When a land lords sells to an owner occupiers does it push up rents? In the article Landlords who own one property ‘left without relief’ under new Victorian Government package posted on 15 April 2020 on the domain website. Barry Plant chief executive Mike McCarthy Makes the claim that landlords selling to owner-occupiers will push up the price of rent by reducing the available pool of rental properties as below.

  “We are going to have landlords that are going to have to sell their
  property and while that’s great for first-home buyers what it does is
  reduce the pool of properties for tenants and over time that will push
  up rents,” Mr Webb said.

There is a similar claim which was made by PETER VERWER chief executive of the Australian property council in this 2013 discussion about a Grattan institute report (Check the transcript for full details.

  They create 1.8 million homes available for rent. They’re not new homes, but they are 1.8million homes that would not exist unless a
  private investor is satisfied with the high compliance costs, the
  quite moderate rent and the maintenance costs to create all of this
  rented space

Does this claim add up, my understanding is that its a zero sum game. e.g. A landlord sells the property and a owner occupier moves in. Then there is one less property available for rent however one less person (or group of people) looking for somewhere to rent.

OR am I missing something?

Notes this is based on content in Australia.

https://www.domain.com.au/news/landlords-left-without-relief-under-new-victorian-government-package-949032/

Your argument is sound (as a first approximation). In fact this is one of the basic examples discussed in chapter 1 of Varian's Intermediate Microeconomics (a standard textbook).

  Suppose that a developer decides to turn several of the apartments
  into condominiums. What will happen to the price of the remaining
  apartments? Your first guess is probably that the price of apartments
  will go up, since the supply has been reduced. But this isn’t
  necessarily right. It is true that the supply of apartments to rent
  has been reduced. But the demand for apartments has been reduced as
  well, since some of the people who were renting apartments may decide
  to purchase the new condominiums.

(quote from pg 10 of the 8th edition)

If you make some additional assumptions e.g., that all buyers are former tenants and that there is no friction in the market (rent changes may be larger when there are new tenants to avoid tension), the equilibrium price will be the same.


Coefficient omitted because of collinearity I have a panel data that includes a decade of firm-year observations (1995- 2005). These companies are from different countries.

A law has passed in (almost) every country at different points in time. For example, if a law passed in France in 2001, the variable 'law' is equal to 0 for firm-year observations in France from 1995 to 2000 and to 1 from 2001 to 2005.
France is a developed country. The variable 'developed' is equal to 1 for all firm-year observations in France over the decade 1995-2005.

I ran this line of code with Stata:

areg payable i.law##i.developed i.year, absorb(firmid) vce(cluster countryindust)

I want to know what is this impact of the law alone, market development (developed country or not) and the interaction between the passage of the law and market development on accounts payable.

The problem is that the coefficient 'developed' is omitted. It says that '1.developed omitted because of collinearity'. Is it because my model has a constant? I don't understand because people use this specification all the time.

Note: I also have time and firm fixed effects. I cluster for country-industry.

Am I doing something wrong? What should I do so that no coefficient is omitted?

You have firm fixed effects. Presumably, every firm is in the same country throughout your observation period. Moreover, no country ever changes its development status (I assume). Hence, for a given firm, there is no variation in the development status. Therefore, you can't identify an effect.


Help finding historical data for velocity of money (M1 or M2) for any country except USA Can anyone point me to a data set of money velocity for at least 20 years back for any other country than the US?

If you're willing to expand your definition of money, then yes, and easily: You can get broad money measures (M2, M3 and M4) as a percent of nominal GDP ($\frac{M}{PY} \times  100%$) from the World Bank for several decades for many countries (mileage will vary depending on particular country).

Just divide by 100 and invert.  By the quantity theory of money,  $V = \frac{PY}{M}$, Bob's your uncle.  Note that this will underestimate V compared to values reported by e.g. the Federal Reserve, because M includes M3 and M4.


Is there a way to trade currencies several times and end up with more money than one starts with? Conjecture: The foreign price value of a currency is not absolute.
Scenario:
If the euro appreciates relative to the British pound and the price of the US dollar stays the same relative to the euro, what would happen to the US dollar?
Would the US dollar also appreciate relative to the British pound? Or, would it cost the same amount of dollars to buy one British pound?
I'm trying to determine whether it is possible to trade currencies several times and end up with more money than one starts with; That is, assuming that there are no transaction costs involved in trading currencies. If it is possible then, it would essentially be a loophole.

You might be interested in triangular arbitrage. In efficient markets this should not be possible, I don’t think...


Cross price elasticity of demand vs Price elasticity of demand Is the cross price elasticity of demand between two goods always lower in magnitude than the price elasticities of demand of each good?

Not necessarily.

For example if the utility function is $U=\min\{x,y\}$, then the demand function for x is given by $D=\frac{M}{P_x+P_y}$.

The own price elasticity of demand for x is: $-\frac{M}{(P_x+P_y)^2} \frac{P_x}{x}$.

The cross price elasticity of demand for x is: $-\frac{M}{(P_x+P_y)^2} \frac{P_y}{x}$.

If these elasticities are evaluated at $P_x=P_y=p$, then for any value of x, you have the same elasticities.


Questions of the type "What do you think other people would think?" For a study in the adoption of new technology, a student and I are developing a questionnaire that will poll domain experts on their opinions of what their colleagues would think about benefits/drawbacks of adopting a particular technology. This is research in social science/business but not strictly game theory, and as we are not economists, we don't know the literature.

Have economists/game theorists investigated questions of the type What do you think other people would think? If several experts can, say, draw technology acceptance distribution functions that reflect their own beliefs about the community's attitude toward a particular strength or weakness of a new technology, then the geometrical average of those distribution functions could be a starting point for inquiry into ranking the relative importance of a set of several strengths and weaknesses. Has this been done before? By whom?

We are not asking for a tutorial here, just a pointer to where should we should start looking for prior art.

Full disclosure: I asked this question on SE/Psychology and Neuroscience and did not receive meaningful answers.

Epistemic game theory would be the closest (sub-)field that deals with questions involving higher order beliefs among interacting agents.

The introductory article by Dekel and Siniscalchi is a good entry point to the literature. From its introduction:

  Epistemic game theory formalizes assumptions about rationality and mutual beliefs in a formal language, then studies their behavioral implications in games. Specifically, it asks: what do different notions of rationality and different assumptions about what players believe about ... what others believe about the rationality of players imply regarding play in a game?

"Epistemic Foundations of Game Theory" on the Stanford Encyclopedia of Philosophy has a less technical introduction.

There is also a strand of literature in behavioral economics that studies cognitive hierarchies. The theories there are developed mostly to explain behaviors in the lab settings. Crawford, Costa-Gomes, and Iriberri (2013) provide a good summary.


Reverse of broken window fallacy for file sharing/piracy Adult Swim roughly brings forward the following argument in the video 'film piracy feeds babies':

  While jobs may be lost in the movie or music industry, they might be created in another. Money that a pirate doesn’t spend on movies and songs is almost certain to be spent elsewhere. Let’s say it gets spent on skateboards — the same dollar lost by Sony Pictures may be gained by Alien Workshop, a company that makes skateboards. - Source

Is this the opposite of the broken window fallacy?

If so, is it correct or still a fallacy (much like survivorship bias and its reverse)?
If not...is it right or wrong? (I guess its relationship to the broken window fallacy doesn't affect my second question)

I discovered such from answer in related question.

If I understand correctly, the claim is is:

  Proposition: Take a budget as given, and consider a world with two goods, $A$ and $B$. In the first scenario, the price of $A$ is positive, and the household spends $E_A$ on $A$, and nothing on $B$. In a second scenario, the price of $A$ is zero.The household will now spend the same amount $E_A$ on $B$.

How did this abstraction work? A represents the copyrighted work, B contains all other consumption goods. I don't think there is strong empirical evidence for or against the claim. So then, what does the theory say?

Neoclassical Theory

The rational agent under a general class of preferences does first decide his optimal consumption level given (permanent) income, and then decides how to allocate that consumption expenditure between different goods. For him, the answer would be Yes.

Caveats

However, what happens if we depart from the rationality assumption? Many weird things can happen. For example, instead of optimally choosing how much to save, the consumer could first decide, what he wants to consume, and then save the remainder. In this case, since he already has A "for free" he might be contempt with that, think that "having some B" is sufficient, and then save the remainder. In that case, it may very well be that the answer is No (or at least, not necessarily). Not all the money not spend on copyrighted material will be used for consumption on other goods.

There are many reasons to believe why the rationality assumption is not always giving us the full story, especially when you look at life-cycle consumption, saving rates and divergence of savings at retirement ages.


Confounding versus endogenous variables. What is their relative hierarchical position? There are valuable resources on the lexicon of types of variables quickly accessible, such as here. However, some of these concepts appear side-by-side often enough to make them confusing.

For example, Wikipedia mentions two causes for endogeneity:

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

This is in line with the Encyclopedia of Health Economics formulation

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

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

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

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

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

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

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

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

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

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

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

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

  ...

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

QUESTION:

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

The question is not totally clear, but I will attempt to give you some guidance.

To answer your first questions, confounding variables are not a type of endogenous variable. We do not observe nor are we interested in the confounding variables, which means they are not endogenous variables in our model.

You later give the correct definition of an endogenous variable "An explanatory variable in a multiple regression model that is correlated with the error term". Hence, there can be several reasons why a variable would be endogenous, but they all have to do with correlation with the error term.

An endogenous variable is one, which cannot have a causal interpretation in a regression model. When something leads to a variable being endogenous, we call this a source of endogeneity.

