texts: Marginal rate of substitution interpretation

texts: I am trying to interpret the marginal rate of substitution stidied in an article. The article in question is Burbidge, J. B., Robb, A. L., 1980. Pensions and retirement behaviour. The Canadian Journal of Economics 13 (3), 421–437. https://www.jstor.org/stable/134702?seq=1. I paste a screenshot of the equation in question. $U^{'}$ is utility from retirement. $U^{o}$ is utility from full-time work. $Y$ is labor income. $R$ is retirement age. $P$ is pension income. $T$ is how many years the agent lives. $r$ is the discount rate. The left-hand side of this equation is the discounted ratio of the marginal utility of another year of retirement to the marginal utility of an increase in consumption per year, that is, the marginal rate of substitution (MRS). I question when this MRS is larger. I consider the right-hand side of the equation, and in particular the term $Y(R)-P(R,\alpha)$. The first component of this term is work income if one was to work full-time at age $R$. The second component is the pension income if one was to retire at age R. Assuming that $\theta = 0$, the term represents the difference between full-time work income and pension income at age $R$. Suppose the term is positive. This means that income from work is larger than income from retirement if one decided to work instead of to retire at age $R$. Suppose that we increase the magnitude of this term. Then working pays more than retirement does. This makes the right-hand side larger. Then, the left-hand side must be larger. A larger left-hand side means that the marginal utility from retirement, relative to the marginal utility from consumption, is higher. But this looks odd. If working pays more (right-hand side), why would the agent derive more utility from retirement (left-hand side)?


texts: Difference type of crowding out effect in economics

texts:
In macroeconomics I came across two type of crowding out. First, in IS LM model where in classical case, when LM curve is vertical increase in government expenditures have no increase in output i.e. full crowding out.
Secondly, in AS AD model due to increase in government expenditures when AD curve shift in classical case i.e. Vertical AS curve there is no effect on output. What's the difference between these two cases of full crowding out.


texts: What is Production Possibility Frontier (PPF) diagram drawn on consumption-leisure?

texts:
When explaining basic macroeconomics model involving consumption-leisure tradeoff, often diagram showing production possbility frontier (PPF) is drawn with leisure on x-axis and consumption on y-axis. But what exactly is the meaning of this production possibility frontier?

Production Possibility Froniter diagram is often drawn on two-goods basis (for example, like butter on x-axis and milk on y-axis) but I am confused on what PPF might be on consumption-leisure basis.

Reference: http://newmonetarism.blogspot.com/2014/02/rbc-and-nk-in-nutshell.html


texts: Data source for average effective personal income tax rate?

texts:
Anyone know a source for the average effective personal income tax rate for the US. By state also would be great.

Definition: average effective income tax rate = (Total income tax collected)/(Total income earned)

Possibly a source for the data to do the calculation.


texts: Can the social planner problem be reduced to a Pareto problem or a Walrasian equilibrium problem?

texts:
The social planner problem is
\begin{align}
\max_{\lbrace x_i,y_i,x_j,y_j \rbrace } &\theta_i U_i(x_i,y_i) +\theta_j U_i(x_j,y_j) \\
& \text{s.t.}\\
&x_i+x_j = \omega_i^x + \omega_j^x\\
&y_i+y_j = \omega_i^y + \omega_j^y\\
\end{align}
where
$\theta_i,\theta_j$ are weights.

As I understand it, with a proper choice of weights, one can turn the Social Planner's problem into

A Lagrangian optimization problem that solves for a Pareto optimal allocation.
A Lagrangian optimization problem that solves for an allocation that is a Walrasian equilibrium.

Is this accurate? If so, what constraints are there on the weights for each case?


texts: Public debt of European countries, by year

texts:
Where can I find lists with public debt of European countries such as the UK, by year? (or by fiscal year)

If there are such lists on Eurostat but only for the last 10 year or so, I would like to have longer lists, for each country in part.

Later edit: If possible, having both the amount in Euros and in percentage of GDP, would be great. Like for example this list for Spain: http://www.datosmacro.com/deuda/espana

If you know lists for a single country, please mention them. For example if you are from Germany and you have links with such a list for Germany, from the National Institute of Statistics or another site, please let me know about it, I'll vote your answer.


texts: How does low population growth increase the effect of accumulated wealth

texts:
This passage comes from page 10 of the translation of Thomas Piketty's book Capital in the Twenty First Century:

  If the rates of population and productivity growth are relatively low,
  then accumulated wealth naturally takes on considerable importance,
  especially if it grows to extreme proportions and becomes socially
  destabilizing.

Why does low population growth exacerbate the effect of accumulated wealth?

Intuitively, I would think that an increasing population would mean more potential employees, thereby allowing already wealthy people to more easily offer low wages. By contrast, I would intuitively think that low population growth, and the resultant scarcity in employees, would force the wealthy individuals to offer higher wages.


texts: Price elasticity on comparison website. How to calculate price elasticity using the coefficient of the products position on site?

texts:
I am looking at the following paper. Glenn Ellison & Sara Fisher Ellison, 2009. "Search, Obfuscation, and Price Elasticities on the Internet," Econometrica, Econometric Society, vol. 77(2), pages 427-452, 03.
Link: https://www.nber.org/papers/w10570

The model did not include price but did include rank ie. the position of a product on a comparison website sorted by price. They then used the model results to calculate price elasticity.

To summarise, the way they did this was: they treat log(1 + Rank) as a continuous variable and compute estimated elasticity when all variables are at their means by setting the derivative of Rank with respect to a change in Price equal to the inverse of the average distance between the twelve lowest prices. They concluded  "the low-quality 128MB PC100 demand equation corresponds to an own-price elasticity of -25.0".

I can't understand this explanation, how is this price elasticity calculated?


texts:
For a system of equations with $M=2$ endogenous variables, $ Y=\begin{bmatrix}  y_1 & y_2 \end{bmatrix}$ and $K=3$ exogenous variables, $X=\begin{bmatrix}  x_1 & x_2 & x_3 \end{bmatrix}$.
The first equation of the system is given by:
$y_{1i}=\gamma_{12}y_{2i}+\beta_{11}x_{1i}+\epsilon_{1i}$.
The data matrices yield, $X'X$, $X'Y$ and $Y'Y$, which are of dimension, $3*3$, $3*2$ and $2*2$ respectively

I need to

Write the OLS and 2SLS normal equations in terms of cross products of the data matrices.

I tried using the standard procedure for deriving normal equations, that is, by minimizing sum of squared residuals, but I fail to understand how the equations can be modelled in form of the cross products of the given data matrices. I think I'm missing the point of the exercise. Please help me in understanding what the question demands. Thanks!


texts: Are modern conglomerate mergers better or worse for economic competition?

texts:
Modern conglomerate mergers differ from those from decades ago as, even though they takeover smaller companies, they have a more narrow focus on related business and, in order to be successful, have an extremely rigorous financial control and seek to be as efficient as possible.
Research I've read shows that there's not enough evidence to say that old conglomerate mergers (1980's) distorted or reduced competition, however, I can't find research on modern firms.
Do you have any knowledge on this? If you can link articles it would be great.


texts: Difference between Nash equilibrium and Pareto Efficiency

texts:
Nash Equilibrium is defined as a solution concept referring to a best outcome which players won't want to unilaterally deviate given the response of other players doesn't change. To me it seems like Nash equilibrium demands that there is no individual blocking (ie it is indivtually acceptable). So, in sense, it talks about individual level welfare.

While Pareto efficiency is an outcome where one or all cannot be made better off without harming someone. To me, Pareto condition is demanding two things - outcome should not be individually blocked (ie they are better off or at par with their endowments at this pareto outcome) and neither should it be jointly blocked ie it should be acceptable to all. So, in sense it talks about societal welfare.

