texts:
Do quasi-linear indifference curves have MRS's that depend only on the nonlinear variable?  For example, for a U(x) = √(x) + y, I calculated that the y would not be in the MRS.  Does that mean that a consumer does not factor the consumption of a "linear" good y into their utility maximization?

If this is the case, can someone explain to me, practically, what it means for a good to be "linear" and for an MRS to exclude one variable?


texts:
Company I work at provides software services. After customers sign up, they then can go and order different combinations of services and consume them.

We do not expose prices within the flow of them ordering services, however we do provide detailed bills to them outlining costs as well as make all prices available on the separate documentation side that we link to.

Personally I believe it is a bit strange that we do not show prices when they order those services (even though they are just a few a clicks away). My theory is that once we will start showing those prices, it will increase customers trust (because we are transparent) and satisfaction (because it will help them avoid surprises in the bill).

I'm wondering if there is any research on the subject of price transparency and its effects that can help prove or disprove my assumptions.


texts: Network goods in competitive markets vs. socially optimal network size

texts:
In networks economics, the socially optimum equilibrium is bigger than the one in perfect competition (see for instance, Easley and Kleinberg 2010, Ch. 17).

Why is that so? Could you provide me with an example?


texts: Effects of finding infinite gold reserve

texts: Suppose an infinite reserve of gold was found. What would be the consequences to the economy in general. Would it have major negative effects?


texts: What impact would falling oil prices have on the natural rate of unemployment?

texts: My intuition is that as the price level falls, cost of inputs is falling for suppliers and their output increases. More people are then employed to increase production - correct?


texts:
Can someone please explain why the concept of a core is equivalent to a competitive equilibrium?
I am just writing a term paper for my matching theory class and I'm having a hard time following along with the literature.
In particular I'm referring to Gale and Shapley (1962), Shapley and Shubik (1971), and Crawford and Knoer (1981).
Thanks


texts:
QUESTION: What are the major or systematic applications of post-1960s mathematics to microeconomics?

For example, in the late 19th century, Fisher first used the mathematical ideas of Gibbs to construct modern utility theory. In the 20th century, Mas-Colell incorporated topological ideas to study general equilibrium. What about the late 20th, early 21st century?

For example, consider directed graph theory, measure theory, topology, the category theory and modern homology or cohomology, topos methods, functional integration, etc.

Note 1: econometrics/statistics, without modelling, is excluded. The only modern mathematics used there is random walk theory, and the ergodic problem, solved via complex analysis. RW and EP are not specific to economics.

Any appropriate economics publication is an answer. This included also those published in non-strictly economics journals, e.g. the Journal of Mathematical Psychology.

Note 2:
Yes, I know, this type of work is rarer (not to be confused with obscurity: some of it is well known). That is what makes it easy to miss such a reference when it is published. Hence the question.


texts: Levelized cost of electricity, to calculate the absolute costs?

texts:
I'm doing my master thesis about the renewable energies. So my goal is to calculate how much it will cost to switch our fuel based energy generation to renewable energy generation. So my first thought was I use the levelized cost of electricity. I found some forecasts of how they will develop to 2050. So I made different scenarios in my thesis on of fast/slow the switch will be and now wanted to calculate the cost of them. So what I wanted to do is take those levelized costs of electricity (LCOE) and multiply it with the amount of electricity production different technologies have in my scenarios. After I did all those calculations I started to become sceptical if this all makes sense at all. Because I thought to myself if I look at the formula of LCOE, if you would change the amount of generated electricity it will also effect your LCOE, so lets say I produce more electricity through coal, this will decrease my LCOE and so on.

I am kinda stuck in the middle of nowhere now, because one part in me tells me that this are basically the costs per unit so it makes sense what I did and the other thoughts I have is, it makes no sense.

in other words:
Can I use the LCOE forecast of 2030 from those studies and multiply that with the amount of electricity produced for example in my 'scenario B' in the year 2030 ?

sidenote: scenario A, B, C and D have a different approach of how fast/slow the switch should be done, so lets say in scenario B I decided that in 2030 there will be already 60% of renewable energy, while scenario C is more conservative and the renewable energy is still beyond 20% of the whole generation.

Can someone please help me with my logical dilemma ?


texts: Is Debt Monetization Equivalent to transferring money from rich to poor?

texts:
I'm reading Ray Dalio's "How the Economic Machine Works", and he says that there are four factors contributing to deleveragings in economies:

1) Debt Reduction

2) Austerity

3) Transferring wealth from the haves to have-nots

4) Debt Monetization

However, to me it seems like debt monetization is equivalent to transferring wealth from the haves to have-nots -- am I correct in my assumption?

Debt monetization leads to inflation which means that cash and Accounts Receivable get cheaper. That would mean that cash holders and creditors would get punished. Since creditors are wealthy people, aren't we basically reducing the dollars received by wealthy people and giving that money back to poor people through job creation?

Just want to make sure I'm understanding correctly.

Thanks!


texts: Comparative dynamics in forward-looking equation

texts:
I have set up and solved an optimization problem with time $t$ endogenous state variables, $\alpha_t$ and $\beta_t$ and choice variable $s_t$. After some manipulation, the first-order condition for $s_t$ is of the form:

$f(\alpha_t,\beta_t,s_t,s_{t+1})=0$

where $f(\cdot)$ is a non-linear and contains expectations over future realizations of shocks. In some specifications there is no explicit solution for $s_t$.

I want to derive testable implications from the underlying theory. In particular, I am interested in the signs of:

$\dfrac{\partial s_t}{\partial \alpha_t}$ and $\dfrac{\partial s_t}{\partial \beta_t}$.

How should I treat $s_{t+1}$ when I take the total derivative? Should I treat it as a constant, or include it? What's the rationale? If more elaboration is needed, do let me know and I'll be happy to explain in more detail the problem.

Thanks!


texts: Insurance question: need a brief explanation

texts:
Two risk averse people are identical in every way (including wealth, W , amount of loss, L, and utility function, U(W)) except they have different probabilities of loss. Suppose they want to buy insurance from a risk neutral monopoly insurance company. Let p1 and p2 denote the probabilities of loss of each agent, respectively, with p1 < p2. The company cannot distinguish between the two agents.
An insurance policy is a pair (P;I) where P is the premium paid and I is the level of coverage (amount paid out in case of loss).

(i) If the company is restricted to o§er a single full insurance policy what would it be?

I have found its solution:  but I don’t understand a point in its solution.

We consider two situations.

1st Situation: we consider a full insurance only to low types (I.e. people who have high probability of loss (p2))

Let’s characterize the insurance policy

$p_2U(W-P-L-I)+(1-p_2)U(W-P)=p_2U(W-L)+(1-p_2)U(W)=U_L$
$W-P-L-I=W-P \iff L=I$
$P^*=W-u^{-1}(u_L)$

I understand how to write these three steps perfectly.  But,

2nd Situation: we consider a full insurance only to both high types and low types (I.e. people who have high probability of loss (p2) and who have low probability of loss (p1))

I am stuck at this point,

  $p_1U(W-P^L-L-I)+(1-p_1)U(W-P^H)=p_1U(W-L)+(1-p_1)U(W)=u_H$
  $W-P^L-L-I=W-P^H \iff L=I$
  $P^*=u^{-1}(u_H)$
  Firm’s expected profit = $(1-p_1)P^H+(p_1)(P^H-I)+(1-p_2)P^H+(p_2)(P^H-I)$

In yellow box, in 1st and 2nd steps, why do the one side of the equation include $p^H$ and other side of the equation include $p_L$?

And in the 3rd step, why price level don’t include wealth W?

For example, if I solved the question by myself, I wrote the equations in yellow box as follows :

1. $p_1U(W-P^H-L-I)+(1-p_1)U(W-P^H)=p_1U(W-L)+(1-p_1)U(W)=u_H$

2. $W-P^H-L-I=W-P^H \iff L=I$

3. $P^*=W-u^{-1}(u_H)$

4. Firm’s expected profit = $(1-p_1)P^H+(p_1)(P^H-I)+(1-p_2)P^L+(p_2)(P^L-I)$

But what I write above are wrong. why?

In summary, I don’t understand how to write equations in the yellow box? Please do a short explanation for those.

If you have an idea, I will be really glad if you explain.


texts: Understanding Boserup's theories on food and overpopulation

texts:
From what I understand about Boserup's theories, she claims that when populations grow and near the carrying capacity of whatever habitat they live in, businesses will have incentive to invest in new technologies that boost the efficiency of resource extraction and thus raising the carrying capacity (food production will keep up with population growth).

Is there a more specific way to explain why businesses have more incentive to invest in technologies, other than its "demand-driven"? That's the best I can come up with right now. Technologies often require investments to be made before they become commercially viable, and even then, they incur further costs as businesses have to spend money replacing capital and training workers to use the tech. Surely, if this eventually yields a profit however, why would businesses only invest in tech once overpopulation threatens? Why would they just do it whenever they can?


texts: Why do people not all live right on top of each other in monocentric city model?

texts: I'm supposed to learn to derive the monocentric city model from these assumptions: everyone has the same preferences, same income, same work location (Central Business District, single point with infinitely small area) and same transportation per mile costs. They get utility from two goods, c (a composite good of everything but housing) and q (housing as measured by size or quality). The price of housing is a function of its distance from the CBD, x, like this p(x). In the end I'm supposed to see that p'(x) < 0, and population density and structural density both decrease as x increases.


texts:
I want to know the meaning of Semidefinite Integral.

I am used to read definite and indefinite integral but I want to know the meaning of such equation :

$\pi(e)\left(1-F\left[-\frac{a}{\pi(e)}\right]\right) \left(a+\frac{\int_{-\frac{a}{\pi(e)}}\mu f(\mu)d\mu }{\left(1-F\left[-\frac{a}{\pi(e)}\right]\right)}\right)$

Where :

$\pi(e):$ is the probability of finding the information $\mu$ depending of the effort $e$ of the agent.
$\left(1-F\left[-\frac{a}{\pi(e)}\right]\right)$ is the condition for the agent to search this information depending on the parameter $a$ which can be viewed as a reward.

$\mu$ is a stochastic term distributed by $f(\mu)$, the expected value of $\mu$ is 0.

