texts: Why do we model that higher government involvement increases output?

texts:
I have just read about the "real intertemporal" model of a macroeconomy in Macroeconomics by Stephen Williamson. I am concerned about how it says any increase in government spending, even if it is equal to an increase in taxes, increases the output of the economy. This is because taxes don't reduce private consumption spending as much as government spending increases demand. But, if I extend this idea to the extreme, where government involvement is exceedingly high, I don't understand why people will carry on spending more than they earn, with high taxes and no way to pay off their debt. It seems like the autonomous component of private spending is problematic when thinking about tax (as opposed to an equilibrium), because this theoretically causes people to overspend in comparison to their income.

The deduction is that, with any positive multiplier (not just one greater than 1 as mentioned in the textbook), the more the government intervenes in the economy, the higher the GDP will be, ad infinitum, so that this model encourages higher and higher government involvement. In reality, socialist countries such as Russia have had lower output than free-market countries such as the United States, and it is well known that government bureaucracies are more inefficient than the private sector. What I'm checking here is where the theory leads. I assume this must be a Keynesian-type model, because it encourages government involvement, and that other models give a different story (neoclassical perhaps?).

As a public administration student as well, I don't like it how government spending is treated so differently to private spending, and this separation here seems to be problematic (as assuming that government departments are efficient in comparison to the private sector).


texts: How to evaluate if an activity is likely to produce a positive ROI?

texts:
I am trying to establish if it would be worth my while to sell a product in a particular online marketplace but am unsure how to evaluate if it would be financially worth my while.

The marketplace in question allows me to know basic kinds of sales data for any given item in the marketplace such as:

When was the item first offered for sale?
What is the total number of sales for this item?
What is the price of this item?
Who is the seller of this item?
What kind of item is this?

The marketplace also allows me some other high level information such as:

What is the total number of items for sale on the website?
How many user accounts are there on the website?
What are the most popular items for sale on the website?

I would love to know if this information is enough to help me make an educated decision as to if it would make economic sense in order to produce an item to sell in this marketplace and if so how would I go about figuring that out?


texts: Why can we write any lottery as a convex combination of the degenerate lotteries?

texts:
I know that a degenerate lottery is a lottery that yields outcome $n$ with probability $1$ and I also know the definition of convex combination: given $x_{1},x_{2}, \cdots ,x_{n} \in \mathbb{R}$, a convex combination of these points is a point of the form $\alpha_{1}x_{1}+...+\alpha_{n}x_{n}$ such that $\alpha_1+...+\alpha_n=1$.

But I am quiet confused about why we can write any $L=(p_1,...,p_n)$ as a convex combination of the degenerate lotteries $(L^1,...,L^n)$. Can someone please explain this for me? Many thanks!


texts: What is considered a "final product" for gross domestic product?

texts:
Given a territory and a time range, the gross domestic product is the sum of all the values added. The term “value added” is open to interpretation. Since the value added of a product or service is its total value minus the value of the intermediate product and services used to produce it, it follows that in an identical scenario, the GDP will vary according to what is classified as final products. Yet in reports, a single number is quoted as if it was the GDP.

For instance, a factory will need cleaning. Is the service of cleaning a factory considered a final product or intermediate consumption needed to produce whatever the factory produces?. What about the plant's paint, electricity, training of workers and so on?. People need to eat in order to work and produce, and more so the more they work (hence food may be classified as intermediate consumption), and need medical care to live (and hence produce) just like car factories need steel. I have seen these things sometimes taken to be final consumption. The consumption of decoration from a restaurant is a requirement (since people go to a restaurant in part, due to the style) and by that reasoning, it is intermediate consumption, but a luxury in one's house (therefore final consumption). When doing the accounting at an high level (city, state or national), how do the accountants know what part of the paint consumed take as intermediate consumption and what part to take as final consumption?.

The boundary between intermediate and final consumption seems blurry. How, and where is the line drawn. Could you please cite a (preferentially publicly available) relevant document from an organization in charge of computing a GDP about the methodology regarding the intermediate-final consumption?.


texts: How is it decided whether a societal need should be met by using a public project or private enterprise?

texts: I know this is a large question, so I'm looking for a broad, general understanding only. Are there any principles using which it may be decided to meet a societal need using a public project rather than private enterprise, in a free market economy? What are all the factors that need to be considered? Moreover, is the government only supposed to provide public goods?


texts: Sequential vs. trembling hand perfect equilibrium

texts:
For any game, trembling hand perfect equilibria are a subset of sequential equilibria.
What is a simple example where a sequential equilibrium is not a trembling hand perfect equilibrium?
Is it possible to create a normal form example?

Links:

Kreps-Wilson: Sequential Equilibria

Selten: Reexamination of the Perfectness Concept for
Equilibrium Points in Extensive Games


texts: 2 firms production decision for one agent

texts:
I'm trying to solve the optimal production $\{x,y\}$ for a risk neutral agent with weight $w$ in firm $X$ and weight $1-w$ in firm $Y$. Each firm has marginal cost $c^X$ and $c^Y$ respectively. The firms face a linear demand where $P(Q)=a-b Q$ and the total production of the economy $Q=x+y$. This risk neutral agent maximizes profits so his/her utility will be:

$U(x,y)=w(x(a-b(x+y)-c^X))+(1-w)(y(a-b(x+y)-c^Y))$

If I take first order conditions to maximize this utility I get:

$(a-2b x-c^X)w-by=0$

$(a-2b y-c^Y)(1-w)-bx=0$

Which solves to:

$x=\frac{(1-w)(2 c^X w-c^Y+a(1-2 w))}{b(1-2w)^2}$

$y=\frac{w(2 c^Y(1- w)-c^X-a(1-2 w))}{b(1-2w)^2}$

Assuming this is all correct, I don't understand why when $w=0$, then $y=0$!!! and $x=\frac{a-c^Y}{b}$ maxing the utility $U(x,y)=0$.

I think this doesn't make sense and can't be the optimum because having $x=0$ and $y=\frac{a-c^Y}{2b}$ (monopoly production) would give $U(x,y)=\frac{(a-c)^2
}{2b}>0$

I must have something wrong, the derivatives and solutions are correct, does anyone see what I'm missing here?


texts: Articles about police complaints for a lit review?

texts:
I'm doing a research paper about how different cities have different quality of police service. I want to do a regression where the dependent variable is number of sustained complaints per 10 officers that year received by that agency. But maybe there is a better measure. I want to avoid using crime as a measure of police quality though, because I think crime is only partly affected by police service in the area.

Anyway, the thing I need to do first of all is get an idea of other work people have done in this area. And this area to me would be analyzing markets for public police, analyzing police service quality, analyzing demand for police service and whether it relates to quality of police service- same with supply, analyzing changes in police force for different cities, identifying factors that improve/diminish city-wide quality of police service.

Could someone suggest articles about measuring the quality of police service in a city? Or equilibrium quantity of police service in a city? Or things related to what I want to research? Especially if they do not focus on crime?


texts:
I want to calculate the TFP by using the estprod function (I use R 4.0.2). As far as I understood the only way to calculate the TFP is manual following this logic .
omega_1 = (data$Y - data$Labor*coefs$statistic[1] - data$Capital*coefs$statistic[2] - data$Materials*coefs$statistic[3]) - this is basically the approach other author on StackExchange suggested to use in order to calculate the TFP. However, after running the regressions (LP, OP, Wooldridge) I get only 2 coefficients in the output, for capital and fo labor only, while for materials the coefficient is missing.
Would really much appreciate any comments and support, the dataset is available here:  https://drive.google.com/file/d/1aedWYABus1fQjKWxkOmYOmxv-qSja7hF/view?usp=sharing
The code is the following so far:
remove(list=ls())

library(plm)
library(dplyr)
library(ggplot2)
library(prodest)
library(estprod)
library(broom)

# Set the working directory
setwd("C:/Users/vadya/Desktop/baka")

# Downloading the survey data
Data <- read.csv("LV.csv", header=TRUE, sep=",")
str(Data)

Data$ID<-as.numeric(as.factor(Data$ID))

summary(Data)

# Creating a panel data frame
PData <- pdata.frame(Data, index = c("ID","Year"))

pdim(PData)
pvar(PData)

DataA <- Data %>%
  filter(NACE == 'A') %>%
  filter(VA > 0, L > 0, K > 0, M > 0) %>%
  select(ID, Year, L, VA, K, M) %>%
  summarise(ID = ID,
            Year = Year,
            l = log(L),
            va = log(VA),
            k = log(K),
            m = log(M))

####################################################################################################################################
mod1LP = estprod::levinsohn_petrin(data = DataA, va ~ l | k | m, id = "ID", time = "Year", bootstrap = TRUE, gross = FALSE)
summary(mod1LP)

mod1OP = estprod::olley_pakes(data = DataA, va ~ l | k | m, id = "ID", time = "Year", bootstrap = TRUE, gross = FALSE)
summary(mod1OP)

mod1W = estprod::wooldridge(data = DataA, va ~ l | k | m, id = "ID", time = "Year", bootstrap = TRUE, gross = FALSE)
summary(mod1W)


texts: Game theory - Definition problem - Strategy vs Action

texts:
A one definition is given by :

  Strategy is one of the possible actions of a player

But I'm having a trouble. When working with games, We specify a strategy set $S$ and a strategy $s \epsilon S$. For instance consider a typical normal form game, battle of sexes for instance. We have $2$ strategies for each player so the set $S$ has two elements. According to the definition here what would be the actions? What is a "possible action"?

I'm asking this because in the definition of Bayesian games we are given an Action set instead of a strategy set. Can anyone clear things up to me?


texts: Why should $dp_2=dm =0$ in this problem?

texts:
I am studying Essential Mathematics for Economic Analysis and in chapter 12 problem 10 there is a problem that I can solve but I do not understand why the solution works.
The problem asks us to differentiate the following system from consumer demand theory:
$$U'_1(x_1,x_2) = \lambda p_1 \\ U'_2(x_1,x_2) = \lambda p_2 \\ p_1 x_1 + p_2x_2=m $$
where system defines $x_1, x_2$ and $\lambda$ as differentiable functions functions of $p_1,p_2$ and $m$. We are asked afterwards find expression for $\partial x_1 / \partial p_1$.
Now I have no problem with the first step - the differentiated system will be:
$$U^{''}_{11}(x_1,x_2)dx_1 + U^{''}_{12}(x_1,x_2)dx_2 = \lambda dp_1 + p_1 d\lambda   \\ U{''}_{21}(x_1,x_2)dx_1 + U{''}_{22}(x_1,x_2)dx_2 = \lambda dp_2 + p_2 d\lambda \\ p_1 dx_1 + x_1 dp_1 + p_2 d x_2 + x_2 dp_2=dm $$
Now my first attempt was to solve 2nd equation for $dx_2$ substitute it into the first and solve for $d x_1 /dp_1$ but I got wrong result. Afterwards in the solution in the back there is a hint that says that to solve this we should put $dp_2=dm=0$ after I follow this hint I get the correct solution:
$$\partial x_1 / \partial p_1 = \frac{[\lambda  p_2^2 + x_1(p_2 U^{''}_{12}-p_1U^{''}_{21})]}{(p_1^2 U^{''}_{22} -2p_1p_2U^{''}_{12} + p_2^2 U^{''}_{11})}$$
But I don't get why we can simply assume $d p_2 = dm = 0$ that seems so arbitrary, how come that  is necessary  to find the correct solution?


texts: How does one do a hypothesis test for elasticity?

texts:
Given the regression output
  $$\widehat{\ln cons} = \underset{(0.6018)}{0.4054} + \underset{(0.0744)}{1.2739}\, \ln m - \underset{(0.1902)}{0.6666}\, \ln p_1 -\underset{(0.2645)}{1.6146}\, \ln p_2$$
  where

  $\ln cons$ is the log of chocolate consumption,
  $\ln m$ is the log of income,
  $\ln p_1$ is the log of the price of chocolate, and
  $\ln p_2$ is the log of the price of sweets,

  test whether chocolate is a luxury good.