My problem is Wikipedia page refers to Nash equilibrium as a broader concept. In what sense is Nash equilibrium broader?


texts:
I was trying to derive a general demand for the good $x$ for this quasi-linear function $u(x,y) = y + 2\sqrt{x}$ subject to standard budget constraint $p_x x + p_y y \leq M$
Using Kuhn-Tucker conditions (my aim was to account the corner solutions) I obtained the following results:
$x = 0$, $y = M / p_y$ when $MRS < p_x / p_y$
$x = M / p_x$, $y = 0$ when $MRS > p_x / p_y$
$x = (p_y / p_x) ^ 2, y = M / p_y - p_y / p_x$ when $MRS = p_x / p_y$
The problem is that I do not how to write down the demand for $x$ with all conditions listed above ($MRS\lesseqgtr$ ) in an explicit form. In other words, I think it is possible to be left only with prices and income as conditions for the demand.
I hope that I was clear


texts: If banks create money by lending it out, how are they taking any risk?

texts: When I lend money to someone and they don't pay it back, I lose my money.  I can only lend out money that I own (or borrow).  I understand that when a bank lends money, that money is created the moment they lend it out.  If that is so, how does the bank take any risk in lending it out, considering they didn't own it in the first place?


texts:
Do free-trade agreements typically include clauses relating to services?

For example, reciprocal recognition of professional qualifications.


texts: Examples of Analysis of Competition in a Latent Product Characteristic Space

texts:
Competition between firms offering heterogenous products is often an exercise of constructing the right kind of spatial model.
There is the famous Hotelling model and many other papers that model competition in a product characteristic space. I can think of examples where cars are differentiated by size, power, gas mileage, etc. These are directly measurable and interpretable features.
However, are there any examples of analysis where latent features/product characteristics (interpretable or not) are used? I am thinking of the kinds of latent features that might be the product of using alternating least squares as an example, though it might be less common in economics.

Below I expand on matrix factorization, which is sometimes used for recommendations. Example article.
We might have a matrix of movie reviews by users,
$$R = \left( r_{ij} \right)_{i\in I, j\in J}.$$
Then features are extracted based on finding $R\approx W F^T$.
Let $R$ be $n\times m$ for $n$ users and $m$ movies. A number of latent features $k$ can be chosen exogenously to extract. Then $W$ is $n \times k$, $w_{il}$ giving the weight user $i$ attaches to feature $l$. A movie's $l$-ness is then given by $f_{jl}$. The user scores movie $j$ according to $$r_{ij} = \sum_{l=1}^k w_{il}f_{jl}.$$
Here, $l$-ness is uninterpretable, simply a result of the matrix factorization and then weights $w$ simply give linear utility weights for these features. Similar uninterpretability might also arise if many non-latent features are condensed via dimensionality reduction.


texts: Marxist Economics: Contradicting Definitions of Capital Intensity?

texts:
As noted in a previous post one method of capitalist exploitation in marxian theory is through an increase in labor intensity as defined by the equation:

$$I=\frac{SV+V}{lh}$$

A fellow user RegressForward helped with the basic mathematics involved in this formula and came up with a decent understanding of the equation in my opinion. It appears to be the same as exploitation via increase via relative surplus value.

However after searching the web for more on this topic I found that there exists a paper which uses a completely different formula which we can use for to get an equation for us who are more econometric ally inclned. A detailed review is in:
Duration, Intensity and Productivity of Labour and the Distinction between Absolute and Relative Surplus-value by Stavros Mavroudeas.

Setup:

Let $T$ be the total daily work time of the workers, and $V$ and $SV$ be their value and surplus value produced during the day. It follows that:

$$T=SV+V$$

He describes this process of increased intensity by including a factor $b$ which denotes intensity.

It follows that effective labor time is defined as:

$$t=bT$$

by extension it follows that effective value production and surplus value production is:

$$v=bV$$
$$sv=bSV$$

Its interesting to note how this affects the marxian labor theory of value:

$$P'=C+b(V+SV)$$

where revenue from sale at price $P'$ is divided based on value added by machinery (C) and effective Labor value and surplus.

In Short: As we can see Stephen Resnick uses a fundamentally different equation from Maveroudeas.  Is there a way to resolve these two equations?


texts: Do real life economists and financial analysts actually use calculus in their jobs?

texts: From what I understand a lot of calculus is used at university level when studying economics and some finance courses (correct me if I'm wrong) but I was just wondering if economists and financial analysts actually use calculus in their actual jobs on a day to day basis.


texts: Should we include some control variables in regressions when we test a moderation effect of a variable?


texts: Best-responding to a stochastically higher distribution of bids

texts:
In Auction Theory, Krishna writes that:

  a bidder who faces a stochastically higher distribution of bids–in the
  sense of reverse hazard rate dominance–will bid higher

(This follows the proof of proposition 4.4 in the section 'Weakness Leads to Aggression'.)

Supposedly, this is 'easy to see' - however, I am having trouble seeing it! I would be grateful if someone could explain why this is true.

My (unsuccessful) efforts so far:

If I bid $b$ when my valuation is $v$, then (under risk neutrality) my expected utility is

$$(v - b)F(b)$$

where $F(b)$ is the cumulative distribution function of all the bids apart from mine (and thus the probability that I win the auction).

Maximising my expected utility with respect to $b$, we obtain the first order condition

$$(v - b)f(b) - F(b) = 0$$

Which implies that

$$b = v - \frac{F(b)}{f(b)}$$

A distribution $G$ is stochastically higher than a distribution $F$ in the sense of reverse hazard rate dominance when, for every $b$

$$\frac{g(b)}{G(b)} > \frac{f(b)}{F(b)}$$

Now, if $f(b)/F(b)$ and $g(b)/G(b)$ do not depend on $b$, it is obvious from the first order condition that I will bid higher when facing a stochastically higher distribution of bids. However, it is not clear to me what happens in the general case where the 'hazard rates' may depend on $b$.

Many thanks in advance!

Bonus question: When my bids increase, will my new distribution of bids 'stochastically dominate' my old distribution (in the sense of the reverse hazard rate)?


texts:
I would like your help to understand the definition of obedience in an incomplete information game at p.7 of this paper.

Let me summarise the definition provided in the paper.

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

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

A basic game $G$ consists of

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

An information structure $S$ consists of

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

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

One way to mechanically understand the notion of the decision rule is to view $\sigma$ as the strategy of an omniscient mediator who first observes the realization $\theta\in \Theta$  chosen according to $\psi$ and the realization $t\in T$ chosen according to $\pi(\cdot|\theta)$; and then picks a probability distribution from $\Delta(A)$, and privately announces to each player $i$, her lottery to play.

For players to have an incentive to follow the mediator's recommendation in this scenario, it would have to be the case that the recommended lottery was always preferred to any other lottery
conditional on the signal $t_i$ that player $i$ had received.

This is reflected in the following "obedience" condition.

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

My question:

I don't understand fully the LHS (or, equivalently, the RHS) expression
$$\sum_{a_{-i}, t_{-i}, \theta} \psi(\theta) \pi(t_i,t_{-i}| \theta) \sigma(a_i, a_{-i}|t_i, t_{-i}, \theta) u_i(a_i, a_{-i},\theta)$$

Saying it in words, this is the sum over $A_{-i}, T_{-i}, \Theta$ of
$$
\text{[Prob that the mediator observes $(\theta, t)$]}\times\\
\text{[Prob that the mediator suggests players to play $a$ under $\sigma$,  given that he observes $(\theta, t)$]}\times\\
\text{[Profit that player $i$ gets from obeying the mediator, given that the other players obey too]}
$$

Let the product just written be denoted by $(\star)$.