I do not understand the second term of the equation where there is only the lower bound:
$\int_{-\frac{a}{\pi(e)}}\mu f(\mu)d\mu$


texts:
My question is about gold standard. But not the version I always see mentioned (trading bills for gold at a set price). I mean having gold coins in circulation.

For example, new currency consists entirely of gold coins (various sizes/purity diluted with worthless metal). The ratio is 1¢/mg with coins ranging from 1 cent to 100 dollars (worth roughly 5x that in current money). The 100 dollar coin maybe being pure gold (quarter-sized, used mostly for saving).

This system seems to have a few good advantages. Simple to understand, minimal inflation (I think), people owning real value instead of worthless paper/plastic being trusted etc. How well would this system function and what possible problems are there with it?


texts:
In Intriligator (2002, p. 143) we find the following statement:

  \begin{align}
 C = \{(x_1,x_2,\ldots,x_n) : x_j \geq 0,~j=1,2,\ldots,n\} \subset [0,\infty)^n
 \end{align}
  Thus  commodity  space is the  nonnegative  orthant  of  Euclidean
  $n$-space,  a closed,  convex set.

I'm rather confused why $C$ is supposed to be closed, because $x_j$ is not bounded from above. However, we may argue that $C$ is closed, because its complement
\begin{align}
C^c \subset (-\infty,0)^n
\end{align}
is open.

Still, isn't it appropriate to say that $C$ is half-closed? Am I hairsplitting here?


texts: A timeline on the the key achievements of Economics and its evolution

texts:
Something I've never seen in Economics but have in Maths and Chemistry and really enjoyed is that when I took it we got to the see the evolution of the science (and yes Economics is a [social] science ) showing us the very building blocks and the story of how it evolved into its modern counterparts.

Like with maths: Something like the basis 1) Indian numbers, $+$, $-$, $x$, $\rightarrow$; 2) fractions, radical numbers, square roots; 3) complex numbers.

Something like that it doesn't come to mind well but I quite enjoyed that. It really set the tone.


texts: Is the BEA double counting benefits in Personal Income?

texts:
The BEA (US Bureau of Economic Analysis) that produces the GDP and GDI also prepares a summary of Personal Income for the nation.

In that it includes employer contributions for both private pensions and insurance as well as the employer contributions for government social insurance such as social security and medicare.

Later on "transfer payments" from both private and government programs are also added.

Finally, personal payments for social security etc are deducted.

To me it seems that including employer contributions that are not available as income and are counted later in transfers seems like double counting and also doesn't agree with elementary macro economic texts that define national personal income as not including such contributions. In fact these contributions are carried into "Disposable Personal Income" which seems clearly wrong. Am I missing something?

6/15

After reading the comments, part of the issue may simply be that I'm not good at accounting, but I understand part of this better. I agree there is no double counting. But, in the image below (just looking at social security)

I'm OK with gross "personal income" at the aggregate level including line 8 and the net of lines 18 and 25. But if one thinks of Social Security as a big savings account, then line 8 belongs in personal savings and not disposable personal income. No?


texts: For stability, is there a limit to the sovereign debt that a Government owes to itself against issued fiat currency?

texts:
Looking beyond the optical illusion of Governments owing debt to Central Banks, Governments effectively owe themselves the sovereign debt created against issued fiat currency.
By definition, there shouldn't be any limit to the debt that an entity owes itself.
Does this mean that Governments can continue to print a limited amount of fiat currency (say 5% of GDP) annually forever?
In other words, is there a problem even if this debt that the Government owes itself, grows to, say, 1000 times the GDP over centuries?


texts: Is there a quantitative model demonstrating the relationship between balance of payments and exchange rate?

texts:
According to conventional analysis, a key factor in exchange rate determination is the state of the balance of payments.

An increase in imports gives rise to an increase in a demand for foreign currency. To obtain the foreign currency importers will sell the domestic currency for it. Obviously, this will lead to the strengthening in the exchange rate of the foreign currency against the domestic currency.

Conversely, if there is an increase in exports, all other things being equal, then once the exporters exchange their foreign currency earnings for domestic currency this sets in motion a strengthening in the domestic currency exchange rate against the foreign currency.

Is there any model which relates the changes in exchange rate with balance of payment quantitatively?


texts:
Eviews,

Just want to know how we can use the below estimation equation using MS-Excel.

Estimation Equation:

CLOSE = C(1)*D(CLOSE) + [AR(3)=C(2),MA(3)=C(3),BACKCAST=1/29/2016,ESTSMPL="1/29/2016 5/27/2016"]


texts: How would a "one-way" fixed exchange rate backed by destroying foreign currency work?

texts:
Note: This question may seem really pointless, but it's actually in the context of a cryptocurrency idea I am developing, but I posed it this way as the question is not really about cryptocurrencies at all, but rather the impact of a bizarre monetary policy on exchange rates.

The Republic of Nowhereland follows a rather peculiar monetary policy: new Nowhereland dollars (NWD) are created by destroying an equivalent number of US dollars, at a fixed 1:1 ratio. Anybody can go to the central bank with any quantity of USD, ritually burn it in front of a bank official, and receive freshly printed NWD. In fact, NWD banknotes are inscribed with text saying

  100 Dollars, Sacrificed to the Gods, at the Central Bank of Nowhereland

or some other denomination. Even the central bank itself is strictly forbidden from creating NWD without destroying an equivalent amount of USD.

Otherwise, the central bank does not interfere in any way with the foreign exchange market, and NWD is fully convertible in every sense. The government does not even have significant foreign exchange reserves.

My question is, what sort of implications, especially on the NWD/USD market exchange rate, would such a system of currency issuance have? Obviously, the NWD will never be valued significantly above the USD, since otherwise burning USD at the central bank would be profitable, and the supply of NWD will rapidly grow until it's no longer profitable to do so.

On the other hand, assuming the Nowherelandish economy grows more than it contracts, it seems like a NWD priced significantly lower than the USD would be unrealistic, as in this case the money supply will never grow. This would cause the NWD to appreciate until hitting the 1:1 ratio when burning NWD becomes profitable again. Also, it seems like this would be anticipated by forex traders, so everybody would buy NWD whenever it's cheaper than USD, so the NWD would essentially be pegged to the USD.

Is my reasoning correct, or am I missing something major? Why are there no real-life currencies backed by such a "one-way" currency board? It seems like it would allow currencies to be soft-pegged to another currency, without incurring any obligations for the central bank to buy its own currency at a fixed rate.


texts: What's the benefit the bank gets on offering me to pay my water/electricity/gas with credit card?

texts:
It says "get extra 40 days to pay your bills" with no interest!

Is it just based on the statistics that people will eventually forget paying and then charge interests from those 40 days, or are there any other things they must be considering to offer this kind of service with no interest?


texts: What are penny auctions? Given the great discounts they claim (up to 95%), how do they make money?


texts:
I am attempting a (very) basic analysis of smuggling from one economy to the other (Venezuela to Colombia) - arising from price ceilings ceteris paribus. e1 are the equilibria without intervention (price controls), e2 are the equilibria after price ceilings, and e3 show what I assume the markets would look like if Venezuelans supplied Colombia (by smuggling) where the Venezuelans' profit =

[Colombia p-hat - cost of smuggling - Venezuela p-hat]

The supply curve for Colombia becomes the sum of the Venezuelan and Colombian supply curves above the [Venezuelan price ceiling + cost of smuggling], while there is a movement along the Venezuelan supply curve to the point of [Colombian price ceiling - cost of smuggling].

Is this correct?

Thanks!


texts: Obvious Dominance and Milipede Games (Question to Pycia and Troyan (2019)

texts:
I stumbled over Millipede Games and obvious Dominance in the paper "A Theory of Simplicity in Games and Mechanism Design" by Pycia and Troyan.

On page 12 the authors define millipede Games.

They explain point 3 verbally in the text: "the last condition ensures that passing will be obviously dominant, since if x becomes impossible, then the agent will at least be able to return to any payoﬀ she was previously oﬀered to clinch."

Then they write that Figure 1 shows an example of a milipede Game. But in my understanding of their definition it is not a milipede Game, because Point 3 of the definition does not hold:

Player j could clinch x in her second move, then player i could not return to that payoff although it was previously offered to her.

What is my misunderstanding here? Looking for help! :)


texts: Best way to measure company size relative to world GDP

texts:
I'm working o a model where corporate revenue / world GDP is a dependent variable of some stuff (based on the model proposed in this paper: http://www.scielo.br/scielo.php?pid=S1807-76922009000200002&script=sci_abstract)

Thing is, I'm not an Economist, so I'm not sure exactly which measures of GDP to use.

On the World Bank website there are four GDP measures: Constant 2010 USD, Current USD, Constant LCU and current LCU.

The companies operate in different currencies and are multinationals, so I was thinking about converting revenues to USD by each year's exchange rate (as recorded by OECD) and dividing it by Current USD GDP values provided by the World Bank.

Does this make sense?

The other way I was thinking is taking constant 2010 USD GDP and inflate/deflate revenues based on CPI Growth (as recorded by OECD) for each currency used in the consolidated income statements of the companies (some companies use Euros and others Yen).

Which one of these would make more sense? If neither one, how would you do it?


texts: Implications of the concepts of combination/expansion of an information structure

texts:
I would like your help to understand the concept of combination/expansion of an information structure in the incomplete information game at p.6-9 this paper.

Let me summarise the game as described 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
$$
\sigma: T\times \Theta\rightarrow \Delta(A)
$$

Combination/Expansion:

Consider two information structures, $S^1\equiv (T^1, \pi^1)$ and $S^2\equiv (T^2, \pi^2)$. We say that $S^*\equiv (T^*, \pi^*)$ is a combination of $S^1$ and $S^2$ if

$T_i^*=T_i^1\times T_i^2$ $\forall i$.
$\pi^*:\Theta \rightarrow \Delta(T^1\times T^2)$ has $\pi^1$ and $\pi^2$ as marginals.

An information structure $S^*$ is an expansion of an information structure $S^1$ if there exists an information structure $S^2$ such that $S^*$ is a combination of $S^1$ and $S^2$.

Question 1:  Is it correct to say that $S^*$ is at least as informative as $S^1$?

Question 2:

The game described above assumes that, before privately receiving the signal, each player $i$ knows nothing about what will be the realisation of the state. I call this "baseline level of information".