As you mention, an important source of endogeneity are omitted variables. If we omit a variable, which affects the outcome variable, then the omitted variable is captured by the error term in our model. If the omitted variable is correlated with an explanatory variable, then that explanatory variable becomes endogenous, because it is now correlated with the error term.

Other important sources of endogeneity are reverse causality and simultaneity, as you mention. For reverse causality, we have that the explanatory variabe is supposed to influence the outcome variable, but if the outcome variable also affects the explanatory variable, then in our regression model, this latter channel is necessarily captured by the error term. This is because such a channel determines the relationship between the outcome and explanatory variable, but we cannot capture it in any variable. Putting the explanatory variable on the left side instead and using the outcome variable as an explanatory variable does not help either, because we then have the same problem. Then the explanatory variable is correlated with the error term, which makes the explanatory variable endogenous.

So overlapping features are that all sources of endogeneity stem from a correlation of an explanatory variable with the error term. Distinctions are the source of this correlation and consequently how to deal with it. For example, omitted variable bias may be dealt with by observing and adding the omitted variable to the regression. This strategy does not work when trying to address reverse causality.


Is a strong foundation in advanced microeconomic theory essential to study environmental economics at the graduate level? Advanced theory of individual economic behaviour in production, consumption, and general equilibrium. Are these topics useful to study environmental economics a the graduate level, or is there not a lot of overlap?

It depends on what you like to do in environmental economics. There are lots of people who are working on moral hazard issues on environmental economics by principal-agent models.

More specifically, an interesting question arises from non-point source pollution. Let's say farmers are using pesticides which cause pollution. Probably, you don't know specifically which of farmers are responsible. How could you create "incentives" in order to avoid this situation(pollution) ?
You can look at the Segerson (1988), published in Journal of Environmental Economics and Management in order to understand this issue more precisely.

Another field could be about social choice theory (and decision theory) in environmental economics, especially on equity between individuals and generations. These issues can be included in microeconomics but more in applied math as they use topology etc. (Geir Asheim, Stéphane Zuber's papers could be interesing for this subject.)

Just to finish, I think there are more things to do in environmental economics at a macroeconomic level. (Note that my opinion could be biased as I am working at macro level.)


How many Nash equilibria are there in the above game? 5 people are eyewitnesses to a criminal incident. Each one of them wants the police to get informed but they prefer a third person to give the information.
Suppose k is one of the 5 people.
If the police receive information from the person l≠k, the utility of k will be equal with v.
If the police receive information from the person k, its utility will be equal with v-c, where v>c.
If the police don’t receive information, the utility of k will be 0.
How many Nash equilibria are there in the above game?

There can't be an equilibrium in which no one tells the police. In that case, it is a profitable deviation to tell since $v-c>0$.
There can't be an equilibrium in which more than one player tells the police. In that case, it is a profitable deviation for one of them to remain silent since $v>v-c$.
There are five pure strategy Nash equilibria in which only one player talks. This one player would be worse off by remaining silent, $0<v-c$, and the silent players would be worse off by telling, $v-c<v$.
Next, you consider mixed strategies. For the same reason as above, there is no equilibrium in which one or more players alway talk and others mix between talking and silence as pure silence is better given someone talks to the police for sure. Similarly, there is no equilibrium in which only one player randomizes and all others remain silent, as this one player would not be indifferent between both actions, talking is always better given the others don't.
There are equilibria in which two players randomize and the others are silent. Wlog, suppose player 1 and 2 talk with probabilities $p$ and $q$, respectively. For each player, talking always gives payoff $v-c$. Both players must be indifferent (otherwise they would not want to randomize). Hence,
$v-c = p v + (1-p)0 = q v + (1-q)0$ which we can solve for $p=q=\frac{v-c}{v}$. Given this indifference condition, it must also be a best response for player 3,4,5 to remain silent. This is true as $v-c\leq p^2 v + 2p(1-p)v$, because $v-c=pv<(p^2+2p(1-p))v$ and $p<(p^2+2p(1-p))$ for any $p\in(0,1)$. There are $\binom{5}{2}=10$ such equilibria.
Similarly, there should be $\binom{5}{3}=10$ and $\binom{5}{4}=5$ equilibria in which 3 and 4 players talk and the others are silent, and one equilibrium in which all five players randomize over both options with some probability $z$ solving $v-c=(1-(1-z)^4)v$.
All in all, there should be $5+10+10+5+1=31$ Nash equilibia.


Current status and trends in the choice of software for teaching econometrics My institution is updating some of its bachelor and master study programs in economics and business administration, and the question of choice of software for econometrics and related classes has come up. I wonder what the leading institutions are using and where the field is headed. Hence my questions:

What software is currently most used for teaching econometrics and related subjects in leading study programs of economics (bachelor and master, or undergraduate and graduate)?
What software is currently most used for teaching econometrics and related subjects in leading study programs of business administration (bachelor and master, or undergraduate and graduate)?
Are there any pronounced tendencies of an ongoing switch to another software or a switch to take place in the near future (say, during 2020-2025)?

The question is intended to be objective. It does not ask for opinions on your favorite software (though I would not mind hearing some core points on that as long as they contribute to choosing an appropriate software for our study programs).
Edit (after the bounty was added): Please try to make the answer specific by including

the year to which your knowledge refers;
study program: economics, business, ...;
type of institution/deparment: university vs. something else, economics department vs. business school vs. ...;
tier: R1, R2 etc. or similar
country;
level: undergraduate/graduate or bachelor/master/Ph.D.;
course: econometrics or some other (in case you may wish to share your experience in a related but different course).

In 2008 the American Economic Association (AEA) created a reproducible research requirement about posting the code and the data for their papers. According to analysis done by the AEA Data Editor Vilhuber, Turrito, and Welch (2020), Stata and Matlab were by far the most dominant software used in these submissions (see figure below, the raw data are here). Given the elite status of this family of journals in the profession, I think this is a reasonable proxy for the software used by elite economists and therefore in elite economics PhD training programs. For what it is worth, Stata and Matlab (and in that order) were also the software I was trained to use in my PhD econometrics classes and my work for my economics PhD, about ten years ago, at an R1 school in the USA. The only exception was my Bayesian econometrics class which I believe used R. As an undergraduate (also at a R1 school in the USA), I used Eviews in my econometrics classes and R in my probability and statistics classes.


Convenient S-shaped production function (i.e. with IRS and DRS) to derive a discontinuous demand for labor Let say that a firm produces a commodity using only one input (i.e. Labor if we suppose to be in the very short run). Then we have a general production function of the following form $y=f(L)$, for $L≥0$, be the output obtained when $L$ units of Labor are employed.

We further assume that the first derivative (i.e. firm’s marginal product) is always $>0$, but ( assuming that f is twice differentiable), $f''(L)≥0$ in $[0,c]$, and $f''(L)≤0$ in $[c,∞)$. Hence, $f(L)$ is first convex and then concave, with $c$ as an inflection point.

When this is the case, contrary to the standard case of a concave production technology (with $f''(L)$ always $<0$), firms do not always make profits if they follow the standard rule for profit maximization (i.e. $\frac{dF(L)}{dL}=w$). Indeed, with IR, there are real wage levels that equal marginal returns for which labor costs exceed revenues. The value of output is less than labor costs for all employment levels lower than a critical employment level (let say $Lc$), that is the level where average productivity maximizes, or, where marginal productivity equals average productivity. For this reason the curve for demand of labor is first decreasing and then at a certain point falls to zero.

What can be a specific functional form suitable to represent this situation and that allows me to derive a curve of demand for work by firms with these characteristics?

I'm not sure but it seems to me that the logistic function $\frac{e^{x}}{1+e^{x}}$ could serve your purpose.

You may need to scale it as its output falls between 0 and 1, but it does have an analytical derivative that you can then use to solve for the labour demand function.


What's an example of a resource, raw material that has become scarce? I'm interested in the elasticity price demand that predicts that as a resource becomes more scarce, it gets more expensive.

Regarding oil price this isn't clear. Is there an example of a resource that has nearly disappeared ? What was the evolution of its price ?

Some examples you might consider:

Fine art when the artist dies (this doesn't reduce the number of works by that artist, but does reduce the number of works that can be expected to exist in the future)
The electromagnetic spectrum - there are a bunch of interesting resources concerning auctions for space on the spectrum
Short .com domain names


Is Foreign investment positive or negative for a country? When a state company is sold to foreigners in a country, people who live in that country generally do not like it. Because the company is sold to foreigners. People are acting with a sense of nationalism.

On the other side if there is an economic crisis or economic recession in that country, foreign investment is needed and the money is very important for the development of the country.

How foreign investment can be interpreted for a country? Is Foreign investment good or bad for a country?

From a purely economic perspective, it doesn't make sense to feel resentful when a national company is sold to foreigners. Imagine a company in my country is sold to a German investor. This shouldn't be a problem, as from the sale price my country could go to Germany and buy a German company instead. So it's all fair game.

However, some countries are growing in influence relative to others. For example, China is growing in influence and economic power relative to the rest of the world. When Chinese companies buy European companies, this is a very obvious sign of that growing influence and this is one reason it raises concerns in the countries that are being targeted. It is hard to accept that one's country might be losing in relative influence.

From a strategic point of view, it might make sense to try and protect national companies from foreign buyers. If the Chinese buy a German company, they might get access to new technology, which can help them develop their own industries. This can lead to increased competition for the German industry. By protecting national companies and proprietary technologies, Germany can limit competition and stay more competitive on the world stage.

The above discussion covers the buying and selling of existing assets, which is usually more controversial. Foreign investment in greenfield projects (when a foreign company builds a completely new factory) is generally considered positive for the national economy as it creates jobs and generates additional tax revenue for the government.


