove this "theorem"?


texts: Determining the elasticity of Hicksian Demands

texts:
If we have Hicksian (compensated) demand functions, how can we determine the income elasticity and own price elasticity?

Is the procedure the same as for Marshallian (uncompensated) demands?


texts: What caused the stagflation in the early 1970s USA?

texts:
I am aware of the conventional reasons: demand push inflation due to much higher oil prices, and a continuation of a mild recession.

Looking for a clearer explanation than I have been able to find, especially wrt monetary policy (IE, printing money)


texts: Does every structural policy change count as structural break?

texts:
I was reading the answers to this question when, the one by Dawson Verley aroused my curiosity. Does every change in structural policy result in a structural break? What conditions are necessary and/or sufficient for break?

Any help would be appreciated.


texts:
I have import values in LOCEUR (LOC is local currency).
How can I obtain these values only in EUR? My data are from Eurostat, where external trade indicator is "Exports in million of ECU/EURO"


texts: How can I prove that a utility function does (or does not) satisfy diminishing MRS?

texts:
I have this CES utility function:
$$U(f, c) = (f^\alpha + c^\alpha)^{1/\alpha},$$
with $\alpha > 0$.
The problem set asks does it "satisfy the principle of diminishing marginal rate of substitution for any value of $\alpha$".
To which the answer is "False, if $\alpha > 1$ the indifference curves are concave, so they don’t satisfy the principle of diminishing MRS"
But short of graphing the indifference curves and hoping that it's visually obvious, I'm not sure how to tell this.
How can one tell from a utility function whether it is or is not non-concave?


texts: Why is the equilibrium network size can be less than the socially optimal size in networks w/ positive externalities for single system?

texts:
For Context, I am reading http://web.mit.edu/rpindyck/www/Courses/NetEx19.pdf. The chapter talks about network externalities in single system like fax machine, email, vaccinations for measles. Paraphrasing from the book "In each of these cases, the
marginal social benefit of one more person joining the “network” is greater than the marginal
private benefit. Hence, the equilibrium network size can be less than the socially optimal
size, so that the competitive market will not be efficient".

Why is equilibrium network size less than socially  optimal?


texts: Generating profit by leveraging fluctuations

texts:
I was writing some code akin to a sound limiter when it occurred to me that if you could find something fluctuating in price between two extremes (what and when those extremes would be isn't relevant I think, just the fact that between those extremes there exists a space where the "signal" would always return to) you could theoretically leverage that in a market setting.
If such fluctuations had sine-wave like properties you could write an algorithm that "buys" below zero and "sells" above zero and generate a profit this way. (I'm using quotes because I really don't mean to exclusively ask about financial markets or stocks, just any exchange that fits the description)
This raises some possibilities:

I'm the programmers answer to Einstein, I should have kept this to
myself and could have made billions.
The type of predictable fluctuations that are needed do not occur in reality ever. This is feels counter
intuitive to me, stocks go up and down, economies wax and wane?
This actually happens but the fact that it does
"closes the gap" so to speak, i.e. it leads to an equilibrium
because even the tiniest fluctuations are "used up" like this. If
so, is this a principle that has a name I could read up on?
This is, when talking about physical goods, entirely impractical because it
implies storage. Similar constraints exist for other kinds of
markets.
This is something very mundane, I'm just thinking about it
in the wrong way.
Something else?

What's going on here?
I've tried finding information on this subject but I'm having a hard time formulating a query. To me, this has all the hallmarks of something that would appear either as a game in game theory or as a problem category in computer science, however it seems to me that it is essentially an economics question, that's why I'm asking it here.
I've also tried asking on another site with an ill conceived practical example, but that never got me past 1, or at least the discussion never really went beyond the practical example.


texts: A profit maximization problem (whole problem has been solved, I just have question about interpretation)

texts:
I would like to discuss with you about the following production function.

$$y=f(t_m, t_l)=\rho t_m^m(n+t_l)$$

where $0<m<1 $ and $n>0$ are fixed parameters.

$t_m$ is manager time.

$t_l$ is labour time.

The manager know the production function freely.

Also let’s define $w_m$=manager’s wage and $w_l$=labour’s wage for $w_m>w_l>0$

$\rho$ is the good’s market price.

Extra Notes:

• the manager’s outside option= the  manager wage in the economy

•the manager is going to  run his own company if he establishes one.

So far, I have defined the production function.

How I have two questions that I would like to discuss with you.

————————

How can I interpret the parameters $n$ and $m$? It is easy to interpret them mathematically, but I could not decide how to make a comment about these parameters in economic terms?