Let $\underline{S}$ denote an information structure that is totally uninformative, i.e., it does not add anything to the baseline level of information assumed (also called DEGENERATE at p.26 of the linked paper). In other words, $\underline{S}$ consists of

(a) for each player $i$, a finite set of signals $\underline{T}_i$, where we write
  $\underline{T}\equiv \underline{T}_1\times \underline{T}_2\times ... \times \underline{T}_N$.

(b) a signal distribution $\underline{\pi}: \Theta \rightarrow \Delta(\underline{T})$ such that $\underline{\pi}(\cdot|\theta)=\tilde{\pi}$ $\forall \theta \in \Theta$ for some $\tilde{\pi}\in \Delta(\underline{T})$. In other words, the conditional probability is equal to the unconditional one and players' belief about the probability distribution of the state is not updated.

Let $\mathcal{S}$ denote the collection of all possible information structures. More precisely,

$$
\mathcal{S}\equiv \{S| T \text{ is a separable metric space}, \text{ $\pi:\Theta \rightarrow \Delta(T)$ is a probability measure on $(T,\mathcal{B}(T))$}\}
$$
where $\mathcal{B}(\cdot)$ denotes Borel sigma algebra.

Note that $\underline{S}\in \mathcal{S}$.

Is it correct to say that: $\forall S \in \mathcal{S}$ where $S\equiv ((T_i)_{i=1}^N, \pi)$, there exists a combination $S^*\in \mathcal{S}$ of $\underline{S}$ and $S$ such that $S^*$ and $S$ are informationally equivalent. In particular, one can set $S^*\equiv ((\underline{T}_i\times T_i)_{i=1}^N, \underline{\pi}\times \pi)$. Therefore, every $S\in \mathcal{S}$ is at least as informative as $\underline{S}$.


texts: Do all mixed strategy Nash Equilibria satisfy Trembling Hand perfection?

texts: Moreover, does it fulfill other criteria automatically, like Myerson's "Proper equilibrium" refinement?


texts: The role of reinforcement learning in Economics

texts: While working on different research projects I got fascinated by RL which got applied to many fields that are focused on agent based modeling. Though it is a field in Machine Learning what interests me is the overlap between that apporach with problems in economics. The latest awesome paper I know is the "AI Economist" by Socher et al.. Do you know more fields/papers where RL is applied to economic decision making? And do you think that this approach can lead to a paradigm shift in economics ?


texts: Under what condition would the law of one price hold?

texts:
Under the consumption-based model for asset pricing, different people will have different prices because of their different utility functions.

What is the force that make the law of one price hold?

You might say that it is a result of no arbitrage, but Kerry Back states in his book Asset Pricing and Portfolio Choice Theory states the following

  The law of one price is a weaker condition than absence of arbitrage opportunities: It is implied by the absence of arbitrage opportunities, but it does not imply the absence of arbitrage opportunities.

Based on this statement, absence of arbitrage is a stronger condition; the law of one price should hold even there is arbitrage in the market.
So What is the force that make the law of one price hold?


texts: Why is infinite recursion on the common knowledge assumption necessary?

texts:
If something is common knowledge in a game, that means that every player knows it, and every player knows that every player knows it, and so on. Are there cases where only one such level of knowing that others know is necessary?

What happens if such 'knowledge of knowing' stops at a certain level? What breaks down if at some level, the 'knowledge of knowing' doesn't hold? E.g., I know that you know, but you don't know that I know that you know.

On the same note, I'd like to understand how this infinite recursion (for lack of a better term...) of knowledge figures mathematically into say, equilibrium concepts.

Thanks in advance!


texts: What is the interpretation of the output matrix of pivoting?

texts:
I have the following matrix:
$$A=  \begin{bmatrix}
    1 & 2 & 3 \\
    2 & 3 & 4
  \end{bmatrix}$$

After pivoting, I got this matrix:
$$B=  \begin{bmatrix}
    1 & 2 & 3 \\
    0 & -1 & -2
  \end{bmatrix}$$

It's very embarrassing, but I know how to pivot, but I don't understand the interpretation of this matrix operation. What is pivoting and why is it important for linear optimization in economics? I only found resources on the mathematical intuition of pivot operation.

In the meantime, thank you so much for your attention and participation.


texts:
One theory of how single payer/universal healthcare systems are less expensive than the US private insurance market is that each country functions as a monopsony: a market structure in which a single buyer substantially controls the market as the major purchaser of goods and services offered by many would-be sellers. For example, with drug pricing, a country can ultimately tell Pfizer, "We don't want to pay more than X for your new drug. If you don't agree, you can take your business elsewhere", and Pfizer is forced to agree because otherwise they lose an entire market. I have two questions on this logic:

Pfizer is a global company, they sell to many countries, how can any single small country be considered a "monopsony" on Pfizer's products? . In a global marketplace, with many payers, it would seem that none of those payers individually can claim to have a monopsony. And this is especially true for small payers, such as Sweden, Norway, Denmark, New Zealand, which are individually a very small part of the global customer base. And this brings me to the next question, the flipside:

Why don't US health insurers have the same "monopsony" power? Why can't Aetna, which is bigger than many countries, tell Pfizer the same thing: "We don't want to pay more than X for your new drug. If you don't agree, you can take your business elsewhere"? How is their "monopsony" any less than Sweden's, which is a much smaller market?


texts: Why do companies push users to use inferior software?

texts:
Sometimes, companies influence users in order to make them use inferior software and other services. For example, Microsoft makes it difficult to use anything other than Bing for Cortana, even though Google is mostly considered to be better. Similarly, Siri uses Safari instead of Chrome and it is difficult to change this, even though the latter is generally considered superior.

At first glance, the answer seems obvious: companies push users to use their products because they are the ones who get revenue from their own products, due to advertisements in search results.

However, this answer seems insufficient. Suppose Microsoft generates $n$ USD in revenue per unit time from using Bing with Cortana. It seems reasonable to suppose that if Cortana had used Google, Google would generate $n + \epsilon$ USD per unit time from her, where $\epsilon > 0$ due to Cortana using a superior search engine, which would cause her her to be at least slightly more popular. If this is the case, why doesn't Microsoft make Cortana use Google under the condition that Google gives $n + \epsilon'$ to Microsoft, where $0 < \epsilon' < \epsilon$? Wouldn't this roughly give Microsoft an additional $\epsilon' > 0$ in profit and give Google an additional $\epsilon - \epsilon' > 0$? If Microsoft using Google would further increase Google's name recognition and decrease Microsoft's, then why not just increase $\epsilon'$ to take this into account?


texts:
I'm trying to show a result that involves utility and money (the latter is in dollars). I would like to know if it is safe to assume that the units of utility is dollars? After all, in auction scenarios, we seem to deduct the bid, which is in dollars from the total utility for the item, and maximize that difference.

Therefore, am I doing the right thing in saying that a utility gain of 10 units can be equated to a gain of 10 dollars?


texts: Dummy variable regressor OLS coefficient formula

texts:
Consider the standard linear regression model: $y_i = \alpha + \beta D_i + e_i$ where the coefficients are defined by linear projections and $D_i$ is a dummy variable. In the population, the coefficients are given by:

$$\alpha = E[y_i \mid D_i =0] \ \text{and} \ \beta = E[y_i \mid D_i = 1] - E[y_i \mid D_i =0]$$

Using OLS to estimate the coefficients, we get:

$$\widehat{\alpha} = \overline{y}_{D_i=0} $$

$$\widehat{\beta} = \overline{y}_{D_i=1}-\overline{y}_{D_i=0} $$

In other words, $\widehat{\alpha}$ is just the sample mean of $y_i$ in the subsample with $D_i=0$ and $\widehat{\beta}$ is the difference in sample means of the two groups. The expressions seem very obvious because they are just sample versions of the population, but my question is, how can we arrive at the above coefficient estimates by using the standard OLS formulas? That is using:

$$\widehat{\alpha} = \overline{y} - \overline{D}\widehat{\beta} \ \ \text{and} \ \ \widehat{\beta} = \frac{\sum_{i=1}^{N}(D_i - \overline{D})(y_i - \overline{y})}{\sum_{i=1}^{N}(D_i - \overline{D})^2}$$


texts: What Was the Accuracy of Macro Model in the Phillips' Machine (MONIAC)?

texts:
One of the most interesting  economic 'artefacts' featured on the campus of my alma mater is the Philips' machine or Monetary National Income Analogue Computer (MONIAC) pictured below.
MONIAC was a hydraulic computer, with a rudimentary macroeconomic model, build by none other than William Philipps as a part of his dissertation. MONIAC could be used to visualize and even predict several macroeconomic variables depending on its calibration (such as interest rates or prices resp. inflation).   The machine was originally intended just for classroom use (Bissell, 2007), but eventually several research/policy institutes around the world decided to commission the machine as well (for example New Zealand Institute of Economic Research bought one). This makes me wonder if the machine was ever accurate enough to be useful outside classroom (e.g. research/policy analysis/forecasting). Since it is based on rudimentary macroeconomic model I would expect relatively large forecasting errors.
I tried to do research on the MONIAC's accuracy but I am finding conflicting reports. According to Wikipedia:

To their surprise, Phillips and his associate Walter Newlyn found that MONIAC could be calibrated to an accuracy of 2%.

but no reference to the work where Phillips and Newlyn made the claim is provided.
I dug bit deeper and managed to find paper (Bissell, 2007) that claims the MONIAC's accuracy was reportedly only $\pm 4\%$ but again the claim is not directly supported by citation. In the next paragraph the paper cites Newlyn (1950) so I thought it might have the answer (since Wikipedia mentions Newlyn as well) but it turned out it does not mention any number for the accuracy of the machine.
This leads me to my question, is there any primary source in the economic literature for the accuracy of the MONIAC? If so what level of accuracy does it report?


texts: What does 'continuation' as in continuation games, strategies, plays, etc. exactly mean?

texts: I am in my first course in grad level game theory. While I was reading through Fudenberg and Tirole's Game Theory, I constantly come into contact with the word 'continuation' to describe some games and strategies but I was never able to find where the authors exactly define what they are referring to. Some sources say continuation game is a game starting at a given information set and including all edges and vertices/nodes until the terminal nodes. But isn't a subgame defined as a part of game tree which starts at a single node and contains all the succeeding nodes and wholly containing the information sets associated with them? Any help in understanding the term would be highly appreciated.


texts: What is the relationship between the demand for loanable funds and investment?

texts: If the demand for loanable funds decreases, investment increases because the real interest rate decreases. Isn't that a contradiction, because loanable funds are used for investment, and a decrease in demand for loanable funds must come from a decrease in investment?


texts: Economic term for relation between drug and companion diagnositic

texts:
I'm looking for economic terminology which must exist, although I don't know what it is.  (I want to look up articles on a particular situation involving two real-world companies.)