Since $1.27 > 1$, it is logical to test whether $\beta_{\ln m}$ could be less than $1$. When I test elasticity, I base the null hypothesis on what is logical, as in this case if $\beta_{\ln m}$ is significantly greater than $1$, one shouldn't reject a (illogical) null hypothesis $\mathrm H_0: \beta_{\ln m} \geq 1$. So,

$\mathrm H_0: \beta_{\ln m} \leq 1$

$\mathrm H_1: \beta_{\ln m} > 1$

$\displaystyle t = \frac{1.2739-1}{0.0744}\approx 3.681$

Therefore, I reject the null hypothesis in favour of the alternative that chocolates are a luxury good.

Do you agree with the way I have set up this hypothesis test? If the estimate were less than 1, I would have stated $\mathrm H_0: \beta_{\ln m} \geq 1$ against the alternative $\mathrm H_1: \beta_{\ln m} < 1$.


texts: Which is safer in the long-term, diffuse debt or concentrated debt?

texts:
I want to deepen my understanding of risks as posed by debt burdens among actors of an economy. After some literature review, it seems the matter is nuanced; points can be made for both sides. I'll present a few points simply for context.

Diffuse

If debt burdens are distributed more uniformly (diffuse), then credit can be extended to many SMEs and likely to benefit employment and other long run growth drivers. Also, less concentrated risk may spread out debt burdens and make servicing more manageable.

Concentrated

If debt burdens are concentrated, then regulators will be able to pursue more effective macroprudential policies. For example, entrusting asset management companies to take care of NPLs and free up bank resources so they may lend more.

Question

Is this a debated position in the broader field of economics or is there clear theoretical framework and/or empirical evidence for one being better than the other for "safe" long run economic growth?


texts: Negative long term effects of wage cap, especially on purpose of money?

texts:
It can be figured that a wage cap could have some noticeable short term effects - mainly, those who are higher paid will not receive as much money anymore, meaning less spending by the richest in the economy (who also happen to own a large portion of the economy's wealth) and more economic downturn for companies.

However, the market could normalize after this as the money earnt by a nation's richest would eventually be more evenly distributed amongst others, hence they would spend more, canceling the downturn.

My question is how will a wage cap (a limit on the amount of income that can be possibly earnt in a year) have negative long term effects that will not be countered by more equal spending in the economy, as provided in the example?

Mainly, I am interested in how will this affect the purpose of money. Would the power of money possibly be restricted in a noticeable way that leads to negative effects in the long-term? Would there also be other negative effects, both on the macroeconomic and microeconomic scale, that would last in the long-term and prove difficult to counter?

Sources, links and further reading is welcome. Thank you in advance.


texts: How do I represent this indifference curve graphically?

texts:
I am not able to visualize this indifference curve.

I consume only two goods: sugar and milk.

I will prefer a bundle X of sugar and milk over a bundle Y only if $x_{sugar} > y_{sugar}$, and $x_{milk} > y_{milk}$.

If $Y_{sugar} > x_{sugar}$ and $y_{milk} > x_{milk}$, then I prefer Y bundle over X.

If neither case is true, I am indifferent between the two bundles.

How do I plot this on a graph? I need to solve a question, and I believe being able to draw a graph will be helpful!

This is how I visualize it. Is this representation correct?


texts: Kiyotaki-Moore v.s. Bernanke-Gertler-Gilchrist - what's the difference?

texts:
What are the key differences between (i) a model which features a "Kiyotaki-Moore collateral constraint"; and (ii) a model which incorporates a "financial accelerator" (a la Bernanke-Gertler-Gilchrist)?

Both have impulse responses which fluctuate due to borrowing being tied to the net worth (or collateral) of borrowers.

So would there be any difference between their modelling outcomes?


texts: Need Advice Debugging MLE Code to Estimate an ARMA(p,q)

texts:
I'm trying to estimate an unknown ARMA(p,q) series via a Kalman Filter & QMLE.

The issue is most of my optimized likelihood values end up around -350, except one or two which are hugely positive! It doesn't seem likely that adding a single AR or MA lag would cause such a drastic jump in my likelihood function.

I've tried messing around with optimization parameters in Matlab such as MaxFunEval, and MaxIter but I am still finding this issue.

If this is the wrong place for a question like this I apologize in advanced.


texts: Why is the price of capital ‘r’ ? (From Cost function)

texts:
according to the Cost formula in microeconomics class,

Total Fixed Cost is represented as “rK” (K as in unchanging, fixed K)

now my economics teacher tells me this ‘r’ is the interest rate at which you rent capital, which is pretty vague and ambiguous to me. If r represents interest “rate” and not the “interest-added cost of capital”, then how can this r be the “price” of capital?

So for example, if the amount of capital is 5 (K=5) I understand that you assume you rent it, or borrow the money from a bank to get the capital, incurring interest. What I don’t understand is the formula. If r is the interest rate (aka rental rate)

isn’t the cost formula supposed to be “K * {P(K) + P(K)*r}”, instead of “rK”?
 (P(K) here represents the price of capital per unit)

so if a unit of capital costs $10, and the interest rate (r) is 3%,

in the end you will be paying $ 5 * (10 + 10 * 0.03) in total , not 5 * 0.03 right?

I mean, r is just the percentge, not the ‘amount’ that you have to pay for the capital. So I don’t really understand why the textbooks and the teachers tell me that the “price” of capital is r when it seems like it’s supposed to be ‘P(K) * (1+r)’ instead of just ‘r’ .

I hope I can get a satisfying answer here. Would appreciate detailed explanations!


texts: How do international organizations collect statistics regarding a country?

texts:
How do international organizations like IMF, WB, and CIA Fact Book collect statistics regarding a country's economic indicators?

What is their primary source of information?


texts: Why are the same set of controls used for both OLS and 2SLS?

texts:
I have been reading several papers that use 2SLS. These papers usually also show the OLS regression results. I noticed that when authors report results for 2SLS, they also include control variables that were used in the OLS regression.

If 2SLS is supposed to solve the omitted variable bias, couldn't we omit the control variables that are included in OLS because we do not have to worry about omitted variable bias? For what reason would authors include those variables?


texts:
I'm struggling with a math concept dealing with unit elasticity at an undergraduate textbook level. In most problems, we are given a starting price and an ending price as well as corresponding quantities demanded. For example:

When bread was ${$2.00}$ a loaf Bobby wanted ${4}$ loaves, when bread prices raised to ${$2.50}$ Bobby wanted just ${2}$ loaves. What is bobby's price elasticity of demand?

To calculate these we say the percent change in price is ${\% \Delta P = \frac{$2.50-$2.00}{$2.00}=25\%}$. The percent change is measured relative to the starting price. Meanwhile ${\% \Delta Q = \frac{2-4}{4}=-50\%}$. Making elasticity ${-2.0}$.

However, I came across a problem where essentially it asked what is the elasticity for someone who wants to spend exactly ${$10}$ on gasoline. I first tried to think about this intuitively, "If price doubles, she'll be able to get half as much quantity no matter the starting price," which seems like elasticity of ${1}$. However, I set it up algebraically I get the following:
$${Q*P=10 \implies Q = 10/P}$$

So I put in some random values of ${P}$, for example ${P_1=$2.00}$ and ${P_2=$2.50}$ for ${\% \Delta P = \frac{$2.50-$2.00}{$2.00}=25\%}$. Meanwhile, For quantity we have ${Q_1 = \frac{10}{2}=5}$ and ${Q_2 = \frac{10}{2.5}=4}$. So that ${\% \Delta Q = \frac{4-5}{5}=-20\%}$.... Which isn't unit elastic.

So I turned to calculus and did the following:

$${Q(P)=\frac{10}{P} \implies \frac{dQ}{Q}*\frac{P}{dP}=\frac{dQ}{dP}*\frac{P}{\frac{10}{P}}=-\frac{10}{P^2}*\frac{P^2}{10}=-1.}$$

Which is unit elasticity. Clearly the discrepancy here is caused by the fact that the derivative has the "starting quantity" = "ending quantity" since it's the same point. But should we be measuring percent change relative to starting price and quantity? Or relative to starting price, but ending quantity? Or does it depend? And why?


texts: Is this a correct way of calculating productivity? And can the proposed data be (accurately) used for doing so?

texts:
I want to know if my thinking for calculating productivity [2019-USD/hour-worked] is correct.
Basics:
Take the GDP of a country and divide by the total amount of hours worked in that country -> voilá you get productivity. Is this correct?
Specifics
I plan to use OECD data for my estimation in the following way:

The total hours worked I plan to get by taking the hours/worker data (https://data.oecd.org/emp/hours-worked.htm) times the size of the labor force [# workers] data (https://data.oecd.org/emp/hours-worked.htm). This should get me the total amount of hours worked.
Get the productivity by dividing the PPP adjusted total GDP [PPP adjusted GDP in 2019-USD] by the total amount of hours worked, where I want to use the GDP data from https://data.oecd.org/gdp/gross-domestic-product-gdp.htm

Questions

Is my thinking correct?
Do you think the data I have chosen is appropriate for my use case?

Thanks!


texts: Is it possible for a firm does not have shutdown point?

texts: If a firm has a quadratic cost function, is it means that the firm does not have shut down point and never shut down? Are the changes in fixed cost do not affect the firm's shutdown decision?


texts: Why does a reduction in money demand lead to a rightward shift in the LM curve?

texts: In my textbook, it says Y must rise to restore money market equilibrium as the justification.


texts: Can a monopoly INCREASE the market surplus compared with a competitive market?

texts:
Monopolies are often blamed for DWLs(Dead Weight Losses), while competitive markets believed to work without DWLs (assuming zero taxes/subsidies and zero externalities).

But I think I found an example when ABSENCE of a monopoly (in this case - a regulated natural monopoly) and presence of a competitive market can lead to smaller market surplus (i.e. DWLs). Am I correct? If not - why?