Why in the second component of $(\star)$ we DO NOT condition on $a_i$ by taking
$$
\text{[Prob that the mediator suggests the other players to play $a_{-i}$ under $\sigma$, given that he observes $(\theta, t)$ and given that he suggests player $i$ to play $a_i$]}
$$
in place of
$$
\text{[Prob that the mediator suggests players to play $a$ under $\sigma$,  given that he observes $(\theta, t)$]}
$$


texts: What is the definition of: 'commodity space'?

texts:
I have seen the concept of commodity space being used multiple times in economics, in particular within microeconomics, but I could not find a general definition of it.
Based on the examples that I have seen, I would guess that it is a vector-space of n-dimensions, in which every dimension coincides with one specific commodity. Furthermore, n is equivalent to the cardinality of the set of commodities.
Is this understanding correct? Is there even a universal understanding of a commodity space?


texts: What are the known / alleged problems against using energy as currency?

texts:
What are the known (and alleged) problems of using Joules (i.e. a measure of energy/work) as a currency? I tried to find such idea in Google (searched terms like "technocracy", since someone told me that technocracy had such idea), but I'm not clear about where to search in.

(Edit : asked in contrast to fiduciary/trust/faith-based currencies)

(Edit 2 : found this link, but i'm not quite an expert in eco to judge the possible problems, not exposed in the article)

(Edit 3 : This one is my fault since I asked a not-so-clear question, becuase my lack of knowledge. I have to clarify that this proposal is not mine, and I want to just study the concept. In this way, many principles I should enumerate are:

Energy taken into account is the "seizable" energy, like solar or fossil.
Fossil energy can be stored. Fossil industry would be credited for that.
Solar energy can be captured, transformed, and injected into the power network to be credited for that [as currently is, in many countries, right now], and have such energy redeemed later; the only difference with the current situation is that [the modern proposals support that] the economy could be based in such energy, instead the vice-versa case.
The exchange act would not involve energy directly, since a wallet of that type could be quite dangerous to carry in the ... ¿pocket?.

In this sense, I think useful answers have already been provided to cover the expressed points, althought I don't want to consider the answer as just-closed, but narrow the extent of the issues I want to understand about).


texts: I have been reading an article about the Phillips Curve. But I got stuck in a part of econometric analysis. I am not good at econometric. Therefore I need help here. In this link you can read the article. If you search 0.97 with Ctrl+F, you can see the first finding that I want to ask about it. She says in there "By applying Equations 5–7 to the data, one need not assume any specific form of nonrationality in expectations. Since the task here is to compare the different models on their own terms, the theoretical restrictions are imposed in the estimated specifications of the New Keynesian models. Thus, in the New Keynesian Phillips curve, the imposed value of β is 0.97 and as seen in Equation 7, the sum of forward- and backward-looking components is restricted to unity for the Hybrid Phillips curve." I confused about if she applied any specific econometric test or not. If she applied, which test did she applied? Please help me.


texts: Identifiability of Non-Parametric Utility Function?

texts:
I recently learned that EU characterized by independence and weak ordering is identifiable, but a utility function like: $U(x)=v_1(x)v_2(x)$ is not identifiable.
Does it mean that "cardinal uniqueness = identifiability"? Or cardinal uniqueness implies identifiability but not the other way?
I found the precise definition of "identifiability" parametric function. But for non-parameteric function, what is the precise definition of identifiability?
For example, does the simplest utility function $u(x)$ characterized by weak order and continuity identifiable by its own? (a.k.a does ordinal uniqueness implies identifiability?)


texts: If all Banks in the world are emptied..?

texts: What would happen if every person in the world pulled their money out of their bank accounts?


texts: Nash equilibrium - mistake in proof of paper?

texts:
I have a question regarding the proof of Proposition 1 in Besley and Ghatak (2007) in Appendix A of their paper. It is a quite highly cited paper but I believe there is a mistake in the proof of their Proposition 1. The model is described in Section 2. of their paper. It is a very simple model that seeks to derive the Nash equilibrium of the market. In particular, they show that $\theta_c^*$ must satisfy $f'(n \theta_c^*) = \alpha$ in equilibrium. In their proof in the appendix they state:

However, I think there is a mistake because the package $(p', \widehat{\theta'})$ does not make each caring consumer strictly better off.

The new package $(p', \widehat{\theta'})$ gives utility:

$$b-p'+f(\widehat{\theta'} + (n-1)\widehat{\theta}) $$

The old package $(p, \widehat{\theta})$ gives utility:

$$b-p+f(n\widehat{\theta}) $$

The new package is strictly preferred to the old package iff

$$b-p'+f(\widehat{\theta'} + (n-1)\widehat{\theta}) > b-p+f(n\widehat{\theta})$$

$$ f(n\widehat{\theta} + \Delta \widehat{\theta}) - f(n\widehat{\theta}) > \Delta p$$

If we make the substitution as stated in the paper: $\Delta p = f'(n\widehat{\theta}) \Delta \widehat{\theta}$ and assuming we want a positive $\Delta \widehat{\theta}$, then the above becomes:

$$\frac{f(n\widehat{\theta} + \Delta \widehat{\theta}) - f(n\widehat{\theta})}{\Delta \widehat{\theta}} > f'(n \widehat{\theta}) $$

If we pick a negative $\Delta \widehat{\theta}$, then the above condition becomes

$$\frac{f(n\widehat{\theta} + \Delta \widehat{\theta}) - f(n\widehat{\theta})}{\Delta \widehat{\theta}} < f'(n \widehat{\theta}) $$

But $f$ is a increasing and strictly concave function, so the above inequalities are always false. So the new package is never preferred to the old package. Everything else in the proof is fine apart from this step and this is the most crucial step of the proof as it characterizes what $\widehat{\theta}$ should be in equilibrium, if this is wrong then many other results in the paper are also wrong.

So, is there a mistake in this part of the proof of the paper? And if so, is there a way to correct it so that the results still hold?


texts: Can I get a more detailed explanation of the Weak Axiom of Profit Maximization?

texts:
In Hal Varian's Book "Microeconomic analysis" on page 35 he gives the following description of a profit maximising firm.

"...If the firm is maximising profits, then the observed net output choice at price pt must have a level of profit at least as great as the profit at any other net output the firm could have chosen. We don't know all the other choices that are feasible in this situation, but we do know some of them-namely, the other choices $y_s$ for $s=1,...,T$ that we have observed. Hence, a necessary condition for profit maximisation is that
$p_ty_t≥p_ty_s$
for all $t$ and $s=1,...,T$.

"We will refer to this condition as the Weak Axiom of Profit Maximisation (WAPM)."

I dont understand this can I get a more detailed drawn out explanation as if I'm five, or a reference to where I can further information on this?


texts: Stock Valuation - Interest rates, Dividends, and Shares Repurchases

texts:
I'm reading a macro book (Blanchard's) and the way he values shares is by calculating the net present value of all dividends we expect to receive by owning some stock, discounted by the interest rates (assuming investors are risk-neutral and only care about expected return). Well, by reading some newspapers and some chapters of a book on corporate finance, I've noticed that not many firms' shares pay dividends, being the paid dividends concentrated in a few firms only. In fact, in corporate finance, it seems managers are taught that with the existence of taxes on personal income(dividends apply), it's preferable to repurchase shares which increase the earnings per share ratio (EPS), which in turn multiplied by the price-per-earnings of the industry the firm is in, gives an expected price for the stock. My question is why should we value stock if no dividend is paid? Aren't selling stock and receiving dividend the only two sources of current income that owning shares give?

Any help would be appreciated


texts: Does Dogecoin or Bitcoin have a more appropriate rate of monetary inflation?

texts:
The supply of new Bitcoins and Dogecoins is depicted in the graph below.

The Bitcoin inflation rate is currently higher than the Dogecoin rate, but it reduces sharply to a rate close to zero. It eventually reaches 0% in 2140, after which there will be no new Bitcoins.

There are currently 100 billion Dogecoins. The Dogecoin inflation rate is fixed at an additional 5.256 billion coins per year for every year henceforth.