How does Net Foreign Assets (NFA) differ from Net Foreign Investment (NCO)? How does Net Foreign Assets (NFA) differ from Net Foreign Investment (NCO)? Yes, the former counts assets, and the latter counts investment, but I can't quite wrap my head around the difference.

One is a stock another is a flow.
Net Foreign Assets are:

Net foreign assets (NFA) determines whether a country is a creditor or debtor nation by measuring the difference in its external assets and liabilities. Net foreign assets (NFA) refer to the value of overseas assets owned by a nation, minus the value of its domestic assets that are owned by foreigners, adjusted for changes in valuation and exchange rates.

Net Foreign Investment is:

Foreign investment involves capital flows from one country to another, granting the foreign investors extensive ownership stakes in domestic companies and assets.


backshift operator in time series confusion Hi All: In time series econometrics, if one has a relationship say

$y_{t} = \frac{x_{t}}{1- \rho L} + \epsilon_{t} $ where L is the backshift operator, then the expression can be re-written as the following infinite series:

$y_{t} = \sum_{i=0}^{\infty} \rho^{i} x_{t-i} + \epsilon_{t}$.

But, what is the expression ( and can it be derived easily ) when the original expression is

$y_{t} = \frac{x_{t}}{1- \rho (L)^{k}}$ where $k is some positive integer greater than 1. Just to be clear, since this is coming out so small when I look at it, the rho is not raised to k but the backshift operator is.

Thanks for the wisdom.  Also, if it's too complicated  or too long to explain, then any reference that explains it is appreciated.

From your last comment it seems that you might have already figured out how to proceed, although I'm not following some of your reasoning. I just want to point out that there is no need to initialize $y_0$.

The absolute value of ρ is typically assumed to be lower than 1 (otherwise, the series would be "explosive"). Because of that, the terms $ρ^ny_{t-n*k}$ and $ρ^nϵ_{t-n*k}$ will be zero when taking the limit of $n->∞$ in the expansion of $y_t$.

The expression for $y_t$ is
$$ y_t= ∑_{i=0}^{∞}  ρ^ix_{t−i*k}+ϵ_t.$$

This means that the effect of $ρL^k$ is to model $y_t$ from $x_t$, $x_{t-k}$, $x_{t-2k}$, $x_{t-3k}$, and so forth. $k=1$ is just a special case of this expression.

I feel too lazy to plug my scanner and scan my derivation right now, but I'll do so if you really want to see it.

Edited to add scan and explanation of the derivation

Here's a walk-through of the derivation. Hope my handwriting is legible enough; if not, it's the scanner's fault.

(1) shows the equivalent way of writing $y_t$ by applying the
backshift operator $L^k$ (of course, after multiplying everything by $1-ρL^k$ ).
(2) and (3) apply the backshift operator to $y_{t-k}$ and
$y_{t-2*k}$, since each one appears in each one's preceding equation.
(4) substitutes in (1) the expressions obtained from (2) and (3).
Multiplications by ρ are developed in (5). Notice the resulting pairs of
(underlined) terms offsetting each other.
(6) is (5) after removing the underlined/offsetting terms.
The pattern is discernible from (6) and expressed in (7) for $n$.
(8) is (7) but with summation notation for the terms involving $x$.
(9) is the limit of (8) when $n$ tends to infinity. There, the
assumption of |ρ|<1 is essential for convergence of the summation
(as justified in the 2nd paragraph I wrote this morning).

Since $|ρ|<1$, then $|ρ^n|<<1$ for sufficient large $n$. Therefore, the term $ρ^ny_{t-nk}$ in (8) will tend to zero regardless of the value of $y_0$. In other words, the influence of $y_0$ on $y_t$ decreases as $t$ departs from 0.


Why economic rent does not exist in perfect competition My question is from production side. Firms which are using better resources will have low cost curves than other firms and earn more profits. To ensure the supply of these effecient resources firms have to pay more than transfer prices and this difference is economic rent. So, their whole profit is used as these economic rent and their average cost is same as theother firms which are not using better resources.

Is this type of situation possible in perefect competition?

Panel(a) are the firms using efficient resources.

Suppose the competitive price is P. If you quote at a a higher price Ph2>P, then someone else, say firm 2, will quote at a slightly lower price than you, say Ph2, and Ph1>Ph2>P. Since competition is perfect, firm 2 will capture all the market and you will go bankrupt. But firm 3 may put price Ph3 such that Ph2>Ph3>P and capture all the market. This process can be repeated until the equilibrium price is reached.

On the other hand, if you place a price that is below the competitive price, you will go bankrupt.

Hence, there is no economic rent because all firms in the competitive equilibrium will choose the equilibrium price which gives them an economic profit(rent) of zero.


In perfect competition, why is there economic loss if marginal cost > marginal revenue? Here's a graph for reference:

In the left graph, I read from a book (CFA L1 notes) that

  At any output above the quantity where $MR = MC$, the firm will be generating losses on its marginal production and will maximize profits by reducing output to where $MR = MC$."

But now consider this:

$Q'$ is an output level above the one at which $MC=MR$. Shouldn't the yellow region represent a positive economic profit in this case? I can understand that at any output level above the one at which $ATC=MR$, the firm would start making losses. But isn't the quote above incorrect, or am I missing something? Sure, you might be making a suboptimal profit at output $= Q’$, but you’re certainly not making an outright loss.

There is no loss at Q' and you are indeed right that the yellow area represents the firm profits. However, if you were to compare the yellow area to the blue area you would find that the latter is greater. So profit for the firm is not optimal at Q' but is optimal at Q*. This is what the quote refers to, it says the firm will be generating losses on its marginal production (so on the quantity Q' - Q*). It does not say that the firm will generate losses on production in general. This will only happen beyond MR=ATC or TC=TR


How to interpret fixed effects? I want to interpret the output of a fixed effects regression and need help with interpreting the country-fixed effects.
The regression is the following:
pm.alldata <- pdata.frame(alldata , index = c("country", "year") )
a.fixedtwo <- plm(log(production) ~ log(temp) + log(rain) + drought + flood + storm + log(labour) + log(fertilizer) +log(capital) +log(area) , data = pm.alldata, model = "within", effect = "twoways")

The dependent variable is agricultural production. I want to look at how temperature and precipitation affect agricultural production (although this is rather irrelevant to the question I have). The country fixed effects refer to 28 countries. The county-fixed effects are as follows:
As I understand it, we can say that country 5 (Ecuador) has an unobservable negative effect (-5,99469) on agricultural production. Am I right?
Now I come to my main question:
I have divided these 28 countries into two subgroups (poor and rich countries).
If I regress only the 14 poor countries, the coefficients of the country-fixed effects change to the following:

Now the effect of country 5 (Ecuador) is suddenly positive (7.5768). This would mean that Ecuador has positive unobservable effects on agricultural production. Is it normal for the signs to change when this is subdivided into a subgroup?Which of the two values of Ecuador should I use for interpretation when comparing the value of Ecuador with the value of a rich country (e.g. Argentina)?

Fixed effects model is estimated as:
$$   y_{i t} − \bar{y_i} = ( X_{i t} − \bar{X_i} ) \beta + ( \alpha_i − \bar{\alpha_i} ) + ( u_{it} − \bar{u_i} )$$
So the country fixed effect is always relative to the average fixed effect.
If a country has negative fixed effect that means it is less productive than average country in your sample. If you choose different sample results might change.


Chinese tarriffs (pre-tradewar) I am trying to understand to what degree tariffs (or other restrictions like quotas) were the cause of the trade imbalances between the US and China. One might imagine that it was simply a matter of the Chinese making goods more efficiently... So what exactly were (pre-Trump) the level of tariffs (or other restrictions) in US-China trade? Were they actually asymmetric?

EDIT: I found a page about quotas by country on Wikipedia here. It suggests that typical Chinese import tariffs are 7.5% and those in the US are 1.66% - that doesn't feel like enough of an asymmetry to explain the massive trade imbalance... maybe there are some legal or quota issues I have yet to discover...

First a disclaimer: Trade imbalances are something that we should expect to happen, especially between two massive economies like the US and China. In fact, it will probably be very hard to find a pair of countries that don't have a trade imbalance (unless they don't trade at all).

This does not mean that there is something wrong necessarily, however, a lot of the discussion seems to think that tariffs are solving a problem or making it worse when trade balances are not necessarily positive or negative.

Now, more directly to your point, the trade balance depends on many things. To list a few: the economic growth of both countries, their relative efficiency on tradable goods, the terms of trade, the relative exchange rates, and whether they are controlled or not, the tariffs or restrictions to trade, the relative purchasing power, the real interest rates in each country, etc. I think that the US and China are very different countries, so it will be quite heroic to try to explain everything with a single variable like tariffs. The trade imbalance is certainly  the result of multiple economic conditions.

Sure enough, if you want to reduce how much you import from a country, tariffs will help, but the real question is why would you want to do this?


What is the graphic intuition behind Marginal rate of subsitution So I think I understand the math, but I don't understand the intuition on a 3d graph. Why does the ratio of partial derivatives give us a tangent line on a level curve(indifference curve)? My understanding is  $\frac{\partial U(x_1,x_2)}{\partial x_1}$ Will give a tangent line parallel to the $U(x_1,x_2), x_1$ plane and $\frac{\partial U(x_1,x_2)}{\partial x_2}$ Will give a tangent line parallel to the $U(x_1,x_2), x_2$ plane. So why does dividing them end up with a tangent line parallel to the $(x_1, x_2)$ plane?

This isn't a perfect answer to your question, but I tend to show all my students pages 1-4 of Dixit's Optimization book. It describes exactly what the MRS is doing and why it must be tangent to the budget constraint.

https://www.scribd.com/document/390573490/Dixit-Optimization-in-Economic-Theory-pdf (pages 1-3 here unless you sign in)


What is the wealth of a company? I would like to better understand what is the wealth of a company and what is made of.