Let's assume there is a competitive market for a specific medicine. The competition is tough. Economies of scales aren't exploited to their maximum because in this case, only one firm would be able to survive (there is enough demand only for one Gigafactory) and for this reason, the state puts limit on maximum size of factories in order to prevent full exploitation of economies of scale.

So many people can't afford the medicine despite fierce competition. And if you don't buy anything, then obviously you can't have surplus. Not to mention, that in their totality the producers have lower surplus due to higher costs and lower sales.

Now let's suppose that one day the state decided that maybe a monopoly isn't so bad thing if it's properly regulated. So the state let the firms increase their exploitation of economies of scale and soon only one firm was left. Of course, it was regulated in order to prevent abuses. Now the market surplus increased. The surplus of consumers increased because now more people can afford to buy the medicine. The surplus of the producer's also greater than the total surplus of producers of the existed competitive market because the production of the medicine is less costly and it has more buyers.

But if we increased the market surplus compared with the existed competitive market, then what does it mean? Shockingly, it means that said competitive market had DWLs! Even if there were no taxes/subsidies and externalities.

UPDATE 01:

Ok, there is my try to formalize my thought.

Let's suppose that there is a perfectly competitive market for a particular medicine. There are NO taxes/subsidies or externalities.

The aggregative demand is Qd=1000-P

The aggregative supply is Qs=-2+0.2*P

P = 835 is the equalibrium price, thus we will have Q=165 as equalibrimum quantity.

The total surplus of consumers is equal to (1000 - 835)*165*0.5 = 13612.5

The total surplus of producers is equal to (835 - 10)*165*0.5 = 68062.5

Thus the market surplus is 13612.5 + 68062.5 = 81675

Now let's replace the competitive market with a regulated natural monopoly that can fully exploit economies of scale.

The aggregative demand is the same, it's Qd=1000-P

P=ATC=200 by the law, while the price without dead weight losses is P=183.(3)
It means that Q=800.

The monopolist's MC=-100+5*P

The total surplus of consumers is equal to (1000 - 200)*800*0.5= 320000

The total surplus of the monopoly is equal to 180*800*0.5+800*(200-180)=88000

Thus the market surplus is 320000 + 88000 = 408000.

As you can see, the total market surplus is bigger. Much bigger.

UPDATE 02

I found book "Intermediate Microeconomics" by  John Hey, it seems to support my conclusion. And there is nothing radical. I will quote some places from the chapter 29.

"One very obvious reason why a single large firm might be more appropriate in some industry is simply that a single large firm might have access to a more efficient technology than lots of small firms. This is a plausible case if centralisation of the industry has consequences in terms of
increased efficiency – contrariwise, if splitting it up into lots of little units causes losses of efficiency and increased bureaucratic costs. ... Even if it behaves like a monopolist – and there is an associated deadweight loss as a consequence – the end product for both consumers and producer might be better."


texts: What is the economic strategy of the UK?

texts:
The UK has run a current account deficit running into billions of GBP per annum since the turn of the century.

If we apply the mindset of a household to the economy then clearly this would appear to be unsustainable. But presumably the household mindset does not exactly map onto a country's economy.

What macroeconomic strategy is this and why can the UK get away with this (or can't it)?


texts: Take It Or Leave It Strategy: Social Optimum

texts:
Here is what I understood

Using Backward Induction, I inferred that buyer offers a price, say, $P$ and the seller will sell only if $P \geq c(I)$. Setting the lowest possible Price that will ensure that Seller sells the good would mean that buyer offers $P=c(I)$

The payoff to Seller would be
$U_S=P-C(I)-I$
Putting $P=C(I)$ gives
$U_S=C(I)-C(I)-I$
which would be negative.
Therefore, seller would choose not to invest, that is, $I=0$

The subgame perfect strategy is Seller chooses to not invest, and Buyer offers $P=C(I)$

Is this the correct way to write the Subgame Strategy? Also, for the Social Optimum, I understand that we are supposed to find optimal $U_B+U_S$, i.e., $P-C(I)-I+v-P$, but I don't know how to proceed. Help would be appreciated!


texts: Relationship between Real Interest Rate and Employment

texts:
The country of Kingsland is considering the introduction of a
  compulsory retirement saving scheme. Under this scheme all workers are
  required to save ten per cent of their annual wages and salaries until
  they retire. Use the supply and demand model (and a diagram) for
  saving and investment to explain the likely effects of this scheme on
  national saving, investment and the real interest rate in Kingsland.
  Explain the effects on employment of the saving scheme. (You can
  assume that Kingsland is a closed economy).

Since the level of national savings has increased, I understand how the savings curve shifts to the right and thus decreases the real interest rate and increases the levels of savings and investment in the economy. I am unable to understand how I can relate this back to the level of unemployment in the economy.


texts: What is the correct way to calculate a selling price from margin and a cost?

texts:
There seems to be two formula to calculate a selling price.

The first formula that I came upon would be

Cost * (1+Margin) = Selling price
Example : 10 * (1+0.25) = 12.5

However, a lot of people uses the following :

Cost / (1 - Margin) = Selling price
Example : 10 / (1-0.25) = 13.33...

This gives a very different number.

As far as I know, the margin and selling prices can be anything you want for most products.

Also note that the second formula fails if you have a margin of more dans 100%.

My question is why is the second formula the most popular ? Is it only a gimmick to get a bigger price?

Am I missing something subtle at work here ?

Also, what should I do if the wanted margin is more than 100% ?

Thanks!


texts: Why did the inverse correlation of stocks and commodities stopped working in 2008?

texts:
Usually, the commodities asset class is considered being inversely correlated with other asset classes, due to its nature of an input for manufacturing (if the prices of commodities go down, the manufacturers can produce for less, and have a larger profit, and vice versa).

Therefore, why during the stock market crash of 2008, the commodities also went down, by far? What happened macro-economically to stop this inverse correlation from working?


texts: Technological shocks and Labour supply in RBC and NK models

texts:
In the class notes of Eric Sims on RBC and New Keynesian models, in his site,  we get to see several graphs with the impulse response functions (IRF) of real variables such as output, labour hours, consumption, etc.

One thing, I don't get is why for the basic RBC (and some extensions) whenever we get a positive tech shock, the labour hours($N_t$) increases, but for the New Keynesian models $N_t$ decreases... Why is that?

Any help would be appreciated.


texts: What would mortgage payments be if monthly payments were constant in real terms?

texts:
From the Wikipedia:

The fixed monthly payment for a fixed rate mortgage is the amount paid
by the borrower every month that ensures that the loan is paid off in
full with interest at the end of its term. The monthly payment formula
is based on the annuity formula. The monthly payment c depends upon:
r - the monthly interest rate, expressed as a decimal, not a percentage. Since the quoted yearly percentage rate is not a
compounded rate, the monthly percentage rate is simply the yearly
percentage rate divided by 12; dividing the monthly percentage rate by 100 gives r, the monthly rate expressed as a decimal.
N - the number of monthly payments, called the loan's term, and
P - the amount borrowed, known as the loan's principal.
In the standardized calculations used in the United States, c is given by the formula:
$$c = \begin{cases}
  \frac{r P}{1-(1+r)^{-N}} = \frac {rP(1+r)^N}{(1+r)^N-1}, & r\ne 0; \\
  \frac{P}{N}, & r = 0.
\end{cases}$$

The "issue" with this monthly payment schedule is that, if inflation is positive, the amount you pay in real terms the first year is more than the amount you pay the last year. Assuming constant inflation $\pi$, what would the monthly payment formula look like if it had to be constant in real terms?


texts: In Black-Scholes model $r$ is defined as risk-free interest rate. What I have understood is that risk-free comes from the yields on sale of government bonds. What does that mean if the interest rate(fed fund rate) are negative? Does the yield on government bonds then also go negative? I understand the price of the bond will go up, but is that yield correlated with the fed fund rate?


texts:
Please help me to understand how the hypothetical introduction of wealth tax will affect the markets.
In my understanding, many of the super-rich own most of their wealth in shares of their own company (take heads of tech giants as an example).
Let's say that country X introduced an annual wealth tax of 3%. Let's also assume that a wealthy individual A owns 75% of their company B. The capitalization of B remains on about the same level. This would mean that after 37 years after the introduction of the tax, individual A will keep less than a quarter of company B shares ($0.75 * (1-0.03)^{37} ≈ 0.24$) and will hand more than a half over to the government. Would it mean that the government can take over the company by means of collecting a wealth tax? (unless the original owner has some kind of a super-voting stock)


texts: How can a country grow with so much debt?

texts: I was going through the Indian budget (Indiabudget.gov.in), and I noticed something very strange. The overall liability of the govt was many times more than the revenue estimated in the budget. How can such an economy grow when the govt has so much debt on itself and it continues to grow over the years. At what level does the debt seem to be dangerous?


texts: Binding constraints at second-best optimum

texts:
I am dealing with ex-ante asymmetric information problems, i.e. adverse selection and in particular I cannot understand what's the intuition behind the fact that only two out of four constraints imposed in the second-best maximization problem are binding.

To be precise, when there is asymmetric information with two types of agents, the optimum is found maximizing the utility under two individual rationality (or participation) constraints and two incentive compatibility constraints. In order to simplify the computations, it can be proven that the IC for the high type agent and the IR for the low type agent are binding, whereas the other two constraints are redundant.

I have seen the proof and it is pretty clear but what I cannot understand is the economic intuition behind the proof; Is there someone that has this kind  of intuition?


texts: Can debt to GDP ratio be reduced transfering debt to local autorities?

texts:
It is my understanding that not only government but also local authorities issue bonds.
This answer on Money and Finance Stack Exchange suggests that such debts are not accounted in the computation of the government debt  (At least for the US).

Questions:

Is there an estimate of the total municipal bond per countries?
Could a very indebted country try to reduce his debt to GDP ratio forcing local authorities to issue more bond and thus reducing the government spending? If yes, is there any country that attempted this strategy?


texts:
Why does inflation occur?  To an outsider, inflation appears somewhat mysterious.  Is there an extremely simple mathematical model where inflation naturally occurs?  I would like something that even someone with zero understanding of economics can appreciate.

UPDATE: I am hoping to find an agent-based model which is not defined in terms of inflation, but in terms of more basic (to me) things like supply, demand, et cetera, but where inflation occurs.  For example, the agents' goal could be to optimize revenue and they could have a limited set of possible actions.  Iterating their decisions could then lead to inflation.  Maybe such a model is nonsense, but I'd imagine that if it is not there would be papers about it.


texts: Why isn't the Federal Reserve bothered by the drawbacks of its unlimited Quantitative Easing?

texts:
On Mar. 26 2020, Fed announces unlimited QE and sets up several new lending programs : finance. I know little on the U.S., as my B.A. economics degree is from a Ontario university. If I remember the IS-LM model, the Fed's Quantitative Easing so far can be pictured below. I reversed the arrow in the original diagram.

Putting All Markets Together: The AS-AD Model - ppt video online.