Which inflation rate is more appropriate for a general-use currency intended for use for transactions of all sizes? I realise this isn't necessarily the stated aim of either currency.

Answerers should assume that the inflation rates are sacrosanct and can't be altered in years to come.


texts: Is there some commonly known indicator that is defined as:  Minimum wage divided by cost of living? I mean, I could call it that way, but perhaps people already have this indicator with a certain specific name or they have a better one for the purpose I'm looking for.


texts: Why Certainity Eqivalence in PIH only holds for quadratic utilities

texts:
In my current macro economics course, it has been stated that there is certainty equivalence in the random walk permanent income hypothesis ("which implies individuals act as if future consumption was at its conditional mean value and ignore its variation") only holds if the utility is assumed to be on form $$ u(c) = c - ac^2/2 $$
I have consulted the coursebook but could not find any rigorous proof or intuition of this. Could anybody help please?


texts: What are some similarities and differences between the 2001 recession and the 2007 recession in terms of causes and the effects on the economy?

texts: I know the two were caused by the burst bubbles and worsened by rising interest rates. I also know that the the 2001 recession had a long jobless recovery but did not experience as many bank failures as the Great Recession. I'm assuming the stock market fell for both?


texts: Classical Theory of Inflation - Money Supply, Money Demand and Prices

texts:
In every textbook, website I read when talking about the classical theory of inflation,  I see the diagram below which depicts the value of money, prices etc. This one below is from Spark notes (https://www.sparknotes.com/economics/macro/money/section2/) or Mankiw (chapter 28 Money, growth and inflation).
These sources all go through a shift in the MS to the right to demonstrate inflation. No problem with that conceptually. Makes sense.
But what about the demand curve? If the demand curve SHIFTS to the right (due to a thriving economy and an increase in transactional demand for money) and the central bank keeps the money supply the same, the result would be deflation? An equilibrium with lower prices than before. i.e. A higher point on the supply curve (see my doodle below).
It would seem that no source considers a shift in the demand curve like any other S & D diagram. And I can't rationalise it for myself.
It seems totally counter intuitive. Could anyone explain the logic of this model when it comes to shifts in the demand curve (keeping money supply fixed).


texts:
Consider two people have a mutually advantageous relationship. That is, if both dedicate more effort to the relationship both improve. Specifically, each individual chooses a level of effort
$x_{i}\in [0,1]$ and the payoff of the person $i$ is

$\pi_{i}(x_{i},x_{j})=cx_{i}+x_{i}x_{j}-x^2_{i}$. where $c$ is constan $c\in [0,1]$

Verify conditions that guarantee the existence of Nash equilibrium in pure strategies and determine such equilibrium.

QUESTIONS:

Q1: for the equilibrium.

$\pi_{i}(x_{j})=cx_{j}+x_{i}x_{j}-x^2_{i}$

$\max_{\mathbf{x}_{i}\in [0,1]} \pi_{i}(x_{j})=\max_{\mathbf{x}_{i}\in [0,1]}(cx_{i}+x_{i}x_{j}-x^2_{i})$

First order conditions $c+x_{j}-2x_{i}=0$
                        $$x_{i}=\dfrac{c+x_{j}}{2}$$
$\max_{\mathbf{x}_{j}\in [0,1]} \pi_{j}(x_{i})=\max_{\mathbf{x}_{j}\in [0,1]}(cx_{j}+x_{j}x_{i}-x^2_{j})$

First order conditions $c+x_{i}-2x_{j}=0$
 $$x_{j}=\dfrac{c+x_{i}}{2}$$
So then I can say $x_{i}=x_{j}=c$ is nash equilibrium.

Is correct?

Q2: (Conditions for existence).
I think that I must verify the conditions of the theorem(Debreu. 1952;Fan, 1952;Glicksberg, 1952): Let $G$ be a game in strategic form such that, for each $i=1,2,...,n, S_{i}\subset \mathbb{R^{m}}$ is compact and convex, and the function $\pi_{i}:S_{1}\times...\times S_{n}\rightarrow \mathbb{R}$ is continuous in $s=(s_{1},s_{2},...,s_{n})$ and quasi-concave in $s_{i}$.Then, the game $G$ has a Nash equilirbium in pure strategies.

$\rho:[0,1]\rightrightarrows [0,1]$ where $\rho_{i}(x_{j})=arg \max_{x_{i}\in [0,1]}\pi_{i}(x_{j})$

*$S\neq \phi$

*$S=[0,1]$ is compact.

*$\rho_{i}(x_{j}) \neq \phi$ and convex...

...

...

But
The teacher indicates that it is not the theorem that must be analyzed. But I think he can be wrong.
Do you recommend that I continue with this?

Or who will be asking me to apply?

Thanks for your help.


texts: Question about Gilboa and Schmeidler "A Maxmin Expected Utility With Non-unique Prior" 1989

texts: I have a question on  the proof of lemma 3.3: Let $g\in L_0$ satisfy $u \circ g = b$, $z\in Y$ satisfy $J(z)=0$ where $J$ satisfy lemma 3.2, and let $f=\alpha g + (1-\alpha)z$. Then $u\circ f = \alpha u\circ g + (1-\alpha) u \circ z$. It is then stated that $\alpha u\circ g + (1-\alpha) u \circ z = \alpha b$. This implies that $u \circ z = 0$. Why is this the case?


texts: What is the difference between personal consumption expenditure price and PCE quantity?

texts: What is the difference between these two things? How is PCE price different from PCE quantity? Also, I am confused about the difference between PCE quantity and measure of real output. For example, what is the difference between PCE quantity and Industrial Production?


texts: Why does the violation of a preference axiom not invalidate the discipline of economics?

texts: There are many examples of the preference axioms of consumer theory being violated. I feel like there are very few cases where at least one of these axioms isn't broken, so is any theory or model created under these assumptions representative of the real world?


texts: Exercise 4.7 in SLP (dynamic programming)

texts:
Exercise 4.7 (b) : Show that under Assumptions 4.10 and 4.11, $T:H(X) \to H(X)$.

$H(X)$ is the set of continuous and homogeneous of degree one functions and $Tf(x) = \sup_{y \in \Gamma(x)} \{F(x,y) + \beta f(y)\}$. The continuity follows from the theorem of maximum. I am a little confused with showing $Tf$ is homogeneous of degree one. According to the solution,
\begin{equation}
\begin{split}
Tf(\lambda x)& = \sup_{\lambda y \in \Gamma(\lambda x)} \{F(\lambda x,\lambda y) + \beta f(\lambda y)\}\\
& = \lambda \sup_{y \in \Gamma(x)} \{F(x,y) + \beta f(y)\} \\
& = \lambda Tf(x).
\end{split}
\end{equation}
$\lambda$ can be taken out of functions because they are homogeneous of degree one. But, how can we justify the change from $\Gamma(\lambda x)$ to $\Gamma(x)$? More precisely,
\begin{equation}
\begin{split}
Tf(\lambda x)& = \sup_{\lambda y \in \Gamma(\lambda x)} \{F(\lambda x,\lambda y) + \beta f(\lambda y)\}\\
& = \lambda \sup_{\lambda y \in \Gamma(\lambda x)} \{F(x,y) + \beta f(y)\} \\
& = \lambda \sup_{y \in \Gamma( x)} \{F(x,y) + \beta f(y)\} .
\end{split}
\end{equation}
I do understand the second equality, but I do not understand the third equality.
Assumption 4.10 and 4.11 are as follows:


texts:
I am looking for an up-to-date survey paper or a book chapter on panel data models.
I know there are excellent textbooks out there like

Wooldridge "Econometric analysis of cross section and panel data" (2nd edition, 2010) and
Hsiao "Analysis of Panel Data" (3rd edition, 2014)*,

but I am looking for a briefer introduction/overview. Among survey papers,

Baltagi & Raj "A Survey of Recent Theoretical Developments in the Econometrics of Panel Data" (1992) is no longer recent.
Chudik & Pesaran "Large Panel Data Models with Cross-Sectional Dependence: A Survey" (2013) is more recent but seemingly a bit narrow and rather technical.

