texts: Books and resources on how policies/regulations are made on exchanges like NYSE, NASDAQ, LSE, etc?

texts:
Different stock exchanges (for example, NYSE vs KRX) have similar but different regulations overall. Each exchange has different concerns and each exchange has a different approach to handle problems like volatility, etc.

How can I learn more about the thought process that goes into making policies/regulations to handle such problems?

Is there a specific discipline that studies financial exchanges and their regulations? Market Economics? I think that's too broad a term.

Bonus question: How do governments decide when to intervene on bad regulations/policies made by financial exchange marketplaces (? by this I mean: stock markets, foreign exchange markets, etc)

Maybe I don't have a clear question. In that case, can you provide some relevant introductory references or keywords to research?

If my question is not appropriate here, can you suggest where else I can get answers?


texts:
In my study, I have 5 independent variables which contains 21 observation each. However one of my independent variables have 3 gaps. What should I do?

e,g

I would need to know the effect of education to inequality and I would like to conduct standard OLS method. However, I have one unbalanced data which have gaps unlike the rest of the data... what should I do?
per say in 1997 (no data) 1998 (0.2345) 1999 (no data) 2000 (0.3453) and then from 2001 - 2017 it has continuous data....should I just drop it and start from 2001?


texts:
Consider a simple dynamic consumption-saving problem. A solution can be characterised using a Lagrangian approach that generates a set of first order conditions and some boundary conditions.

An alternative approach is to set use a Bellman equation. What I don't understand is how come a Bellman equation approach does not seem to use information regarding the boundary conditions in the solution methodology? That is, a Bellman equation does have a tradeoff between time period t and t+1 but not some overall budget constraint does not seem to be represented.


texts: Intuition behind a cournot duopoly nash equilibrium producing a higher output than a monopoly?

texts:
I am just wondering if someone could explain the descriptive, not mathematical intuition behind why a cournot equilibrium for a duopoly produces a higher level of output than a monopolist but lower level of output than a perfectly competitive maket?

I can understand why a cournot model with many firms would result in a perfectly competitive outcome but why would a duopoly necessarily result in a more efficient outcome than a monopoly?

Thanks in advance


texts: Have any economics papers used unified cure models?

texts: Does anyone know if there are unified cure models (aka split population models) in time-until-employment studies that combine the mixture cure approach with the promotion time approach as described in this paper in epidemiology: https://journals.sagepub.com/doi/abs/10.1177/1471082x0800900202


texts:
Consider Solow model with $Y=(AL)^{1-a}K^a$. Then output per effective labor is $y=k^a$ where $k=\frac{K}{AL}$.

"If markets are competitive, the rate of return on capital equals its marginal product, $f'(k)$ minus depreciation $\delta$"?

How does market competitiveness deduce formally/mathematically the rate of return on capital equals its marginal product, $f'(k)$ minus depreciation $\delta$"? The statement seems plausible but I can't prove it mathematically. What is the formal definition of rate of return on capital here?

The relevant equations are the following.

$\frac{d}{dt}K=sY-\delta K$ where $s$ is saving rate. Assume labor $L$ and knowledge $A$ grows exponentially at rate $\delta,g$ respectively.

Reference. Romer Advanced Macroeconomics, Chpt 1, Sec 1.5


texts: If the industry is dominated by a few major large retailers like Walmart and target with thousands of many other small supermarkets around the country, what is the market structure of the industry? is it a perfect competition or an oligopoly?


texts: I would like to know how important combinatorics is. I am an undergraduate student looking to take more math courses and I saw and intro to combinatorics as an option. The reason I am asking is because the course seems cool to me but preference is usually given to compsci majors thus there are hurdles when enrolling which is why I was wondering what application of combinatorics are there in economics?


texts: Find high resolution market data for a single ticker?

texts:
I'm doing my dissertation at the moment and for it, I need high-resolution market data. The only problem is I'm a student and haven't got much money. A lot of sites I have seen want monthly subscriptions or big upfront fees, I do not have this.

What's the cheapest way I can get 6/3 months of Tesla market data at say 1-second resolution?

Thanks.


texts: What are the justification of using 1990 or 2010 as benchmark in studies?

texts:
Normally, many international studies and documents using multiple-of-10 years (for example 1990, 2010) as the benchmark year.
For example: Dong,2019, p.899 used 1990 as the benchmark to calculate the Export Market Leniency Laws variable as discussed here, or WorldBank converted GDP to $USD 2010 as discussed here.
I have some justifications for this usage:

These numbers look round and are convenient. If you used the benchmark as 1991 or 2011, the readers will think you had some reasons to omit 1990 or 2010, you will be questioned about cherry-picking data.

Multiple-of-10 years do have an advantage in the USA and some other countries because these are the census years, so the macro-level data would be up-to-date and better in demographical.

Could you please justify these ideas and offer me some more reasons for these choices?


texts: Ex-post vs Ex-ante Budget Balance in Auctions

texts:
Have I understood this correctly?

When I say my auction mechanism is ex-post budget balanced it means that in practice (I have done market simulations) and according to the results my mechanism is budget balanced. whereas, if the mechanism is ex-ante it means we only anticipate that it is budget balanced?

A reviewer of my paper has asked me to explain in the paper what ex-post and ex-ante means. How would you suggest to explain it?


texts: Confounding versus endogenous variables. What is their relative hierarchical position?

texts:
There are valuable resources on the lexicon of types of variables quickly accessible, such as here. However, some of these concepts appear side-by-side often enough to make them confusing.

For example, Wikipedia mentions two causes for endogeneity:

Uncontrolled confounder (omitted variable bias);
Loops of causality between dependent and independent variables (simultaneity).

This is in line with the Encyclopedia of Health Economics formulation

$$Y=X_1β_1+X_2β_2+C_oβ_o+C_uβ_u+\varepsilon\tag 1$$

where the generating true model in the equation is opaque to the researcher because of $C_u$ - an unobservable confounding variable which, unlike $C_o,$ may be suspected, but cannot be controlled for, resulting in a flawed $Y=X_1\beta_1+X_2β_2+C_o\beta_o+e$ model. In this case, if $X_1$ was correlated with $C_u,$ we could say that $X_1$ is endogenous because of the presence of an unobservable confounder.

Based on this, should confounding variables be considered a type of endogenous variable? Endogenous > Confounding?

But, then in this Stata blog it seems to have a different mathematical formulation as compared to confounders and OVB. In this linked document $X_1$ would be endogenous if

$$\begin{align}
Y &= X_1\beta_1 + X_2\beta_2+\varepsilon\\[2ex]
&\mathbb E(\varepsilon \vert X_1)\neq0\\[2ex]
&\mathbb E(\varepsilon \vert X_2)=0
\end{align}$$

It is evident that this may just be a different mathematical formulation of the same concept in equation (1): the omitted unobservable confounder manifests itself through residual lack of independence of $X_1$ and $\varepsilon,$ a rather theoretical mathematical equation since $\varepsilon$ cannot be directly measured, and the actual residuals are orthogonal to the model matrix by construction.

According to this blog, confounders and endogenous variables are two separate issues.

Perhaps the true understanding of the differences comes from graphical causal models:

  one only needs to consider the three elementary causal structures from which all DAGs can be constructed: chains $A\to C\to B$ (and its contraction $A\to B$), forks $A\leftarrow C\to B,$ and inverted forks $A\to C \leftarrow B.$ Conveniently, these structures correspond exactly to causation, confounding, and endogenous selection.

Here, confounder = common cause while endogenous selection = common outcome.

There may be some field dependency. From J Epidemiol Community Health 2008;62;858-861 F Imlach Gunasekara, K Carter and T Blakely:

  Endogenous explanatory variable: An explanatory variable in a
  multiple regression model that is correlated with the error term,
  either because of an omitted variable, measurement error, or
  simultaneity.

  ...

  When endogeneity is discussed in biostatistics texts with
  respect to longitudinal data it is mainly a factor of reverse
  causation. An endogenous exposure variable is a predictor of
  the outcome at time $t$ and is also predicted by the outcome at
  time $t–1.$ This can be controlled for by adding time-lagged
  variables to the model.

QUESTION:

Could we precisely define the differences and overlapping features of these two types of variables with emphasis on any hierarchical structure? Can we formulate their respective definitions in a precise (linear) algebraic equation, or through directed acyclic graphs (DAGs)?


texts: Was the aid in the Marshall Plan a loan?

texts:
In the aftermath of the Second World War the USA organised the Marshall plan for the post-war reconstruction of Europe.

I take it this was actually a loan of some kind; on what kind of terms was the loan given? How long did it take a country, for example the UK or France to pay this off - or are they still paying it off? How much was the loan worth in real terms if the interest due on the loan was discounted?


texts: Why is it important to open up the economy before a cure for COVID-19?

texts:
This is a multi-part question:

Why are we leaving quarantine so soon?
If it's to increase economic activity, why is it important to keep it so high?
At what point is economic activity worth more than thousands of people's health and livelihoods?


texts: What is the logic of Bagehot's policy of high interest rate?

texts:
I have a doubt about monetary policy, as suggested by Walter Bagehot. He wrote a book "Lombard Street" in 1873, to comment on a recent banking crisis. There he recommends these measures to stop a banking panic:

That the central bank lend freely.
At a high rate of interest.
On good banking securities.

The second point is particularly puzzling. In his own words:

  First. That these loans should only be made at a very high rate of interest. This will operate as a heavy fine on unreasonable timidity, and will prevent the greatest number of applications by persons who do not require it. The rate should be raised early in the panic, so that the fine may be paid early; that no one may borrow out of idle precaution without paying well for it; that the Banking reserve may be protected as far as possible.

(From Wikipedia: https://en.wikipedia.org/wiki/Lombard_Street:_A_Description_of_the_Money_Market)

This goes counter the main narrative in the press today, which is that central banks have to lower the interest rate in order to increase lending and economic activity, not to increase it. Bagehot's policies could actually exacerbate the crisis! A high interest rate might produce deflation, which exacerbates debts, like in the Great Depression. What is going on here?


texts: Minimalist example of voter profiles yielding different outcomes

texts:
Let the set of alternatives be $\left\{a,b,c,d\right\}$.

Let there be $n$ types of voter profiles, each type with a different strict ordering over the set of alternatives.

The number of voters belonging to the profile types need not be the same, let us denote these by $v_1,v_2,...,v_n$.