Isn't the Federal Reserve supposed to be rattled by inflation or increase in the Price Level, as per the right shift in AD'?

Let me know of other drawbacks. I haven't brought up lower interest rates because this doesn't appear a drawback. After all, the Federal Reserve aims for more investments and for people to spend money rather than deposit in securities that depend on high interest rates.


texts: Why's it always better to choose a lump sum than periodic payments over time?

texts:
Gill, Madura. Personal Finance, 4th Canadian Edition 2019. p. 56.

  True or False? It is always better to choose a lump sum than periodic payments over time.

p. 519

  T

Doesn't the answer depend on the amount of lump sum vs. periodic payments and inflation?

Or are the authors assuming that if lump sum = P, then you get n periodic payments of $\frac{P}{n}$ (for a total of $n × \frac{P}{n}$)? Then inflation will cause each P/n to be worth less.


texts: STATA: Estimation of Own-Price and Cross-Price Elasticities for Logit, Nested Logit, and BLP Models

texts:
I am working with some data on automobile sales and characteristics in a small country. It is an unbalanced panel dataset taken over 6 years and over 5 market segments. I am trying to construct some discrete-choice demand models using Stata, using two OLS models (one where Price comes in linearly, one where Price is logged) and a nested logit. I will do my BLP instruments model next.

The OLS models are: δj=ln P(j)-ln P(0)=βxj-αpj+εj

and

δj=ln P(j)-ln P(0)=βxj-αln(pj)+εj

The nested logit is as follows:

δj=ln P(j)-ln P(0)=βxj-αpj+σ[ln P(j)- ln P(g)]+ξj for j∈g.

Where P(j) and P(0) represent, respectively, the probability of buying good j and the probability of buying an outside good. Xj is a vector of the characteristics of each good j (in this case, I am using CC/weight, Maximum Speed/100 and Size = Length*Width/10000), and pj is the price of good j.

The code I have used to define my variables and then runmy regressions is as follows:

gen lnPj=ln(Sj)
gen lnPg=ln(Sg1)
gen deltaj=ln(Sj/S0)
gen MSP100=0.01*MSpeed
gen LW10000= Length*Width*.0001
gen diffPjPg= lnPj-lnPg
reg deltaj CCW MSP100 LW10 P, robust
reg deltaj CCW MSP100 LW10000 lnP, robust
reg deltaj CCW MSP100 LW10 lnP diffPjPg, robust

So far, I have computed the own-price elasticities with the code:

gen OPE_PLogit=-.4894868*P*(1-Sj) for the first model and

gen OPE_lnPLogit=-1.959741*P*(1-Sj) for the second model

where Sj is the market share of that particular car for that particular year. I do know that in Stata, generally, one computes the elasticity using the -margins- command.

Let kk be any good but jj, α be the coefficient on price, η be the price elasticity, Sj be the own-market share, Sg be the share for a particular class of cars, e.g. Sedans, Sk be the share for all cars within a group except car j, and S0 be the overall share for cars other than J. The question is this: given that I have directly specified the regression equation and obtained good regression coefficients, is it still appropriate to use the formula η=αPj⋅(1−Sj)η=αPj⋅(1−Sj) normally used to compute the own-price elasticity and η=αPk⋅Skη=αPk⋅Sk (.) for the cross-price elasticity if I am using an unbalanced panel dataset? I think I recall my professor saying that an unbalanced panel dataset will adversely affect the elasticities, but I'm not sure how to adjust for this.


texts: If a weak preference relation is complete and transitive, why is the strict preference relation negatively transitive?

texts: My textbook says that "if a weak preference relation is complete and transitive, the strict preference relation MUST be asymmetric and negatively transitive". Now, I think I understand why it must be asymmetric - all strict preference relations are asymmetric, correct? However, I don't understand why it is negatively transitive. If the weak preference is transitive, couldn't the strict preference also be transitive?


texts: Ireland wholesale electricity prices are higher during the weekends

texts:
Some data from Ireland SEMO (weekday electricity prices) and quarterly prices from the European Commission imply that Irish weekend prices are greater than weekday prices.

The same datasets used showed the correct relationship (weekend prices lower) for France, Denmark, Netherlands, Belgium, and Norway.

Is this actually the case?
If so, why is it the case? Typically wholesale electricity prices are lower during weekends in most countries.

To clarify, I have wholesale hourly prices for weekdays only for Ireland in 2013 and 2014, from the power exchange: http://sem-o.com/marketdata/Pages/default.aspx For intellectual property reasons I cannot upload them, but taking the mean across these weekday-only prices gives quarterly means in 2014 which are lower than that reported by the European Commission Quarterly Report on European Electricity Markets. An example of a quarterly report: https://ec.europa.eu/energy/sites/ener/files/documents/quarterly-electricity_q3_2014_final_0.pdf (page 14, in the little map of Europe with average prices on the map)

Since the mean of weekdays only is below the mean of all days in a given quarter, this implies that the weekends have higher mean prices than the weekdays. This isn't usually the case for most countries, since generally factories and offices use up more energy than people relaxing at home.


texts: Impact evaluation of a policy when different individuals adopt the policy at different times

texts:
Let there be a policy $T$ which can either be implemented or not implemented by an organisation. Suppose there are $n$ organisations and the outcome variable $Y$.
The policy is not centrally imposed- different organisations have adopted the policy on their own will at different points in time. Which suggests that there is a significant possibility of self-selection bias.
I wanted to know if there is any technique to find out if such a policy is effective or not.
I have read about Difference-in-Difference and Discontinuous Regression-- but as far as I have understood-- they need a policy implemented at a particular point in time, and two groups, one of which is treated and the other is not.
In my case, there are two groups-- one that is treated and one that is not treated, but the time of implementation is different for different organisations.
I may be unclear, so I present a simplistic example. Suppose there are 6 firms A, B, C, D, E and F, having all walls in their respective offices white or green. The $Y$ variable of interest to me is the total productivity of employees (suppose I have a way to measure that perfectly) for example.
In the beginning (suppose in the year 2000) all the firms had white walls. Then in 2003, firms C and E changed to green. Then in 2005 firm B also changed to green. The other firms have not made any changes till now (say, 2010).
I have the employee productivity data (monthly) of all the five firms from 2000 to 2010 and also the data of when they switched from white to green.
Is their any method to find out if green walls have any advantage over white walls with this data? I am aware of the possible self selection bias (maybe the firms decide to change to green when they see an unusual drop in productivity etc.) Is there any way to overcome this and evaluate if the policy of switching to green works?
If yes, where can I read more about it, the assumptions, how to test them, then how to actually conduct the analysis using software etc.


texts: Monopolistic Competition- productive efficiency

texts:
In my textbook, it says that monopolistic competition will never lead to productive efficiency (where $MC=AC$) in the short run and long run. I understand that they are meant to be producing at the profit-maximising level of output (where $MC=MR$), but all the diagrams showcase scenarios where the $AC$ curve is always positioned such that the points where MR=MC does not intersect where $MC=AC$.

My question is, is there any possibility that the profit-maximising level of output will also happen to be where we've achieved the lowest possible unit cost (lowest $AC$)? So that $MC=MR=AC$, and the firm can be both productively-efficient whilst also being profit-maximising? Why is this not possible?


texts: Calculating marginal tax rates when near a cliff

texts:
When using tax and transfer microsimulation models, a common approach for calculating marginal tax rates is to recalculate the tax liability when adding $1 to earnings. This will take into account various tax laws that interact in complex ways.

However, this will generally miss the effects of cliffs, such as losing Medicaid, ACA subsidies, or SSDI, unless a household is $1 below the threshold.

Is there a best practice to deal with this? A couple ideas come to mind:

Recalculate the tax liability for multiple changes to earnings, such as $1, $100, $1,000, etc., and weigh the results by the distance (e.g. 1/x).
Make copies of the underlying data, varying the initial earnings within some range, e.g. +/- $1,000, possibly oversampling near the true earnings (e.g. triangular distribution).


texts: What determines rent prices of houses? Does it depend only on interest rates?

texts:
My hypothesis: the renting is determined by the opportunity cost of selling the house and gaining interests in a bank or some investment company. That is, instead of renting, sell it, put the money in a bank, and gain interest on them.

In other words, the renting prices of real state are determined by only two factors: The price of the house + the interest rates.

However, it has been my observation here where I live, in very few houses (thus lacking some statistical weight), that house renting for commercial entities is around the same as selling the house and gaining interest, but, house renting for a physical person is around half than selling house and gaining interest.

Questions:

The hypothesis of renting determined by interest rate is a good one in the context of theoretical microeconomics, or merely simplistic understanding?
In the real world, is renting primarily determined by interest rate and house price? In other words, is the relationship causal? Or just a correlation? Is there a correlation anyway?
Are there more mechanisms for determination of the prices of renting a house?
Why sometimes the renting price can be lower than if gaining on interest? Why would anyone prefer to keep the property of the house, if they could gain more by selling it and gaining interest?


texts: Can a government invest in public companies so their dividends can finance the government

texts: Is it possible that a country could use the money in its sovereign wealth fund to invest in different country's Stock Market and use the dividends to finance its government thus increasing spending while keeping down taxes?  Or could a country grant a corporate total monopoly on its domestic market and force it to compete in international markets to bring in foreign exchange and take a reasonable amount of dividend from the company to finance the government activities?


texts: Non-cooperative Nash Equilibrium in political game

texts:
I have difficulties deriving the non-cooperative Nash Equilibrium of this problem.

The objective function is to maximize the expected total rent over the two periods, that is:

\begin{align}
\max_{S_i} (1-e_i S_i + P_i(S_i, S_j) \delta(1-\underline{S}))
\end{align}

with $P_i(S_i, S_j)=\frac {S_i}{S_i+S_j}$, and $i,j \in \{A,B\}$, and $e_A=1-d$ and $e_B=1+d$

$S_i$ denotes the quality of the service, $e_i$ is a parameter that captured the spending needs in $i$, $P_i(S_i, S_j)$ is the re-election probability, $\delta$ is the discount factor and $\underline{S}$ is the minimum service quality.

The solution of the Nash Equilibrium of the game is
\begin{align}
(S_A^*, S_B^*)=\Big(\frac{\delta (1+d)(1-\underline{S})}{4}, \frac{\delta (1-d)(1-\underline{S})}{4}\Big)
\end{align}

I have tried but I don't get that same solution.

This is what I have done:
I solve the maximization problem
\begin{align}
\frac {\partial{U_i}}{\partial{S_i}} = -e_i+\dfrac{\delta(1-\underline{S})S_j}{(S_i+S_j)^2}\stackrel{!}{=}0
\end{align}

and get the best respond function for $i$ and $j$ respectively as follows
\begin{align}
\delta(1-\underline{S})S_j=e_i(S_i+S_j)^2 \\
\delta(1-\underline{S})S_i=e_j(S_i+S_j)^2
\end{align}

I impose symmetry $S_i=S_j=S^*$ to the reaction function and I get this:
\begin{align}
\delta(1-\underline{S})S^*&=e_i(2S^*)^2 \\
S^*&=\dfrac{\delta(1-\underline{S})}{4e_i}
\end{align}

I am not sure though.


texts: how to find whether trade is possible between two nations

texts:
In the following image, we have U.S. and U.K. producing wheat and cloth in bushels/hour and yards/hour respectively.