*Chapter 13 looks pretty nice as it summarizes the entire book; it might be a good starting point.


texts: Why is saved money sitting on a bank account bad for the economy?

texts:
I've seen several news that were concerned about effect of the unspend savings that just sits on a bank account to the global economy.
Given that bank uses to money invest in things, or simply lend them to other people, isn't that money still on the market and contribution to the whole economy?


texts: Won't countries be in trouble if all sovereign debtors demand payment?

texts:
I'm trying to understand this r/explainlikeimfive analogy. I rectified typos, and simplified some  names and numbers.

Won't Cal demand  his principal back at some time in the future?

Similarly, won't countries' sovereign debts demand their principal?

For example, China holds much US treasuries and US sovereign debt. If China thinks COVID-2019 will cripple the US and wants to park its money else where, won't China demand all of its principal from the US so that it can buy Australia or New Zealand sovereign debt instead?

'Country A owes \$10  to country B, and has agreed to pay 2% interest annually. Call this Debt X.
Country B owes \$15  to country A, and has agreed to pay 1% interest annually. This is Debt Y.
Investor A is willing to purchase Debt X for \$12, because he values the steady rate of return, and believes country A is very likely to pay its debts. He isn't as sure about Debt Y, but he is willing to pay \$16 for it. Investor B thinks that investor A is going to change his mind about Debt Y and value it more highly, so he is willing to pay \$17 for it today.
Debt is traded constantly and it's valued differently. Just because 2 countries owe each other similar amounts of money, doesn't mean the value cancels out in any meaningful way.
Think of debt this way. You and your three brothers all own a house together. Each year you take up a collection of \$1000 a head for \$~4k annual upkeep on the house. One year, a tree falls on the roof, and the house needs another \$4000 bucks. Everyone could just chip in 1k each, but one brother is having a tough year, so instead, you loan the house \$4k, with the expectation that it will pay you 1% interest a year.
Your brothers agree, and over the years, this comes up a few more times. You even use debt to finance installing a new hottub. You now own \$20k in debt from the house, 1 brother owns \$5k, and for some weird reason, your neighbor Cal wants to purchase the debt from you. (He really thinks your household is trustworthy, and wants somewhere to park \$20k for 1% interest).
Now C owns \$20k of debt from your house, so C owns 80% of all your house's debt. Would you say C owns your house now? Well of course not, your house is likely worth many times more what C has claim to. If someone in your house is super worried about the situation, they could take up a collection in the house to buy the debt back from C, but it's not a popular idea, because most people can think of better things to do with their money than pay off C so they don't have to make the small yearly interest payments.


texts:
Consider the following 2x2 game:

\begin{array}{|c|c|c|}
\hline
&C&R\\\hline
M&0,0&3,5\\\hline
D&4,4&0,3\\\hline
\end{array}

This game has two distinct pure-strategy Nash equilibria.

I recall that in cases like this there is almost always a third mixed NE, and this had to do with the index theorem and having an odd number of equilibria.

Can someone provide the idea behind the index theorem and why having two distinct pure strategy NE in 2x2, 2 person game, static, complete information results into a third mixed NE with probability 1?


texts: Is a spatial effect a random or a fixed effect?

texts:
Below is the definition taken from Wikipedia(with some minor alterations)

Consider the linear unobserved effects model for N
observations and $T$ time periods: :$y_{it} = X_{it}\mathbf{\beta}+\alpha_{i}+u_{it}$ for $t=1,\dots,T$ and
$i=1,\dots,N$
Where:

$y_{it}$ is the dependent variable observed for individual $i$ at time $t$.
$X_{it}$ is the time-variant $1\times k$ (the number of independent variables) regressor vector.
$\beta$ is the $k\times 1$ matrix of parameters.
$\alpha_{i}$ is the unobserved time-invariant individual effect. For example, the innate ability for individuals or historical and institutional factors for countries.
$u_{it}$ is the error term.

The fixed effects (FE) model allows $\displaystyle \alpha _{i}$ to be
correlated with the regressor matrix $\displaystyle X_{it}$. Strict
exogeneity with respect to the idiosyncratic error term $\displaystyle u_{it}$ is still required.

Firstly, how does the definition usually used in Econometrics(I don't know which is it) relates to this one?
Reading this definition, I would say that a spacial effect term would be highly correlated to $X_{it}$ and therefore it 'fitted' the definition of a fixed effect. I'm thinking for example in a situation where (innate)ability can be highly correlated to the pollution in a certain region.
However, in the answer to this question, definition 4 of a random effect seems to also 'fit' perfectly to a spatial effect.
Maybe a spatial effect can be both... like a $\alpha_i \sim S(X_{it})$?


texts: Why low labour productivity for Govt Services in UK and USA in 2000s?

texts:
My labour productivity data for USA and UK show that the "Government services" sector for both countries are below their economies' average.

This trend is observed in the 2000s.

Are there any reasons for the low labour productivity in the sector for the 2 countries?

Referring me to some reliable sources will be helpful too.

Thank you


texts:
I won't go into detail of this model because it's really just one point that i'm confused about. This question is based on a model by Matsuyama (2007).

Agents are deciding whether to invest in a project or not
The project gives a payoff of R units of capital
R is a random, uniformly distributed variable over the interval [0,1]
Agents only decide to
invest if return on investment > return on saving; let's call this
cutoff level of capital R*
Question: what is the total level of
capital in this economy?
Answer: capital = the integral of R from R*
to 1.  [1]: http://i.imgur.com/daYZz4A.png

I understand that an integral is like a continuous sum... I just don't quite understand how we can just sum of all the R's to obtain the total level of capital? What if all the R's don't actually occur?

Thank you!


texts:
Find Pareto optimal allocations and the core for the following economies.
There are two consumers and two goods. Utility functions are $u_1(x_1,y_1)= 10x_1-(y_1-2)^2$ and $u_2(x_2,y_2) = 10y_2 − (x_2 − 2)^2$. The endowments are (0,4) for agent 1 and (4,0) for agent 2.
I have its intuitive solution but I don’t understand this.

Please help me to provide a solution by calculation. Thanks a lot.


texts: loanable funds theory: why is the supply of loanable funds equal to saving (+ dishoarding + new money)?

texts: It seems that the loanable funds theory suggests that all that is saved is supplied in the market for loanable funds. This makes sense when we are talking about 'household saving' (i.e. household income minus consumption). This money will be put on a savings account (or used to buy bonds), and if not, counts as hoarding per definition. I have a hard time grasping why it would be true for 'firm saving'. Let me explain what I mean by that: Assume a production volume of 1 million $ in a given period. Assume further that 800.000 are paid out as wages and that 500.000 of those are consumed. Overall saving is 500.000, household saving is 300.000. It's obvious that the households will want to loan out those 300.000 (and in the case that they hoard some of this money, it constitutes hoarding, i.e. negative dishoarding, and gets subtracted from the supply of loanable funds = saving + dishoarding + newly created money). But I don't understand why the firms would supply the remaining 200.000 as loanable funds. Is there some assumption that profits are rules out in principle, i.e. that production has to equal household income? I'd be very grateful for some clarification, thx in advance.


texts: Two interpretations of the Lagrange Multiplier

texts:
A question about the second answer on this thread:
Help understanding Lagrangian multipliers?