What is the minimal number of $n$, for which you can construct the voter profiles in such a way that the plurality rule (a.k.a. first-past-the-post), simple run-off (election with two rounds) rule, elimination rule and the Borda count all yield different outcomes? (Assume non-strategic voters. Outcomes should not be ties.)

EDIT:
Plurality rule has one round of voting and whoever has the most votes wins.  Example: United Kingdom parliamentary elections

The simple run-off rule has two rounds of voting. The two candidates with the most votes in round 1 advance to round 2. In round 2 voters vote for their favourite remaining candidate, and whoever has the most votes wins. Example: French presidential election

The elimination rule is similar to the run-off rule but has three rounds (number of alternatives minus one). In each round the candidate with the least votes is eliminated (figuratively). Others proceed to the next round.  Example: Academy award (Oscar) vote

Minimalist guesses ("here are some profiles with $n = 4$") are fine, ideal solution would provide a proof that $n$ is minimal.


texts: Arguing uniqueness of Bayes-Nash equilibrium in an auction setting

texts:
In an auction setting with interdependent values, let $\theta_i$ denote the type of player $i$ and $m_i$ that player's message (a bid, essentially). I have calculated the best response function as:
$$m_i^* = \theta_i + \gamma \sum_{j \ne i} (\theta_j-m_j)$$
Obviously, then, truth-telling by all parties ($m_k = \theta_k$ for all $k$) is a symmetric BNE, regardless of $\gamma$. I want to also argue that it is the unique BNE. If $\gamma = 1$, it seems like there would be assymetric BNE if there are only two players in which one player's positive misreport ($m_i - \theta_i$) would equal the other player's negative misreport ($\theta_j - m_j$). If $\gamma<1$, it looks like the truth-telling BNE is unique, but how would I prove that?

Also, so far I have not used a common prior assumption. Do I need it here to argue the existence of the truth-telling BNE, or to argue it's uniqueness? If so, we can suppose $\theta_i$ is drawn i.i.d. uniformly from $[0,1]$.


texts: Interpretation of IMF Balance of Payments Data - Financial Account

texts:
While I understand the meaning of the components of the Financial account what I don't understand is the concept of "assets" and "liabilities" after direct investment, portfolio investment etc.

A lot of studies have looked at gross capital inflows, gross capital outflows and net capital flows but don't mention exactly the procedure to find these.

I would really appreciate if anyone can explain.


texts: Recommended ratio of sells of software of basic and advance edition

texts:
Our company is selling one software in two edition: - cheap one with basic features - expensive one with basic and advance features

According to sells statistic, more than 90% of people are buying the expensive one edition. I would like to know if the sells model is suitable. Isn't the expensive variant too cheap? I know that Microsoft is selling Windows Office in Home edition and Professional edition, but they don't sell more than 90% of in Professional edition.

It seems to me that such product configuration is different in software development, because production price of creating software copy is same for cheap and expensive edition (which differs for example from automotive where production of luxury car is ore expensive).

Is there some recommended ratio in sells for cheap and expensive edition of software to maximize revenue?

I ask my colleague about it and he answered: "Isn't it good that we sell the highest edition at most?" It is reasonable argument?


texts: Does immiserizing growth exist outside of theory?

texts:
For a course in international trade, our professor touched on the idea of immiserizering growth.  He emphasized that immiserizing growth was a theoretical outcome from specialization of trade and did not provide the class with examples on the global market.
What are some real world examples of immizerizing growth?


texts: The effect of inflation differentials on the relative prices of goods across countries

texts:
I am struggling to understand the answer to this question (the answer was given as C):

  If inflation in South Africa is lower than that in the United States (US), US exports are becoming relatively _____ in South African markets. This shifts the demand curve for US dollars to the _______ and the supply curve of US dollars to the ________.

  A. cheaper, left, right

  B. more expensive, right, left

  C. cheaper, right, left

  D. more expensive, left, right

  E. cheaper, left, left

I selected B. Firstly, I think  that if you have to pay more for US exports because of inflation, they are more expensive compared to before. Secondly, using the equation E = RER x P*/P (where E is the exchange rate, RER stands for 'real exchange rate', P* is the foreign level of prices, and P is the domestic level of prices) I think that the rand depreciates and the dollar appreciates, which implies that the demand for dollars increased (presumably because more dollars are needed to pay the higher price), and the supply of dollars decreased (presumably because traders see that they should hold on to dollars until a later date, given the appreciation caused by increased demand).


texts:
Why is the bliss point utility function convex even though it has concave portions to it ?

According to Nicholson and Snyder (authors of Microeconomic theory - Basic principles and extensions) a function has diminishing MRS and is convex only if it is quasi-concave. Accordingly, I checked quasi concavity for the bliss point utility function $U (x, y) = 12x + 16y –x^2 – y^2$, and it showed that the function is quasi concave throughout. This means that the function should be convex throughout, but that is not the case here.


texts: What's the Difference Between Being Pro-business and Being Pro-market?

texts:
In a recent interview I watched a economist say something along the lines of:

"There is a distinction between being pro-business and being pro-market. There should be rules in place so that businesses can compete in a way that is good for the economy and not just good for their shareholders."

Question: What is this distinction exactly? In other words, what is he probably referring to?

The only thing that comes to mind when I think about that statement is how many corporations are using large amounts of profits to buy back their shares as opposed to investing in capital. Am I on the right track, or is there more to it than that?


texts: How to simulate changes in quantity demanded when several prices change?

texts: I am not sure if this is a straightforward question or not. Basically, I have a set of products along with their prices and quantities demanded. I also have own and cross price elasticities for each product as well as the cross price elasticity with my outside good. I want to figure out how quantity demanded will change when the prices of several products changes. For example, if my products are different types of beers and the outside option is wine, I want to know how quantity demanded of all beers and wine will change when several beers change their price. I want to assume that total quantity demanded of beer and wine remain constant (but expenditure can increase). Finally, I do not want to estimate a demand model I just want to use the elasticities that I already have access to (from an outside source).


texts:
What effects could the growing use (and abuse) of Decentralized crypto-currency have on the rest of the world economy? For example, one cause for concern is the simplicity of laundering the currency. Is there any comparable event in history that could help forecast what might be in store? Is there even any cause for worry?

I want to get some outside opinions on this thought experiment.


texts: Fair and efficient allocation of "family goods"

texts:
Consider an exchange economy with two goods, e.g. home furniture (x) and electrical equipment (y). The interesting thing about these goods is that, when a family owns a bundle, all members of the family enjoy the same bundle (it is like a "club good" but only for the family).

There are two families. In each family, there are different members with different preferences over bundles. Assume that all preferences are monotonically-increasing and strictly convex.

An allocation is a pair of bundles, $(x_1,y_1)$ for family 1 and $(x_2,y_2)$ for family 2.

An allocation is called envy-free if:

All members of family 1 believe that $(x_1,y_1)$ is at least as good as $(x_2,y_2)$;
All members of family 2 believe that $(x_2,y_2)$ is at least as good as $(x_1,y_1)$.

An allocation is called Pareto-efficient if there is no other allocation of bundles to families such that all members of all families weakly prefer and at least one member of one family strictly prefers.

Under what conditions does a Pareto-efficient envy-free allocation exist?

If each family has a single member, then a Pareto-efficient envy-free allocation exists; this is a famous theorem of Varian. Has this theorem been generalized from individuals to families?


texts:
The Allais paradox, is an  experiment set up as follows, where you are free to chose between gambles $A$ and $B$:

(the table on wikipedia is much more readable if you prefer)

  Experiment 1

  Gamble 1A

  \$1 million, 100% Chance

  Gamble 1B

  \$1 million, 89% Chance

  \$0, 1% Chance

  \$5 million, 10% Chance

  Experiment 2

  Gamble 2A

  $0, 89% Chance

  \$1 million, 11% Chance

  Gamble 2B

  \$0, 90% Chance

  \$5 million, 10% Chance

The paradox arises when one chooses both Gamble 1A and Gamble 2B.

This paradox is portrayed as a proof, or evidence of inconsistency in von Neumann–Morgenstern utility theory with it's status as a "rational" decision theory. In particular it is intended to show inadequacy of the independence axiom of that theory.

However, while I find that while {Gamble 1A, Gamble 2B} is an acceptable and even desirable set of choices (which would be logically inconsistent with the theory), this observation doesn't seem strong enough to show the theory is absurd -- it seems fair to argue that if one refused to accept 1% chance of gaining nothing, one would desire a 10% greater chance of winning anything (versus gaining nothing) to be the correct choice in Experiment 2. In other words, both choices {Gamble 1A, Gamble 1B} and {Gamble 2A, Gamble 2B} seem perfectly logical. In fact, if all choices were approximately the same utility, the inconsistency would disappear (which seems entirely plausible to me).

Is there another set of parameters, or another example entirely, which more convincingly shows an absurdity of the independence axiom, or are the parameters above as strong as it gets?


texts: Why is a solution concept of Bayesian Persuasion a subgame perfect equilibrium?

texts:
Many papers on Bayesian persuasion adopt SPE as a solution, by arguing that the sender has no private information.
This does not make sense to me: Regardless of whether the sender has private information, we need to restrict the belief of the receiver about the state of the world after the receive observes an off-path disclosure policy, which SPE has no bite. Should we understand SPE in Bayesian persuasion literature as something that does not really mean subgame perfect equilibrium?


texts: Fair voting procedure when there are many issues

texts:
When several people have to decide about a single yes/no issue*, the natural decision rule to use is the majority rule.

But when there are many issues to decide upon, the majority rule is "unfair" in the following sense: it is possible that the majority's opinion will be accepted on all topics and the minority's opinion will not be accepted on any topic. As an extreme example, it is possible that 51% of the population will decide about 100% of the issues.

I am looking for a decision rule which prevents this unfairness.

Formally, define a "uniform group" as a group of people who always vote in the same way. Define the "acceptance rate" of a uniform group as the percentage of issues on which the opinion of the uniform group got accepted.

Define a "fair decision rule" as a rule for which, for every uniform group containing X percent of the population, the acceptance rate tends to X when the number of issues tends to infinity.

MY QUESTION IS: Does there exist a fair division rule as defined above?