Is the wealth of a company similar to GDP of country, like a "gross company product" ?

As example: can we say GDP as total market value of good a services produced by a country in a certain amount of time, and wealth of a company is the market value of assets and services produced in a certain amount of time?

Could the two measures be compared ?
Or is the market value of a company conceptually a different thing than a "gross company product" ?

The "wealth" of a company is not a well-defined term. The worth of a company, its market value, is whatever someone is willing to pay for it. The market's best guess of that value, for listed companies, is equal to the share price multiplied by the number of shares in circulation. In theory, for both listed and unlisted companies, the worth of a company is equal to the sum of of all discounted future cashflows arising from the company.

As such, it is a stock variable, not a flow variable.

Conversely, the GDP of the country is a flow variable, not a stock variable. It's the total value of transactions in the economy in a year; as such, it's somewhat analagous to a company's turnover.


How to integrate a piece-wise function and what are semicolons in function notation? I'm trying to get the cdf from a pdf, which, according to this MIT open courseware video, is as simple as getting integral from -$\infty$ to $\infty$. Like this:

$$
F_z(z) = \int_{-\infty}^\infty f_z(z)dz\, = 1
$$

And that works for functions like this: $f_x(X)$

But what about a function like this $f(X;\beta)$?

Yeah, this is a homework problem, so I don't expect an exact answer, but hopefully some general principles. I have a hard time googling to learn how to do this because I don't know what to call this kind of function $f(X;\beta)$, and I don't know how to type a $\beta$ into google.

The pdf I have is:

$$
f(X;\beta)=
    \begin{cases}
      \frac {e^{-X/\beta}}{\beta}, & \ X\geq0 \\
      0, & \text{otherwise}
    \end{cases}
$$

and the cdf it comes out to is:
$$
f(X;\theta)=1-e^{-X/\beta}
$$

Part of my question is also, why did the $f(X;\beta)$ become $f(X;\theta)$?

CDF = integral of PDF from $-\infty$ to $x$, or:

$F\left(x\right) = \int_{-\infty}^{x} f\left(u\right) du$.

Functions like $f\left(x;\beta\right)$ take $\beta$ as the parameters, the $\beta$ index different probability density functions.  You don't need to integrate over them to get the CDF.

$F\left(x;\beta\right) = \int_{-\infty}^{x} f\left(u;\beta\right)du$.


What is the opportunity cost of going to a football match? According to this video:

Opportunity Cost of a choice is what you gave up to get it.

Now, let us read the following question:

You are going to a football match next Saturday evening, you have already bought the tickets and cannot resell it. You have just learned that on this Saturday evening, there is also a rock concert that you are interested in. The ticket for the concert costs 40\$ but you value this concert as much as 50\$.
What is the opportunity cost of going to a football match?
a) price of football match’s ticket
b) 40\$
c) 50\$
d) 10\$

My answer was (c). Coz, I gave up the concert which costs 50\$.
However, my teacher says that the correct answer is (d).  Why?

Note that the opportunity cost is what you gave up to get it, not necessarily the price of what you gave up to get it. Your opportunity cost is not what you perceive as the value of the rock concert since you haven’t even bought the tickets to the concert yet.
If you had bought the tickets to the rock concert already, then the opportunity cost of going to the football game would be $50 since that’s the value you placed on the concert and you’ve already bought the tickets.
But in this case, you haven’t purchased the tickets yet so your opportunity cost should be 10 dollars since that is the net gain of that activity: the tickets cost 40 dollars, you value them at $50. You can kind of picture opportunity cost as potential profit. Your ‘potential profit’ of the concert is 10 dollars since the value you think it’s worth outweighs the cost by 10 dollars.
tl;dr
You haven’t bought the tickets to the rock concert yet so you have to account for the cost of the tickets as well.


McCloskey's example of fungibility in basketball To illustrate the concept of fungibility, Deirdre McCloskey (1985, p. 7, PDF) gives an example from basketball.

She claims that the last two points scored are no more important than any two points scored earlier:

  The University of Iowa beats the University of Michigan for the Big
  Ten basketball championship by two points in double overtime, 70 to
  68. Whose two points won the game? One's first thought is to look to the last points made. But points are fungible. Any two points can be
  viewed as the crucial points that make the difference between a score
  of 68 to 68 and 70 to 68. The shot that Weisskoff made in the first 5
  minutes of play counts as much as the last. For the purpose of making
  the score what it is, there is effectively no last, no crucial, point.

Is this analysis correct? And if not, in what sense are the last two points more important than any two points scored earlier?

Two examples to illustrate the connection here to economics:

Example 1. Two politicians A and B are running for village mayor. The electoral process in this village is unusual — the two politicians have 12 hours to take turns going door-to-door soliciting votes. The end result is that politician A beats politician B by 35 votes to 34.

Question: Is the first vote scooped up by politician A just as important as the last vote?

Example 2. Two Girl Scouts C and D go door-to-door trying to sell boxes of Girl Scout cookies. The Girl Scout who sells the most wins Girl Scout of the Month. The final score is 35 to 34, with Girl Scout C winning by one box.

Question: Is the first box sold by Girl Scout C just as important as the last box sold?

In economics and finance, fungibility means that we cannot distinguish between instruments. For example, we normally do not care whether we have one \$20 bill or two \$10 bills.

McCloskey's example is poor. In one sense, it is correct: when points are scored do not matter in the final tally. However, it is psychologically incorrect when applied to sports.

For example, in ice hockey, it is somewhat common to pull your goalie if you are behind at the very end of the game. You have a slightly greater chance of scoring since you have an extra attacker, but it is very easy for the other team to score if they get control of the puck. If you were leading 1-0, and then scored a second goal because the other team pulled their goalie, no sensible hockey fan would weigh the second goal as much as the first. The game was already effectively won by the earlier goal, and the second was just a statistic.

More generally, a team's effort during the game probably reflects the score. Piling up points early may be dangerous, as the team will then relax and sit on its lead. Therefore, later points are effectively more valuable. In order for McCloskey to be correct, we have to believe that the score of the game does not influence behaviour.

These problems do not crop up when using \$10 bills in your example.


Violation of completeness axiom (simple everyday examples) Simple everyday examples of violations of transitivity are not difficult to come up with, but I'm having trouble thinking of some for the completeness axiom.
One possible formulation of the completeness axiom in plain English:

Given any two alternatives A and B, exactly one of the following is true: (1) I strictly prefer A to B; (2) I strictly prefer B to A; (3) I am indifferent between A and B.

One example that I was hoping could work (but didn't) came from the book/movie Sophie's Choice, where Sophie is made to choose between the following two alternatives:

A: Send her son to the gas chambers (and her daughter to the children's camp).
B: Send her daughter to the gas chambers (and her son to the children's camp).

She is initially very reluctant to express a preference for either alternative. So one possible interpretation is that she is exactly indifferent between A and B. Another is that she does not obey the completeness axiom.
However, she is then pressed further and told that if she doesn't choose, she'll simply be given alternative C: "Send both children to the gas chambers."
Faced with this alternative C that is clearly inferior to both alternatives A and B, she then does indeed choose one of the alternatives (B: Send her daughter to the gas chambers), hence strongly suggesting that she does indeed obey the completeness axiom.
The above is of course merely my interpretation of the story in Sophie's Choice. Maybe someone can give an alternative interpretation where the above turns out to be an example of the completeness axiom being violated.
(One possibility might be along these lines: Sophie's preference relation is incomplete over {A,B}. When faced only with A and B, she doesn't prefer A to B, doesn't prefer B to A, and isn't indifferent between A and B. However, when given an additional option C that is vastly inferior to A or B and which she must default to in the absence of a choice, she now prefers B to A.)

For those who seem to believe the completeness axiom is inviolable and are  unaware that "within economic theory, criticism of the axioms of transitivity and completeness have quite a long history" (Putnam, 2002, p. 163), please see the following three examples of economists criticizing the axiom of completeness:
Von Neumann and Morgenstern (1953, Theory of Games and Economic Behavior, 3rd edition, p. 630):

The axiom (3:A)—or, more specifically, (3:A:a)—expresses the completeness of the ordering of all utilities, i.e. the completeness of the individual's system of preferences. It is very dubious, whether the idealization of reality which treats this postulate as a valid one, is appropriate or even convenient.

Aumann (1962, p. 446):

Of all the axioms of utility theory, the completeness axiom is perhaps the
most questionable. Like others of the axioms, it is inaccurate as a description of real life; but unlike them, we find it hard to accept even from the normative viewpoint.

Anand (1987, p. 190):

Whilst completeness is one of the first assumptions used in any" formal"
theory of rational choice, it is probably less acceptable as an axiom of
rationality than either transitivity or independence.

There is a problem in how you translate completeness into behavior. Let $R$ be any binary relation, representing preferences, on a set $X$ of alternatives and $A\subseteq X$ be a nonempty set of alternatives available. The usual assumption is that the decisionmaker chooses an alternative $a\in A$ optimally according to the relation $R$. Here are three ways to interpret this:

$a R b$ for all $b\in A$.
$b R a$ for no $b\in A$.
$b R a$ implies $a Rb$ for all $b\in A$.

One usually uses 1. for weak (reflexive) preference relations, 2. for strict (irreflexive) preference relations, and 3. works in both cases. If we define $R'$ by $xR'y$ iff $\neg(yRx)\vee(xRy)$, then $R'$ is complete and satisfies 1. iff $R$ satisfies 3. If $R$ is irreflexive, $R'$ satisfies 1. iff $R$ satisfies 2. So completeness in itself has no behavioral implications from this perspective. It can interact with other properties. For example, transitive and complete is more restrictive than transitivity alone- completeness forces transitive to be applicable to more comparisons.