When I take derivatives

$\partial y/\partial t_l= t_m ^m>0$ which means that as labour’s time increases, production increases, revenue increases and so profit increases.

$\partial y/\partial t_m= m t_m ^{m-1}(n+t_l)>0$ which means that as manager’s time increases, production is diminshingly increases (since $m-1<0$) and revenue diminishingly increases so profit diminishingly increases. ( I did this comment. But I don’t think it is enough or correct in economic view. How can I say it correctly?)

———————-

My important question is that!

Under Which conditions does the manager establish a company and decide to enter the industry?

For that, I firstly establish the manager’s decision problem as follow:

Revenue = $\rho y= \rho t_m^m(n+t_l)$

Cost= $t_m w_m + t_l w_l$

Profit = $\pi = \rho t_m^m(n+t_l) -( t_m w_m + t_l w_l)$

So his decision problem:

$$\max \rho t_m^m(n+t_l) -( t_m w_m + t_l w_l)$$

Subject to $w_m>w_l>0$ and $0<m<1$ and $n,p>0$

When we solve it

$\partial \pi/\partial t_m= \rho m t_m ^{m-1}(n+t_l) -w_m=0 $

$w_m= \rho m t_m ^{m-1}(n+t_l)$

$\partial \pi/\partial t_l=\rho t_l ^m-w_l=0$

$w_l= \rho t_m ^m$

So we know that $w_m>w_l>0$

$$ \rho m t_m ^{m-1}(n+t_l)> \rho  t_m^{m}$$

$$n+t_l>{t_m\over m} $$

I only find this condition in order to establish a company. ( I am not sure but I hope it is true) But I cannot say something about it in economic view.

I solved everything, just discuss what I did. Is it correct or false? Or how can I interpret them in economic aspect?

Thanks a lot.

EDIT

From the above maximization problem, I obtained the following solutions:

And from $w_l= \rho t_m ^m$

I get $$t^*_m=(w_l/\rho)^{1/m}$$

From $w_m= \rho m t_m ^{m-1}(n+t_l)$

I get $$t^*_l= {w_m\over m}p^{1-m/m}w_l^{1-m/m}-n$$

When I insert these two $t^*_l$ and $t^*_m$ into the profit function, I get

$$\pi^*=w_l^{1/m}w_m \rho^{1-m/m} {1\over m} (2-mp^{1/m-1})-nw_l$$

Then, when I compare this with the outside option $w_m$, then I get

$$\pi^*=w_l^{1/m}w_m \rho^{1-m/m} {1\over m} (2-mp^{1/m-1})-nw_l>= w_m$$

But this result doesn’t make sense. I could not make any reasonable interpretation.


texts: Sovereign debt market learning resources

texts:
I'm trying to understand this paper, but I'm having some difficulties in understanding some parts. Is there good quick introduction about how the sovereign debt market works?

The paper is about greek debt 2012 restructure:

http://scholarship.law.duke.edu/cgi/viewcontent.cgi?article=5343&context=faculty_scholarship


texts: Check for concavity, quasi-concavity with given value of function

texts:
I am studying for an upcoming exam in microeconomics and I have always struggled with proving concavity, convexity in different exercizes. This one I can't solve for the life of me. It is kind of hard to find the exact point I struggle with, because I'm pretty confused on this one overall.

We are given sets of points for which the value of the function is f(x) = 1, 2, 4.

We are then asked if these curves are consistent or inconsistent with the function being either concave or quasi-concave.

We are given tips:

Write down the definition of concavity:

$f: D -> \mathbb R$ is concave if for all $ x, x' \in D, t \in (0,1):$

$f(tx + (1-t)x') \geq tf(x) + (1-t)f(x')$

Select two points in the domain (1,3) and write down the convex combination for the points.

???

Evaluate the value of the function.
Evaluate the value of the convex combination for each of the points for this function.
Use the defintion to show where the function is concave and/or quasi-concave

What throws me off here is that there is no actual function given, but only values for the function. If I had a function, say $f(x,y) = x^\beta y^{1-\beta}$, I could choose a point and check with a certain t against the concavity defintion, right?

I hope this doesn't fall under the no homework-clause. I don't have to turn this in, I'm just lost :)


texts: What are the implication of state-run oil production vs. private production from leases?

texts:
I'm not any kind of expert in this area, so please be gentle.

It seems that we speak of oil (and other natural resources) as though control of output and revenue from extraction adheres to the national government (as in "Saudi" oil), but is this true of countries like the US as well? Is it accurate to speak of "US" oil in the same way we speak of "Saudi" oil, given that from what I gather the US does not directly control production and does not directly sell product, while the Saudi government controls oil extraction as a state-owned monopoly?