In all cases except in case D, given in the figure, trade is possible between U.S. and U.K.

how did we reach this conclusion?

step 1: U.S. can exchange 4W for 1C domestically if she gets any ratio of exchange lesser than 4W/1C say, 3W/1C or 2W/1C or 1W/1C then U.S. shall be willing to exchange wheat for cloth.

step 2: U.K. can exchange 1W for 2C domestically if she gets any ratio of exchange greater than 1C/2W say, 1W/1C then U.K. shall be willing to exchange cloth for wheat.

Conclusively, if the ratio lies between 4W/1C and 1W/2C, both U.S. and U.K. shall be willing to trade.

if we apply this formula in all cases, we can find whether trade is possible or not between the two nations.

My question is whether this method is foolproof?


texts: Difference between 'surplus' and 'welfare'

texts:
I see these two terms used interchangeably but I have the feeling they are not exactly the same. My gut feeling tells me this:

1)
Surplus is the additional aggregate utility from the existence of one market, while welfare is the additional aggregate utility from all existent markets

$$\implies  [ W(u_1,u_2,\dots,u_N) \ \mathrm{with} \  u_i=u(c_1,...,c_M) ] \gg [ S(u_1,u_2,...,u_N) \ \mathrm{with} \ u_i = u(c_i) ]$$

Change in surplus is thus an approximation of the aggregate gain in welfare, and is only equivalent under the conditions that: policy changes do mainly affect one market and consumers’ utility is assumed to be quasi-linear in the good at focus.

2) Or a second idea/notion, surplus is only the difference between supply and demand curve (i.e. it entails all aspects of the good that can be monetized), while welfare also includes non-monetizable aspects of a good.

Any thoughts on this?


texts:
What is the financialization process of wealth in the economy? What
  are the determining factors? What are its consequences?

  What is the role of financialization in the economic crisis of 2008?

I do not know if my ideas are right, but

Financialization of the economy would not be the process of selling debt in the form of financial securities?

The relationship between financialization and the 2008 crisis would be the fact of the credit facility and the sale of debts caused an imbalance in the economy.


texts: A weaker definition of local non-satiation can also imply indifference "curve"

texts:
Let $u$ be a continuous utility function on $\mathbb R^2_+\setminus\{0\}$. Consider the following three conditions:

Local non satiation says that for any $x \in X$ and $\epsilon > 0$, there exists $y \in X$ such that $d(x,y) < \epsilon$ and $U(x) < U(y)$.
Local non satiation* says that for any $x \in X$ and $\epsilon > 0$, there exists $y \in X$ such that $d(x,y) < \epsilon$ and $U(x) \neq U(y)$.
The indifference sets of $U$ are curves.

As a standard result, (1) implies (3) and (3) implies(1).

Obviously, (1) implies (2) so (3) also implies (2).

Can (2) also imply (1) and (3)？


texts: How can I write a conditional expectation of finite state markov process in matrix notation

texts:
NOTE: This question is related to the econometric method explored in the following two questions:

Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/eigenvector
Example of the change of measure proposed in Hansen (2012)

QUESTION: Suppose that $X_t$ is an $n$-state Markov chain with transition probability matrix $\mathbb P$ and realized values given by $n$-dimensional coordinate vectors. Suppose that $\{W_{t+1} \}$ is an iid sequence of multivariate normally distributed random vectors. How would I represent an equation of the form
$$
E[\exp(D'X_t + X_t' F W_{t+1}) e(X_{t+1}) \mid X_t = x] = \exp(\eta) e(x)
$$
as an eigenvector problem for a matrix $\mathbb M$? How can I represent $\mathbb M$ in terms of the primitives of the problem?


texts:
Are there any countries in which banks do not need to follow any special regulation other than the regular business regulations. If not, are there any countries that come close?
For more information https://en.wikipedia.org/wiki/Free_banking?wprov=sfla1 .


texts: Can the benefits provided by the Ex-Im Bank of the US be considered a Public Good?

texts:
With the debate surrounding the upcoming re-authorization of the Ex-Im Bank of the US, I wanted to hear from someone who might know. What is the best case to be made for its continued operation? I understand the "loans as corporate welfare" case, but I think you could probably classify improved export conditions and the resulting job growth, tax revenue, etc. as a Public Good.

If this is true, do these benefits justify the bank's existence despite the corporate welfare?


texts: Market competitiveness → Capital earns its marginal product. But why?

texts: Why is it possible to tell that, in the case markets are competitive, capital earns its marginal product? What's the formal explanation and what is the economic intuition behind it?


texts: Quantity restriction in model with fixed factor of production

texts:
I'm trying to see the effect of a restriction on production in a model where one factor of production is perfectly elastic and the other is fixed.
Specifically, suppose the production function is Cobb-Douglas: $y = k^\alpha l^{1-\alpha}$. Then cost minimisation gives
\begin{align}
k &= \left(\frac{\alpha}{R} \frac{W}{1-\alpha} \right)^{1-\alpha} y \quad \quad \quad (1) \\
l &=  \left(\frac{1-\alpha}{W} \frac{R}{\alpha} \right)^\alpha y \quad \quad \quad (2)
\end{align}
where $R$ is the price of $k$ and $W$ is the price of $l$. The goods market is perfectly competitive, so price equals marginal cost:
$$
p = \left(\frac{R}{\alpha}\right)^\alpha \left(\frac{W}{1-\alpha}\right)^{1-\alpha}. \quad \quad \quad (3)
$$
Demand for the good is given by
$$
y = \frac{\phi}{p} \quad \quad \quad (4)
$$
where $\phi$ is a parameter. Equations (1) - (4) give four equations in the six variables $y, k, l, p, R, W$. Now suppose $k$ is perfectly elastic and $l$ is perfectly inelastic, i.e.
$$
R = \bar{R} \quad \quad \quad (5) \\
l = 1 \quad \quad \quad (6).
$$
I can solve these six equations in six variables. But now suppose I want to introduce a quantity restriction, $y \leq \bar{y}$ (where $\bar{y}$ is sufficiently low as to be binding). To avoid an overdetermined system, which of the six original equations do I drop? Alternatively, do I redo an optimisation equation, including this extra constraint, so that there is an additional Lagrange multipler variable?
Intuitively, I think that the price $W$ of the inelastic factor of production $l$ will be bid up, but I'm not sure how this mathematically arises.
Thanks!


texts: Does the demand for bad quality products increase when there is information asymmetry?

texts:
Situation 1 In a situation where we have two markets one with good quality products and the other with bad quality products, if we are in a situation where the buyer knows which is the good product and which is the bad we can say that the demand for good quality products is superior to the bad quality ones.

Situation 2 Now if we go from situation 1 to situation 2 where the buyer does not know which is the good or the bad product we can say that the demand for good quality products decreases since the buyer is willing to pay less because he does not kbow if what he is buying is a good product.

Now what I dont understand is why do we say that the demand for bad quality products will increase when the demand for good quality products decreases?

Is it just because the decrease in demand for the good products is the same quantity as the increase in demand of bad product since the two products are the same type but not quality? Or is there another explanation for this ?


texts: Repeated game with stage game has more than 1 NE

texts:
Given the game like Prisoner's dilemma (infinitely undiscounted) and each person has 3 actions in every period: confess defect and kill, and the payoff matrix have 2 NE as (D,D),(K,K).

Can I still use the property that if in any stage NE is played, then that kind of strategy is SPNE.

It seems work for me to prove that any sequence like dd,kk,kk,kk,dd....randomly combination of dd,kk, is SPNE.

Is that correct? Can I generalize that property?


texts: Finding the conditional input demand function

texts:
Find the conditional input demand function and cost function for the given production function $$f(a,b,c,d)=\min\{ a,2b\} + \max\{3c,4d\} $$
In The solution, The production function is defined as $f(x,y)=x+y$ which is perfect substitutes.
Therefore, when $P_x >P_y$, $x=q$ and $y=0$. And when $P_x < P_y$, $y=q$ and $y=q$.
So far, everything is okay. The point that I don’t understand is how to define $P_x$ and $P_y$. In the answer, these are defined as follows
$P_x= P_a+(P_b/2)$ and $P_y= P_c/3 $ if $P_d/P_c >4/3$ and  $P_y= P_d/4 $ if $P_d/P_c <4/3$
Why does he sum of the prices of goods a and b to find the $P_x$? But while finding $P_y$, he separates it under a condition? What is the difference ? In short, how to define Px and Py? My question is this.


texts: Does GDP count both the investment and the house rental?

texts: Suppose you bought a new house in the year of 2010. Then the price of the house in counted toward the 2010 GDP. Say then you live in the new house in the following years. So in these years, the GDP includes the housing rental you paid yourself. But then why is it not an overcount? I mean, when we counted the house price into GDP in2010, we have already counted all the utility of the house in one year and there is no need to count the de sequent rental.


texts: Shapley Value - Any Real World Applications?

texts:
The Shapley Value has been around for seven decades now. It is intuitive, tractable, and has many desirable properties. To my surprise, however, its actual applications in the real world are not readily available (as defined by a simple Google search). Most of the "applications" of the Shapley Value I could find are theoretical/hypothetical in nature. For example, the Investopedia entry lists the pricing of airport runway usage and marketing analytics as two applications without reference to actual real world cases.
My question is: Are there any real world applications of the Shapley Value in pricing transactions and/or allocating profits/costs among cooperating parties?
More specifically, I'm looking for answers in any of the following forms:

"As documented in [news/professional/academic] Publication X, Company A used the Shapley Value (or its variant) to price its transaction with Company B and Company C."
"As documented in [news/professional/academic] Publication X, Company A used the Shapley Value (or its variant) to allocate its [R&D/marketing/overhead] costs among its subsidiaries B, C and D."
"The empirical study by Author et al. (20xx) in Publication X found that
the profit/cost sharing practice within a [firm/industry/multinational enterprise] is consistent with the prediction of some model based on the Shapley Value."
"The empirical study by Author et al. (20xx) in Publication X uses [a structural estimation/an empirical strategy] that is based on the Shapley Value."

Please do provide links/references to the sources. Thank you.

Note 1. While I'm primarily interested in the application of the Shapley Value in a business context, pointers to its use in other domains such as politics would also be appreciated.
Note 2. I found a paper by Littlechild and Thompson (1977) where the authors applied the Shapley Value in calculating the prices of airport runway usage based on actual data from the Birmingham Airport. It is unclear, however, whether those prices were subsequently adopted/implemented by the airport authorities.


texts:
I read on cnbc.com (mirror):

Tenev also advocated for real-time settlement instead of two-day settlement in order to help combat some of the chaos that occurred during the GameStop saga.