(* I restrict the question to yes/no issues, since when the issues are not binary the problems are much more complicated).


texts: Basic Solow Growth Model: Stability Proof

texts:
I am reading through McCandless "The ABCs of RBCs" this summer to get a preview of what I need to know for the coming Fall semester. It did not take long to find a statement that I can easily accept but cannot prove. On Page 9 after deriving the steady state condition of $(\delta + n)\bar{k} = \sigma A_0 f(\bar{k})$ in a zero-technological growth regime (where $\delta$ is depreciation and $n$ is growth rate of the labor force), the author says that "the stability of the positive stationary state can be seen from the equation $$ k_{t+1} = g(k_t) = \frac{(1-\delta)k_t + \sigma A_0 f(k_t)}{1+n}$$ Notice that between 0 and the positive $\bar{k}$, the function $g(k_t)$ is above the 45 degree line, so that $k_{t+1}$ is greater than k_t." He provides a standard-looking Solow model state diagram where I can verify this graphically, but not analytically.

I'm trying to prove every statement in the book in order to better familiarize myself with the details of macroeconomic theory before diving deeper, but I am absolutely stumped as to how I would prove that $k_{t+1} > k_t$ when $0 < k_t < \bar{k}$ and vice versa. I first tried manipulating the capital motion equation to prove it directly, and I could not reach a proof. The next strategy I have been trying to employ is to differentiate the capital motion equation and prove that its derivative is less than 1 at the steady state point, but it fails:

$$
\frac{\partial k_{t+1}}{\partial k_t} = \frac{(1-\delta) + \sigma A_0 f'(k_t)}{1+n} > \frac{(1-\delta) + \sigma A_0 f'(\bar{k})}{1+n} = \frac{(1-\delta)+(\delta+n)}{1+n} = 1
$$

Does anyone have an alternative strategy I can follow? It's been driving me nuts for two days.


texts:
I am trying to do this problem, and I am  not getting the answer.
I need to find the fixed cost of system 1, and system 2.
I know that the fixed cost will be the y-intercept of the equation.
Fixed cost for system 1 is 1000, and fixed cost for system 2 is $5000.
When I tried to find the variable cost per map dispensed, I am not getting the answer.
I know that the variable cost changes with the output. Therefore, it is the slope of the equation. In this case, the variable cost for system 1 is supposed to be 0.90, and the variable cost per map dispensed for system 2 is 0.1. However, the solutions manual shows that the variable cost per map dispensed for system 1 is 0.8, and variable cost per map dispensed for system 2 is 0.16.
Did I do something wrong?


texts:
I'm very inexperienced in mathematical economics, so when I came across the idea of the consumption set in Arrow-Debreu, I was a little confused. So for each element x in consumption set X, what does x represent? This also applies to element y in technology set Y. Are x and y values?

And as a side note, how can one analyze something like a Value Equilibrium on a macroeconomic scale? What kind of variables and analysis goes into looking at equilibrium/efficiency of allocations?


texts: Use of mathematics and imprecise definition of terms

texts:
As a postgraduate student of economics I've been trying to expand my mathematical "toolset". While doing so I've talked to engineers, physicists and mathematicians, many of which have disdained the use of mathematics in economics. Their arguments vary, but one common theme is summed up by mathematician Michael Edesess' critique:

Economics pretends to be mathematics, but it is not mathematics. There
is a major difference. No mathematician uses a term in a formula, or a
statement of a theorem, unless that term has first been defined with
excruciating precision.
And while economists may think they’ve defined terms like "aggregate
demand" or "economic growth", they should try reading some real
mathematics to see what a precise definition truly is. The economists,
I think, leave the work of definition to be inferred from the way the
terms are used in the formulas.

I believe I know the precise definition of (quite a few) economic terms, but maybe Edesess is pointing out to some more profound mathematical foundations which I may not be familiar. Could someone expand on his argument and maybe even counter back?


texts: How do I find the probability mass function of an individual observation for a multinomial logit model?

texts: I know what the probability mass function of a multinomial logit model is.  However, I do not know what the probability mass  function of an individual observation i, f(yi|xi), is for a multinomial logit model.  I would really appreciate if someone could explain how to get the answer and knows the correct answer.


texts: What is the monotone hazard rate assumption used for?

texts:
I was reading this article on advance purchase discounts and pricing in which the author uses the monotone hazard rate assumption. Why does the author use it?

The article is Advance-purchase discounts as a price discrimination device (PDF) by Nocke Peitz and Rosar

Below you can find a screenshot of the part in question.

Thank you very much!


texts: Consumer behavior with constrained demand

texts:
Suppose there is a linear demand function $D(p)$ describing the demand of an individual consumer. This is derived from a utility function or is just observed, but let us assume it is correct. Now suppose that the product is available at price $p$, but the store insists that each consumer buys a minimum amount that is in fact larger than $D(p)$, but only by very little.
 Say it is $D(p) + \epsilon$, where $\epsilon < D(p)/100$.

Can I say without additional assumptions that given the options of buying a quantity $q$ where $q \in \left\{0\right\} \bigcup \left[D(p) + \epsilon,\infty\right)$, the consumer will choose to buy $D(p) + \epsilon$?

My argument is that this will maximize her consumer surplus given the constraint on $q$. As I specified that this is a linear demand function and $\epsilon < D(p)/100$ you can do the math, but it is easy to see that the surplus will be positive for any continuous demand function given a small enough $\epsilon$.

Is this an accepted line of argumentation?

In most models it is accepted that consumers seek to maximize their utility. I am not sure however if one can argue absent a utility function that surplus maximization is the goal.
 A workaround would be specifying a quasi-linear utility function supporting $D(p)$ but I would like to avoid this if possible.


texts: Utility function types - request for review

texts:
I am working on a Wikipedia page that compares several common utility functions. Although I found some information about these topics on the web, I didn't find it all in one place, and often got confused by the different terms. I will be happy for any comments or reviews. Most importantly: are the facts in this page correct?

EDIT: to make the question self-contained, I copy its current contents below. Because StackExchange markdown does not support tables, I used Senseful Solutions to create the text table.

This page compares the properties of several typical utility functions of divisible goods. These functions are commonly used as examples in consumer theory.

The utility functions are exemplified for two commodity types, $x$ and $y$. $p_x$ and $p_y$ are their prices. $w_x$ and $w_y$ are constant parameters.

+---------------+-------------------------------------+-----------------------+-----------------------------------------------------------------------------------+----------------+-------------+-----------------------------------------+----------------------------------+
|     Name      |              Function               |  Indifference curves  |                                   Demand curve                                    |  Monotonicity  |  Convexity  |                Good type                |              Example             |
+---------------+-------------------------------------+-----------------------+-----------------------------------------------------------------------------------+----------------+-------------+-----------------------------------------+----------------------------------+
| Linear        |  ${{x\over w_x}+{y\over w_y}}$      |  Straight lines       |  Step function: only goods with minimum ${w_i p_i}$ are demanded                  |  Strong        |  Weak       |  Substitute good|perfect substitutes    |  Potatoes of two different farms |
| Leontief      |  $\min({x\over w_x},{y\over w_y})$  |  L-shapes             |  hyperbolic: ${\text{Income} \over w_x p_x+w_y p_y}$                              |  Weak          |  Weak       |  Complementary good|perfect complements |  Left and right shoes            |
| Cobb–Douglas  |  $x^{w_x} y^{w_y}$                  |  hyperbolic           |  hyperbolic: $\frac{w_x}{w_x+w_y} {\text{Income} \over p_x}$                      |  Strong        |  Strong     |  Independent good|independent           |  Apples and socks                |
| Maximum       |  $\max({x\over w_x},{y\over w_y})$  |  ר-shapes             |  Discontinuous step function: only one good with minimum ${w_i p_i}$ is demanded  |  Weak          |  Concave    |  Substitute good|substitutes            |  ?                               |
+---------------+-------------------------------------+-----------------------+-----------------------------------------------------------------------------------+----------------+-------------+-----------------------------------------+----------------------------------+

Are the details in the table correct?

EDIT: Many thanks to all commenters and answerers. I revised the page accordingly.


texts: What quasi-experimental/econometric technique can I use to measure the impact of a policy using longtitudinal tax data?

texts:
I have two cohorts of workers with very similar characteristics (e.g. same demographic profile, skill level, industry) that were laid off at different points in time. Say one group was laid off between 2002-2004 and the other was laid off between 2009-2012.
The first group were laid off with no additional support from their employer. The next group was provided a range of services to help them transition to a new job (call this the treatment group).
I have income tax data, which also includes details such as sex, age marital status etc for the years following these events for much of the two cohorts.
Where would one begin in using this data to attempt to measure the quantitative impact of the treatment (receiving transition support)?
Are there any precedents for such use of tax data? What kind of data analysis or modelling techniques would one use?


texts: Can people lack a comparative advantage and a comparative disadvantage?

texts:
Source: Question 9b, p 61, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw
= Question 8b in Principles of Microeconomics, 4 Ed, 2008

  9. Are the following statements true or false? Explain in
  each case.
  b. “Certain very talented people have a comparative
  advantage in everything they do.”

  Answer: b. False; it is not true that some people have a comparative advantage in everything they
  do. In fact, no one can have a comparative advantage in everything. Comparative
  advantage reflects the opportunity cost of one good or activity in terms of another. If you
  have a comparative advantage in one thing, you must have a comparative disadvantage
  in the other thing.

Abbreviate comparative advantage as CA. Mankiw's question above motivates the titled one.

E.g., suppose in a 3-person economy: person A's CA is cooking and person B's foraging, yet person C does nothing.


texts: Numbers of right and left gloves Question?

texts: I assumed that numbers of right gloves at the horizontal axis and numbers of left gloves at the vertical axis. Therefore, two goods are essential and indifference curves are L-shaped. However, I want to ask that if my left hand is broken and I cannot wear the left glove for 12 months, does the indifference curve look like https://ibb.co/BfmF53H  Also, what can I say about its utility function? Can I say that its utility function looks like $U(x,y) = x^\alpha$


texts: Bank Charter Act of 1844 vs banking landscape 2021 - regulatory capture or policy obsolescence?

texts:
A driving motivation for the Bank Charter Act of 1844 was to institutionalize/centralize seignorage and impose limits on how much influence commercial banks have in terms of money creation (along m4 lines). Background here:https://wcfia.harvard.edu/files/wcfia/files/471_01-05broz-grossman.pdf
In today's digital world, issuing actual notes is somewhat trivial. In effect, credit/deposit accounts can be created largely at the discretion of commercial banks. At first glance it would seem that the 90%+ money in the form of commercial bank accounts is a modern manifestation of a nearly-identical issue identified by Sir Robert Peel and supporters centuries earlier.
I would like to see where conventional economic thinking stands on this issue.
Question
Has legislation simply not caught up with digital disruption in money creation or is this more about lack of political will (regulatory capture)? Or perhaps there is an entirely separate, more benign explanation as to the disconnect of policy and industry over the past 200 years?


texts:
In a book on Corporate Finance, the author writes that 'all other things constant' the higher the rate of growth in sales or assets, the greater will be the need for external financing(bank loans, debt securities, or equity). His reasoning is based on the $\text{Assets}=\text{Liabilities} + \text{Equity}$ equation. My question is why can't a company manager use his cash, in the current-assets, to drive the growth in sales or assets? And why should this equality be maintained in this situation? To answer just that by def. of equity, i.e. assets minus liabilities, in this last question seems to be not answering at all...