What if any are the implications of the apparent differences here?


texts: Nonparametric estimation: Interaction of two continuous variables

texts:
The probability of observing a binary outcome y is a function of two variables, y = f(x1, x2).

Both x1 and x2 are continuous, and I have no prior on the functional form of f. I have shallow knowledge of kernel density estimation, but have only seen that done in the case of a univariate variable. How should I proceed here / is there some basic literature on this?


texts: Perfect Substitution with a Continuum of goods?

texts:
Imagine I have a continuum of different goods indexed by $\omega \in [0,1]$. I have a household which consumes a quantity $C(\omega)$ of good $\omega$, and pays a price $P(\omega)$. The household has a budget equal to 1, and has a linear utility function.

$$U(C) = \int_{0}^1 C(\omega) d\omega $$

The consumer chooses her consumption bundle by solving the problem

$$\max_{C} U(C) $$
$$ \text{Subject to}:  \int_{0}^1 P(\omega) C(\omega) d\omega \leq 1.$$

My question is with regards to the fact that this problem seems ill-defined. If I were to go ahead solve the optimization problem, I would have the consumer choose

$$C(\omega) = \begin{cases} \frac{1}{P(\omega)} \text{ if } P(\omega) =  \min_{\omega'} P(\omega') \\ 0 \text{ otherwise.} \end{cases}$$

However, this means that  $U(C) = \int_{0}^1 C(\omega) d\omega = 0$, and $\int_{0}^1 P(\omega)C(\omega) = 0$ since $C(\omega) = 0$ almost everywhere.

Is there a mathematically more robust way of defining this problem? One approach I've seen is using Dirac delta functions, but I'm not sure that's right. That is, defining

$$U(C) = \int_{0}^1 C(\omega) \delta_{\omega} d\omega$$
where $\delta(\omega)$ is a ``function'' which is equal to $+\infty$ at $\omega$ and $0$ everywhere else.


texts: Economics of exclusive supercars with limited number of items sold

texts:
I understand that rarity increases price, and that maximum profit may not be to sell every car you can but still the production of supercars looks weird to me.
T.50 production will be 100. Allegedly they sold most of them already.
Ferrari Enzo(quoting Wikipedia):

The company sent invitations to existing customers, specifically, those who had previously bought the F40 and F50. All 399 cars were sold in this way before production began.

It seems that in both cases manufacturers could sell much more cars than they choose to do(without reducing the price)
So is there a well know economical reason for this strategy(assuming car manufacturers are not lying about the demand).


texts: Find Price elasticity of demand in this example

texts:
ln(Q) = 10-0.7ln(P), where P is price and Q is demand.

What is the price elasticity of demand?


texts: Preference over lotteries without independence axiom

texts:
Suppose a set of $N$ outcomes can be ranked in the following order: $1\succ 2\succsim\cdots\succsim N$. Further, suppose a decision maker has preference over lotteries over these outcomes. Assume the preference over lotteries is rational, continuous, but not necessarily consistent with the independence axiom.

Does it follow that the best lottery in this case is the degenerate lottery $(1,0,\dots,0)$?

What if the independence axiom is violated?


texts: Can the central bank interest rate policy still control inflation?

texts:
Historically, central banks have been using interest rate policy to control inflation.

In current times, most rates have been going ever lower, but it seems to be incapable of driving inflation up.

Do cheap loans really encourage people to start and expand businesses, or at least increase consumption? In my own country, Canada, it seems that all that those cheap loans do, is encourage buying more expensive homes.

Would the average citizen really use loans to increase consumption, buy cars or holidays? I may be wrong, but I would guess most people are reluctant to borrow for something that is not a home?

If that is the case, would it not mean that setting interest rates is no longer an effective monetary instrument when it comes to consumer price inflation?


texts:
Suppose the government wants to determine the efficient price of a certain commodity for which there is no competitive market. One way to do this is to take a sample of the potential buyers and ask them how much they are willing to pay, take a sample of the potential producers and ask them what their costs are, calculate an optimal price on the sample and use it as an approximation to the real price.

I am interested in references about this and similar problems. Particularly, my goal is to calculate bounds on the error of approximation. This seems like a fairly standard question in statistical economics, but I could not find references.


texts:
On June 11, 1782, John Adams secured a much needed loan for the new Republic from Holland. How exactly did this work in the days of strictly paper currency? What did it mean to loan internationally back then (and even today)?