Why would using real-time settlements have helped combat some of the chaos that occurred during the January 2021 GameStop saga?


texts: Proof on weak axiom of revealed preferences

texts:
I read the following statement.
“ A utility maximizer with strictly convex and strongly monotonic preferences
satisfies weak axiom of revealed preferences.”
How can I prove or show this? I cannot realize this statement on my mind. Please show me it’s proof in order to understand its statement.


texts: Too much of a good thing - examples of production (or utility) functions that are initially increase in a factor and then decrease

texts:
I'm attempting to build a spatial model that estimates labour distributions after climate change impacts agricultural production. The key point to note is that some rainfall is good, and some temperature is good, but only up to a point - too much rain will drown the plants, and too hot a temperature will cause them and the soil to lose moisture too quickly.

In the model, I use the data I have to calibrate and get values for productivity in the context of the model, and I would like to use those estimates to estimate the parameters of some production function, so that to run the counterfactual, I can apply projections of climate data to estimate productivities in each country. Does anyone know of production functions with the required property?


texts:
I would like to analyse how COVID-19 has impacted the aviation industry by looking at how the demand for airlines + holidays has fallen via an indifference curve analysis. However, I'm not sure where to start
Would the indifference curve shift inwards?


texts: Why do increase in firms profit margins cause cost push inflation?

texts: I read somewhere that this was the case. I get what profit margins and cost-push inflation are, but don't see how increase in marginal profit causes cost-push inflation? Also, how does increase in money supply cause cost-push inflation?


texts: How can one compute the CPI All items index from the component indexes?

texts: How can one compute the CPI All items index given the CPI energy index and the less energy index? I used the relative importance as component weighted value but it isn't true.


texts:
What impact did monetary policy actions taken during the Great Recession (2007-09) have on U.S. economic performance?

Quantitative easing and unconventional policy actions such as asset purchases and "forward guidance". I think I'm missing some things.


texts: Reasons for the recent rise in long-term unemployment

texts:
Kroft et al document the raise of long-term unemployed in the US during the recent crises. This is an impressive figure from their paper:

They show that the raise does not come from compositional effects. However, they cannot find the reason for this phenomenon. For some reason, apparently, long-term unemployed are less likely to find a job, and hence their stock accumulates.

Potential reasons I could think of are

Human capital deterioration
Discrimination of employers
Shrinking motivation of searching

What other reasons does the literature find? Is there empirical support for any of this?


texts:
I have a little doubt in the Job Market Signalling Game. I am referring to A Primer in Game Theory: Gibbons, Chapter 4, Signaling Games
The attached paragraph refers to a Separating Equilibrium case wherein, the High Ability type player chooses to signal $e_s>e^*(H)$, so that the Low Ability type has no incentive to mimic High Ability type, since he/she will mimic only when $e$ is between $e^*(H)$ and $e_s$.
I understand the reasoning behind this. However, I cannot seem to understand why a High Type player would choose to signal thus is he/she gets a lower payoff by doing so (since it is not optimal). Is it the case that the 'loss' due to Low Ability Type mimicing him/her is greater than the 'loss' ny not playing optimal action? Does this have anything to do with sequential rationality?

I'm sure I'm missing something. Please help me understand the concept and what I'm wrongly inferring. Thank You!


texts: Is there an alternative metric to GDP that measures a country's assets rather than flows?

texts:
The Gross domestic product measures the value of all final goods and services produced in a period.

This has some limitations.  For example, if a car hits a lightpost and both need to be repaired and some parts replaced, that contributes to the GDP, even though at the end we're in roughly the same situation as before and the reparation process has used resources (labour and material) that might have been used elsewhere.  From Wikipedia:

  The UK's Natural Capital Committee highlighted the shortcomings of GDP in its advice to the UK Government in 2013, pointing out that GDP "focusses on flows, not stocks. As a result an economy can run down its assets yet, at the same time, record high levels of GDP growth, until a point is reached where the depleted assets act as a check on future growth". They then went on to say that "it is apparent that the recorded GDP growth rate overstates the sustainable growth rate. Broader measures of wellbeing and wealth are needed for this and there is a danger that short-term decisions based solely on what is currently measured by national accounts may prove to be costly in the long-term".

I'm aware of numerous alternative measures focussing well-being, such as the Human Development Index,Gross National Happiness, and the Happy Planet Index.  They don't really measure either wealth or well-being (the latter may be impossible to measure), and their exact definition is somewhat arbitrary.

Is there any reasonably well-established alternative to GDP that measures the total value of the stocks of a country?  Wikipedia has a financial assets list, but it relates only to households (and on this list, Greece is almost twice as wealthy as Norway, which is so vastly against expectations that I wonder if the definition is useful).  I can reasonably well estimate the value of my own assets (except for the value of my education/skills, which is harder to quantify).  Is there any metric that is used to estimate the value of all assets in a nation: infrastructure, real estate, machines, goods, farmland, but also education, human capital, unmined natural resources, etc.?


texts: Are FedWire transfers and volume tracking exchanges of reserves between banks that have accounts at the Federal Reserve?

texts: Looking at Fedwire® Funds Service - Monthly Statistics it appears that these transactions are between banks but I'm trying to confirm is whether the stuff they are exchanging is classified as reserves. That is, FR liabilities shown in "Deposits with F.R. Banks, other than reserve balances" in H.4.1?


texts: Resolution - Ramsey growth model with per capita variables

texts:
Let's say that we have the sum of the utility of a social planner
$$\int_{0}^{\infty}U\left(C\right)e^{-\rho t}dt$$
where $C$ is the total consumption. If we want to write this by a per capita variable $c=\frac{C}{L}$ where $L=e^{nt}$ is the total number of population that grows exogenously at rate $n$. We can reformulate this such as
$$\int_{0}^{\infty}U\left(c\right)e^{nt}e^{-\rho t}dt$$
Until now, everything is straightforward. However, if we have started by a specified functional form such as a CRRA utility
$$\int_{0}^{\infty}\frac{C^{1-\sigma}}{1-\sigma}e^{-\rho t}dt$$
We would not have reached the result above and should have some exponent term with $\sigma$.  What is the  logic behind? There is something I miss.


texts:
I am a student, currently working on my Bachelor's Thesis. And as the next deadline approaches, I hope someone could give me a hand on my constant issue:
I need to estimate the next model with GMM estimator:

So far I was using pgmm function in plm package. You can check other topics of mine with the issues I have faced, and I still did not solve them.
Hence, I tried to move to another package pdynmc authorized by Dr. Markus Fritsch.
Here is a part of my dataset filtered with firms having at least 5 years of observations: https://drive.google.com/file/d/1dFUgXp8e1K0CdqMTpbtfviDq9vgJNOxW/view?usp=sharing
I am not sure you can get a context of it, but I need to estimate similar to this model as:
A change or growth in the dependent variable from t to t+1 (ΔTFPt+1) = GMM instruments, as far as I understood, of the, lagged dependent variable (so lagged change in the dependent variable) (ΔTFPt, and ΔTFPt-1) + change in one other variable (ΔDebt), the measure of needed variable (financial friction) + interaction between last 2 variables (financial friction * ΔDebt) + control variables (firm age, firm size or log(TA), change in sales or ΔSales).
In my dataset, needed variables are:

ID - is an ID of the companies
Year - the year of observation
ta - log of total assets
ff1-5 - financial friction variable of the companies
LVomegaACF_A - is a TFP measure
domegaACF_A - is ΔTFP measure
ddebt -  ΔDebt variable
dsales -  ΔSales variable
Age - age of the companies

I tried to use the package as follows:
model <- pdynmc(dat = LVcheck, varname.i = "ID", varname.t = "Year",
                varname.y = "domegaACF_A", lagTerms.y = 2,
                fur.con = FALSE, varname.reg.fur = c("ddebt", "ff1", "Age", "ta", "dsales"),
                lagTerms.reg.fur = c(1,1,1,1,1),
                fur.con.diff = TRUE, fur.con.lev = FALSE,
                include.dum = TRUE, dum.diff = TRUE, dum.lev = FALSE, varname.dum = "Year",
                w.mat = "iid.err", std.err = "corrected", estimation = "onestep", opt.meth = "none",
                use.mc.nonlin = FALSE, use.mc.diff = TRUE, use.mc.lev = FALSE, include.y = TRUE)

And the error I receive:
Error in pdynmc(dat = LVData_A, varname.i = "ID", varname.t = "Year",  :
  Insufficient number of time periods to derive linear moment conditions.

The question is the following, why the number of periods is insufficient if the only firms are displayed that have at least 5 years of observations?
And also, is my code written accordingly to my model specification, and all the arguments needed are written correctly.
I would really much appreciate your responses and any support from your side. Here is the package description https://rdrr.io/cran/pdynmc/man/pdynmc.html
Despite the fact, everything is quite detailed there, I still do not understand what is wrong with what I am doing.
Thank you very much in advance.


texts: Why are simple returns additive over securities?

texts:
I've found a few sources for instance this one, that makes the claim that over a portfolio, simple returns are additive. I can see why it doesn't make a difference if we use net or gross returns as long as the weights add to one, but I can't see why we should get this additive behaviour for a quantity that has a division in it. Perhaps I am using a bad definition of weight?

If someone could share a derivation for a portfolio of two assets that would be sufficient.


texts: Road to equilibrium in a basic economic model

texts:
I am reading a (macro)economics book which introduces a model of a small, closed economy. Two relations are presented. The IS relation (savings equals investments, or demand equals production) and the LM relation (money supply equals money demand).

The book then goes on about what happens in an economy given by this model .... but is the model's equilibrium one that occurs naturally? Is real-life money supply equal to money demand? Is real-life investment equal to savings?

My question in short: why does the economy converge to these equilibriums?


texts: Pigouvian subsidies for non-linear marginal external benefits

texts:
Suppose an agent is choosing how much $x$ to consume and $p_x=200$. If the agent's marginal private benefit is $MPB(x)=300/x$ and $x$ takes only integer values, then he will choose to purchase just one unit of $x$. But suppose his consumption of $x$ yields a positive externality such that the marginal external benefit is $MEB(x)=2700/x$ (essentially there are nine other people similar to the agent who benefit as much from the agent's consumption as the agent does). Then the social optimum is where the marginal social benefit equates with the marginal social cost ($p_x$):
$$MSB(x)=MPB(x)+MEB(x)=\frac{3000}{x} = 200 \Longrightarrow x^* = 15$$
If I were to ask what the appropriate Pigouvian subsidy was to implement this societally optimal outcome, I can envisage two possible answers:

Set the marginal subsidy equal to the marginal external benefit: $MS(x)=\frac{2700}{x}$. Note that, in this case, the government would end up paying the agent $\sum_{x=1}^{15}\frac{2700}{x} \approx 8959$ in subsidies, which is substantially more than the agent's outlay ($200 \cdot 15 = 3000$).
Set the marginal subsidy equal to the marginal external benefit evaluated at the optimal output: $MS(x)=MEB(15)=2700/15=180$. Total subsidy is $180 \cdot 15 = 2700$.
Set the marginal subsidy as low as possible to get him to purchase each unit up to 15: $MS(1)=0$. $MS(x) = 200 - \frac{300}{x}$ for $2 \leq x \leq 15$. Total subsidy is $\sum_{x=2}^{15} 200 - 300/x \approx 2105$. I suppose here I could even tax the first unit to bring the total net subsidy down further!