Any help would be appreciated


texts: How is matching theory used in context of Marriage market difference in terms of which is used in context of labour and housing market?

texts:
I am looking for an overview as most of the introduction to matching talks about the work done in the Marriage market, Job Matching which is axiomatic. Then while looking at Labour and housing market it very different and at a very macro level.

Marriage: https://web.stanford.edu/~niederle/Palgrave%20Matching.Approved.pdf

Labour: https://economics.mit.edu/files/7400

Housing: http://www-2.rotman.utoronto.ca/facbios/file/Search%20and%20Matching.pdf


texts: Size and influence of the regulatory/supervisory sector

texts:
I am interested in the size of what I call the regulatory/supervisory sector in Western economies. A regulatory/supervisory (R&S) activity involves either:

Determining a set of rules economic agents must comply with under penalty of retaliatory action (regulation).
Monitoring and enforcing the compliance of economic agents with a set of rules (supervision).

These functions can be accomplished either by public or private actors: for example, in the UK the Financial Conduct Authority is responsible for regulating and supervising the behavior of individuals working in the financial sector; on the other hand, auditing companies such as EY and PwC are hired to monitor whether companies comply with accounting standards.

Is there any paper which studies the size of the R&S sector in the economy or its impact of the economy? Is there any economist which specializes in this? These can also be old economists from XIXth or XXth Century which thought and wrote about it.

Why do I ask this? Roughly speaking, as economies (such as countries or regions) grow over time, their economic fabric becomes more complex and sophisticated as they transition to activities with higher value added. My impression is that economies will experience a continuous, long-term upward trend in the number of R&S jobs both in the public as well as in the private sector, with the portion of economic activity belonging to the R&S sector converging towards some sort of equilibrium point (I do consider the existence of R&S cycles). The need for these positions comes from different structural factors, among which:

As economies become more complex and sophisticated, certain systemic risks gradually emerge and R&S jobs are needed to monitor and control these risks (e.g. the development of the banking systems in Western countries has generated the risk of systemic financial instability, as seen in the numerous banking crisis throughout the last centuries);
Growth often comes through innovation, which brings disruption through the formation of new sectors of activity which tend to replace or substitute old ones. As these new sectors grow and become more mature, the limitations and risks they pose become gradually apparent to society which will ultimately demand to regulate and supervise them either through private or public action (e.g. the current debate around the use of personal data by social networks and the need to regulate it);
Rogue economic actors can exploit institutional loopholes or lack of oversight to perform illegal or borderline illegal activities for their profit. Once society identifies these shortcomings, R&S is improved to avoid repetition of these unfair practices (e.g. the Enron scandal and the resulting Sarbanes-Oxley Act in the US).

On the other hand, it could be argued that the size of R&S activity is not intrinsically increasing: for example, regarding point 2 above, it can be argued that as new industries replace old ones, so too do new R&S roles replace old roles.

Given I believe the R&S sector can only grow in relative size over the long term, I am logically interested in understanding how this sector influences the economy and how an economy evolves as a consequence of the increasing importance of regulation and supervision. For example, it might be the case that an outsized R&S sector has similar negative effects to those due to the proliferation of rent-seeking activities.


texts: How is expected inflation measured for policy purposes? Is it based on some economic model or some survey?


texts: How do companies with shareholders close up shop?

texts:
How can a company with shareholders stop operations without being acquired or going bankrupt?

How is a company with shareholders that is closing up shop able to give shareholders money back for their shares if the shareholders invested more money than the value of the company's assets?

If a company with shareholders has closed up shop in the past without being acquired or going bankrupt, what are some well-known examples?


texts: How would privately minted coins enter circulation?

texts:
I read a great article about private minting in early America that talks about some of the private minters whose copper, silver, and gold coins were widely circulated throughout the country without the federal government having anything to do with the process. I had some questions about how exactly that would work, so in the absence of a historian, I thought I would ask here for some answers that would have to make sense economically.

These coins would have to be considered commodity money rather than fiat money since the government wasn't involved. In order for this to work, would the face value of the coins have to be really close to the intrinsic value?

If the face value and intrinsic value were the same, how would the minters profit without any seigniorage?

Without a central bank, how would money minted by private minters enter circulation?


texts: Is there any academic paper documenting the importance of the Operating Cycle?

texts:
Content from a website that :

The Operating Cycle offers an insight into a company’s operating
efficiency. A shorter cycle is preferred and indicates a more
efficient and successful business. A shorter cycle indicates that a
company is able to recover its inventory investment quickly and
possesses enough cash to meet obligations.

I am wondering if there is any academic paper that documented the same thing for citation purposes and I am also looking for academic papers talking about the operating cycle in a quite comprehensive context.


texts: How do central banks create money to pay interest on reserves

texts:
Referring to this answer (https://economics.stackexchange.com/a/15321/12013) for the technical process of money creation.

How do central banks create the money to pay interest on its reserves (assuming positive interest rate)? I don't see the process being backed by any asset. And if the money is fiat-ly created with no asset backing, would raising interest rate not have the opposite effect of driving inflation and devaluing the currency (rather than slowing inflation and appreciation)?

Yes I am aware of the PQ=MV formula of conventional central bank wisdom, that raising interest rate has the effect of restricting money supply and slowing inflation. I would like to know if the factor mentioned above exists, and if yes, when will each factor/force dominate net inflation and exchange rate.

Since there are many types of interests, the answer can be limited to IOER or this.


texts:
What are the exogenous variables that drive demand for and supply of money? Are there variables in common between the two? I think I'm getting caught up with interest rates, as adjusted by the Feds vs the natural return from investment etc.
Thanks in advance for any help!


texts:
I was just thinking about the question

  How does a firm choose the optimal input vector as to maximize profits when the firm produces more than one final product

More precisely if $\mathbb{R}_{\geq 0}^{\ell}=\{x \in  \mathbb{R}^{\ell} : x \geq 0\}$, the production function would be
$$
f:\mathbb{R}_{\geq 0}^{\ell}\rightarrow \mathbb{R}_{\geq 0}^{n}, \quad n\geq 2
$$
For simplicity we can assume the firm operates in a competitive market so that the price is given.

My question is, how does the firm choose the input vector $x \in \mathbb{R}_{\geq 0}^{\ell}$ as to maximize profits?

I did some research and apparently the type of problem this is a “multi-objective” optimization problem, and it appears to be an active field in engineering. Some of the methods to solve this kind of problems use pareto-dominance style arguments.

I wanted to know if anyone could clarify the specific question of multi product profit maximization, and more generally I would also appreciate any literature or books on this topic (multi objective optimization), written for economists, as I have been searching in google and every book I find appears to be written for engineers.

I suspect that a treatment of this topic from an economics point of view would involve some discussion of social choice theory.

Any help is most welcomed!


texts: EMH: Difference between market price and fundamental value?

texts:
I am confused by the relation between stocks market prices and fundamental (or intrinsic) values stated by Efficient Market Hypothesis. How these deviates regarding to efficient market theory or are these the same according to EMH?

Why I am asking this is because among the literature, there can be found two kind of statements.

This is the very general statement that can be found from here and there:

  Investopedia: This principle is called the Efficient Market Hypothesis (EMH), which asserts that the market is able to correctly price securities in a timely manner based on the latest information available. Based on this principle, there are no undervalued stocks to be had, since every stock is always trading at a price equal to its intrinsic value
  **.

The another one what can be found from academic literature and books, states:

  Fama (1965) In  other words,  in  an  efficient  market  at  any  point
  in   time   the   actual   price   of   a   security   will   be
  a good estimate of its intrinsic value.

and line with previous, other source states :

  Market efficiency
  does not require that the market price be equal
  to true value
   at every point in time. All it requires is that errors in the
  market price be unbiased,
  i.e.,
  that
  prices
  can
  be
  greater
  than
  or
  less
  than true value, as long as these deviations are random

I also saw algebraig illustration where it was shown that the market price estimates the fundamental value of security better any individual trader can estimate it. (with certain assumptions)

So the question is, why here and these is stated, that in efficient market, the market price of stock is trading at a price equal to fundamental (or intrinsic) value? Which is right?

And if the market price is at the best good estimate of intrinsic value, how can it be stated that in efficient market there are not under- or overvalued stocks, if the market price is only best estimate of instrinsic value?

I am not very familiar with algebraig definitions, but some kind of clarification behind this issue would be appreciated.

Thank you for clarification.


texts: Differentiating through this integral in banking loans?

texts:
Working through the math which gives the following profit function for a bank but I can't seem to solve this first order condition. The profit function is defined as follows,

\begin{equation}
\pi_t = p_{k,t-1} R^L_{k,t-1} L_{k,t-1} + (1-p_{k,t-1}) \frac{L_{k,t-1}}{\int_0^1 L_{k,t-1}dk} \tau \theta_{t-1} a_{t-1} - R^D_{t-1} L_{k,t-1} + \mu_t^B \bigg( \int_0^1 \bigg[\bigg(\frac{R_t^L + \eta \frac{1}{\theta_t}}{R^L_{k,t}+ \eta \frac{1}{\theta_{k,t}}} \bigg)^{\epsilon} x_t + \gamma^L s_{k,t-1} \bigg] dj - L_{k,t} \bigg)
\end{equation}

and the FOC they get for $L_{k,t}$,

\begin{equation}
\partial L_{k,t}: p_{k,t} R^L_{k,t} + (1-p_{k,t}) \frac{\tau \theta_t a_t}{\int_0^1 L_{k,t} dk} - R^D_t - \mu_B =0
\end{equation}

I can't seem to make sense of this differentiation of the integral. I have been looking at Leibniz integral rule all day. My understanding was that the following holds when the bounds of the integral are constants,

\begin{equation}
\frac{\partial}{\partial x} \bigg( \int_0^1 f(x) dx \bigg) = \frac{\partial}{\partial x} f(x) dx \Big|_0^1
\end{equation}

Using this rule I can't get what the result showen is. Am I incorrect or is this example incorrect?