Now one can try to make a distinction between indifference and incomparability. But such a distinction necessarily uses a different framework than the usual maximization paradigm.


Proof of Expected utility theorem with three outcomes I am trying to prove the expected utility theorem with three outcomes. The expected utility with $n$ outcomes is rather cumbersome and long in the economics textbook Mas-Colell. But I was hoping that the proof with three outcomes is shorter, however, I am having some difficulty proving it.

Suppose I have three lotteries $x \succeq   y \succeq   z$. We can think of $x$ as the "best" lottery and $z$ as the "worst". The can set  $u(x)=1$ and $u(z)=0$ and then $u(y)=p$ where $p$ is the probability at which a gamble with a $p$ chance of $x$ and a $1-p$ chance of $z$ is indifferent to $y$.

How do I proceed from here to prove the Expected utility theorem?

For $n$ outcomes, the EU states that given $\succeq $ satisfies independence and continuity axioms, there is a utility function $ u:Z\rightarrow \mathbb{R}$ such that if $$p\succeq q\Leftrightarrow \sum_{i=1}^{n}p_{i}u(z_{i})\geq \sum_{i=1}^{n}q_{i}u(z_{i}).$$

Edit: Letting $u(x)= 1$ and $u(z) = 0$ linearly scales the utility function.
So we want to show $$u(y) = u\left ( px + (1-p)z \right ) = pu(x) + (1-p)u(z) = p \text{ by the independence axiom}.$$

Since we have assumed $x \succeq  y \succeq  z$ then it follows that $u(x) \geq u(y) \geq u(z)$, where $p \in [0,1]$. Does this make sense?

I am not sure about the part: $u\left ( px + (1-p)z \right ) = pu(x) + (1-p)u(z)$. Is this a legitimate way of writing the proof for the case of three outcomes?

In order to do that, you need to define $u(·)$ as a utility function on "sure things" rather than on lotteries. In your example, you need to think in terms of the set of possible prizes to the lotteries. Say the set of possible prizes is given by $R$ and asume that is finite. For any $r\in R$, define $w_r$ as a lottery that pays $r$ in every state of nature. Then, it should be clear that

$$x \sim \sum_i p_i w_i,$$

(and similarly for $y$ and $z$) where $p_i$ denotes the probability of state $i.$ Given that, as you mention, it must be the case that two equally desirable lotteries receive the same expected utility, the utility assigned to $x$ needs to be

$$H(x)=H\left(\sum_i p_i w_i\right).$$

The first chapter of Huang, C. and Litzenberger, R.H. Foundations for Financial Economics, North Holland, 1988 explains in detail why the function representing the preferences $(H(·))$ has to be linear, and, with linearity stablished, you get the expected utility representation because

$$H\left(\sum_i p_i w_i\right)=\sum_i p_i H(w_i).$$

The only thing left is to define $u(r) \equiv H(w_r),$ i.e, $u(r)$ is defined on outcomes, while $H(w_r)$ is defined on lotteries. This is why we say that $u(r)$ is a utility function on sure things, because $r$ receives the same utility level that a lottery paying precisely $r$ in every state of nature.

Of course, expected utility is most useful in settings with large outcomes spaces and/or large lotteries spaces. In a restricted setting such as yours, you're probably best served by assigning values ("utilities") to lotteries themselves (as you did in your question). Again, a more rigorous proof can be found in Huang and Litzenberger, op.cit.


How to deal with a singular Leontiev inverted matrix? I am currently studying and experimenting the input-output methodology. It is a 1930's method based on national accountings that allows to measure the interindustry flow of good and services.

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

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

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

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

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

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

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

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

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

I am not sure exactly what you divided by what, but suppose your input-output table looks like this:
$$
A =
\left[
\begin{array}{lll}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{array}
\right]
$$
If you proceed to divide the first column by $\sum\limits_i a_{i,1}$ the second by $\sum\limits_i a_{i,2}$ and the third by $\sum\limits_i a_{i,3}$ then your new matrix will have 1 as an eigenvalue. (You can show this by showing that the norm of any vector is unchanging upon multiplication with the matrix by straightforward calculation.) This is problematic, because if $s$ is an eigenvector then
$$
A \cdot s = s = I \cdot s
$$
which implies
$$
(I - A) \cdot s = 0
$$
which in turn implies that $I - A$ is not invertible (singular). So my guess would be that the problem is the division.

I thought (incorrectly, see comment below) that input-output models usually deal in physical goods, not the value of physical goods, so the unit of measurement for $a_{11}$ would not be euros by say liters (of milk). In this case you would not have to divide the value of individual inputs by the sum of the value, but the number of goods used in the individual inputs by the total output of a good. This may make your problem go away.


Fractional reserve banking and the value of someone else's currency Suppose there are two countries: $A$ and $B$. $A$ is a large, stable, democratic country with its own currency, the dollar. $B$ does not have its own currency. All prices and financial transactions in $B$ use the dollar and $B$'s citizens have a positive quantity of dollars that they hold domestically.

Country $B$ has a monopoly retail bank that is required to hold 5% of the value of its deposits as reserves in the safe keeping of an independent central bank, also located and controlled within $B$.

My question is: does this suffice for the bank in country $B$ to practice fractional reserve banking? If so, am I correct in thinking that the bank in country $B$ is exerting an externality on the people of country $A$ by devaluing their currency every time it creates a new loan? Is there anything that $A$ can do to prevent this?

When the retail bank in country B multiplies the money supply, it does so by creating an asset (money owed by the borrowers) and a liability (the obligation to honor the loan it gave to the borrowers) on its books, and an asset (money to spend) and a liability (the loan to pay back) on the books of each of the borrowers.

Now, if these borrowers are all spending their money amongst each other, this probably isn't going to be a problem. It by no means affects inflation in country A, because there's no additional demand on country A's resources.

But lets say instead all of the borrowers then go to use this money to import some goods from country A. This will be, on the face of it, inflationary. Suddenly you have all this extra demand, for no additional supply.

One of two things happens:

The borrowers say to country A's exporter, 'I would like to buy some widgets, get the cash from my bank' and exporter (or rather, the exporter's bank, who is based in country A) says to the bank 'Cash please!'. Country B's bank doesn't have the cash to honor every loan they've made, so they're unable to honor the payments and the loan they gave the borrowers is essentially worthless. The exporter doesn't send the goods.
The exporter in country A's bank is ok with the promise of payment from the bank in country B. Afterall - there are also exporters in country B selling goods to people in country A, and this will balance out the loan.

In this second scenario - the there is also an increase in supply because country B is also exporting to country A, so it's not necessarily inflationary.

Bottom line: The inflationary effect of multiplying the money supply will be tempered by the bank's ability to honor the loans. A bank can make all the on paper loans it wants, but unless it's able to actually honor them, they are meaningless. In our modern banking system, there's a high degree of trust which means when a bank lends us money, and we see that money in our bank account,  we assume that that money is actually going to be able to buy us goods.


Sanity of lending out made-up money Background
I've done some research to get an understanding into the issue I want to ask about. Regrettably, I found out general descriptions of the mechanism and/or evidently biased explanations, which I've got no means to question. Please excuse me if I refer to a concept in a less than optimal terminology. I'm a bright guy but definitely not a scholar of economics.
Please note that I'm not asking for how fractional banking works in mathematical terms. I'm questioning the sanity of it. Well, not questioning - rather not grasping how it differs from hiding the lack of funds.
The traditional approach
Alice owns X units of currency but doesn't use them. Bob comes by and asks to borrow it for a period of one unit of time. As a reward, he promises to return 5% higher amount. Carol comes by and makes the same request with the difference that he promises 10% return on the investment.
Alice considers the chances of the money being paid back in full including the interest as corresponding to the pay-off (e.g. Bob pays up 1.05 X with the probability of 95% and in any other case he's good for nada, zero, ziltch). Alice regards the offers and realizes that there are three options (partial investment of X units isn't of interests).

Keep the money in the mattress (0 risk, 0% gain).
Present the money to Bob (5% risk, 5% gain).
Present the money to Carol (10% risk, 10% gain).

Here, Alice might ask himself if the inflation forces him to invest into anything, if there's any slightest difference in correlation (5% gain but 5.01% risk) etc. But that's not the aim of the question.
The mechanics of the above is obvious to me. The bigger the risk (time the money invested), the bigger the gain. If at loss, only the amount being risked is lost. I.e. only the money risked to get the gain is being risked to getting lost. This part I view as sane and self-controlled.
The banking approach
Suppose there's this typical bank, Bank of Scandinavia. As far I've understood the regulations, it's allowed to lend more money than it actually possesses, as long as it doesn't go bananas. The government of Scandinavia decided that the bananas level starts at 50%, meaning that if BS owns 10 X units, they can lend out 20 X without being considered unstable.
This part puzzles me, because the gain of the bank is being generated based on equal parts of the money risked to getting lost and some money that doesn't even exists.
It's my understanding that the stimulation of the economy is far greater using this approach. I also hear that the wealth created this way is sustainable, at least if we keep the bananas level fairly modest.
As far my research went to its conclusion (and by that I mean that I got tired of googling and watching suspected cartoons on YouTube claiming to reveal the ugly truth), I've learned that some governments set the bananas level to 10% (meaning that BS could lend out 100 X). In fact, during a period, there was the level of 3% in US and it was frown upon as too restrictive.
Main question
Is it correct to regard the lending set-up as unhealthy, bound to implode and cause mayhem (at an extremely low risk, which in practice guarantees that such won't take place)?
Or is there a regulatory system covering either the tiny-whiney risky part or, alternatively, a means to recreate and pay back the part of the lost money that wasn't really there? Are there other gains to this set-up except boosting the economy (at incrementally larger risk)?