Are all of these correct? Is any of them a better answer than the other two?


texts:
I've read that, concerning the CAPM, in equilibrium all portfolio weights are strictly positive. Why is that? You can also go short in the risk free asset right? And then you're on the right of the Tangency Portfolio.

Furthermore, I read that by definition, the MVP can contain short positions. How does this relate to my first question?

Hope you can help out!


texts: How can two countries of roughly the same size, population and GDP have such big differences in minimum wage?

texts:
We could answer this question theoretically, or give a real-world example of two such countries.

Is there anything more interesting to say than: that's just something decided by the government? Could geographic location play a role? Is an equal GDP an indication of equal minimum wage, or isn't it?


texts: Difference between shocks, innovations and disturbances

texts:
In macroeconomics and macroeconomic models, shocks, innovations, and disturbances are very prominent and often mentioned in the literature.

In general, is there a difference between macroeconomic shocks, disturbances, and innovations, or can these terms be used interchangeably?


texts:
Continuous trading economies. I see this expression in many papers but I do not know what it means in the precise technical sense. And I'm not an economist.

Maybe it could refer to an economic environment in which agents are allowed to trade continuously. But in what way? In time and goods to trades? E.g., in time: there is a subset $S\subset \mathbb R$ s.t. $t\in S$? Or, in goods: there is a subset $U\subset \mathbb R$ that represents all the possible goods that agents of this economy can trade?


texts: Ratios to determine company's current purchasing power

texts: what are the parameters which will affect a company ability to buy a new product based on its current financial situation.  Is there any metrics or ratios which will tell the current company purchasing power?


texts: Is there an economic theory that explains what happens when a market is saturated with a precious resource?

texts:
The theoretical situation is this. What if a record breaking amount of platinum were discovered. What would happen to the economies that use, store, and/or produce platinum?

I would like to apply this theory to any kind of precious material or element. Other examples would be gold, uranium, or oil.


texts: Which economist suggested solely printing money to borrow and not have bonds?

texts:
I remember reading this really interesting idea by some economist that a government need not issue fixed-term debt such as bonds, notes or bills. Instead all it could do is print money and use it to pay for everything, thereby borrowing.

It would repay by levying taxes, which it would vary based on the rate of inflation. I. e. if the rate of inflation would be too high, it would increase tax rates to bring it down and vice versa.

My question is -- who was this economist? I need to cite this idea and need a name or better yet a citation to a paper.


texts:
This should be a very simple question for most of you, but I can't seem to get an answer so I decided to ask the question here. So please be as simple as possible and excuse my ignorance.

This is a chart of the US debt as percentage of GDP versus time. It is obvious that WW1 and WW2 have greatly increased the debt. Let's take the WW2 case as an example. the US military/defense spending reached 38% of GDP in 1944-1945, and as far as I understand, GDP is value of the all the products and services in a country within a specific time, a year in this case.
So my question here is, why does the debt increase during a war ? And why can't governments "direct" the products and the services they already own and which are already accounted for in the GDP to their war effort instead of borrowing ?

In other words, what could have happened if the US spent on the war entirely from its production and services (GDP) without borrowing a penny ?


texts:
$$
L_t = \gamma(\pi_t - \pi_t^\otimes)^2 + \hat{Y}_t^2
$$

Central banks loss function is given by the equation above. This loss is increasing and convex in the distance from the inflation target, i.e. the marginal loss increases at a faster rate than the increase in the distance from the target.
In Figure 1, we can visualise the preferences using indifference curves, where the ellipses have the center being the desired point (0, $\pi_t^\otimes$ = Target inflation point.) (saturation point - bliss point)
It is hard for me to see how the different ellipses are indifference curves, or convex from in the difference from target?. Any explanation would help a lot.


texts: With whom does the US have the largest deficit using the trade in value-added (TiVA) methodology?

texts:
The US has the largest gross trade deficit with China. But some economists have argued that this is misleading, e.g. using the iPhone as an example in which most parts don't orginate in China.

There's actually a more academic version of this analysis called "trade in value-added", which can be roughly summarized as:

  Global imbalances: accounting for trade in value-added (specifically accounting for trade in intermediate parts and components) and taking into account “trade in tasks” does not change the overall trade balance of a country with the rest of the world – it redistributes the surpluses and deficits across partner countries. When bilateral trade balances are measured in gross terms, the deficit with final goods producers (or the surplus of exporters of final products) is exaggerated because it incorporates the value of foreign inputs. The underlying imbalance is in fact with the countries that supplied inputs to the final producer. As pressure for rebalancing increases in the context of persistent deficits, there is a risk of protectionist responses that target countries at the end of global value chains on the basis of an inaccurate perception of the origin of trade imbalances.

This does look like quite an involved method to follow for all imports though. My question for here is: with whom would the US have the largest trade imbalance if one uses the "trade in value-added" (possibly recursively) to track US imports to their components?


texts: MLE estimation with serially correlated errors

texts: I want to estimate the parameters of $a_t = a_{t-1}+\theta+\epsilon_t$ using MLE. Assume errors $\epsilon_t$ are serially correlated, then how would I choose the likelihood function?


texts: I am curious how to solve the utility maximization problem if the representative agent has borrowing constraint.


texts: I understand the concepts of risk-aversion, risk neutrality and risk-attraction. I wonder if it possible to compare risks between two lotteries without giving the utility function. For instance,  Let X = (10, 20, 30) and consider two lotteries L1 = (1/3, 1/3, 1/3) and L2 = (5/12,1/6,5/12). Can we say that one lottery is riskier than the other?


texts:
I am currently reading Dying of Money by Jens O. Parsson and he criticizes the way price level is calculated. Basically he tries to make a case that since money are not only used to purchase goods but also used for investing, there are two money supplies and two velocities at the same time:

There are at all times two distinct money supplies and two distinct
velocities of money, one each in the market for national product and
the market for national wealth ["investments"]. The comparison between
the total supply of money and the gross national product alone, as is
made in computing the so-called "income velocity" of money, is
meaningless.

First, I wonder what does he mean by two distinct money supplies? Where does the second supply come from? Is it like borrowed money?
Second, is there a velocity metric for investments or maybe even inflation metric too?


texts: Effect of lower Government spending on Loanable Funds Market

texts:
I'm having trouble with understanding what the results would be...

Let's suppose the situation where the newly formed government act to cut government spending and, by doing so eliminate the current federal government budget deficit.
Does this shift the demand curve or the supply curve in the loanable funds market?

I watched a Youtube video and it said demand would increase (crowding out) but my lecture notes contradict that by saying supply will decrease (crowding out) or does that result to the same thing?


texts: Effect of a permanent increase in government expenditure in an open economy?

texts: In Krugman & Obstfeld's International Economics, 8e, Chapter 16, an involved argument is given showing that a permanent fiscal expansion will not affect output even in the short run. It seems to me that this is a saddlepoint stability argument in disguise. Am I right in thinking this? Can someone please help me with a differential equation formulation?


texts: Why is CRRA utility often used in macroeconomics DSGE model?

texts:
As title says, why is CRRA utility often used in macroeconomics DSGE model? That is, the form of

$$u(c_t) = \frac{c_t^{1-\sigma}}{1-\sigma}$$

I cannot find any theoretical background around this..... After all, there is often no risk involved in DSGE models..


texts:
I estimated the CES function (https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution) using national accounts data for France. I got (using notation in wikipedia):

a = 1.19
r = -0.48

so the term next to capital is negative (-0.19). Is this possible? What does it mean? I don't see anywhere in that website a restriction on the sign of "a". My textbook does not state restrictions either. Is it fine? Or is it a problem?

Any thoughts on the issue?


texts: Can anybody explain to me Nett Gross, Adjusted Nett Gross and Total Nett Gross through an example? I am new to this subject and from an engineering background. This knowledge is required for my research work. Thanks in advance.


texts:
I want to derive the Euler Equation for the following:

$$max \sum\limits_{t=0}^{T} = \beta^{t}U(C_t)$$

$$s.t. C_t+K_{t+1} \leq f(K_t) , t=0,1,2,...,T-1$$
$$-K_{T+1} \leq 0$$

I'm a bit confused about why the F.O.C. have that:

$$\frac{d\mathcal{L}}{dK_{t+1}}=-\lambda_t+\lambda_{t+1}f'(k_{t+1})$$

and how we combine the F.O.C to yield the Euler equation:

$$U'(C_t)= \beta U'(C_{t+1})f'(k_{t+1})$$

I assume the F.O.C w.r.t. $K_{t+1}$ is such because of the inclusion of the intensive form of the production function but I am not exactly sure how and I really want to understand this completely.  I also need to make sure I understand how we are using the FOC to produce the Euler Equation.
Can anyone provide a bit of clarity?


texts:
Consider the following income fluctuation problem. An agent lives for two periods, 0 and 1, and faces stochastic income in period 1. We are given this utility maximization problem: $$\text{max}\ U(c_0)+\beta E_0U(c_1)\ \text{s.t}\ $$
$$c_0+a_1=y_0$$
$$c_1=(1+r)a_t+\tilde{y_1}$$
where $\tilde{y_1}$ is stochastic: $y_1=y_0+e$ with probability $1/2$ and $y_1=y_0-e$ with probability $1/2$. We consider $\beta(1+r)=1$
We are asked to show  that if $u'''> 0$ (i.e. $u'$ is convex) and $e > 0$, then $a_1 > 0$. And how can we interpret this result?
In regards to interpretation, the third utility is usually related to prudence. Now what my train of thought was:
$$u'(y_0-a_1)=E_0[u'((1+r)a_1+\tilde{y_1})]>u'[E_0((1+r)a_1+\tilde{y_1})]=u'((1+r)a_1+y_0)$$
$$\implies y_0-a_1<(1+r)a_1+y_0$$
Suggesting that $a_1>0$. Meaning that the agent is prone to save?
Is this correct?


texts: It's unclear how market equilibrium is reached in case of overproduction

texts:
Let's assume that there is disequilibrium, namely that $P=P_2$, thus $Q_s > Q_d$. In other words, there is overproduction. This is perfectly competitive market, so competition between producers will make them lower prices in order to get rid of excessive production, thus allowing the market equilibrium (in the point $E$) to be reached. But wait a second! When we said that producers will change price we said nothing about quantity of production. But you can clearly see that in point $L$ (before producers lowered prices) the quantity was equal to $Q_2$, while in point $E$ it's equal to $Q'$, and $Q' < Q_2$.