Much appreciated.


texts: Is NIIP a good measure of a country economical development?

texts:
In another question I asked someone pointed me to an answer where NIIP (Net International Investment Position) was mentioned as a measure of economical development, which I already heard about it and it makes sense since it takes into account not only the actives but the pasives of a country

But then you see this list, and you find out that first world countries like United States, Australia, Sweeden or Spain are in big red. What does this mean? Does it mean that NIIP is a poor index to measure economical development or wealth? Or does it mean those countries are in a serious bad situation which could lead them to be in a crisis in the future?


texts: Could a hike in interest rates cause a country to be unable to pay back it's debt burden?

texts:
Sometimes I read in news articles, that a central bank can't hike the interest rates much higher, because then the government would be unable to pay the interest rate burden of it's government debt.
Is this really true? In my understanding this should only be true for government debt that will be issued after the interest rates are already high.

I mean, the biggest part of government debt that has been already issued is only traded at the secondary markt at a fixed nominal interest rate.
(except of an usually much smaller part of floating rate notes)


texts: How to measure quality of education across countries?

texts:
For my research, I need a measure of the quality of education that I could apply to multiple countries. It must include quality of tertiary education.

Standard measures like HDI Education Index are not precise enough. For example in HDI Education Index, Kazakhstan is ranked along Hong Kong, Belarus above Singapore, etc. Such absurd discrepancies destroy any hope for good results for my model.

Please, if you have an idea (no matter how wild it is) what I can use as a proxy for quality of education, please share it.


texts: What is the economical advantage coming from the ability to speak English?

texts:
I'm very much interested in the difference between anglophonic and non-anglophonic countries stemming just from the language skills. I'll be grateful for any references regarding the topic.

What is the approximate annual economical gain of a country stemming purely from investments in English language classes?


texts: What will giffen goods and Veblen goods peform in general equilibrium model?

texts:
I'm a beginer of microeconomics.
According to consumer behavior theory, a consumer possesses a set number of money as budget constraint at first. And their is negative income elasticity of demand and extremely positive income effect for giffen goods. In contrary, the man who demand Veblen goods will increase his quantity demanded if price increase.
But in chapter general equilibrium, I was informed that their is no money in this model, and the 'number' of price are used to indicate relative price, not absolute one (I learned that from Intermediate Microeconomics:A Modern Approach by Hal R. Varian, and a textbook self-complied by the school). I am confused that if their is no money,  are the changes of income and price samely relative in partial equilibrium model? Or the 'number' of them are absolute? How can we witness giffen effect and Veblen effect in general equilibrium model?


texts: Kelly criterion wealth allocation alternatives

texts:
Thanks for your patience with answering my question.

I am interested in building an optimal wealth allocation strategy across multiple betting opportunities, correlated or uncorrelated and with different types of constraints.

I've been looking for relevant papers and literature.

What I've found so far is all Markowitz theory, Kelly criterion related. My question is if there are other alternatives to such strategies that may have very different idea behind them.

Also if there are some papers that you yourself found very relevant to Markowitz and Kelly. Papers about informed betting strategies, investments across multiple opportunities, wealth allocation etc.


texts: How to derive utility possibility frontier?

texts:
I'm trying to derive the utility possibility frontier of a economy whose consumption contract curve is $$y_A = \frac {y} {x} x_A$$ and $$y_B = \frac {y} {x} x_B$$where $x_A + x_B = x$ and $y_A + y_B= y$.

$$U_i = \sqrt {x_iy_i}$$

While deriving the UPF. they have added up $U_A$ and $U_B$, and I don't understand why. Why do we add up utilities while deriving UPF?

(I gave all the details of the question because I'm not sure if they added the utilities only because of the peculiarities of the question or if its an algorithm. )


texts: Ricardian Model: Trade pattern rules (ch. 3 Krugman's book)

texts:
I'm reading chapter three of International Economics by Paul Krugman et al. I have two questions that are somewhat related.
Question 1: Let $P_{c}$ = price of cheese, $P_{w}$ = price of wine, $a_{Lc}$ = unit labor requirement to produce cheese, $a_{Lw}$ = unit labor requirement to produce wine.
How does $\dfrac{P_{c}}{P_{w}}=\dfrac{a_{Lc}}{a_{Lw}}$ produce the flat portion of the world relative supply curve? I know the textbook says it is because the home country is willing to produce either good. Still, how does that translate to a flat portion of the world relative supply curve?
Question 2: Also, in chapter three Krugman talks about how to determine patterns of trade by looking at relative productivities. Take the variable definitions I gave in question one and let $a^{*}_{Lc}$ = unit labor requirement to produce cheese in the foreign nation and $a^{*}_{Lw}$ = unit labor requirement to produce wine in the foreign nation. Krugman says that one should order the goods $i$ to $N$ so that the lower the number $i$, the lower the ratio $\dfrac{a_{Li}}{a^{*}_{Li}}$. That is, we order the goods in such a way that
$\dfrac{a_{L1}}{a^{*}_{L1}} < \dfrac{a_{L2}}{a^{*}_{L2}} < \cdots < \dfrac{a_{LN}}{a^{*}_{LN}}$
He says that the relative wage $\dfrac{w}{w^{*}}$ fits somewhere in that chain of $\dfrac{a_{Li}}{a^{*}_{Li}}$'s. He says that any goods left of the relative wage will be produced at home and any goods to the right of the relative wage will be produced in the foreign nation. But then he says something that I think contradicts what he has already laid out. He says that a good will be produced at home if $\dfrac{a^{*}_{Li}}{a_{Li}} > \dfrac{w}{w^{*}}$. It seems that these two rules can contradict each other right? Is this a typo or is there something that I'm not understanding?


texts: Why are pricing charts treated as continuous series?

texts:
I understand that prices are set by actors' offers to buy and sell within the market, however, when analyzing the data it seems to often be treated as though the price is continuously varying like some natural process that is independent of the actors' choices to buy/sell at certain prices... said offers being what actually creates the discrete datasets.

Is there a reasoning/rationale behind this? Does it make a difference? Am I missing something here?


texts: Literature on factors affecting number of houses built

texts:
Is there any existing literature on the various factors affecting the number of houses constructed in a particular city over, say, a given month? Factors might include: quality of housing stock, a lagging value of housing sale price, house price to earnings ratio.

Preferably, I would like to see literature that describes the relative importance of these factors, perhaps by running a regression--so that way, when I do my own regression on the factors, I can compare the magnitude and direction with existing research.

Anything related to this would be useful too; for example, if there is no paper which predicts the number of houses built, then something which gives, say, a utility yield for constructors would be helpful.


texts: Is the set of optimal strategies convex in a single-agent decision choice problem?

texts:
EDITED with insights from the comment below.

Consider a decision maker who has to choose an action among $\mathcal{Y}\equiv \{1,2,...,L\}$. The payoff from choosing action  $y\in \mathcal{Y}$ depends on the state of the world, $V$, with support $\mathcal{V}$. Specifically, choosing action $y\in \mathcal{Y}$ leads the payoff $u(y,v)$, where $u:\mathcal{Y}\times \mathcal{V}\rightarrow \mathbb{R}$.

Suppose the decision maker has complete information about the realisation of $V$ drawn by nature.

A (mixed) strategy of this choice problem is a probability kernel, $\mathcal{P}_{Y|V}\equiv \{P_{Y}(\cdot| v)\in \Delta(\mathcal{Y}): v\in \mathcal{V}\}$,  collecting probability distributions of  $Y$ conditional on every realisations $v$ of $V$.

Hence, $\mathcal{P}_{Y|V}$ is an optimal strategy of the choice problem  above if  $\forall v\in \mathcal{V}$ such that $P_{Y}(y|v)>0$, and  $\forall \tilde{y}\neq y$
$$
\begin{aligned}
u(y, v)  \geq u(\tilde{y},v). \\
\end{aligned}
$$

Let $\mathcal{Q}^*$ be the collection of all optimal strategies of the choice problem  above, that is
$$
\mathcal{Q}^*\equiv \Big\{\mathcal{P}_{Y|V}: \forall v\in \mathcal{V}, \forall y \in \mathcal{Y}\\
\hspace{6cm}\underbrace{P_{Y}(y|v)>0 \Rightarrow u(y, v)  \geq u(\tilde{y},v)\text{ } \forall \tilde{y}\neq y}_{\text{This is not a linear constraint because of the form "IF ... THEN ..."}}\Big\}
$$

Question 1) The definition of $\mathcal{Q}^*$ just given seems to highlight that $\mathcal{Q}^*$ is not a convex set. This is because it is defined by a constraint of the type "IF ... THEN ...", which is not linear.

Is this comment correct?

Question 2) Consider a payoff function $u(1,v)=u(L,v)>u(y,v)$ $\forall y \neq 1,L$ and $\forall v \in \mathcal{V}$. Consider the following strategies
$$
1) \mathcal{P}_{Y|V}\text{ s.t. } P_{Y}(1|v)=1 \text{  and }P_{Y}(y|v)=0 \text{ }\forall y\neq 1, \forall v \in \mathcal{V}
$$
$$
2) \tilde{\mathcal{P}}_{Y|V}\text{ s.t. } \tilde{P}_{Y}(L|v)=1 \text{  and }\tilde{P}_{Y}(y|v)=0 \text{ }\forall y\neq L, \forall v \in \mathcal{V}
$$
$$
3) \mathcal{P}^*_{Y|V;\alpha}\text{ s.t. } P^*_{Y}(1|v;\alpha)=\alpha P_Y(1|v) \text{, } P^*_{Y}(L|v;\alpha)=(1-\alpha) \tilde{P}_Y(L|v) \text{,  and }P^*_{Y}(y|v;\alpha)=0 \text{ }\forall y\neq 1,L, \forall v \in \mathcal{V}, \forall \alpha \in (0,1)
$$
I believe that the set
$$
\mathcal{B}\equiv \{\mathcal{P}_{Y|V}, \tilde{\mathcal{P}}_{Y|V}, \mathcal{P}^*_{Y|V;\alpha} \text{ }\forall \alpha\in (0,1)\}
$$
is convex. Indeed it seems to me that $\mathcal{B}$ is the convex hull of $\{\mathcal{P}_{Y|V}, \tilde{\mathcal{P}}_{Y|V}\}$.