If we have a standard utility maximizing problem
$$
\max_{x,y} U(x,y)
$$
with the constraint $p_{x}x + p_{y}y = B$, where $p_{x}, p_{y}$ are the prices of $x,y$, and $B$ is the budget/income. The Lagriangian would work as
$$
U(x,y) + \lambda(B-p_{x}x - p_{y}y)
$$
and we would proceed to take partial derivatives and find critical points. My question is on the interpretation of the Lagrangian function above and specifically the multiplier $\lambda$:

1) In what way is $\lambda$ the "price we pay for not obeying our constraint"? (as one of the explanations in the linked post has it)

2) Intuitively, not mathematically, how is this equivalent to the interpretation of $\lambda$ as a "shadow price"?  What exactly is a shadow price?

3) What difference does it make to $\lambda$ if our constraint was written as $p_{x}x + p_{y}y - B$ instead? (i.e. in reverse order)


texts:
Consider a seller offering a single object for sale to two buyers with
  independent valuations – each bidder’s value is uniformly distributed
  on [0,1]. Assume that buyer 1 submits a bid that buyer 2 observes.
  Buyer 2 then has the ‘first refusal’ right to buy the object at that
  price. If she refuses, buyer 1 gets the object at the price he bid. What is the optimal strategy for buyer 1?

I have attempted the following:

$$\pi_1(v_1,v_2)=p(v_2<\beta(v_1))(v_1-\beta(v_1))$$
$$=(1-\beta(v_1))(v_1-\beta(v_1))$$

If this is an equilibrium, we must have that

$$=(1-\beta(v_1))(v_1-\beta(v_1)) \geq (1-\beta(w))(v_1-\beta(w))$$

for all $w\in[0,1]$. Hence,

$$\left.\frac{\partial \pi_1(v_1,v_2,w)}{\partial w}\right|_{w=v_1}=-v_1\beta'(v_1)-\beta'(v_1)+2\beta(v_1)\beta'(v_1)=0$$

$$\iff\beta(v_1)=\frac{1+v_1}{2}$$

But this strikes me as clearly wrong, if $v_1=0$ why should the player overbid? What am I missing?


texts: Why does an economic slowdown lead to deflation?

texts:
Usually economists say that in recession there is deflation, so increasing the money supply does not lead to a high level of inflation.
According to the Quantity theory of money, the price level is defined as such:
P = M*V/Y

Which implies that if the economy slows down, the V (velocity of money in circulation) goes down as well, leading to lower price level, hence lower inflation.
But what I don't understand, that at the same time the Y (Real GDP) goes down as well, cause of the recession, which should lead to a higher price level, hence higher inflation.


texts: Employing numerical techniques for Hotellings location model

texts:
I am trying to program a numerical solution for Hotellings locational model (with regards to the firms' respective locations). However, I have very little experience with numerical techniques. Let's assume that we are analyzing a duopoly where the firms:

choose locations in the first stage
compete in prices in the second stage

Model Specifics:

Notation:

$P_i=prices $

$x_i=locations$

Demand functions

$$F({D_1}) ={ {\frac{{{P_2} - {P_1}}}{{2t({x_2} - {x_1})}} + \frac{{{x_2} + {x_1}}}{2}} }$$

$$F({D_2}) ={1- [{\frac{{{P_2} - {P_1}}}{{2t({x_2} - {x_1})}} + \frac{{{x_2} + {x_1}}}{2}}] }$$

Profit functions

\begin{array}{l}
{\pi _1} = {P_1}F({D_1})\\
{\pi _2} = {P_2}F({D_2})\\
\end{array}

Solving through backward induction.

First-order conditions:

$$FO{C_1} =\frac{-2\,P_1+P_2+\left(x1+x2\right)\,\operatorname{t}\left(- x1+x2\right)}{2\,\operatorname{t}\left(- x1+x2\right)}$$

$$FO{C_2} =\frac{P_1-2\,P_2+\left(- x1-x2+2\right)\,\operatorname{t}\left(- x1+x2\right)}{2\,\operatorname{t}\left(- x1+x2\right)}$$

Equilibrium prices:

$$P_1=\frac{\left(x1+x2+2\right)\,\operatorname{t}\left(- x1+x2\right)}{3}$$

$$P_2=\frac{\left(- x1-x2+4\right)\,\operatorname{t}\left(- x1+x2\right)}{3}$$

First-stage profit functions:

$${\pi _1}=\frac{\left(x1+x2+2\right)^2\,\operatorname{t}\left(- x1+x2\right)}{18}$$

$${\pi _2}=\frac{\left(x1+x2-4\right)^2\,\operatorname{t}\left(- x1+x2\right)}{18}$$

I am looking for a numerical solution to find the Nash equilibrium for the problem. That is, how do I solve for the optimal locations on the [0,1] interval using numerical analysis? Do you have any tips to which methods I might use to solve it?

Any help would be appreciated!


texts: Effects between price level and interest rate

texts:
I'm looking at the relationship between the price level and the interest rate in an economy.

If the price level goes up, with fixed nominal money supply, the real money supply goes down, therefore, the real interest rate should go up.
But if real (?) interest rates go up, people would defer current consumption and prefer to consume in the future, because investing instead of consuming benefits them more than before. Thus, the price level should drop.

Is there something wrong? Am I overlooking further mechanisms, or mixing up real and nominal rates? Or is it indeed that there is a positive effect in one direction, but a negative one in the other direction?


texts: Simple Keynesian model of income determination

texts:
When determining equilibrium, we take consumption equal to C= ¢ + c' y where ¢ is the autonomous consumption or minimum consumption that would take place even in absence of income.
What could be the consequences on equilibrium income if the autonomous consumption ¢ was negative?


texts: British inflation up again, but crisis might come. What should the BoE do?

texts:
According to the latest ONS report, inflation is rising as a consequence of the (pre/post) Brexit devaluation. This graph about the Input PPI is pretty revealing (taken from here):

Yet, with the risk of an oncoming economic crisis, and interest rates at record low (probably at the ZLB), what can the Central Bank do?

Some say inflation is a good thing, as it "greases the economy" by lowering real wages. But that surely will only hit the demand even more. I'm puzzled!


texts: In Blackwell's condition for T to be a contraction mapping, we require that satisfies discounting. What is the intuition of discounting?

texts:
The discounting condition is as follow:

There exists some $\beta \in (0, 1)$ such that $[T(f + a)](x) ≤ (T f)(x) + βa$, for all $f ∈ B(X), a ≥ 0, x ∈ X$.

While the monotonicity condition makes sense, I can't give a nice meaning to this property.


texts: What is the economic meaning of a differentiated variable cost function

texts:
Given the total cost function $C(Q)=Q^3-5Q^2+12Q+75$, write out a variable cost function. Find the derivative of the variable cost function and interpret the economic meaning of that derivative.
Note: the derived variable cost function is 3Q^2-10Q+12


texts: How to calculate marginal utility with two goods?

texts:
I'm just getting started as an amateur into microeconomics and I really can't understand this thing about marginal utility when more than one good is involved:

Let's say I have the utility function U = x(y+1).

Now, from what I've studied, I  think that the marginal utilities for x and y should be:

MUx = y+1
MUy = x

I just don't get how to arrive there "mathematically", and I fear I wouldn't be able to find the marginal utilities of a more complex function, for example U = x(x+y)

Could you help me?
Thank you!


texts: Are there examples of businesses that profit from helping consumers coordinate better?

texts:
In economics, its often assumed that individuals are unable to coordinate. Moreover, its often assumed that one of the roles for the government is to help consumers coordinate. However, its also possible that businesses that find a way to help consumers coordinate could fulfill that role.
Are there examples of businesses dedicated to and profiting from helping consumers coordinate better?


texts: Relation between marginal cost and output elasticities

texts: Does anyone know of any results that show the link between marginal cost and the output elasticities analytically? I am looking at production and cost theory books but can't find any results that posit a direct dependence.


texts:
For solving this question, which assumptions/axioms should be used and should Lagrange multipliers be equal or different?