What happened with all these ${\bf Q}_2$ minus ${\bf Q}'$ goods? It looks like producers collectively decided to destroy part of their excessive goods in order to reach the point of equilibrium. Because if producers will change only price of their goods (i.e. $Q_s$ is constant) there is NO way they can reach equilibrium without moving their supply curve (or alternatively - without moving the demand curve).


texts: Why we need to control for the interation of year and industry fixed effects?

texts:
Normally, we control for firm and year fixed effects, but in some case I saw people control for the  firm along with yearxindustry or firm and yearxregion fixed effects.
Could you please hint me why they need to do so?


texts:
How much of previous economics (historically) is still relevant today?

How is it determined?

Is e.g. 18th century economics still relevant today? Is it accurate/useful to cite Adam Smith for example?

It's clear that people still cite e.g. Smith or Marx, but one could question, whether such citing serves a "purposeful" description of contemporary reality or whether it's merely made plausible to "apply Marx today", because one can.


texts: Why does China spend so much on agricultural/farming subsidies?

texts:
I use the OECD's Total Support Estimates (TSE), which I think is a proper measure of total agricultural subsidies (but correct me if I'm wrong).

China's TSE is by far the largest at \$239B in 2017 and even its per-capita TSE (PPP*) is higher than the US's.

Here are some explanations I have come across for why agriculture is heavily subsidized in the rich democracies:

Rural voters wield disproportionate power.
The costs (of the subsidies) are diffuse and so no single voter has much incentive to organize/lobby against the subsidies.
Voter inattention: The voters who pay for the subsidies are simply unaware that they are doing so.

However, China is not a democracy and so it would seem that the above explanations do not apply. So what explains China's large agricultural subsidies?

*I think (but am not sure) the TSEs given by the OECD have not been corrected for PPP. And so, I have taken the liberty of converting them.

Google spreadsheet with data and sources.


texts: Why solving the model for a benevolent social planner gives an efficient allocation?

texts:
Probably this question is really dumb - and I'm sorry if it is - but why solving the model for a benevolent social planner, gives an efficient allocation?

What's the criteria for this efficiency?

I'm asking this because in several NK models in macro, when we're comparing the 'desirability' of simple rules, we take as efficient the allocation obtained from solving the model as stated above.

Any help would be appreciated.


texts: Understanding annualized percentage rate of interest, real interest and nominal interest rate

texts:
I am having issues finding a solid example online that explains how the concepts surrounding the word interest relate to each other. I am after an example that presents a concise mathematical formula that I can ultimately use to write a computer application.

Let us start with nominal versus real interest rates. My understanding is that the simple concept of interest on a loan is called nominal interest. If we consider an inflation rate, then their difference is called real interest. Mathematically:
$$
r_r = r_n - r_i,
$$
where $r_r$ denotes the real interest rate, $r_i$ denotes the inflation rate, and $r_n$ denotes the nominal interest rate.

The so-called "annualized percentage rate (APR)" is an interest rate that accounts for any additional costs the loan may incur in. According to [1] the following is a formula for APR:
$$
\begin{aligned} &\text{APR} = \left ( \left ( \frac{ \frac{ \text{Fees} + \text{Interest} }{ \text {Principal} } }{ n } \right ) \times 365 \right ) \times 100 \\ &\textbf{where:} \\ &\text{Interest} = \text{Total interest paid over life of the loan} \\ &\text{Principal} = \text{Loan amount} \\ &n = \text{Number of days in loan term} \\ \end{aligned}
$$
When algebraically manipulating the latter expression, it seems like an equivalent expression can be derived as follows: Let $f$ denote the sum of all fees incurred by the loan, and let $p$ denote the amount borrowed (i.e. principal). The APR for a loan period of $n$ days is then defined as:
$$
r_{APR} = 100\times\frac{365}{n}\times\left(\frac{f + p}{p}\right)\times r_n,
$$
where $r_n$ denotes the nominal rate of interest.

Examples:

Let $r_i = 0.04$ and $r_n = 0.1$. Then $r_r = 0.06$, or 6%. Then, let $p = 200,000$ USD and $f = 5,000$ USD for a $n = 365$ days loan period, so that $r_{APR} = 0.615$, with a total amount to payback of 212,300 USD, meaning the cost of the loan is 12,300 USD. Note, in this example, I’ve used the real interest rate rather than the nominal interest rate to compute the APR.

Core questions:

Is the definition of real interest rate correct?
Is the second definition for APR correct?
What if $n = 365$, thus making the coefficient $365/n = 1$? Wouldn't this make this coefficient worthy of the name annualization coefficient?
What if instead of using the nominal interest rate to compute the APR, we use the real interest rate?
Isn't APR a misnomer? The word "annualized" may be correct... but "percentage rate" seems like a very general noun phrase. Specifically, the word "percentage" only applies if we take it as a percentage, and the word "rate" is valid, but anywhere in APR the word interest appears.  Wouldn't a better name for this interest rate be "annualized cost-of-borrowing (real) interest rate", in where the word "real" could be used in the case in which the formula used the real interest rate, rather than purely the nominal interest rate?


texts: Are there any other rational preference relations without utility function representations, besides Lexicographic?

texts: It seems like lexicographic isn't that "special". Like yes it is special in that supposing it has a utility function gives you a bijection from the rationals to the reals, but I mean unique in some sense. I know that it satisfies a bunch of nice properties, but it still feels like there should be plenty of other (rational) preference relations that don't have utility representations.


texts: Deriving aggregate output from labor demand and supply

texts:
I was reading the following paper:
http://eml.berkeley.edu//~moretti/growth.pdf
I got stuck at equation (7)
The firm's production function is $Y_{i}=A_{i}L_{i}^{\alpha}K_{i}^{\eta}T_{i}^{1-\alpha-\eta}$
Labor supply is $W_{i}=V\frac{P_{i}^{\beta}}{Z_{i}}=V\frac{\bar{P_{i}}^{\beta}L_{i}^{\beta \gamma_{i}}}{Z_{i}}$
Labor demand is $L_{i}=(\frac{\alpha^{1-\eta}\eta^{\eta}}{R^{\eta}}\frac{A_{i}}{W_{i}^{1-\eta}})^{\frac{1}{1-\alpha-\eta}}T_{i}$
The paper says that if we impose aggregate labor demand is equal to aggregate labor supply (normalized to one), then the aggregate output $Y=\sum_{i}Y_{i}$ is
$Y=(\frac{\eta}{R})^{\frac{\eta}{1-\eta}}[\sum_{i}(A_{i}[\frac{\bar{Q}}{Q_{i}}]^{1-\eta})^{\frac{1}{1-\alpha-\eta}}T_{i}]^{\frac{1-\alpha-\eta}{1-\eta}}$
This step looks drastic to me. How can the aggregate output be derived from the above conditions?


texts: A question about Lagrange multiplier(when $\lambda=0$)

texts:
I need help in a maximization problem(finding the optimal investment portfolio).

where $R_s$ and $\Phi$ are $n$ by $1$, with other variables being scalars.
$C^s$ is consumption (or wealth) of an investor, $R_s$ (or $R$) is the return rates of risky assets while $R_f$ is the return rate of a risk-free asset(say government bond), $\Phi$ is the quantities of risky assets, $\phi_f$ is the quantity of the risk-free asset, $\omega$ is the quantity of all the assets(so $\phi_f+\Phi' \cdot 1=\omega$), and $u(\cdot)$ is the investor's utility function.
The solution to this problem gives the following first order condition(FOC) i.e. taking derivative w.r.t. $\Phi$ (assuming integration and differentiation can be exchanged):

But there's actually a constraint: $\phi_f+\Phi' \cdot 1=\omega$, so I tried Lagrange but couldn't get the same result:
$$L(\Phi, \lambda)=E[u(c)]+\lambda(\omega-\phi_f-\Phi' \cdot 1 )$$ with FOCs:
$$\partial L/\partial \Phi =E[u'(c)(R-1\cdot R_f)]-\lambda \cdot 1=0$$
$$\partial L/\partial \lambda =\omega-\phi_f-\Phi' \cdot 1 =0$$
I couldn't get the same result from above. To have the result in the solution I must have $\lambda=0$ but I'm not sure in what cases it can hold. Please let me know which parts I did wrong.


texts: Statistical models which represent the impact of strict measures vs no strict measures (and less economic impact), enforced due to Covid-19

texts:
I have been wondering whether there are statistical models like this one, (which estimated the deaths caused by the virus itself) that estimate the deaths caused by the economic turndown. There is an estimate of how much the pandemic would cost the Israeli health system, and just a general economic analysis of the impact of the pandemic. I was wondering if there are for example models which show the impact of the strict measures(deaths caused by the economic crisis due to lockdown) and just models which show how much more deaths would occur if there was no strict lockdown (and hence the no economic crisis, or at least not as drastic as after complete nationwide lockdowns) than the economic crisis itself.

I am not particularly interested in any specific country, just examples if such exist.

I'm looking for a model that shows the consequences of lockdowns and its economic impacts. ie how much more/fewer people will die from economic collapse rather than the virus given there was no lockdown (but social distancing and mass testing involved).


texts: Term for when using a single number is used instead of a function?

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A cost per unit could be 20, but it could also be 20 + 2q (in the cast of the latter, the cost per unit is a function whose result increases with each unit produced).
What is the term to describe when a single number is used where we could also expect a function?
I have in mind 'scalar', but I'm not sure if that's the best term.


texts: Optimal strategy in a single-agent choice problem under uncertainty

texts:
Consider the following single-agent choice problem under uncertainty.

Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{v})$. First, let nature draw a realisation $v$ of $V$ from $P_V$.
Then, let the decision maker choose an action $y\in \mathcal{Y}$, with $\mathcal{Y}$ finite, without observing $v$. Upon the decision has been made, the decision maker gets a payoff $u(y,v)$.

For example, suppose that $\mathcal{Y}\equiv \{1,2,3\}$. $V$ is a $3\times 1$ random vector, $V\equiv (V_1,V_2,V_3)$. $P_V$ is the 3-variate standard normal distribution. $u(y,v)\equiv v_y$.

What is the definition of an optimal strategy for the decision maker in this setting?

I'm thinking about using "a sort of" Bayesian Nash equilibrium for a single-agent setting, i.e., an optimal strategy is $P_Y\in \Delta(\mathcal{Y})$ such that, $\forall y\in \mathcal{Y}$ such that $P_Y(y)>0$ and $\forall \tilde{y}\neq y$,
we have that
$$
\sum_{v\in \mathcal{V}} u_i(y,v)P_V(v)\geq \sum_{v\in \mathcal{V}} u_i(\tilde{y},v)P_V(v)
$$
that is, in my example,
$$
\sum_{v\in \mathcal{V}} (v_y -v_{\tilde{y}}) P_V(v)\geq 0
$$

But maybe a pure strategy is what people use?

Is existence and uniqueness obvious (at least in my example with a normal distribution)?

Could you also provide a reference discussing definition, existence, multiplicity?