Correct?

What is the relation between $\mathcal{Q}^*$ and $\mathcal{B}$?

I think that $\mathcal{B}\subseteq \mathcal{Q}^*$. This is because for each element in $\mathcal{B}$, the "IF ... THEN ..." condition defining $ \mathcal{Q}^*$ is satisfied.

Does  $\mathcal{Q}^*\subseteq \mathcal{B}$ too? If my assertion is question 1) is correct, then it should be $\mathcal{Q}^*\supset \mathcal{B}$ because otherwise $\mathcal{Q}^*$ would be convex. But here I'm lost: which element of $\mathcal{Q}^*$ does not belong to $\mathcal{B}$?


texts: Does Modern Monetary Theory (MMT) provide a useful insight into how to manage the economy?

texts:
According to advocates of MMT, the primary risk once the economy reaches full employment is inflation, which can be addressed by gathering taxes to reduce the spending capacity of the private sector. Deflation is not seen as a risk because the Government of any country with sovereign control of its own internationally accepted currency can print money to create as much inflation as it wants at will (depending on who receives that money).
It appears to me that this must be true to some extent, but my concern is that the feedback mechanism where the extra money generates inflation might not be smooth and free flowing for various reasons and a vast excess of money might accumulate in an unstable way in certain areas of the economy. After a period of time some trigger event might cause a sudden uncontrollable cascade flood of that money that could destroy public confidence and the currency itself. Is this an unfounded fear?
https://en.wikipedia.org/wiki/Modern_Monetary_Theory


texts: How are economic principles applied to non-financial models, such as a democratic election?

texts:
Economic agents make decisions in particular models. These models do not need to be related to financial contexts, and economics can be used to describe how agents will act in any other field in which humans act.

As an example, how would economic principles be applied to the process of a democratic election?


texts: What is aid money for natural disasters spent on?

texts:
It's often said that the best thing you can do to help after a natural disaster is to give money.

I have a simple question about how and where that money is sent. I imagine often resources can be donated, but money is still required to utilise them.

Is there a study showing the breakdown?


texts: Does land value tax create an incentive to merge land ownerships?

texts:
LVT is "a tax on the unimproved value of land", and "in theory, it does not distort decision making". But if I own land then improvements such as buildings on my neighbour's land can easily increase the value of mine.

It seems like the total LVT payable would therefore be reduced if I sold my land to my neighbour and they paid tax on the entire estate at the value it would have had not been improved. This seems like a major distortion of decision making.


texts: Can 10% of the population provide super-abundance for the entire world?

texts:
In a discussion at the Watson Institute for International and Public Affairs on Nov 9, Mark Blyth, a political scientist, said that

  We live in a world where literally 10% of the population could provide super-abundance for everyone.

Despite not being defined by Blyth in that talk, I'm assuming that super-abundance in this means:

3500 kcal (14.6 MJ) per day in nutritionally complete food
100 sq meters of appropriate shelter
clothes
entertainment (including vacations)
healthcare, education, sanitation and everything else related to the first two levels on Maslow's hierarchy of needs

Can 10% of the population working full time or the entire working population (I'm assuming that 50% of the population is work capable) working only 20% of the time provide for the entire world ?


texts: How To Program Finite General Equilibrium Models

texts:
I am wondering the best way to find a numerical solution to a finite general equilibrium model with Matlab. The model is a basic neoclassical growth model with equilibrium equations:

$c_t+k_{t+1}=k_t(1-\delta)+k_t^{\alpha}$(budget constraint)

$c_t^{-\gamma}=\beta c_{t+1}^{-\gamma}(1-\delta+\alpha k_{t+1}^{1-\alpha})$(Euler equation)

This is on a 500 time step time horizon. I tried to solve this using fsolve, but the program does not like the negative exponents in the expression. Is there another way in Matlab to program these? Also there are boundary conditions, let's just say they are $k_1=1$ and $k_{500}=0$.


texts: Why do banks need to write-off the debt against Shareholders capital invested

texts:
I have seen the basic equation that rules this system:

$$ Assets = Liabilities + Equity $$

@Alecos Papadopoulos has a really great answer that totally makes sense for this question.  But, I would like to ask, why does the bank need to write-off the debt against Shareholders capital invested?  Why cannot they act like the Pope and say, "I forgive your debt" then move on and not write off the shareholder's capital?  Would this not be better for everyone?

Further, I have read Jeffrey Sachs has argued for debt forgiveness for developing countries that have trouble paying back their debt, is this a similar situation replacing Person $A$ with country $A$?


texts: Long-term interest rate and stock market correlation

texts:
What correlation is there between (1) long-term interest rates and (2) the stock market valuation? Please provide a simple intuitive explanation.

For example, as I understand it from recent news reports, rising long-term interest rates put pressure on the stock market. Why?


texts:
The Wall Street Journal claims that:

  Some are concerned over the likelihood of the U.S. adopting trade
  tariffs on imports from China. This policy option would risk
  retaliatory measures and hurt U.S. exports, a blow to growth momentum,
  while making imports more expensive in the U.S., fueling inflation
  pressure. (emphasis added)

An academic article also says that the relationship is universally agreed upon by economists (gated link):

  If there is one idea on which all orthodox economists concur, it is
  that tariffs raise prices, that protectionism, without exception, is
  inflationary. Professor Samuelson, for instance, argues that tariffs
  reduce labor productivity and enhance “the cost of living” (1976, p.
  694). In the words of Coughlin et al., “protectionist policies
  increase prices” (1991, p. 25). According to the 1992 Economic Report
  of the President, “Trade barriers not only raise the prices of
  imported goods to consumers but also the prices of domestically
  produced goods” (p. 196).

I understand that tariffs reduce labor productivity by disallowing countries to produce in accordance with their comparative advantage. However, how does this lead to inflation? Is it because a decrease in goods produced plus the amount of money kept the same leads to inflation?


texts: Phenomenon of equal prices without price collusion

texts:
Some time ago, I came across a term describing a specific phenomenon observed in free markets. I'm now looking for this term.

When comparing prices of certain staples in some countries, one quickly notices that their prices are exactly the same in different supermarkets and discounters. For example, in Germany, the cheapest price for 1 kg of sugar in any supermarket or discounter is 65 ¢. I have never seen a different price for this for years. The exact brand of sugar is different for different supermarkets or discounters, but the cheapest offer is always 1 kg for 65 ¢. It's the same for eggs, milk, flour, yeast, salt, curd, and many other staples.

This price does not change as its in every competitor's interest to keep it exactly where it is:

If a market participant increases the price to make more money off the specific product, many people will avoid the supermarket or discounter because their prices are perceived to be higher in general as the staple in question serves as a price comparison between shops for many people.
If a market participant decreases the price to attract more customers, any competitor will decrease the price of their equivalent product to not appear to have higher prices than the participant that decreased their price.

This phenomenon results in supermarkets and discounters limiting the amount of a product customers can buy rather than increasing prices when running short of resupply or taking losses.

Note that I'm not looking for the term "price collusion". The term describes the exact phenomenon described above and does not suggest that price collusion is happening.

I'm not 100% sure this term exists in English. I only know that it exists in German because I read about this phenomenon on the German version of Wikipedia, but no one I asked in real life can tell me what it is. I guess that it exists in English, too, as it is an economic phenomenon not limited to any specific geographic region. Now I need the English term (if it exists) for usage in an English document.


texts: What does the introduction and expanded availability of credit cards do to money velocity?

texts:
Consider the quantity theory of money: $MV=PY$.
"Consider an example of a demand shock: the introduction and expanded availability
of credit cards. Because credit cards are often a more convenient way to
make purchases than using cash, they reduce the quantity of money that people
choose to hold. This reduction in money demand is equivalent to an increase in
the velocity of money. When each person holds less money, the money demand
parameter k falls. This means that each dollar of money moves from hand to hand
more quickly, so velocity $V (= \frac{1}{k})$ rises."

This is the argument given in Mankiw's intermediate macroeconomics text. I found this argument not correct in some sense. First of all, Mankiw's says people reduce the demand of money. This is not right. The total amount of money in the economy is a given. I think what Mankiw is trying to argue is people have less cash and less money in the demand deposit account. But then the money go to their saving account, or maybe they invest in some securities. But all these money they invested will become someone else's deposit account and an increase in saving account balance and the decrease in checking account balance does not change the total money supply. The money supply is inherently fixed then.

Mankiw also argues that each person hold less money so velocity goes up. The problem is although ordinary consumers are holding less money, banks are actually holding more cash to pay for people's purchases associated with the credit card. This is because merchants are not going to wait until people's statement balance get due in the next two months to collect their money. They want to settle the payment ASAP, which is why banks have to pay them earlier. And consumers will pay back the money to the bank later.

I believe another problem is what is the difference between real money supply and real money demand. In the problem Mankiw assumed Price Level does not change, and since the money supply is exogenous, $M/V$ does not change, i.e., real money supply does not change. So there is no way people is holding less money. They have to hold it somewhere, maybe in saving, maybe in checking. And like I said before, if they invest in securities, the balance they've invested show up on someone else's deposit account.

I really struggle with this seemingly easy problem. Any comments, corrections, and help is appreciated.


texts: Is poverty rightly measured internationally?

texts:
According to the World Bank, Argentina has 3.63% or people living in poverty. As a subjective assessment of someone living there, this is completely ridiculous. Rates measured by Argentine government and Argentine private institutions set it around 32% to 34%, and they are widely accepted as representative figures of Argentina's today reality.

As far as I understand, the definition used by the World Bank to define a person as poor says someone is poor when he earns less than US\$ 3.1 a day. That makes US\$ 90.30 dollars a month. Now I understand that the living costs are different in different countries, but how could they reach a figure of US\$ 90.30 a month to cover basic needs? How can a person with US\$ 90.30 dollars a month cover basic needs anywhere?


texts: Inflation leads to loss of gold reserves

texts:
I am reading Murray's Rothbard What has government done to our money? and this is his reasoning for inflation leading to loss of gold reserves to other countries (assuming everyone is on gold standard)

Lets assume everyone is on gold standard. Then

Credit expansion in country A
Prices in A increase
Increase in imports from country B because foreign goods become cheaper
Country B redeems A's currency for gold. Hence gold outflow from A to B.

What I am confused about is how does inflation lead to increase in imports in 3. As monetary supply increases, A's currency would lose purchasing power and so imports would become equally expensive at that point. Why would that not be the case?