Think of an agent with utility function u() and wealth w. Assume that u() is continuus and represents a locally non-satiated preference relation. The utility maximization problem of this agent can be stated as:

max  u(x)
 s.t. p.x ≤ w

On the other hand, when the agent’s constraint is to attain a utility level h, her expenditure minimization problem can be stated as:

min  p.x
s.t. u(x) ≥ h

Show that if x* is optimal in the utility maximization problem when w > 0, then x* is optimal in the expenditure minimization problem when the constraint is to attain a utility level u(x∗).


texts:
I am reviewing old midterms to prepare for my upcoming midterm and ran across this question:

Let $\alpha , \beta \in (0,1)$. Now, let $f_{\alpha}$ and $f_{\beta}$ on $\mathbb{R^2}$ be defined as $f_{\alpha}(x)=x_1^{\alpha} x_2^{1 - \alpha}$ and $f_{\beta}(x)=x_1^{\beta} x_2^{1 - \beta}$

Now, let R be a binary relation on $\mathbb{R_x^2}$. Let ${x,y} \subset R_+^2$ We have that: $$xRy \leftrightarrow f_{\alpha}(x) \geq f_{\alpha}(y) \land  f_{\beta}(x) \geq f_{\beta}(y)$$

For which combinations of $\alpha$ and $\beta$ is this binary relation complete, for which combinations is it transitive and for which combinations is it continuous.

My thoughts

It seems this can only be complete if $\alpha=\beta$ but I can't quite finish the proof whenever I proceed WLOG with $\alpha < \beta$ Can anyone here offer an attempt at formally proving that this is complete iff $\alpha = \beta$ ?
I think that anytime we have xRy, yRz we will necessarily have xRz. That is. And so, I think this is transitive for all combinations of $\alpha,\beta$. My proof involves using the well-ordering of the reals and the definition given for this particular relation. If anyone thinks that this is not true for all $\alpha,\beta$ please let me know why/how.
I know what continuity is and how to prove it. However, I am not sure for which combinations of $\alpha,\beta$ this relation is continuous. I suspect it is continuous for all combinations of $\alpha,\beta$. Is this true? If so, can you prove it?


texts: From single-consumer-multi-units to multiple-consumers-single-unit

texts:
When I took a course in consumer theory, the economy always had a single consumer, represented by a monotone positive utility function $u(x,y)$ and an income $I$. Given prices $p_x$ and $p_y$, it is possible to calculate the demands of the consumer for products $x$ and $y$.

Now, I deal with a different type of economy: there are many consumers, each of them wants only a single unit of each product. Each consumer is represented by three positive values: $u_x$ (utility for having $x$), $u_y$ (utility for having $y$) and $u_{xy} \geq \max(u_x,u_y)$ (utility for having both $x$ and $y$). Given prices $p_x$ and $p_y$, each consumer buys either $x$ or $y$ or both, whichever gives the highest net utility (utility of product/s minus price). So it is possible to calculate the aggregate demands for $x$ and $y$.

MY QUESTION IS: Is there a natural/standard way to convert between these two types of economies?

I.e, given a utility function $u(x,y)$ and income $I$ for a single consumer, is it possible to construct a set of consumers with different $u_x$, $u_y$  and $u_{xy}$, such that the demand curves in both economies are the same?


texts: Why are most of open market orders so far from the mid price?

texts: Say there is an exchange with open buy and sell orders, why are there so many orders placed. So far away from the mid price. So for example is lowest sell order is say 1.01 and highest buy order is 1.00. It seems there is a trend that most of the open orders will reside away from the mid price. That is the total amount of orders at a given price is proportional to the distance from the mid price.


texts: Show a compound function is increasing and supermodular given its components

texts:
If $f:\mathbb{R}^n \to \mathbb{R} $ is twice continuously differentiable, has a non-negative gradient, and is supermodular, and $g: \mathbb{R} \to \mathbb{R}$ is twice continuously differentiable and convex, then $g(f(x))$ is increasing and supermodular

To show increasing I think we can just show $\displaystyle \frac{d}{dx} g(f(x)) > 0$

$$ \displaystyle \frac{d}{dx} g(f(x) = g'(f(x)) f'(x) $$

Since $f(x)$ has a non-negative gradient $f'(x) \geq 0$, but I'm not sure how to show $g'(f(x)) > 0$ as given convex tells us $g''(x) > 0$

For supermodularity, let $l, l' \in \mathbb{R}^n$; $g(f(x))$ will be supermodular if the following inequality holds:

$$ \displaystyle (g \circ f)(l \vee l') + (g \circ f)(l \wedge l') \geq (g \circ f)(l) + (g \circ f)(l') $$

I think if we had $l_i \leq l_i', \; \forall i$, then we will have equality as $(g \circ f)(l \vee l') = (g \circ f)(l') $ and $ (g \circ f)(l \wedge l') = (g \circ f)(l)$, but don't know what to do for the other cases.


texts: Can I recreate an experiment on Allais paradox using student grades as payoffs?

texts:
For a project in experimental economics, I thought of doing something related to expected utility theory/prospect theory, but using grades instead of money.

Is this reformulation of the Allais paradox conceptually right or not?

Problem 1.1:
Consider the following scenario:
A.1 – you can get an B+ with probability 100%
B.1 – you can get A with probability 10% or get B+ with probability 89% or not passing the exam with probability 1%.
+
A.2 – you can get B+ with probability 11% or not passing the exam with probability 89%,
B.2 – you can get A with probability 10% or not pass the exam with probability 90%.*

Then I will modify the problem to see if for higher stakes student's preferences change.

Edit:
If we consider that not passing the exam gives utility = 0, (as in the Allais paradox we have the same case because it corresponds to receiving 0$) the graph of the utility function, assuming constant marginal utility of grades would look like this:


texts: How was the CES production function derived?

texts:
The Constant Elasticity of Substitution production function is defined as:
(Taken from Wikipedia)
$$Q=F \boldsymbol{\cdot}\left(a\boldsymbol{\cdot}K^r+(1-a)\boldsymbol{\cdot}L^r \right)^{1\over{r}}$$
Where:
$Q=$ the quantity of output
$F=$ factor productivity
$a=$ Share parameter (i.e. $0 < a <1$)
$K, L=$ Quantities of production factors
$r= {\left(s-1 \right)\over{s}}$
$s= {1\over{1-r}}=$ Elasticity of subsitution
My question:
Though this is a quite elegant formula, how is it derived?


texts: How to find equilibrium price with inverse demand?

texts:
So I know how to do it when it is a function of Q but as a function of P I'm confused about what steps I have to take
demand:
p = 1000-0.025q
supply:
p=150+0.033q


texts: If house prices appreciate, why do developers sell them?

texts:
In many parts of the world, people buy a house expecting its value to increase over time.

But if is widely believed that the building's value will increase, what incentive is there for the developer to sell the property?  Why not hold onto the property, and sell it later at a higher price?


texts:
Pilbeam's textbook on International Finance (p. 106) says:

  (...) the immediate effect of a devaluation of exchange rate from $S_1$ to $S_2$ is to make domestic good competitive (...)

How can be possibile that an exchange rate devaluate from $S_1=\frac{p_1}{p^*}$ to $S_2=\frac{p_2}{p^*}$ with $S_2>S_1$? Here $p_1$ and $p_1$ are domestic prices and $p^*$ is a foreign country prices.

Shouldn't be the otherwayround instead, since the domestic currency is gaining value against $p^*$ ($\uparrow{S} \rightarrow \uparrow{p} $ via $S\cdot p^*=p $)?


texts: Can I use the released data on AER and JPE in my own research without permission?

texts:
I don't think JPE has suggested a specific license. However, the journal did say that the data policy is adopted from American Economic Review (AER). AER did suggest a license of Creative Commons Attribution International 4.0 (CC-BY).
That license allows reuse of data without asking permission (I just have to cite it). So my question is, may I also use the data released by JPE without asking permission?