Here is the situation:  Company A is developing a diagnostic test which will warn of a particular type of deadly antibiotic resistance.  Company B is a pharmaceutical company developing a drug to treat that kind of resistance.

Is there an economic terms that describe concepts relevant to this situation?   The important features are that

1)  Product B will never be bought without product A.
2)  Customers will only buy A with the intention of possibly buying B.
3)  Product B will certainly sell at a very high price if product A works perfectly, because A will identify those patients for which B is life-saving.  A deserves some of this return, but the many customers buying A each will have only a low-probability of being one of the few to benefit.

Similarly, one could imagine a related case that there are exactly two bicycle wheel manufacturers, and by law A can only sell front wheels and B can only sell back wheels.  There will be some sort of odd price hostility between A and B, because the two products are each useless without the other.  The natural thing to happen is for the producers A and B to merge, although wrangling about the terms of a merger may make this impossible.

In my real-world case the cognizant shareholders of A should oppose any buyout by B at anywhere near current market prices, because A's technology will extend to many many other applications.


texts: Meaning of innovation in the wealth creation process

texts:
Is there a formal definition or measure of wealth that captures the notion that with improving technology "life gets better"?

A stupid example of what I mean would be the invention of the iPhone. I know that with the iPhone new markets were and new profit possibilities were created and in that sense the economy got richer. That effect could be measured by let's say the GDP.
But apart from that I can now watch Netflix on the bus or text people everytime, everywhere. So personally my life got a whole lot more pleasant.

Also is there an accepted connection between innovation and "wealth" in the sense that I described above?

Cheers,
FL


texts:
Some authors makes the difference between these two terms.

Could somebody explain what is the difference between division of labor and division of work?


texts: How to econometrically identify perfect complements in production?

texts:
The production

$$f(x_i,...,x_n)=\min\{x_i,...,x_n\}$$

is pretty straight forward and usually with smaller size data sets and can usually be picked up on rather quickly in an intuitive sense.

However if one has a very large set of data with a firm that produces $n$ products, how does one go about analyzing the production process and say that such a relationship exists in production of a given good?


texts: Measuring demand for banking services - (Maximum) Market Size

texts:
I am in need of a variable measuring "demand for banking services" in general, on a country level. Specifically the (maximum) size of the market for banking services for a given country. This will be used as a control variable.

Does anyone know any standard proxies or measures used in the literature to measure something like "total demand for banks"? I need something general, not a specific banking service. Something that summarizes the different sources of demand for banking services, such as some kind of constructed index or so. Something that summarizes everything/most services through which banks make profits. If that is not possible, are there maybe two standard measures that each cover demand for deposits and demand for loans?

What variables are generally used? If nobody knows what is standard, does anyone have any plausible suggestions of proxies/measures for "demand for banking services"? Further, any suggestions on data sources I could use to get country level data (preferably a panel starting around the '80s or '90s) for such a variable?

The proxy/measure need not be perfect. The only important thing is that it captures "the size of the market for banking services (in general)" in some way. Especially a measure of demand that would determine the (maximum) number of banks in a given country.


texts: I learnt that giffen good doesn't satisfy the law of demand, but can we draw an offer curve to represent giffen good?


texts: Divergence of a variable in forward-looking models. Blanchard-Khan conditions

texts:
(1) This post is, first, regarding the issue from Romer's Advanced Macroeconomics, 4 ed. Chapter 6.4 on nominal rigidity, pp. 264-266 to be precise.

He sets out a simple model with microfounded IS curve, AS curve and MP curve, using standard notation with $\pi$ as an inflation, $y$ as an output and $r$ as an interest rate.

My question is why agents in this model cannot expect $y$ to diverge? Is this due to mathematical and/or economical reasons? Or did I miss some assumption in the text?

Also, does diverge here mean rise ad infinitum or only rise fast enough to offset the convergence of $\phi^n$? [I know, this is a rather math than econ question, but entirely a propos the problem considered].

So here's the model:

(2) Secondly, later in the text a similar issue recurs in chapter 11.5 when analyzing the model of optimal monetary policy in a forward-looking setting. Romer considers cases where self-fulfilling equilibria arise (I guess Blanchard-Khan conditions):

So why do we have to assume that our variable is bounded? Again: is this due to mathematical and/or economical reasons?

(3) Finally, when I elswhere read about Blanchard-Kahn conditions there is stipulated that "Blanchard-Kahn conditions apply to models that add as a requirement that the series do not explode". Why is that? Isn't that possible for an economic system to have such a property? Or why are we ruling out from our analysis models with that property?

Do all these 3 issues touch the same problem and have the same solution or this is just the coincidence that I don't get this assumptions/results(?) in different contexts?

PS
This comment is really helpful claryfing some math related issues, but it does not pertain to the reason for the assumption/result(?) in question.

Edit:
For the clarity reasons I've included more of Romer's solution to the (1) problem.


texts:
I have one year sales data of a retail company and lets say I am forecasting the next month sales for the product. I have got the sales using time series in R. Now I want to forecast the price as well. I want to build a model using both the demand and price. My function should be f(DP) where D is demand and P is price. I want to maximize Revenue or Profit where Revenue=DP.

As of now, I forecasted sales and did a linear programming on Price itself to get optimal price of a single product. I want my model to be robust but this is chicken - egg theory where demand forecast is dependent on the price and price is dependent on demand. Please help by sharing some theories which would better fit for this or some R models.


texts: Is the symmetric equiblirium in congesstion games always inferior in terms of social-welfare?

texts:
Let $G$ be a finite, symmetric, congestion game. According to Nash theorem, a (mixed) symmetric equilibrium surely exists. Congestion games also known to admit pure-strategies Nash equilibrium as they are exact potential games.

  I was wondering if a symmetric (i.e. one in which all players play a strategy with the same probability) can yield higher social-welfare (sum of payoffs for the players) than any other equilibrium for the game.

The intuition is that if all players are using the same elements, this has to incur higher cost than if they partition across multiple actions, as the payoff per player depends directly on the number of players using the same elements.

  Also, is there always a single symmetric equilibrium for congestion games?


texts: Formal definition of perfect information

texts:
I am looking for the formal definition of 'perfect information' in game theory.

Please direct me to a book or preferably an online paper where I can find it.

On a related note:
The Wikipedia page for the term is not very useful. It only offers an informal definition:

  In game theory, an extensive-form game has perfect information if each player, when making any decision, is perfectly informed of all the events that have previously occurred

Given this definition the simultaneous move examples seem strange. The games mentioned (e.g. iterated prisoner's dilemma) could easily be altered to have sequential moves where the second mover is simply not aware of the first move. This game would have the same extensive form but would no longer fit the informal definition.


texts: Income effect $-\frac{\partial x_i}{\partial m} x_i$ or $\frac{\partial x_i}{\partial m}x_i$?

texts:
Recall that the slutsky equation is:

$$\frac{\partial x_i}{\partial p_i}=\frac{\partial h_i}{\partial p_i}-\frac{\partial x_i}{\partial m}x_i$$

I know $\frac{\partial h_i}{\partial p_i}$ defined as the substitution effect, the second part of the equation is the income effect.

My Question: is the income effect defined as  $-\frac{\partial x_i}{\partial m}x_i$ or $\frac{\partial x_i}{\partial m}x_i$ (is the negative sign a defining characteristic?)


texts: Game Theory PSNE of a two player simultaneous game

texts:
Consider a two player simultaneous game where each player chooses a non-negative value, $x_i$, $i=1,2$. The payoff to each player is $π_i(x_1,x_2)=2x_i+2x_1x_2-x_i^2.$

a. What are the pure strategy Nash equilibria of this game?

b. Suppose that the set of strategies is limited to $[0,M],M>0$. What are the pure strategy Nash equilibria of the game now?

For a) I got the answer that there are no PSNE since there's no intersection between the best response function of both players. Please correct me if that's wrong!

For b) I got very confused because I'm unsure how bounding the values of $x$ will make the conclusion any different from a). I realize that the payoff function provided doesn't necessarily mean that the larger $x_i$ is, the larger the payoff will be.

Below is my proof:

Consider $π_i(x_1,x_2)=2x_i+2x_1x_2-x_i^2.$. We first assume $x_1> x_2$. In order to find out if a larger number leads to a higher payoff, i.e.

if $2x_1+2x_1x_2-x_1^2>2x_2+2x_1x_2-x_2^2$

$2x_1-x_1^2>2x_2-x_2^2$

$x_1(2-x_1)> x_ 2(2-x_2)$

Following from $x_1>x_2$,

$2-x_1<2-x_2$

$x_1(2-x_1)> x_ 2(2-x_2)$ for $0<x_1\leq 1 $ and $0<x_2< 1$

and

$x_2(2-x_2)> x_ 1(2-x_1)$ for $x_1>1 $ and $x_2\ge 1$, where $x_2<x_1$

Therefore, in order to maximize the payoff of each player and find the intersection of their best response such that they will have no incentive to deviate, with the condition that $[0,M]$, we find that:

As long as $0<M\leq 1$, the PSNE will be {$P1: M, P2: M$}. When $M>1$, the PSNE will be {$P1: 1, P2: 1$}.

I'm quite unsure if I'm right though, and would love to get some input!


texts: Does good geographical location count as land in economics?

texts:
For example, the North pole is in the northern part of the earth and is very cold, making it suitable to build a site to study polar bears. Is the cold and northern location of north pole counted as land? But since the site is already built so the place should be counted as capital?

Sorry I know this example sounds a bit stupid but I'm very confused and couldn't think of a better one.


texts: How does the self-corecting mechanism put the economy back to long run equilibrium following a negative shock on the stick-wage SRAS?

texts:
According to some lecture notes, apparently it is possible for the economy to return to long run equilibrium if via the self-correcting mechanism if there is a temporary shock to the stick wage (horizontal) SRAS. I believe the situation can be graphed as below (SRAS shifting to SRAS1).