There are two ways I can think of interpreting this question.

My first thought is that a single bank doesn't lend out more money than it has, but the banking system does. So let's say someone deposits 100 dollars in Bank A and the reserve requirement is 10%. Then Bank A can lend out 90 dollars. Let's say that money is deposited in Bank B eventually. That bank can then lend out 81 dollars. This money then gets deposited in Bank C eventually, and it can lend out 72.9 dollars. This process continues, and if you take the sum of all this lending, you get that the money supply is now:

$$\sum_{n=0}^\infty 0.9^n(100) = \frac{100}{0.1} = 1000$$

So the banking system can lend out 1000 dollars without being considered unstable under this 10% reserve requirement. Notice how it kind of looks like we are double counting the money that is in the economy, and that's the point of fractional reserve banking. There isn't actually 1000 dollars, but there is credit worth that much floating around in the system.

The second way you could argue though is that individual banks in fact can lend more money than they have in their account. It creates an electronic record crediting the borrower's deposit with the sum of credit. So here, the limitation is still the reserve requirement. Say Bank A gets a deposit of 100 dollars. It can then lend out 1000 dollars at a 10% reserve requirement. Since it doesn't have 1000 in cash, it gives out credit.

I think that the real economy will use a combination of these two methods to get its lending out, but regardless, the result is the same. A simple money multiplier.

Edit: To reiterate (read: copy-pasted) from the comments below, how can a bank lend out credit that isn't backed up by paper/physical money?

FDIC insurance from the central bank, but more to the point,
The bank isn't going to back up all the credit at the same time. Say in our above scenario (100 dollars, 10% req.) the bank lends out "air money" of 5 dollars to someone, who then spends the credit purchasing from a business. The business then claims on that credit, and the bank still had some reserve (10 dollars in cash) to pay the business. Meanwhile, the bank, because it lent out so much credit, is also collecting a lotttt of interest, and borrowers pay back that interest...in cash. That replenishes the reserve. So in an equilibrium money market, hopefully the rate at which the bank gets cash in interest is the same as the rate which they pay back the "air money" with that actual cash.

Take the car example from in the comments. That is, say you "promise both your friends a car, but you only have one car and both friends know this". Well, the analogy is a little stilted, not quite parallel to what a bank is like. If you were a bank, you would only lend (not give away forever) out the car if you were promised to get it back with some interest, (maybe more gas or something). Problems only happen if both friends want the car the same time.


Can we add well-being into macro model as an endogenous variable? People talk a lot about well-being as an objective of macro policy (together with gdp growth). So if well-being is an objective, i'm wondering if we can add well-being into macro model as an endogenous variable? and we can see the response of this variable to a shock just as we did for other endogenous variables?
Thank you for all your help.

One can model anything, that's why it is a model. The real question is what the value of such a model would be.

More to the point, I think this would be a very hard thing to do sensibly because how are we going to measure well-being? It encompasses way more factors than our economic models typically capture, such as social relations, health and mental state. Even if we include all of those, the relation between all those variables among each other and well-being is often unknown. We could theorize about it, but actually finding out what the relations are would be very hard to do.

For example suppose I model well-being as a combination of health, income and social relationships. That would mean that my macro-economic model would have to contain some kind of measure how social relationships evolve. Moreover, not only are increases in my income going to improve my well-being directly, but it is also going to affect my health (positively up to a point probably) and social relationships (those I guess could go both ways depending on income inequality or the possibility to be generous or visit friends and relatives).

If one really wants to capture well-being there are so many variables affecting that, that the model essentially becomes a black box. We don't know what's driving the results anymore.

What has been done, is trying to measure these things in retrospect. There are various macro-economic/social indicators and indices that try to capture how well-being has evolved over time. These retrospective studies are then used to judge what has gone well and what has not (the latter is also a hard thing to do because we typically have no good counterfactuals)


What Does "Quantity" Represent When Looking at Supply and Demand? There are several possible scenarios involving changes in supply and demand that people are supposed to memorize in AS Economics. For example, when Either Demand OR Supply Move on Their Own:

Rising Demand - Increase in Qty - Increase in Price
Falling Demand - Decrease in Qty - Decrease in Price

While price is pretty self explanatory in every situation, I have yet to fully understand what "Quantity" represents.

What does Quantity mean in these examples?

Does it mean "Equilibrium Quantity"? If so, can somebody please explain how the "Quantity Demanded" and "Quantity Supplied" are related to each other, and how the theory behind quantity as a whole relates to/ties in with each of the examples above?

Each curve simply shows the amount of goods that producers would supply at given prices and how many units of goods consumers would demand at all the different prices. Let's say the price of wooden chairs would be 5 million Euros. Producers would want to supply a large quantity of wooden chairs, since they're so profitable. Consumers would likely demand very little though. However since no one suppliers want to sell more than people want to buy the price will have to change and will not stay there in equilibrium. We only have an equilibrium when all parties agree, otherwise transactions don't take place. That's one intuitive way of thinking about it if it helps you.

The quantity at which suppliers want to supply exactly as much as consumers demand and consumers want to demand exactly as much as suppliers want to supply is given by the intersection of the two graphs. In this case neither party is unhappy with the outcome (both agree on the quantity to buy and sell). This means we are in equilibrium (i.e. no one wnats to change behavior). That one point is the equilibrium quantity.

Note that consumers cannot buy more than producers are willing to sell and vice-versa. If that would be the case, then they would have to change somthing, which means we wouldn't be in equilibrium.

So in short:

The Demand curve shows the quantity demanded.
The Supply curve shows the quantity supplied.
For the two curves we have several not easily observed hypothetical quantites. One quantity for each possible price.
The intersection is the observed equilibrium quantity.


Why is it a problem if China starts "dumping" US Treasuries? What does it mean to be dumping? China has 1.2 trillion dollars worth of us treasuries. Why would it be a problem for them to get rid of all of them? Why would that destabilize the US economy?

It would increase the total supply of US treasuries available at any point in time, which would require a higher interest rate for the market to clear. Higher interest rates would increase the cost of capital in the US economy, which in most conditions will reduce investment.

However, higher supply would also decrease the exchange rate of the USD, which could be beneficial for exports (which needs to be considered in a context of higher cost of consumer imports and higher cost of production inputs).

"Dumping" would be fine as a descriptive word for many informal contexts, but "dumping" has specific meaning in an international legal context, such as in the WTO, and so regarding the specific question of what it would mean to unload large volumes of US treasuries at the same time, e.g. for the purpose of negatively impacting the US economy, "dumping" would not be the correct term.

It should also be mentioned that China would immediately lose significant financial assets if the 1.2 trillion in treasuries were to lose 100 billion or 200 billion dollars in equivalent value. Considering the relatively large volume of credit extended in the Chinese economy relative to financial assets, this implies a relatively major economic cost to China if it were to make such a move. On the matter of strategic reasons to hold large volumes of US treasuries, the face value argument of the Chinese government is legitimate, if not the complete story: What else should they be holding if not US treasuries?


Arrow-Debreu Theorem of Existence: Non satiation Let $n$ be the number of consumers and $m$ be the number of commodities.
The Arrow-Debreu theorem requires closed and convex consumption sets $X_i \subset \mathbb{R}^m$ for all buyers $i \in [n]$. Additionally, it requires the utility function of any consumer $i$, $u_i: \mathbb{R}^m \to \mathbb{R}$ to be continuous, quasi-concave and non-satiated over the consumption set $X_i$, where non satitation is defined as $\forall \mathbf{x} \in X_i, \exists \mathbf{y} \in X_i$ such that $u_i(\mathbf{y}) > u_i(\mathbf{x})$ (pages 268-269).
It seems to me like these assumptions are contradictory. How can the utility function be non-satiated if the consumption set is closed, i.e., compact since it is a closed subset in $R^m$. Doesn't compactness and continuity of the utility function guarantee that there exists a bundle within the consumption set that maximizes utility which implies that non-satiation cannot hold?

Converting my comments into an answer:
At the bottom of p.268, the authors say:

The set of consumption vectors $X_i$ available to individual $i$ $(=1,\cdots,m)$ is a closed convex subset of $R^l$ which is bounded from below.

[Emphasis added.]
Since the Heine-Borel Theorem establishes that $S\subset R^n$ is compact if and only if $S$ is both closed and bounded (from below and above), one cannot conclude necessarily that $X_i$ is compact. (A counterexample is that $[0,\infty)$ is closed but not compact.)


Which countries impose family income taxation? I'm looking for a comprehensive overview of international income tax systems (OECD countries would be sufficient), showing which countries apply some sort of family taxation, i.e. married partners undergo some sort of Income Splitting. The Wikipedia Article mentions Germany, U.S. and Canada. France also applies splitting. What are the remaining ones?

I have finally found this: OECD (2005), Taxing Working Families A little old, but mostly accurate still.


Bounded rationality with Quantal Response Equilibrium model for an Extensive Form game I am working on my Master thesis based on bounded rationality in behavioral game theory models, I wanted to know if QRE(Quantal Response Equilibrium) can be applied to games where players have different strategy sets as opposed to what I have seen in resource allocation games, if yes, how?

I'm not sure what capacity allocation games you're applying QRE to. But here's a very stylized example where QRE is applied to an asymmetric game where the strategy spaces of the two players are (nominally) different:
\begin{array}{c|cc}
&L&R\\\hline
T&1,0&0,9\\
D&0,1&1,0
\end{array}
This game can be easily represented in the extensive form as well.