Did Holland send their own currency? Did they send it in the form of some standard, i.e gold bullion? How did the U.S. pay this back? In some other standard? I just have no concept of how an international power could lend anything other than goods in the 18th century.


texts: How to estimate market risk using only publicly available data?

texts:
How can I calculate market risk for the US Stock Market (NYSE or NASDAQ) using only freely accessible data? I'm only interested in the market risk of the whole economy not of different industries, companies or sub-sectors.

Somebody suggested to me to download market index data and construct the volatility as a measure of market risk. But I can't find a proper explanation how I do this.

Thank you.

p.s. Is the following procedure correct?:

I get data US Stock market (for example https://fred.stlouisfed.org/series/SP500) calculate the growth rate and in the last step I compute the variance of the growth rate to get the market risk?


texts: Why isn't the Fed funds rate greater than interest rate on loans to the pubic

texts:
First of all, fed funds rate is the rate banks borrow reserves' from each other. Interest rate on loans is the rate the bank charges to public for its loan. From one line of logic, we think of the rate bank charges to public should clearly be greater than the interest rate itself bear to borrow since banks are making a margin. And empirical data clearly support it.

However, another line of logic does not quite support it. We know the banks borrow reserve money in fed funds market, which is clearly better than the money it lends to the public in the following sense: one unit of fed funds can support 10 units of additional deposit if the reserve-deposit ratio is 10%. So the banks with this addtional 1 unit of reserve, can theoretically make 10 more units of loans and therefore creating 10 more units of deposit. So reserve is better money. Hence, theoreticaly, the fed funds rate should at leastbe higher than the rate banks make loans to the public, if not 10 folds.

My question being whether there is a logical fallacy in my understanding and if not, what kind of reality deviated it from theory.


texts: What are some good Phd or research programs for Economic History / Economic Thought History?

texts: Please correct me if I am wrong, but my impression is that most "mainstream" economics programs are now focusing less and less on economic thought history. So, in order to do research on economic thought history or some comparative studies on economic development, perhaps history department is a better place to study? What are some good programs for that? Thank you!


texts: Interest rate determination in the real world

texts: I have just learnt about the demand and supply framework for money and how the equilibrium interest rate in an economy can be determined. In theory, based on that framework, an increase in nominal incomes would lead to an increase in the demand for money, causing interest rates to rise. However, in reality, I don't see that occurring. In fact, in reality, say in the United States, rates are often set by the Federal Reserve through manipulation of the money supply. To me, rates don't seem to change as a result of changes in nominal incomes. Why is this so?


texts: What is the trade-off between? Consumption and Leisure or Income and Leisure?

texts:
When first presenting the utility function and its arguments, textbooks typically start by stating that utility is a function of consumption and leisure. See for example https://sites.hks.harvard.edu/fs/gborjas/publications/books/LE/LEChapter2.pdf.

On the other hand, some consider that the utility is a function of income and leisure, and claim that this is more familiar than if the utility was a function of consumption and leisure. See for example https://www.jstor.org/stable/1911308?seq=1#page_scan_tab_contents.

What are the different motivations behind the two approaches? Which one is, or should be, the standard? What should be the reference point in determining the arguments of the utility function?


texts: Question about using elasticities to compare difference rates but with different normalization

texts:
Lets say I am estimating a regression of a death rate per 100k people on an economic shock, so:
$y = \beta_o + \beta_1 * X+ error$
where the dependent variable is the death rate, and x is the measure of the shock.
First, I can calculate an arc elasticity by doing $\hat{\beta}$ * $\frac{\bar{x}}{\bar{y}}$, correct?
and given this, I want to compare this elasticity to another paper in the literature that uses a different shock by creating the same arc elasticity given their regression results and summary statistics. However, their dependent variable is a death rate per 100k people aged 18-54.
Since elasticities are unitless, if I calculate my elasticity, and say it is 2, and their elasticity is 2.5, are these still roughly comparable measures?


texts: Does the H-1B visa program have the effect of reducing wages in the U.S

texts: In either the short or long term, does the H-1B visa program have the effect of reducing wages in the U.S. for U.S. citizens?


texts: Economic valuation of green spaces using GIS

texts:
I was wondering if there are any standard methods that are employed to obtain insight of the economic value of tree cover in a particular area. I assumed using negative difference vegetation index coupled with economic value of ground cover as proxy but this is not supported by any literature in my search.

So if there any datasets (preferably free) that show the spatial value variations for green spaces, their suggestion would be appreciated.


texts: Why stochastic dominance is "stochastic"?

texts: I think the CDF is pretty much fixed, so the FOSD (first order stochastic dominance) is pretty much non-stochastic. Why does it have a "stochastic" in its name?