The problem is I don't see an explanation as to how it will return to long run equilibrium ($Y_f$), other than to let labour markets adjust itself over long periods of time??


texts: What is the difference between Stochastic game and Bayesian game ?

texts: I was studying definitions of Stochastic and Bayesian game and it appears that Stochastic game is a generalized form of Bayesian game. Could anybody please explain the fundamental differences between Stochastic game and Bayesian game and imperfect information and incomplete information games ?


texts: Is there any variable commonly used as a proxy for the inflation target set by the Central Bank?

texts: I have been asiggned to estimate a monetary policiy rule à la Taylor for my macroeconometrics class. There are no explicit inflation targets stated by the Central Bank (of the country I am the estimating the model for (Costa Rica)) for a part of the period whose data I must use. I would like to know if there is some variable commmonly used as an aproximation of proxy of the inflation target chosen by the Central Bank. Any help, commentary or reference to any bibliography is deeply aprecciated. Thank you.


texts: Why does equity have historically poor performance after rate cuts?

texts:
I am struggling to understand why equity markets seem to suffer shortly after fed rate cuts. Here is a rather telling chart:

Question

Assuming not some kind of spurious relationship, what's the intuition behind the  connection between rate cuts and equity dropping?

Maybe the rate cuts draws investors attention to the weakness of the macro conditions and makes them more risk-adverse?


texts: Creating utility function with certain properties

texts:
This is a fun little task I need help completing. Im creating a game-theoretical model for the utility a government get from labour rights (R) and FDI (F), and I need a utility function to have certain properties to be a good model of the theory Im using. An important factor is the average level of labour rights (C) in other countries. The point of the theory is that states cuts competitively in labour rights to attract more FDI. So, Im hoping someone on this forum could pick up the challenge of making a Utility function for me that I can use.

Here are the Rules. P is a function of R and F (Higher R and F gives higher P), F is a function of R and C, higher R relative to C gives lower F. There has to be a parameter alfa(a) that gives the "sensitivity" of a state to P and beta (b) that gives the sensitivty to F. a+b=1 Higher a means that the government gets more utility per increase in R. Higher b means that the government gets more utility per increase in F.

P<0

F<0

The optimal choice of R for a government should be a function of a,b and C in which the entire idea of this is that the more a government prefers FDI instead of labour rights, the lower R should be set relative to C.

I need the function itself, its first derivative, and the value of R at which the first derivative is zero.

I hope this makes sense and that someone will find this challenge to be fun.

Best regards Magnus


texts: Tactical voting when the voting rule is unknown

texts:
The Gibbard-Satterthwaite theorem implies that, in every non-dictatorial voting system with 3 or more candidates, there is a preference profile in which some of the voters can gain by lying about their preferences. However, usually this gain requires that the voters know the voting rule.

For example, consider a voting system with 3 candidates, A B and C, and 12 voters with the following preferences:

3 voters prefer A>B>C;
4 voters prefer B>C>A;
5 voters prefer C>A>B.

Consider the following two voting rules:

plurality - in which C is elected;
Instant-runoff - in which B is elected (after A is eliminated in the first round).

Consider the 5 C>A>B voters, and assume all other voters are truthful:

In plurality voting, they should of course be truthful so that their favorite candidate C wins.
But in instant-runoff voting, they can gain by lying and saying that their best candidate is A, since this will prevent the election of their worst option B.

So without knowing the voting rule, these voters cannot know whether lying about their preferences will help them or harm them.

The situation is different with the 3 A>B>C voters:

In plurality voting, they can gain by lying and saying that they prefer B, as this will prevent the election of their worst option C;
In instant-runoff voting, although they won't gain from lying, they also won't lose.

So even without knowing the voting rule, these voters can know that voting for B will either help them or at least not harm them.

For the sake of this question, assume that all voters are truth-biased. This means that, if they are not sure whether lying will help them or harm them, they will be truthful. They will only lie if lying may help them and may not harm them. So in the above example, the C>A>B voters will be truthful and the A>B>C voters will lie (assuming the B>C>A voters are truthful).

MY QUESTION IS: Is there a collection of reasonable (non-dictatorial, monotone, etc.) voting rules, such that, in all preference profiles, no truth-biased voter will want to lie?

In other words: we look for a collection of voting rules so that, for every preference profile and every group of voters, there exists a voting rule in our collection where their best response (when all other voters are truthful) is to be truthful.


texts:
I'm wondering if there is a method by which we can visualize a firms decision to rely on volunteer labour. I have an idea but I'm unsure if it is correct, please tell me if there is an issue with my understanding.

I posted here about the issues with looking at volunteer labour with labour market models driven primarily by wage rate to determine the individuals decision of entry to a given labour market, however from the firms end I think there might be a way to look at its decision to primarily employ volunteer labour.

In the picture below I have a slightly modified version of a the labour market to describe the non-profit sector. The labour demand $N_d$ is the same however the labour supply $N_s$ is shifted right and some of the curve is below the wage of zero, indicating the individuals on this end of the labour supply curve would pay to do such work for such a firm.

This abnormal behaviour of an individual working for free or even paying his employer can be in reference to what is called by Richard Freedman  the purchase of "conscious goods or services".

The implications this graph has is that there is an "oversupply" of labour or a specific type of labour (usually general labour in the case of the volunteer sector), to the point the firm does not need any more workers, "Maxing out their inputs" therefore they won't pay for such readily available labour at all.

Again I am posting this model here to see if there is an issue with my understanding or if there is anything for the SE community to add.


texts: Did Zimbabwe have an inflation of 89.7 sextillion percent?

texts:
From a Cato Institute article by Steve Hanke1 (emphasis added):

The Economist’s most recent infraction on Zimbabwe’s hyperinflation appeared in the May 2016 issue. The magazine claimed that the hyperinflation peaked at an annual rate of 500 billion percent. Where did this figure originate? You guessed it. That figure is buried in the IMF’s 2009 Article IV Consultation Staff Report on Zimbabwe.
In reality, Zimbabwe’s annual inflation rate in September 2008 was 471 billion percent, not 500 billion percent. More importantly, Zimbabwe’s hyperinflation peaked in November, not September. It was then that Zimbabwe recorded the second-highest hyperinflation in history: a whopping 89.7 sextillion percent. This is 179 billion times greater than the IMF’s figure.

Did Zimbabwe, at one point, record a hyperinflation of 89.7 sextillion percent? Wikipedia cites the IMF figure.

How did Steve Hanke come up with the number 89.7 sextillion?

Is Steve Hanke's methodology accurate? Reasonable? Trustworthy?

Why are the two numbers so different?

Note: Steve Hanke certainly seems to believe that inflation for some countries is higher than actually reported (e.g. the Zimbabwe article I cited, this tweet regarding Sudan from 9 hours ago, and this tweet regarding Argentina from 11 hours ago). Maybe this could be considered in an answer?
1Professor of Applied Economics and Co-Director of the Institute for Applied Economics, Global Health, and the Study of Business Enterprise at The Johns Hopkins University in Baltimore


texts:
I live in a student dorm with 16 people and we share a kitchen. Every week someone has to clean the kitchen. Right now we just take turns in a way determined by the numbers of our respective rooms. This is obviously not very efficient. I was thinking about the possibility of using auctions to determine who should do the cleaning. One possibility could be a sealed bid type thing where everyone states how much money they want in order to do the cleaning. Then the person who wants least does the cleaning and the other people fund this by contributing an equal amount.

Is there a more efficient mechanism? Some points I am considering: Should the amount of funding of each person depend on his/hers bid? Should the person cleaning also contribute to the funding? Will it be better to pay the lowest bidder the amount of the second lowest bid?

I am well aware that this kind of thing might be socially/morally objectionable. It is more of a thought experiment.


texts: Event Study vs. Difference-in-Differences

texts:
I am trying to perform Event Study methodology to analyse impact of group of events on group of stocks from certain sector. I noticed that I am getting surprisingly lot of positive results (very low p-value like ~0.00). When I sampled set random dates from my time period and run same Event Study analysis I got multiple low p-values again. Approximately 50%-60% per 100 random dates for each company. I assume that high volatility of my companies (and index) might one reason however I need confirmation here. But I have started wondering about different thing. I use same events for all companies from one sector. Not events specific for each company (like m&s for example). So I started wondering whether I should use Difference-in-Differences here? I heard that:
“Difference-in-Differences (DID) is more appropriate for systematic events that affect the whole market while event study is designed to examine impact of events specific for single company”
How true is that statement? As I said before in my analysis I examine impact of same set of events for each company like change in regulations for entire sector. Are there other alternatives beside Event Study and DID?


texts:
I am doing exercises in the book Steve Tadelis An Introduction to Game Theory. I have answers to the even questions from chapters 1 to 8. But I would like to check the other remaining chapters' answers. I thought I could ask here as people here may know.

  Where can I find answers to Steve Tadelis An Introduction to Game Theory  answers for chapters after the 8th one?


texts: Crypto-tokens: how do they function in a latter stage of company?

texts:
I am newbie to cryptocurrencies and just read an article about ICO (Initial Coin Offerings). However, I didn’t quite get the functioning and role of tokens. Lets say there is a company that plans to build a marketplace that operates on blockchain, where you can buy and sell many different things. To use the marketplace the user however needs to buy company’s tokens.

To raise money to build the marketplace, the company one day decides to participate in an ICO, where it will issue its tokens for a low price. The ICO is very successful and the company manages to build the platform and attract a reasonably sized customer base.

Let’s say that in a few years the value of the company goes up, which means that the value of the token will also increase. Then come new users who are attracted to the platform and want to participate in it. This is the part which I don’t understand. Because they need to buy the tokens to participate in the market, wouldn’t the high price of tokens (compared to their original price at ICO) significantly deter new users from coming to the platform? The new users would have to pay high costs (buying the tokens) just to enter the platform. How do blockchain companies (like Status.im) solve this problem?

Thanks a lot for clarifying the problem.


texts: Estimating the cost of an assett that needs to be replenished

texts:
I am working with hard drives.  For simplicity,  let's say all drives have the same capacity, 1TB and all cost $100.