Thanks,


texts:
There are a plethora of examples of weaknesses in my textbook, such as:

The Walrasian assumption
Not including nominal shocks
Not including indivisible labour
Not including distortionary taxes
Not including multiple sectors and sector specific shocks

In my opinion the greatest weakness is the Walrasian assumption, as I think this is not too realistic in the real world.

I think we want to measure degree of weakness by how closely we see the results posited by the model exhibited in the real world.

So if you have read some articles that improve on the basic RBC model, what are the common extensions (1-5, or other) that you see that address these weaknesses?


texts: How to test if the effect of one regressor entirely comes from other regressors?

texts: I have a regression model that includes IQ test scores as the dependent variable; my own education, my father's education and my mother's education as independent variables. Suppose I want to know whether the only way parents'education increases my IQ test score is through my own education. How would I test that hypothesis?


texts: Any pointers to reviews or data-sets or meta-analyses looking at the relationship between household fertility rate and family income/wealth (possibly with other factors like education and geographical region also measured) ? I assume there is some US census data with these values ? Perhaps also from other countries ?


texts: Gold Standard: Settling Up -- how were large transactions handled between companies?

texts:
I got the impression that the purchase of Alaska from Russia required at some point what would have been at 20 bucks/ounce (I think gold was at one point much less than 20) 350k ounces or roughly 10 tons of gold to Russia. If this is so, the expense of moving that much gold would have been very significant -- not just normal freight but cost of security, etc.
Did it ever become normal for banks to simply shift ownership between parties without moving gold out of its vaults?
And for large but lesser transactions, like buying a ship or a mansion, did that require someone carting, say, 1000 pounds of gold between banks?


texts:
For a Cournot Duopoly game with Linear Demand functions, we need to find the optimal quantity of each firm such that profit is maximised. Given the linearity of the Demand curves, we will obtain a quadratic profit function. Since profit function is strictly concave and quasiconcave, we can ensure a unique maximum, i.e. a unique optimal quantity for the firm to produce. The above explaination is for a 'standard' game with Linear Demand function, say, $max(a-bq,0)$, with cost function, say, $C_i=c_iq_i$ for, say, a duopoly, $q=q_1+q_2$

What I need to understand is that if we have non-linear demand function, such that we cannot ensure a unique optimal quantity for profit maximisation (which would be the Best Response function), how would the Nash Equilibria or Equilibrium be obtained? That said, is it possible for a Cournot game, or for that matter, any game to have more than one Best Response?

I'm still a bit rusty on the concepts, please bear with me. Is what I'm trying to understand, right conceptually? What am I missing?


texts: elasticity of income if price changes by 10 percent

texts:
Arista always spends  10
 % of her income on whatzits. Assume that her income increases by some percentage while the price of whatzits remains constant (and that all whatzits cost the same). What is her income elasticity of demand for whatzits?

I know elasticity of demand is either less than 1 or more than 1.
Since the equation for elasticity of income is quantity divided by income I dont understand what number to put for the numerator.

? / 10 %.  = 1

Will the answer be positive 1 or negative 1.


texts: Expectation conditional on a sum of random variables

texts:
The setting is a simple OLS regression where the true model has regressor $x$ and error term $u$, but we can only measure $\bar{x}=x+v$ where $v$ is iid with mean 0.

According to the textbook:

$\mathbb{E}(u|x)=0$ is satisfied, but $\mathbb{E}(\bar{u}|\bar{x})=\mathbb{E}(u-\beta x|x+v)=-\beta v$

I can see that $x$ and $u$ are correlated, but why am I allowed to just take $\beta x$ out of the expectation when I "only" condition on the sum $x+v$, and not explicitly on $v$?


texts: Isn't money moving towards central bank in the long run?

texts:
Central banks typically pumps money into the system by :

lending out to private banks
buying govt bonds

But in both these cases won't the central bank get back more money when it ends it's position (ie., initial money along-with the interest) and in the end more money from the system would get accumulated with the central bank.


texts:
I am studying for an exam in marketing, and there's the following sample question:

The main reasons that people choose products in category X is: 1. Brand 2. Price. Where the importance ranking is 50% Brand and 50% Price. Brand A’s utility is 50 and Brand B’s utility is 30. What is the maximal pricing among the following of Brand B’s product so that it will be preferred by the market if the pricing of A is $80?

a: $54.9

b: $59.9

c: $64.9

d: $69.9

The correct answer is (b). How do they get to this number? My only idea of how to solve this would be to multiply $80 by 30/50 but that's not even an option. Thank you.


texts: Usage of natural gas in 1970 (where was the demand elasticity?)

texts:
The following historical graph of US Marketable Natural Gas volume has me puzzled:

How was the gas used in 1970 (a peak production period), given that we would seem to be using a lot more gas now? Normally, I think of natural gas as having relatively inelastic demand because it relies on fixed distribution networks which are time-consuming and expensive to build.

In 2010, the graph shows less gas being produced than in 1970, but considering the huge increase in the retail use of natural gas for heating in recent decades, how can this be? Apparently there was some huge, elastic demand in 1970, which I presume was some industrial process. What would that have been? Before you say "power generation" look at this graph:

So, we are using a LOT more natural gas now compared to 1970 both in homes and for power generation. So, what is this huge extra use of natural gas in 1970? Where was it going?


texts: Confusion about the convexity of the best response correspondence

texts:
I am recently reading the proof of the existence of the Nash Equilibrium. As a math student, I do understand the use of Berge's maximum theorem and Kakutani's fixed point theorem, but I am not sure why the mixed-strategy space and the image of the best response correspondence are convex.

For example, if I have two mixed-strategies $\sigma_i,\sigma_i'\in BR_i(\sigma_{-i})$, why is the mix of these two strategies, $\lambda\sigma_i+(1-\lambda)\sigma_i'$ ($0\leqslant\lambda\leqslant1$), also a best response? Since $\sigma_i,\sigma_i'\in BR_i(\sigma_{-i})$ suggests $u_i(\sigma_i,\sigma_{-i})=u_i(\sigma’_i,\sigma_{-i})=\max\{u_i(x_i,\sigma_{-i})\}$, how to prove that $u_i(\lambda\sigma_i+(1-\lambda)\sigma_i',\sigma_{-i})$ also equals to maximum?


texts: Can somebody explain to me why exactly people necessarily had to starve under "communist rule"?

texts:
So, all my life, I've been told certain things. One of the least controversial is the "truth" that if you pick communism for a country, people will automatically starve. Allegedly, this is because the rulers will (I frankly have no idea if this is even really part of communism) insist on having centralized factories producing food, and then ship this out to every corner of the country so that everyone gets fed, but due to human flaws (or something), the food never ends up where it should?

I've always been confused about this. If that does happen, surely they would not keep doing it for long? Surely their plan isn't to starve their own people to death? Why is it so important to have huge centralized factories and then ship out all the food/goods?

And I don't understand why "the human factor" applies here but not in a capitalist system (or other). And why can't they just have a bunch of local sub-factories which operate according to the same principles, for practical purposes?

I cannot imagine that all the factory workers and food truck drivers just sit around with their hands in their pockets and whistle all day while their fellow men starve, just because they are in a communist country. As lazy and stupid as people tend to be in general, it doesn't go to that extreme... does it?

Surely they have managers/bosses even in a communist factory/food distribution system?

I really hope that somebody will finally clear this up for me, because I'm clearly missing some crucial detail about all this, which people never want to tell me when they say that communism is so bad.

PS: I'm not a communist.


texts:
I am reading "Principles of Economics" by N. Gregory Mankiw.
Why doesn't the supply curve shift to the left in the following situation?
Why do producers respond to the surplus by cutting their prices?

Suppose first that the market price is above the equilibrium price, as in panel
(a) of Figure 9. At a price of $5 per cone, the quantity of the good supplied (10 cones)
exceeds the quantity demanded (4 cones). There is a surplus of the good: Producers
are unable to sell all they want at the going price. A surplus is sometimes called a
situation of excess supply. When there is a surplus in the ice-cream market, sellers
of ice cream find their freezers increasingly full of ice cream they would like to sell
but cannot. They respond to the surplus by cutting their prices. Falling prices, in
turn, increase the quantity demanded and decrease the quantity supplied. These
changes represent movements along the supply and demand curves, not shifts in
the curves. Prices continue to fall until the market reaches the equilibrium.


texts: It seems firms spend a lot of time and energy "capturing" market share. Why is that?

texts: Are consumers just silly and once they like a firm they go for it regardless of the price? Or is there something more complex going on?


texts: How to find the "cost function" given the production function *as well as* the cost per unit produced and the fixed costs?

texts:
I'm working on the following homework problem, transcribed verbatim:

  A firm has a production function defined as $y = 8L^{1/4}K^{3/4}$. The firm faces costs of \$20 wage, \$60 rental rate of capital, \$2 per unit produced, and a \$42 fixed cost. Find the cost function, and average total cost, average variable cost, and marginal cost functions.

I'm confused on two levels.

(1) Does "cost function" mean short-term cost function, holding capital constant, or does it mean long-term cost function, allowing both inputs to vary? How can the professor possibly be so clueless as to fail to realize that the question is ambiguous as written?

(2) If the firm faces costs of "\$2 per unit produced and a \$42 fixed cost," shouldn't the cost function simply be $c(y)=2y+42$? But this answer contradicts the solution I get when I use the Lagrangian approach.

According to the minimization problem, the cost function $c(y)$ is the minimum value of $20L+60K$ subject to the constraint that $y=8L^{1/4}K^{3/4}$. The Lagrangian condition says

$$20=2\lambda (K/L)^{3/4}$$
$$60=6\lambda(L/K)^{1/4}$$

so

$$10(L/K)^{3/4}=10(K/L)^{1/4} \implies L=K$$

Therefore $y=8K$ and thus the cost function is $c(y)=80K=10y$. This is not the same thing as $c(y)=2y+42$. What is going on here?


texts: Why is the supply curve in the foreign-currency exchange market vertical?

texts:
In the book 'Economics' by Mankiw and Taylor the demand and supply curves on the foreign-currency exchange market are shown as follows:

The supply equals the Net Capital Outflow (NCO). I would have assumed that the exchange rate influences NCO in the same way it influences imports and exports, for example a higher exchange rate makes it more profitable to invest abroad than domestically, leading to an increased NCO. However, the supply isn't influenced at all by the exchange rate according to Mankiw and Taylor and that's what I don't understand.


texts: Book Recommendation for Microeconometrics of Discrete Data

texts:
I am looking for a few good books pitched at different levels to help analyse discrete data.