In the standard formulation of QRE, each player $i$ plays a mixed strategy $\sigma_i$, where the probability of pure strategy $s_i$ being played is determined by the following formula:
\begin{align}
\sigma_i(s_i)&=\frac{\exp(\lambda u_i(s_i,\sigma_{-i}))}{\sum_{s_i'\in S_i}\exp(\lambda u_i(s_i',\sigma_{-i}))},
\end{align}
where $\lambda\in[0,\infty)$ measures the precision of the response; the larger the $\lambda$ the more precise the response.

Applying to the game above, let $p$ be the probability that player 1 chooses $T$, and $q$ the probability that player 2 chooses $L$. Note that $p$ and $q$ parameterize the two players' respective mixed strategy. Then, player 1's quantal response to any given mixed strategy by player 2 (parameterized by $q$) is to play $T$ with probability $p$ and $D$ with $1-p$, where
\begin{equation}
p=\frac{\exp(\lambda\cdot (1q+0(1-q)))}{\exp(\lambda\cdot(1q+0(1-q)))+\exp(\lambda\cdot(0q+1(1-q)))}.\tag{1}
\end{equation}
Similarly, player 2's quantal response to any given mixed strategy by player 1 (parameterized by $p$) is to play $L$ with probability $q$ and $R$ with $1-q$, where
\begin{equation}
q=\frac{\exp(\lambda\cdot(0p+1(1-p)))}{\exp(\lambda\cdot(0p+1(1-p)))+\exp(\lambda\cdot(9p+0(1-p)))}.\tag{2}
\end{equation}

In a quantal response equilibrium, $(\sigma_1,\sigma_2)$, the two player's strategies must be quantal responses to each other; that is,
\begin{align}
\sigma_1(T)&=\frac{\exp(\lambda \cdot \sigma_2(L))}{\exp(\lambda\cdot\sigma_2(L))+\exp(\lambda(1-\sigma_2(L)))}&\sigma_1(D)&=1-\sigma_1(T)\\[12pt]
\sigma_2(L)&=\frac{\exp(\lambda\cdot(1-\sigma_1(T)))}{\exp(\lambda\cdot(1-\sigma_1(T)))+\exp(9\cdot\lambda\cdot\sigma_1(T))}&\sigma_2(R)&=1-\sigma_2(L)
\end{align}

In the following graphs, the dashed lines plot the best responses of each player; the solid curves represent the quantal responses under different levels of precision. That is, the solid curves plots equations $(1)$ and $(2)$ above. The intersection of the two solid curves is the quantal response equilibrium point, described by the last set of equations above.


How did Cowen and Tabarrok calculate the probability of Hewlett-Packard sales? The discussion on prediction markets in the chapter on the price system in Tyler Cowen and Alex Tabarrok's Modern Principles of Economics, Second Edition (pp. 123-124) contains the following paragraphs:

Members of HP’s sales team bought and sold shares that paidoff when sales fell within a certain range. A typical security would pay out $\\\$1$,
if and only if future sales were, say, between $10,000$ and $15,000$ units. Another
might pay off if sales were between $15,000$ and $20,000$ units. The market con-
tained $10$ types of securities—a range broad enough to include all the relevant
possible sales outcomes.
By examining the prices of all $10$ shares, HP could assign a probability to any
combination of outcomes. For example, if the price of the $5,000–10,000$ unit
sales security was $10$ cents and the price of the $10,000–15,000$ unit sales security was $20$ cents, this suggests that the probability of selling $5,000 –15,000$ units
was $30\%$.

How did the authors arrive at this figure of $30\%$?

It is this probability that is consistent with shares trading for their expected value. The expected value is given by:
$$E(S_1+S_2)=E(S_1)+E(S_2)=p_1 \times1+p_2 \times1=p_1+p_2$$
where $S_i$ is the payment of share $i$, $p_i$ is the probability of payment of share $i$ (due to the sales figure falling in some range). So if the expected value is to equal the price of the security, then:
$$E(S_1+S_2)=P_1+P_2 \Rightarrow p_1+p_2=P_1+P_2 $$
Where $P_i$ denotes the price of share $i$. So the probability of one of them paying off equals the sum of their prices (note that the events of share 1 and 2 paying off are mutually exclusive).
In your case
$P_1=$$\\\$$$0.20$
$P_2=$$\\\$$$0.10$
Of course these calculations totally disregard the many complications that go into asset pricing (like discounting cash flows, accounting for having to wait for payment), but I assume the authors want to keep it simple to prove a point. The bigger picture you should take away from this answer is that share prices can be interpreted as reflecting information about (what investors believe to be) probabilities of future events.


How do calculate whether selling a product leads to profit? To simplify things, imagine a company which sells two products, A, and B, and it has two types of revenues, two types of variable costs, and 1 type of fixed costs.

I can calculate margins by taking revenue A - variable cost A, and revenue B - variable cost B.

This tells me how much I make by selling each product.

However, then I have fixed costs, and I can't really "attribute" them to A and B.

My question is, how do I then decide which product is profitable to sell or not?

How do I "apply" fixed costs to my products?

Do I give use weights? For example, if 50 % of my sales are of product A, then it gets 50% of fixed costs attributed to it, and thus my profits from selling A is

revenue from A - variable costs from A - 50 % of fixed costs = profit from A

My interest lies in deciding whether I should scrap a product, or invest more in a product.

The process for solving this type of problem is very general--it's not a set of rules.  You don't need to attribute fixed costs to one good or the other (if there is only one fixed cost).

Here's the procedure:

Write out the whole profit function
Find the maximum of the profit function

If the maximum is less than the scrap value, then scrap it.

If your profit function is continuous, then you can maximize it by differentiating with respect to the quantity produced of the two inputs, setting the first order conditions to 0, and solving.  Just be sure to check that you have found the maximums and not the minimums.  If it is not continuous you will need to use a different method to find the maximums.

How to write the profit function?

$$
\pi= TR(q_1,q_2) -TC(q_1,q_2)
$$

$TR$ is usually easy.  It's

$$
TR(q_1,q_2) = P_1(q_1,q_2)\cdot q_1 + P_2(q_1,q_2)\cdot q_2
$$

Insert your price functions (which will be constants if you are a price-taker) and your cost function so that $\pi$ is a function only of $q_1$ and $q_2$.  Then find its max.  The $q_1$ and $q_2$ that maximize $\pi$ are what you want.

This type of problem seems hard if you get caught up letting your right brain trying to figure out how to solve it heuristically.  Don't do that.  Write out the profit function and maximize it.


Homothetic production function and Profit Function I know that homothetic production function implies that cost function is multiplicatively separable in input prices and output, and it can be written as
C(w,y)=h(y)C(w,1). Can some one help me derive the functional form of profit function in case of homothetic production functions?

I have figured this as the answer to this question;
As we know profit maximization problem is given as,
$$
\pi(p,w) = \mathop{max}_{\textbf{y}}\quad p.y - C(\overrightarrow{w},y)
$$
When $f(\overrightarrow{x})$ is homothetic,

$$
C(\overrightarrow{w},y)=h(y).C(\overrightarrow{w},{1})
$$

Substituting in the profit function gives;

$$
\pi(p,w) = \mathop{max}_{\textbf{y}}\quad p.y - h(y). C(\overrightarrow{w},1)
$$

First order condition gives us;
$$
p=h'(y)C(\overrightarrow{w},1)
$$

Which can be written as;
$$
h'(y)=\frac{p}{C(\overrightarrow{w},1)}
$$

or

$$
y=(h')^{-1}\frac{p}{C(\overrightarrow{w},1)}
$$
$$
\Rightarrow y= \gamma(p).\beta(w)
$$

Therefore $y(p,w)$ is separable.
Since
$$
\pi(p,w)=\int{y(p,w)}dp
$$

$$
\pi(p,w)=\int{\gamma(p).\beta(w)}dp
$$

$$
\pi(p,w)=\beta(w)\int{\gamma(p)}dp
$$

$$
\pi(p,w)=\beta(w)\alpha(p)
$$

Thus $\pi(p,w)$ is also separable in factor prices and output prices.


Basic question i guess I'm not in economics, I'm actually studying sociology and I'm doing a subject about labor economics. I'm reading an article that talks about automation and says "The employment impact of technological progress in larger countries depends on the relative product elasticity-if the fall in price arising from the labor savings more than proportionately increases demand, we will see an expansion of employment. Since more open developing countries are often assumed to be price takers, we should therefore see any domestic innovations in productivity rewarded massively with a huge expansion in employment."
what does it mean by price from the labor savings?
http://documents1.worldbank.org/curated/en/869281482170996446/pdf/WPS7922.pdf

fall in price arising from the labor savings

The price of a product is usually determined in part by its cost. (This holds in almost all theoretical models without strict capacity constraints, even in the extreme case of monopoly.)
If automation can replace some of the labor with cheaper machines, cost will decrease, hence the product will be sold at a lower price.


If automation implicitly increases wealth, why is it generally considered undesirable? When it comes to the subject of automation, I read that the wide majority of the arguments assume that the profits/savings "vanish", alongside the jobs loss.

I see the reasoning above as flawed though: if automation lowers the prices of the goods (both by increasing productivity, and by reducing costs; I'm ignoring the automation industry itself) in general, this leads implicitly (in the long term) to an increase in wealth, and by extension (again, in the long term), to an increase of the jobs offer.

In practical terms, if producing, say cars, would cost less, people would save money and spend it through other markets, say going (more) to theater; the increase of demand in other markets would create new jobs, in this case, theater companies.

I see the net of all of this as positive. Am I missing some important factors?

I can see as argument (by some) that this phenomenon could/would only lead to increased profits for the "Top 1% of the evil capitalists©".
Although undesirable, this is irrelevant - such (evil©) people would certainly spend or reinvest the money, again, leading to the mentioned consequences.