They typically last about 4 years,  when they need to be replaced.    They drop in price about 50% over that period of time.  They cost 100 dollars for the first for years,  $50 for the next 4 years, etc.

What's the usual way of estimating the cost of something like this?


texts: Difference-in-Difference on State Sales Tax Rates

texts: In an attempt to evaluate a potential U.S. National Sales tax rate, it was suggested on this forum before that I consider a difference-in-difference on state sales tax rates before and after they changed.  How would I go about doing this?  Would I do a difference-in-difference on each of the states sales taxes, and then aggregate the data?  If so, how do I aggregate the data?


texts:
I am reading Optimal Time-Consistent Fiscal Policy with Finite Lifetimes by Calvo and Obstfeld.

Here is the paper :

Calvo and Obstfeld (1988)

In fact, their model consists of two stages. In the first part, there is an OLG model with individuals who have an individual discount factor (the same individual discount rate for all individuals). After, once the OLG is solved (consumption distributed optimally in a static way), the model reduces to a standard agent model.

There is a sentence that I can not understand on the page 418 of the paper

  Notice that the optimal aggregate accumulation path is entirely
  independent of private time preference

How is this possible? The utility function depends on a parameter $\Phi$ which contains the private time preference (i.e individual discount rate). Then, the steady-state levels will be different with respect to different individual discount rates. It follows that the dynamics of the consumption and capital will depend on the individual discount rate.


texts: VAR, SVAR, BVAR, TVP-VAR, etc, I have a feeling that the persistency of the impulse responses will not change much irrespective of the model, even if impulse responses in the first period of the shock changes, for example, from negative to positive (or vise versa) depending on the model of choice. I mean persistency here is a feature of the data, not the model, right?


texts: How does the federal funds rate compare to the federal discount rate?

texts:
The federal funds rate is the interest rate charged to banks when they borrow from each other overnight in the federal funds market to satisfy their reserve requirements. This rate is influenced by the Fed through open market operations. The federal discount rate is the interest rate charged to banks when they borrow from the Fed to satisfy their reserve requirements. This rate depends on how much money banks are in need of and how much the Fed is willing to provide.

It seems to me that both of these rates should be almost equal most of the time. If the discount rate is lower than the federal funds rate, then the depository institutions would borrow from the Fed, instead of from each other. Thus, this additional demand for the central bank's reserves drives up the discount rate such that it equals the federal funds rate. The opposite would occur if the federal funds rate is lower than the discount rate. Is this correct?


texts: What are some benefits of local currencies?

texts: Lets say that we have in my country Greece there is an Island Crete that it has big production (agriculture,small banks etc.) and produces big surplus compared with other parts of Greece and the people there wanted to create there own currency in order to influence their economy and economic policies. What are some benefits for those people in such scenario?


texts: Stochastic Dynamic Programming: Deriving the Steady-State for a Lottery

texts:
I am working through the basic examples of the stochastic RBC models in the book by McCandless (2008): The ABCs of RBCs, pp. 71 - 75

A Standard Stochastic Dynamic Programming Problem

Here is a formulation of a basic stochastic dynamic programming model:
\begin{equation}
y_t = A^t f(k_t)
\end{equation}

\begin{equation}
A^t = \cases{A_1 \text{ with probability } p \\ A_2  \text{ with probability } (1 - p) }
\end{equation}

\begin{equation}
k_{t+1} = A^tf(k_t) + (1 - \delta)k_t - c_t
\end{equation}

With an agent maximizing the expected utility function:
\begin{equation}
E_t \sum_{t}^\infty \beta^t u(c_t)
\end{equation}

Substituting consumption from the previous equation and using the recursive formulation of the problem gives the following problem:
\begin{equation}
V(k_t, A^t) = \max_{k_{t+1}} \left[u(A^tf(k_t) + (1 - \delta)k_t - k_{t+1}) + \beta E_t V(k_{t+1},A^{t+1})\right]
\end{equation}

Then McCandless proceeds saying that the algorithm to solve to the problem is almost identical to the deterministic case. One finds the first-order conditions (a derivative of the value function with respect to $k_{t+1}$) for the control variables, then does the same for $k_t$ and applies the Envelope theorem to get an analytical solution. Steady-states found, model written, paper submitted. Profit.

A Lottery Augmented Version

Now I want to investigate a little different case. Take the very same model but introduce another control variable. Call it $s_t$ for a security:
\begin{equation}
l_{t+1} = l_t + s_t
\end{equation}

And the $l_t$ enters the problem through the variable $A^t$:
\begin{equation}
A^t = \cases{A_1 \text{ with probability p} \\
A_2l_{t} \text{ with probability (1 - p)}}
\end{equation}

The main difference is easy to see if one writes the equation for income in a period $t$ explicitly opening up the expectation sign:
\begin{equation}
y_t = pA_1f(k_t) + (1-p)A_2l_tf(k_t)
\end{equation}

In this case we have a deterministic control variable $l$ "turning on" when a certain event happens (as if you would win in a lottery, which increases your income by the factor of how much you invested in it - yes the example makes little sense but I am interested in the principle itself).
The Question: Does the following lottery augmentation changes the process of how to solve the model? If yes, what is the idea behind and what does change? If no, why is that?

P.S. If someone could point me a paper with an example model, which is very close to the one I described, that would be brilliant.


texts: General equilibrium - exchange economy with time and perishable goods

texts:
I am attempting to solve a general equilibrium problem from the textbook Jehle and Reny. However, I am slightly confused if my approach is correct. The question is as follows.

Consider an exchange economy with one good and two time periods. Two consumers have the following utility functions:

$U_A (x_{A1}, x_{A2}) = \sqrt{x_{A1}} + \sqrt{x_{A2}}$

$U_B (x_{B1}, x_{B2}) = \sqrt{x_{B1}} + \sqrt{x_{B2}}$

where $A1$ corresponds to time period 1 and $A2$ corresponds to time period 2.

Each consumer is endowed with one unit of the good at time period 1, BUT only B is endowed with 1 at time period 2 (A is endowed 0 at time period 2). Note that storage of the good is not possible, but consumers can engage in trade in period 1. Calculate the competitive equilibrium allocations.

I am not sure if I am overthinking the problem, but since the good is perishable. Will both agents just consume their endowments (e.g., agent 1 consumes 1 in the first period, and agent 2 consumes one in the first and one in the second).

Is there a scenario where agent 1 would want to sell some of his endowment in period 1 to purchase some in period two? Given his utility function I believe this would be the case, but showing it seems much different than the typical GE problems I have been solving.

Thanks


texts: Economic theory journals for a refinement theorem about utility function representation

texts:
I would like to ask which are the (mathematical) economics journals that publish papers about economic theory and that focus mainly on the mathematical aspects of it. Let me be more precise. If I have a refinement of a representation theorem for preference relation axiomatization, which journals are most suitable to get the paper accepted?
Of course, I mean a significant generalization of the theorem and, of course, I am not thinking about Econometrica or Journal of Economic Theory since I understand my question is about a refinement of a theorem, and not a completely original economic issue. Nevertheless, I think my generalization fills an important gap in the subject and I would like to ask for a list of economics journals (maybe listed by ranking of importance) that may be the right target for my result. Thank you in advance!


texts: Why isn't there an "ideal value" for a given currency?

texts:
If a currency can be worth too little (e.g. needing \$10,000,000,000 to buy a loaf of bread) and worth too much (e.g. being able to buy a loaf of bread for $0.00001), why isn't there an "ideal value" (a point, range, or a shifting set of priorities based on market conditions) that a currency could be fixed or drawn toward?

Many everyday transactions are still done in cash, requiring mental calculations from the transacting parties. Too large numbers and too small numbers create transaction costs that, at least for the extremes, cannot be ignored.  So conceivably, some "middle" point could be considered "ideal" as regards the efficiency of money as medium of transactions.

What forces may prevent such an "ideal value" for a currency from being established?


texts: In the Ramsey model, how does it make sense to say that capital equals wealth when wealth can be negative and capital cannot?

texts:
In the Ramsey model, $K_t$ denotes capital, and $A_t$ denotes the assets/wealth of the households.

However, each household is identical. Since the economy is closed, the assets of each household equal their share of the capital. So, $A_t = K_t/H$, where $H$ is the number of households.

However, in theory, $A_t$ can be negative. Obviously a household can accumulate debt at some point in their lifetime. But $K_t/H$ can never be negative, since $K_t$ itself, total capital in the economy, cannot be negative.

So I do not understand how it makes sense in the Ramsey model to talk about "wealth" and "borrowing" and "debt" since $A_t$ is forced to be positive?


texts: Do products which are only produced and consumed locally contribute to GDP value?

texts:
According to Wikipedia:

  Gross domestic product (GDP) is a monetary measure of the market value of all the final goods and services produced in a period of time, often annually or quarterly. Nominal GDP estimates are commonly used to determine the economic performance of a whole country or region, and to make international comparisons.

But what if a country has a product which is massively or at least moderately produced and consumed only locally, either for tradition or any other reason. And the exports of this product are non existent or at best minimum. In the case the exports are non existent, the international market value of this product would be zero, wouldnt be? Or does the national market value counts in this case? Also, if the international market exists but it's minimum, and most of the production can only be consumed localy, does all those unsalable products value contribute to the GDP value?


texts: Piketty's explanation of elasticity of substitution (from his book Capital in the 21st century)

texts:
I have some trouble following the explanation of the elasticity of substitution between capital and labor and its implications on p189.
Take this part:

The relevant question is whether the elasticity of substitution
between labor and capital is greater or less than one. If the
elasticity lies between zero and one, then an increase in the
capital/income ratio β leads to a decrease in the marginal
productivity of capital large enough that the capital share α = r × β
decreases (assuming that the return on capital is determined by its
marginal productivity).

Specifically, when he talks about that elasticity, does he mean something like (dL/L)/(dK/K) with L for labor and K for capital? Assuming that, how exactly does a higher elasticity translate in a lower fall in marginal product of capital?
Thanks


texts: What's the best reference for rigorous study of mixed-strategy nash equilibrium?

texts:
I am studying game theory, but I feel like I do not understand mixed-strategy equilibrium all that much. Yes, I know how to find them in 2x2 cases, and in some 3xn (n <= 2) cases as well where the normal form has been artificially constructed to make finding the mixed strategies very easily (e.g., one of the actions can conveniently be ignored because it's dominated).