Specifically: Specification, Estimation and the application of econometric methods to model discrete choices by individuals, households or firms.


texts:
I calculated the Marginal cost for the below question. But it seems the results are wrong

After coming up with an innovative idea for a new product, you paid 4000 to an industrial designer to draw the blueprints and found a factory in China that agreed to produce the product for you for $3 per unit (the price includes the shipping cost from China to you).

Since this is a totally new and unique product, you have no idea how the demand for it would be. Therefore, before you start pricing the product and ordering large amounts from the Chinese factory, you decide to run an experiment (or a pilot study): you talk to Target and they allow you to sell your product at 11 different Target stores for 11 different prices (a different price at each store). These stores are located in areas whose residents have similar average income, so you can be certain that price (and not income) is the only factor varying among these stores.

I took the fixed cost as 4000
The variable cost was taken as 3.

When the MC was calculated, it was given as 3. I feel this is not correct and there is something not correct here.

Can someone kindly point it out.

Is the fixed price taken was incorrect? or the variable cost incorrect?


texts: Which institutions are in the eurodollar market?

texts:
My main question is: how much of the eurodollar market is claims issued by depository institutions or Bank Holding Companies?

It's about a $4tn market, but who's in it? Who is funding themselves in eurodollars and who are the dominant players?

I'm trying to figure how much of the market is outside the banking system. Any links/research is greatly appreciated.


texts: Do states compete with each other when they emit debt?

texts:
Let's say that, for some reason (a crisis or similar), many first-world countries' states need to emit public debt to be able to pay the services the normally provide (pensions, health etc.).

As I see it, they would be competing with each other to sell these bonds, right? Would this competition make the government bonds' rates to rise?


texts:
We often talk about time preferences in intertemporal utility maximization problems.

Usually we see some variant of:

$$\max_{c_t}\sum_{t=0}^\infty\beta^tu(c_t)$$
subject to:
$$\sum_{t=0}^\infty e_t=\sum_{t=0}^\infty p_tc_t$$

where $e_t$ is some endowment process over a consumers life time and spending is on a specific consumer good.

I have been thinking how exactly we estimate what $\beta$ is.

Our usual demand analysis methods only consist of estimating a expenditure function and then recovering underlying preference parameters. Here its tricky though since we are interested in what a discounting looks like.

how do we approach this problem?


texts: Where can I get Per Capita Income data of states in the USA? Also which are the sources often used in econometric or macroeconomic analysis and how reliable are they?


texts:
I am solving a three-stage game in a supply chain with one buyer and one supplier. The supplier has private information on its production capacity. The supplier also has the option to sell to the market directly. As of now, the game sequences are as follows. In the first stage, the supplier decides on the wholesale price, then the buyer takes the wholesale price as a signal, updates its belief about the production capacity of the supplier and order some of that capacity. In the last stage, the buyer decides, how much it wants to sell to the market directly, and the supplier decides how much to sell to the market if any capacity remains.
For now, the only signal is the wholesale price. I want to add a second signal to the first stage. In other words, the supplier not only sets the wholesale price but also puts a limit on the buyer's order quantity. In the next stage, the buyer solves its expected utility by considering two signals.

Has someone heard about a similar story with 2 signals at one stage?
Thanks


texts: Decomposition of an additive functional into a Martingale part and other

texts:
This question relates to a theorem about the decomposition of additive functionals---a technique especially useful in macroeconomics and finance. This question has two objective. First, I don't have a reference to the theorem that shows when this is possible, and I would like to find it. Second, I would like to know how to actually find this decomposition.

Consider the following autoregressive model:
$$
X_{t+1} = \alpha_0 + \beta_0 (X_t - \alpha_0) + W_{t+1},
$$
where $-1 < \beta_0 < 1$ and $W_{t+1}$ is distributed as a normal with mean zero and variance one. Now, consider the additive functional
$$
Y_t = \sum_{j=1}^t X_j.
$$
How would I produce the decomposition of the form
$$
Y_t = r_1 t + M_t - r_2 (X_t - X_0)
$$
where $\{M_t \}$ is a Martingale? (How can obtain the values $r_1$, $r_2$, and $M_t - M_{t-1}$?)


texts: Oughtn't option premiums increase by the same amount as strike prices?

texts:
Pls see this question's title. In the screenshot below, as the strike prices below increase by  +1, oughtn't the option premiums increase by +1 too?
Why buy the \$104 put  for \$13.71? The \$105 put looks more attractive to me; it has lower IV and costs only 4 cents more!


texts: What is the proof for why border adjustments are exactly offset in theory by currency appreciation?

texts:
Why is it true, in theory, that border adjustments are exactly offset by currency appreciation? I've read the colloquial explanations online, but am looking for something more rigorous.

For example, http://taxfoundation.org/blog/exchange-rates-and-border-adjustment says that

  Standard economic theory states that a border adjustment ends up in a wash for both exporters and importers because prices adjust to leave the trade balance unchanged. Specifically, the value of the domestic currency adjusts upward. Standard supply and demand shows why both the import tax and the export exemption work together to push the value of the domestic currency up.


texts: Policy relevance of the optimal taxation given uncertainty about social welfare specification

texts: One common criticism in the optimal taxation literature is the specification of the social welfare function. The optimal taxation literature (I have the Mirrlees framework in mind) relies on first specifying a social welfare function. However, because we never observe the social welfare function (SWF) and because we're not even sure if a reasonable specification of social welfare can be represented by a utilitarian-like SWF, what kind of policy prescriptions can we get out of these types of models? How much of a problem is this? Are there potential ways in which this problem can be made less offensive?


texts:
I was surprised to find that we did not have a question on this Stack Exchange on this particular problem in decision theory. So I have chosen to add a question on Newcomb's Paradox, though I would like to limit the scope of it to its economic considerations more than its philosophical considerations.

For those unfamiliar with the problem, here is the usual formulation of the problem.

You are presented with two boxes.

Box A is clear and has \$1,000 in it.
Box B is opaque and either has \$0 or \$1,000,000 in it, which is decided by another player, let's say a machine here.

You can choose to take just Box B, or both Box A and B, but before you choose, a machine makes a decision about what is in Box B, based on what it thinks you will do. The machine has played this game many times before and empirically is almost always correct in predicting what the player will do.

If it thinks you are going to choose both boxes, the machine will place \$0 in Box B.
If it thinks you are going to choose just Box B, the machine will place \$1,000,000 in Box B.

Empirically, people are split on whether to play the one box or two box strategy. The intuition for both cases goes likes this.

For those who pick one box, the intuition is that if the machine is almost always right, then the expected value/utility of picking just Box B will be much much higher than picking both boxes. So obviously one should pick just Box B and not be greedy.

For those who pick two boxes, the intuition is that picking both boxes seems to be a dominant strategy. If the machine has already picked putting nothing in Box B, it doesn't hurt, and can only help, if you pick both boxes. If the machine has already picked putting \$1,000,000 in Box B, then...well you should still want both boxes!

So what's the rub? Philosophers like getting into the weeds with this question in discussing causality or free will. But perhaps one criticism of this thought experiment is that the scenario described here is not rigorously defined within the realm of game theory. The machine's only goal is to predict the player's move correctly, but it does not actually have a defined payoff for making the correct prediction. One can map the set of choices and player payoffs as a tree, where the player cannot observe the choice of the machine, but the information set needs more elaboration than this. How does the machine make its prediction exactly so that it is "almost always right"? Why does the machine get to completely preclude mixed strategies and just...know what the player will do most of the time? Essentially, the whole game, strategies and payoffs and information, seems all very hazy. Should it even be considered a game? Or is this just a weird decision theory question?

With paradoxes, trying to add in extra assumptions, or showing why an existing assumption is ill-defined, this can go a long way to providing a possible solution to a paradox. So my question(s) are:

  How could one alter the formulation of Newcomb's Paradox to make it decisively analyzable with game theory or decision theory, and what strategy/decision should the player make in that case?
  If you would choose not to alter the formulation of the paradox, what is the correct analysis of the problem?

Two ending points.

$^1$ I hope I have formulated my question so that there could be multiple correct answers that are objectively correct, and not just opinion based.

$^2$ If you think Newcomb's Paradox is just so incoherent that one can't really alter it without really altering what makes the paradox interesting, you can talk about that too. I am not asking that as a question because I think that would be too opinion based.


texts: Deriving the translog production function

texts:
Ive been having difficulty deriving the translog production function defined as:

$$\ln y=\alpha_0+\sum_{i=1}^n\alpha_i \ln x_i+\frac{1}{2}\sum_{i=1}^n\sum_{j=1}^n\ \beta_{ij}\ln x_i\ln x_j $$

I know we start with a log-log production function.
$$\ln y=\alpha_0+\sum_{i=1}^n\alpha_i\ln x_i$$

the next step from what i recall is to take the taylor series of this function around the point $x_i=0$. the reason why this is an issue is because $\ln(0)$ is undefined.

How exactly is this function derived?


texts: Finding a nash equilibrium in pure or mixed strategies

texts:
The question I'm dealing with:

  Let $x=3$, find any Nash equilibrium in pure or mixed strategies.

I have observed that the pure strategy Nash equilibrium is $(u,r)=(3,3)$.

The answer to this question is:

$(\pi^*,\rho^*)=(1,0)$

Am I correct in interpreting the above as:

Given the PSNE of $(u,r)$, the row player will play $u$ with probability $1$ and the column player will play $r$ with probability $1-0=1$?

Thanks


texts:
Suppose there are 2 firms; Demand curve is given by $P=1400 - 5(q_1+q_2)$ and cost function is given by $C_i = 5q_i^2$.

For cournot, the best response function comes out to be $q_i=70 - 0.25q_j$ giving $q_1=q_2=56$ and $P=840$. Thus $\pi_1=\pi_2$= $840 * 56 - 5*(56)^2 =31360$.

For collusion $MC=MC_1+MC_2=10q_1+10q_2=10Q$. Thus $MR=MC$ gives $1400-10Q=10Q$ which in turn gives $Q=70$ and $q_1=q_2=35$. And $P= 1400 - 5(70) = 1050$. Thus $\pi_1=\pi_2=1050.35 - 5(35)^2 = 36750-6125=30625$.

What I don't understand is, how is profit greater in Cournot duopoly as compared to a collusion. Is it possible? Or did I make a mistake somewhere during the calculation of $MC$ for collusion?