It's important to note that I'm talking about long term. I'm sure that if literally tomorrow automation would take over millions of job, it would certainly be a disaster.
I'm also assuming a healthy economy, that is, the increase of savings/profits wouldn't stay still under the mattresses.

Short-term or long-term, Property rights and distributional issues exist, "evil capitalists" or not, and they will always result in strong scrutiny of any change.  Remember that what is "short term" for society is mid- or even long-term for individuals.

Moreover, there exists the transitional pain: whether we can optimize it downwards, and who is going to feel it.

All these cause the heated arguments and the opposing positions.

But your post starts with a strange assertion: that "almost all times" it is assumed that automation has a negative economic impact. If this was so, it seems a little strange that automation marches triumphantly for the last two hundred years, and it continues to do so. If this was so, people now must live in a much worse material situation than two hundred years ago. Is this the case?


How do Trade Costs work in International Trade? I'm currently reading a paper about trade costs in international trade, but I really struggle to understand the following passage:

  A rough estimate of the tax equivalent of “representative” trade costs for industrialized countries is 170 percent. This number breaks down as follows: 21 percent transportation costs, 44 percent border-related trade barriers, and 55 percent retail and wholesale distribution costs (2.7=1.21∗1.44∗1.55).

What does "tax equivalent of representative trade costs" mean?
"Trade costs for industrialized countries is 170 percent" of what?
How can trade costs exceed 100%?

Please help me out, I'm really loosing my sleep on this one!

The quotation comes from James Anderson and Eric Van Wincoop "Trade Costs"  in the Journal of Economic Literature Vol. XLII (September 2004) pp. 691–75 and a preprint of the article is available

The calculation is trying to find the equivalent to an ad valorem tax by which the price of manufacture increases by the time of retail sale.  Essentially it is saying transportation multiplies price by $1.21$ (a $21\%$ increase), tariff and non-tariff border related trade barriers multiply by $1.44$ (a $44\%$ increase), and retail and wholesale distribution costs multiply by $1.55$ (a $55\%$ increase) combining to multiply by $1.21\times 1.44\times 1.55=2.7$ (a $170\%$ increase).

This figure being over $100\%$ is not an issue.  For example you could imagine a high tax on a packet of bottle of perfume costing $\$10$ before tax: if the tax rate was $170\%$ ad valorem this would add $\$17$ tax and make the after-tax price $\$27$.

There are plenty of caveats: domestic commerce also faces retail and wholesale distribution costs as well as some transport costs.  Some goods see smaller costs, such as high-value low-weight goods seeing lower transport costs, or cross-border trade involving a short distance and a free-trade area, so this is in a sense a weighted average across goods and countries.

The article goes into considerable detail on the methods used for the calculations and possible implications for trade models.


Why is the stock market always rising? I asked myself: How is it that the stocks are always rising? How is money generated every year so that the value of a company rises?

I mean, at some point there is a finite amount of money in the system, isn't it? Right now people assume that the stock market is overheated and not many sources are left where money can come from to make it rise even higher.

Now my question is: How and where is money coming from? I know, people invest, but at some point they take money from point A to B and don't create it.

Is there a basic book out there which explains the basics? Not for dummies but also not for experts who assume to know everything. Maybe a pragmatic economics book?

How is it that the stocks are always rising?

Because companies generate value.

  How is money generated every year so that the value of a company rises?

It isn't. Money is a measure of value, it is not value itself. Suppose you spend the day making a painting that's worth 100 dollars. You added one hundred dollars' worth of value to the economy, but you didn't add any actual dollars to the economy. There's no need for there an extra 100 dollars to be created for you to make the painting. If the market capitalization of a company rises from 10 billion dollars to 11 billion dollars, the amount of money that people are willing to pay for the company has increased, but the amount of money that exists hasn't increased.

  I mean, at some point there is a finite amount of money in the system

Well, the money supply is generally increasing, but that's separate from the rise of stock prices.


Relationship between Growth in Purchasing Power and Real Interest Rate equations My textbook gives these two equations including the real interest rate and says that the second equation (b) can be arrived at from the first (a), but doesn't explain how.

rr = Real Interest Rate, r = Nominal Interest Rate, i = Inflation

Equation (a):
$$Growth\ in\ Purchasing\ Power=1+r_r = \displaystyle\frac{1+r}{1+i}$$

Equation (b):

$$Real\ Interest\ Rate = r_r = \displaystyle\frac{r-i}{1+i}$$

I'm feeling slightly obtuse but I've been away from math quite a while, and can't figure out how to rearrange the first formula into the second one.

What are the exact equation steps necessary to get from: $ r_r = \displaystyle\frac{1+r}{1+i}-1$ ⇒ $r_r = \displaystyle\frac{r-i}{1+i}$ ?

$Growth\ in\ Purchasing\ Power=1+r_r = \displaystyle\frac{1+r}{1+i}$

Also it is given that $real\ interest \ rate=r_r$

So :

$$real\ interest \ rate=(1+r_r)-1=\frac{1+r}{1+i}-1=\frac{1+r}{1+i}-\frac{1+i}{1+i}=\frac{r-i}{1+i}$$


What is business cycle frequency? I am reading a paper by Michal Andrle, Jan Brůha,
Serhat Solmaz (On the sources of business cycles: implications for DSGE models). The authors use data at a quarterly frequency for their empirical analysis. But they also have this statement in their paper, 'Our empirical approach boils down to a multi-country dynamic principal component analysis of data at business cycle frequencies'.
What does the term 'business cycle frequency' mean? And what does it mean to analyze data at business cycle frequency? I have yet found a simple definition for it.

Business cycle frequency is a frequency that has the length of one business cycle.  Business cycle is:

economy-wide fluctuations in production, trade, and general economic activity. From a conceptual perspective, the business cycle is the upward and downward movements of levels of GDP (gross domestic product) and refers to the period of expansions and contractions in the level of economic activities (business fluctuations) around a long-term growth trend.

The length of the business cycle varies but usually, it is at least a few years.


Why do all apartment complexes in Albuquerque have pools? Apartment builders have a constrained optimization problem whereby they balance building different amenities to attract tenants with varying preferences. Recently when searching for apartments I noticed that every single apartment seemed to have a pool. I feel like many people would prefer a small decrease in rent and open space, more parking, a larger fitness center, ect to a pool. Apartments have many other variances in terms of parking, landscaping, price, ect, yet the pool seemed to be a universal. Does this simply reflect that the apartment market cannot be perfectly competitive or that preferences for pools is near universal? Is there an economic explanation or cognitive bias that would explain this kind of convergence?

PS: I will not be offended if this is closed. I'm not sure if this type of question is not on topic for this site.

In most places, it's probably more efficient to invest in more houses than to put pools for the same value in the houses you own. In some place, having a pool might even decrease the renting value of your house: the maintenance cost compensate the rent increase. In Albuquerque, it is possible that it's more relevant to invest in pools than in houses, hence all landowners invest in pools, hence, no more houses to rent without a pool.

With $P$ the cost of a pool, $H$ the cost of an house, $r_H$ the revenue you get for renting a naked house and $r_P$ the revenue you get for renting a house with a pool and $c$ the upkeep of a pool, every house owner is going to build a pool before renting or selling if $$(r_p - c)/P > r_H/H$$

If this isn't true (and it isn't in most places), some people we choose to build a pool for other reasons but not all houses will have pools.


Best strategy to incentivise third party investment How can governments incentivise NGOs and economic consulting firms to invest in national reserve conservation? I guess this would be more political, but what are the more economic aspects of trying to get corporations involved?

There are several possible routes to get conservation investment into national reserves, i.e. geographic areas that are designated for special protection and environmental conservation.

The government could set up a fund that rewarded the protection and enhancement of the reserves; by guaranteeing the returns on investment, then investors would be drawn in.

The government could specify that investment in national reserve conservation was a requirement for other rewarding activities: for example, it could specify that if a corporation wanted to win government contracts, it had to invest at least x% of its turnover in protecting national reserves. Or that planning permission was linked to such investment.

It could create special tax incentives for such investment: for example, the company's tax burden might get reduced by amount equivalent to a fixed percentage of the investment in the national reserve.

I suspect that in any case, an expert panel would be needed, to assess whether something would represent beneficial investment or not; and if it is, then what the suitable size of return on the investment should be.

And any system is prone to gaming, so the scheme would need to put in place measures to detect and curb such gaming.


Why is gold a safe haven investment? To me, it seems like gold is the ultimate example of something where the value should go down when the economy, stock market etc go down.

Just like Ferraris, and other frivolous consumer luxury goods, gold has almost no inherent value, beyond what we choose to assign to it. If the economy plummets, people will buy considerably fewer products that are made of gold, much like they will buy considerably fewer Ferraris.

Why does gold's value increase when times are tough? Why do we not see trouble on the stock market lead to increased prices for consumer essentials such as grains, textiles etc - things that have almost no change in demand when there is a change in income because they have real value (stopping people dying).

Note: Answers should be appropriate for countries that have left the gold standard. If there are any countries still on it, answers for those countries aren't what I am looking for.

You could see it as a coordination game and an example of a rational bubble. Because everybody knows that people start buying gold and the price goes up when the economy tanks, it is actually a good strategy to do just that. Similar things happen for example with the Swiss Franc.
The idea that the stock of gold is fixed and hence its price is stable, is empirically just plain wrong.
First, gold production varies with production cost and the demand for gold, just as in other industries. It is also dominated by a couple of countries and big mining companies with tons of market power.
Second, the price of gold is highly volatile, just as other commodities. The standard deviation of gold prices is much higher compared to for example Treasuries or G7 countries' equity indices.