But if I were to write down an nxn matrix right now, n >= 3, I wouldn't be able to solve for it's mixed strategies.

So I am looking for a really good really rigorous really thorough reference to understand mixed strategy equilibria. Any recommendations?


texts: How does a country devalue its currency?

texts: I recently read an article in the New York Times that talked about China devaluing its currency (which I believe is held to a peg against the US Dollar). My question is: specifically what tools does a central bank of a country employ to devalue its currency artificially and what effects does it have on its foreign trade?


texts:
I have often listen to the old man who criticized the lack of morality in the Chinese people nowadays: "To get more money, break through to the bottom line to get more money!"

Is there a contradiction between economic development and morality? Are there any countries that are highly ethical standards that develop very well?


texts:
I interested in the net effect of buying locally versus abroad.

The UK Government wants to buy a ship. It can buy from a UK or Korean shipyard. The unit price is the same for both yards: £10. A ten pound note. Nice and simple for the purpose of this example.

If the purchase is from the local shipyard, then the ten-pound note is delivered to the local yard directly from the bank account of the Government, having previously been forcibly removed from other UK citizens via taxation. This wealth is then distributed throughout the UK economy, via the employees and suppliers of the shipyard.

Some people advocate buying locally for this reason: they view this local economic stimulus as a positive side-effect of buying locally.

If the ship is purchased from Korea, assuming perfectly efficient currency exchange, then the wealth is transferred (having been converted into the Korean currency by a foreign exchange brokerage) to a Korean company. This wealth is then distributed around the Korean economy in a similar way, and presumably the Korean economy sees the economic stimulus.

But the original ten pound note has not vanished. It is now sitting in the bank account of someone behind the foreign exchange brokerage. This ten pound note will either be saved, or converted into another currency, or spent in the UK, because the UK is the only location where it is legal tender. So the money is STILL (eventually) spent in the UK, but a little more circuitously.

Is my understanding correct?

Does this mean buying locally is in some sense equivalent to buying from another economy? Or where have I gone wrong?

Does the situation change if Korea has the same currency as the UK?


texts: Why are population projections so inaccurate?

texts:
UN in 2015: India's population will surpass that of China in 2022.

Source: https://www.telegraph.co.uk/news/worldnews/asia/india/11770757/Mapped-India-predicted-to-become-worlds-most-populous-country-by-2022.html

UN in 2017: India's population will surpass that of China in 2024.

Source: https://timesofindia.indiatimes.com/india/indias-population-to-surpass-that-of-chinas-around-2024-un/articleshow/59257045.cms

UN in 2019: India's population will surpass that of China in 2027.

Source: https://www.indiatoday.in/india/story/india-population-china-united-nations-report-world-1550962-2019-06-18

No one expects population projections to be 100% accurate but I didn't expect them to be this inaccurate either. What are the possible reasons for the UN getting this wrong so many times and by a margin of several years?


texts: The maximum sustainable yield model: clarifications

texts:
I would like your help to understand the Maximum sustainable yield model. This is what I understood with some questions.

We consider a population of individuals who are born, possibly reproduce themselves, and die.

We assume that the population does not grow indefinitely, but after a certain amount of time the population reaches an equilibrium size, $K$. Time and population size are thought as continuous variables. Time spans an infinite horizon.

Specifically, the evolution of the population size over time is assumed to follow a logistic function as in Figure A of the picture below,
where $N(t)$ denotes population size and $t$ denotes time.

Consequently, one can derive the slope of the logistic curve at each point, which we denote by $\frac{d N(t)}{dt}$. When plotting $\frac{d N(t)}{dt}$ as a function of $N(t)$, one obtains Figure B of the picture below.

$\frac{d N(t)}{dt}$ can be thought of as the "increase of population size that is obtained by natural processes during an infinitesimal amount of time".

Suppose now that a firm wants to harvest individuals and that the firm's profit increases with the number of harvested individuals. Let $H$ be the harvesting rate, that is "amount of individuals removed from the population during an infinitesimal amount of time". Suppose that the firm wants to keep the harvesting rate constant over time. At a given point in time, $H$ cannot be bigger than $\frac{d N(t)}{dt}$ because otherwise the harvesting is not sustainable and the population is at risk for decline to extinction. $\frac{d N(t)}{dt}$ is highest when the population size is equal to $N^*$. Hence the optimal strategy is to wait until the population has reached size $N^*$ and then apply a constant harvesting rate equal to $H^*$ (which, in turn, keeps the population size constant at $N^*$ and does not allow it to grow until $K$).

Questions:

1) Is my summary correct? For the last sentence to be true, are we assuming that "waiting until the population has reached size $N^*$" has no cost for the firm (or that, somehow, costs are compensated after)?

2) I read somewhere that the harvesting activity produces an harvested stock equal to $N^*$. What does this mean? Since the time horizon is infinite, once harvesting starts it will never stop. Therefore, how can one compute the final harvested stock?

3) Which are other underlying assumption of the model that I have not reported in my description above?


texts: Understanding the formulation for the SDF chosen in a paper

texts:
In a Stanford paper they claim the SDF is an affine transformation of the tangency portfolio by citing a textbook and then say a valid formulation of the SDF can be given by $M_{t+1} = 1 - \sum_{i=1}^N \omega_{t,i}R^e_{t+1,i}$.
I'm trying to understand a bit more about how they came up with their formulation. For example, why "$1 - $" and not "$1 - $", also why not wirte "$+\sum_{i=1}^N \omega_{t,i}R^e_{t+1,i}$". I have no reason for these alternative formulations but I'm assuming there's a bit of intuition behind there formulation that I'm not following.
So far the reasons I've come up with is "$-\sum_{i=1}^N \omega_{t,i}R^e_{t+1,i}$" so that the tangency portfolio has larger positive weights on high risk assets. If that's a satisfactory reason, then I'm just trying to figure out why "$1-$". That's going to scale the optimal weights but I don't the reason why for a particular scaling.


texts: Exports: How can a small amount of export make really high income

texts:
I'm currently researching for a school project about Thailand.

I found the wonderful Observatory of Economic Complexity Website.

There are two visualizations I don't quite understand:
https://atlas.media.mit.edu/en/visualize/tree_map/hs92/export/tha/all/show/2015/
https://atlas.media.mit.edu/en/visualize/stacked/hs92/export/tha/all/show/1995.2016/

How can it be that Animal products (light yellow) are only 1.3% of total exports but make the most money.

Maybe I didn't understand the Stacked Visualization right. So maybe that's my mistake.

EDIT: OK; I just found out that I misread the chart. I was a little bit confused obviously. These stacked line charts are completely unlogical to me


texts: Why wouldn't competition prevent "usurious" payday loan rates?

texts:
The current Wiki page on "Payday Loans" claims loans are priced above marginal cost. The justification is that

  If a lender chooses to innovate and reduce cost to borrowers in order to secure a larger share of the market, the competing lenders will instantly do the same, negating the effect. For this reason, among others, all lenders in the payday marketplace charge at or very near the maximum fees and rates allowed by local law. [23]

Doesn't this logic contradict the fact that competitive markets price goods at their marginal cost?

Is there an implicit assumption that the payday loan market is not sufficiently competitive? If so, is this assumption true?


texts: Is profit margin the same as net profit margin?

texts: I'm quite confused by these two terms because different websites define them differently.


texts: IMF adopted Chinese yuan as international currency the other day. Will Chinese yuan be a key international currency someday?


texts: Why is discriminating monopoly better than competitive markets for producers?

texts: In intermediate microeconomics by Hal Varian, It is said that discriminating monopoly is better than competitive markets for producers. Why so?


texts: Do (any) governments or central banks have an explicit or econometrically probable policy to "prop up" stock market prices?

texts:
This assumption (that governments [in the a broad sense of the term] prop up stock prices deliberately) has been taken as a given/assumption in another question here.

Is there evidence that they actually and deliberately do that (i.e. prop up stock prices) though, instead of that being a side-effect of "propping up" the "mainstreet" economy?

Evidence I would accept:

Explicit declarations e.g from relevant government institutions (e.g. central banks, fiscal policy makers) that "propping up" stock market prices is a goal.
Econometric analyses that somehow prove that the "real goal" of stimulus measures is propping up stock prices, "above and beyond" the "real/mainstreet economy."


texts: When we learn about the GDP multiplier, it is portrayed as 1/MPS, because savings are supposedly a leak out of consumer spending. However, what I don't understand is aren't those savings spent anyways in the product market? Don't they go to the financial market and get used by businesses to invest in projects? At that point the GDP multiplier would be infinite and the only thing that would matter is how fast people spend. Am I wrong in thinking this?


texts: Neo Keynesian Modelling and the Lucas Critique

texts:
Some people from the more extreme microfoundations/internal consistency camp keep bashing the Neo Keynesian model for the Calvo pricing being not micro founded and hence the whole model not being immune to the Lucas critique.

However, one could argue that we don't  observe inflation rates far away from the steady state in the US, and, as long as this was true, the lack of micro foundations was minor.

Which argument dominates here? Are there other arguments to be made around NK and the Lucas critique? What is the literature's conclusion?


texts:
Is there an economic theory of quitting an activity? A theory that weighs the investment costs put into something and the opportunity costs of pursuing it.

I am aware of Fershtman and Gneezy Quitting in Tournaments paper that investigates the decision of quitting in the middle of a race or of a tournament. But, I am looking for a more general model of quitting something such as playing an instrument, a sport or even a job. Dropping-out from (grad)-school may obey the same investment-opportunity cost trade-off.

Update: I am looking for some explicit references modeling the exiting or quitting process, even if it concerns some decisions in particular without any generalization.

Edit: Here is why I picked @Ubiquitous' answer.


texts: Are Price and Quantity Conjugate Variables?

texts:
I am taking a thermodynamics class. In this class one of the things that is discussed is how the partial derivatives of the internal energy with respect to extensive parameters (entropy, volume, mol number, etc) give rise to intensive parameters (temperature, pressure, electrochemical potential, etc). For example for pressure and volume:
$$ P = \left(\frac{\partial U}{\partial V}\right)_{S,N} $$
The similarity between pressure volume diagrams and price quantity graphs (see below) got me thinking, is there a similar conjugate relationship between price and quantity? Maybe something like this:
$$ P = \left(\frac{\partial U}{\partial Q}\right)_{D^*} $$
Where $P$ is the price, $Q$ is the quantity, $D^*$ is either demand, supply or the conjugate of either and $U$ is some sort of economic (as opposed to thermodynamic) potential. This $U$ could be found with an intrgral but does it have a name? Can we use Legendre transforms to generate more potentials?


texts: Why is market equilibrium pareto efficient?

texts:
Let us assume that the current price $P$ is lower than the 'equilibrium price' $P^\star$ so that $Q$ is lower than $Q^\star$. If we move from this combination towards the equilibrium one, it may be the case that the producer surplus decreases. I understand that the total surplus (consumers+producers) increases, but it is not clear to me why producers should be willing to reduce their surplus. So it looks like to me that there is not pareto improvement in moving from $(P,Q)$ to ($P^\star$,$Q^\star$), in that consumers are better off but producers may be worse off.
What is wrong with my reasoning? Could you help me with this, please?


texts:
The US Census Bureau's survey of income and program participation (SIPP) has, among others, the following variables:

epdtbhn: Paid job during the reference period
ersnowrk: Main reason for not having a job during the reference period
tpmsum*: Earnings from job received in this month
eeno*:  Across-wave employer index/number Unique job number that will remain the same from wave to wave.

Now, I'm looking at the following individual from the 2008 wave:

br ssuid ersnowrk epdjbthn tpmsum*  eeno* if ssuid == "019925011535"

In May 2012, that individual was reported as Unable to find work, epdjbthn == No.
In the next month, epdtbhn == Yes: He/she had a job (consistent with ersnowrk == Not In Universe). However, all the employment variables (tpmsum*, eeno*) are also all not in Universe.

This is clearly inconsistent data. The allocation flag for epdjbthn says that the data was not imputed. The allocation flag for the employment variables is meaningless (as they are not in universe). Does this mean I can rely on the person to have found an actual job, even if none of the other employment variables are speaking towards it?


texts:
What's the difference? To illustrate, please give examples of

A game with perfect but incomplete information; and
A game with complete but imperfect information.

Related.


texts: How can the abuses of monopoly power lead to market failure?

texts:
So I know that the abuses of monopoly power can cause market failure, but I don't know why that is. I am guessing that because monopoly's face a lack of competition, they have no incentive to improve their product or service, therefore they are not allocating resources efficiently (market failure), however, in my book, a lack of competition is a seperate cause, so I was wondering if there was anything else to it.

P.S. If you could include a logic chain of reasoning and an example in your answer, that would really help me to understand it. I am also revising for GCSEs so the answer need to be extremely advanced. Thanks


texts: I am trying to determine how to write the K-step ahead forecast of a VAR(2), with two variables, as a weighted average of its mean and last observations. I understand that one must use companion form, but am unsure of how to derive the weights from it. Any guidance is much appreciated. Thank you.


texts: How to predict income n years after graduation using income dataset with age, but not graduation year?

texts:
I'm trying to predict the income of graduates of certain Master's programs n years after graduation, using the American Community Survey individual level dataset to calibrate my equation. It gives me observations of individuals listing their income, age, degree program, and other variables, but doesn't tell me years since graduation or years in the workforce. How can I best predict income n years after graduation?

I'd like my final product to be a regression equation of the form:

income_year_n = starting_salary(many variables) * (1+rate_of_raises)^n

My initial approach is along the lines of:

The youngest people with this degree are 23 years old. They all must have graduated the previous year. Use them to calibrate the starting_salary function.
The next youngest group is 24. They must either have one year of experience, or have just graduated. I know roughly the proportion for each, because I know how many 23 year olds there are in the dataset, but I don't know which are the new graduates and which graduated last year.
The next youngest is 25, this group has either 0, 1, or 2 years of experience, and I know the proportions for each.

And so on. This feels like the beginning of an approach that would work, but I can't figure out how to go from this data to a regression equation that predicts income after a certain number of years.

Any ideas? I know there's no perfect solution, I'm looking for a close-enough hack to actually use the equation in the real world. Anything would be greatly appreciated, thanks a ton.


texts: So, I am trying to evaluate the consumer and producer surplus. In my notes it is written that the new consumer surplus (defined by the change of the graph from pre-subsidy to post-subsidy) is G + A + D + E - which I do understand. But now, the new producer surplus is defined as the area H + D + A + B. This, one the other hand, doesn't maky any sense to me. Shouldn't the producer surplus be the area H + the "tunnel" that is not marked below H?


texts:
In an effort to empirically back up merger simulation models (which are rarely used in practice) I am trying to find 'old' papers, working papers, memos, etc. that have data on simulations people ran on mergers at that time. Using this information and the post merger information only available in the present I hope to see how effective merger simulation models were in estimating the post-merger economic effects.

If my request is still unclear here is a paper by Craig Peters with the same goal.

Are you aware of any such references or collection of references that could prove useful?


texts: Data source for the relative frequency of different kinds of expiration date by retailers? (use by, sell by, best by)

texts: I'm not sure if this is the correct Stackexchange site for this question, but I am interested in the economic and environmental effects of food waste reduction. A common policy proposal to reduce food waste is to standardize expiration dates of food so that consumers do not mistakenly discard food before it has spoiled. However it's not easy to assess the effectiveness of the policy without knowing the baseline frequencies of the different types of expiration date (use by, best if used by, sell by, etc.) Is anyone aware of a study or survey that has tried to quantify how often retailers and/or manufacturers use each different type of expiration date label? It would be great to have data for individual food types as well if that exists. This question refers to the USA but I would be interested in data from any country.


texts: Data Set/Database listing NAICS codes for U.S. firms?

texts:
I need access to a dataset that matches firms to their NAICS codes so that I can fill in some missing data in a data set I have for some research.

I was wondering if anyone on here might know of such a database or dataset I could explore?


texts: Where to start learning economics as a mathematician?

texts:
I study pure mathematics at university and I'm looking to get into economics, with pretty much no background knowledge about it.

Are there good sources to learn from with a decent mathematical background in mind, or should I just start learning from "normal" sources, like watching video lectures from introductory courses, which don't assume much mathematical knowledge? Preferably, I'd like to embrace economics without those limitation.


texts: Axiom: More is Better; But when is more better?

texts:
I'm taking an introductory microeconomics course and have been introduced to the 3 axioms of economic preferences. These include

Completeness
Transitivity
Non-satiation

My understanding of non-satiation is incomplete. This is because of how the lecturer has described it. I am told that non-satiation means

More is better
Indifference curves further from the origin are better

From some research on the internet I find that non-satiation is also known as the Axiom of Dominance, described as:

  If any combination A has more of one or of both the goods than B, then
  it is said A dominates B. This axiom states that if A dominates B,
  then the consumer will prefer A to B. This axiom is also known as the
  axiom of non-satiation or of monotonicity.

Given this, my understanding is that given 2 bundles $A(x,y)$ and $B(a,b)$, $A > B$ if $x > a$ and $y > b$.

My questions:

Q1) Is my understanding correct?
Q2) What if $x<a$ but $y>b$? Is the agent indifferent? He will have to be, otherwise completeness will be violated?

Thanks for your help.


texts: Who is the first one to equate "rational" with "complete and transitive preference"?

texts:
MWG taught that, suppose that the menu is finite, "rational" is the same as "complete and transitive". But it seems that it does not cite any sources. Who said this first?
vNM said in 1944 that their EU is rational behavior, which is followed by computer scientists, statistician, and Finance literature. Why didn't MWG also follow this?

MWG equate "rationalizable" with "existence of utility function" or "complete and transitive preference". To be clearer about my question, I am most interested in learning the first literature which argue that the "existence of utility function" or "complete and transitive preference" is rational.


texts: Monthly price elasticity and possibility of using daily values

texts:
I am calculating the price elasticity as a starting point to find a theoretical optimal price that would maximize our revenue.
I am looking at 2 years data and to use the price elasticity formula, I am considering monthly values separately (this also because given the strong seasonality we have, i would expect different elasticity per month and I would like to suggest different prices every month).

To get the monthly Price Elasticity, I calculate for each month Prices and Quantities of the respective year:

$$
\frac{(Q^{2018} - Q^{2017})/Q^{2017}}{(P^{2018} - P^{2017})/P^{2017}}
$$

Question 1: Is this correct? Using aggregated monthly data is enough? What if I had also 2016 data? How could I put this extra information in the formula?

Question 2: Could I use daily data to calculate the price elasticity? Could I plot 2 years data and use the linear trend line for the elasticity calculation?

Thanks in advance, any help is highly appreciated!


texts: Why do we need a restriction of a game to prove the given statement?

texts:
Consider a game $G$. We have to prove that is $s$ is a Nash Equilibrium of $G$, then it is also a Nash Equilibrium of the game formed by removing strictly dominated strategies of $G$.

I looked at the proof for this in https://homepages.cwi.nl/~apt/stra/ch3.pdf (the proof is described in first two pages of it)
They use a restriction $R$ ($R_{i}=$ (possibly empty) set of strategies such that $R_{i} \subseteq S_{i}$)  of a game at every point of the proof.

My question is what good does it do to take the $R$ of the game instead of directly taking the set of all possible strategies for all the players $S$?


texts: Books for microeconomics and macroeconomics for selected topics

texts:
I am a mathematics undergraduate trying to self-learn some economics. I have no background in economics. I wish to know from which chapters of Hal Varian's "Intermediate Microeconomics" (7th edition) should I study for the following topics:

Microeconomics: Theory of consumer behaviour, theory of production,
market structure under perfect competition, monopoly, price discrimination,
duopoly with Cournot and Bertrand competition (elementary problems) and
welfare economics.

Macroeconomics: National income accounting, simple Keynesian Model of
income determination and the multiplier, IS-LM Model, models of aggregate
demand and aggregate supply, Harrod-Domar and Solow models of growth,
money, banking and inflation.

Regarding the macroeconomics part, I still do not know which book to follow and which chapters to read. It would help me a lot, if someone can guide me in this. Since the headings of the chapters differ from the names of these topics, I am unsure which portions to read without any expert's help.

P.S.: I am unsure if this is the right place for me to ask such a question.