One economic professor said if the data is specified as "replication data", then you cannot reuse it without permission.

The data is not specified as a "replication"


texts: Interpretation of coefficients in a regression with a lagged dependent variable

texts:
I have estimated the following dynamic panel data model using GMM:
          $\ln Y_{it}=\beta_0+\beta_1\ln Y_{it-1}+\beta_2\ln X_{it-1}+\epsilon_{it} $
where $Y$ is employment and $X$ is productivity.
Suppose that the estimated coefficient on $\ln X_{it-1}$ is $\hat{\beta_2}=0.3$. If I understand correctly, because of the dynamic structure of the model, it can be considered that the dependent variable is the growth rate of $Y$. Hence, is the following interpretation of the estimated coefficient correct: any $1\%$ increase in productivity would be expected to increase the employment growth rate by $0.3$ percentage points?
If not, what would be the correct interpretation?


texts: How does capital investment (factory, plant, etc.) benefit the region they are located in?

texts:
Generally, capital investment is always good for the economy, but I am not sure about the underlying mechanism. For example, if a car factory is built in a certain state, does it improve the economy solely by creating jobs and generating car sales thereby increasing the regional GDP?

I’ve also another related question. I often read that states in the U.S. frequently fight for large capital investment in their respective regions from a certain company, I’m assuming it would boost the economy tremendously. However, if a factory (lets say it’s located in state A) ONLY ships and sells its products to state B, would it improve state A’s economy as much as if sales were only made in state A?

My hypothesis is that the factory in would still improve the economy in state A due to the creation of jobs and its overall costs of production (purchasing from other businesses in the area), although it wouldn’t boost the economy as much as it would in the other scenario.

Please correct me if I happen to have said anything wrong.


texts:
Are they the same thing?

Is yield the annualized return rate?

Why when yield rise, yearly return increases but price falls?


texts: Developmental studies and industrial policy for the highly developed countries - research trends?

texts:
Developmental studies usually is field of reasearch whose object is developing countries and industrial policy studies similarly are attributed to the developing countries or the things of the past. But still I feel that issues researched by these branches of economics are becoming more and more relevant to the economics of developed countries:

How to make economic more fair and more distributed when technology developments create technological unemployment, when businesses require and reward exceptional talent but the jobs for least educated or least talented is replaced by automation and artificial intelligence
Automation and artificial intelligence create opportunities to relocate manufacturing from the offshore to the onshore, remove back in developed countries. What policy decision about allocation of education, infrastructure spending promotes such relocation, should this trend be supported by the general or local governments and how?
Industrial landscape is changing in current world, e.g. Artificial Intelligence is emering and completely new factor of production (along capital and labour). How this trend should be supported and how this trend should be guided for the benefit of all. What resources and how should be reallocated to increase competitivenes in all the new fields of technology - robotics, AI, ubiquitous computing, etc. Some of the developed countries rely on the traditional industries and they need modernization as well.
Many more question...

So - my question is - how economics and policy planning is responding to these trend. Are there research trends, topics, journals, important monographs with such perspective?

I feel that the current developments put the developed nations in the situation that is somehow similar to developing countries - in need to increase competitiveness and in need to correct social issues raised by unequal social development. So - these topics should be researched.

I know that I have raised many different topics in my question, but my aim is not to receive separate answer on any of those topics. My aim is to get the name and references to the research trend which answers those questions.


texts: Compute Nash Equilibrium in median voter game

texts:
Consider a spatial model in which two candidates A and B compete for office. The policy space ranges from -1 to 1 and each candidate can take one of three positions, -1, 0, and 1 (so that they have only three pure strategies). Voters vote for the candidate closer to their ideal points, but the location of the median voter is not known to the candidates: the median voter is located at either -1 or 1 with probability s < 1/2 and is located at 0 with probability 1 - 2s. Assume that candidate A is slightly more advantaged than B: A prevails if A and B are equidistant from the median voter but B wins if he is closer to the median voter. Winning yields a payoff of 1 and losing 0. The candidates simultaneously choose a position. Answer the following questions.

Draw a 3-by-3 payoff matrix and show if there are any pure-strategy Nash equilibria.

My attempt:
$\begin{array}{r|ccc}
A\backslash B & -1 & 0 & 1\\
\hline
-1 & 1, 0 & s, 1-2s+s & 1-2s+s, s\\
0 & 1-2s+s, s & 1, 0 & 1-2s+s, s\\
1 & 1-2s+s, s & s, 1-2s+s & 1, 0
\end{array}
$

This simplifies to
$\begin{array}{r|ccc}
A\backslash B & -1 & 0 & 1\\
\hline
-1 & 1, 0 & s, 1-s & 1-s, s\\
0 & 1-s, s & 1, 0 & 1-s, s\\
1 & 1-s, s & s, 1-s & 1, 0
\end{array}
$

Computing PSNE:
If A chooses -1
-- if s>1/2, B chooses 1
-- if s=1/2, B chooses either 1 or 0
-- if s<1/2, B chooses 0
If A chooses 0
-- B chooses either -1 or 1
If A chooses 1
-- if s>1/2, B chooses -1
-- if s=1/2, B chooses either -1 or 0
-- if s<1/2, B chooses 0
If B chooses -1
-- A chooses -1
If B chooses 0
-- A chooses 0
If B chooses 1
-- A chooses 1

There's no PSNE.

Or can I say the following? Since the BR for either player should result in a strategy that helps them win the median voter, it can't happen that both players win the median voter. Therefore, there exists no PSNE.

Characterize a MSNE if it exists. Hint: let A's mixed strategy to choose -1, 0, and 1 be p, q, 1-p-q, respectively, and B's mixed strategy be x, y, and 1-x-y, respectively.

For B to be indifferent, EU(-1)=EU(0)=EU(1). Thus, sq+s(1-p-q)=(1-s)p+(1-s)(1-p-q)=sp+sq

Solution: p=s/(2-s), q=(3s-2)/(s-2)

For A to be indifferent, EU(-1)=EU(0)=EU(1). Thus, x+sy+(1-s)(1-x-y)=(1-s)x+y+(1-s)(1-x-y)=(1-s)x+sy+(1-x-y)

Solutions: s=o, y=0, or
x=(s-1)/(s-2), y =s/(2-s)

I don't know how to translate these into MSNE. Can you also let me know if I have got everything right so far?

Thanks in advance.


texts: Why are labor, capital, and land traditionally denoted by the letters L, K, and T?

texts:
AFAIK, at least in the English-speaking world, labor, capital, and land are (in economics) usually denoted by the letters L, K, and T.

Who first popularized the use of these letters and why?

My uneducated guesses are that:

L would certainly make sense in English.
K I think is from the German Kapital.
T I think is from the French or Latin Terre or Terra.


texts: The underlying force for creating specialized areas in the cities of developing economies

texts:
Big cities in developing countries often have streets or quarters that specialize in selling a particular type of good like: books, musical instruments; or giving a specialized service like: haircuts, selling coffee. A prominent example would be the capitals like Hanoi or Bangkok.

This almost never happens in cities in developed countries. Barcelona, Spain for example has its services, shops and even supermarkets distributed uniformly along its blocks.

How to explain it in simple terms?
Is there any economic model that could effectively describe and explain the phenomenon?


texts: Effects of variables on the demand for money?

texts:
I need verification on my understanding as to whether the following factors affect the demand for money, and if so how they affect it:

Changes in Nominal National Income: will affect the transactions motive for money because changes in this will change the amount of money demanded in the economy as more/less will be demanded to buy more/fewer goods and services (shifts the liquidity preference (LP) schedule). Will have little effect on the precautionary motive if nominal national income increases, but the effect may be greater if nominal national income decreases. Changes in nominal national income may change the demand for government bonds (the main asset in focus of the Keynesian model, I presume) and may therefore change the speculative motive of the demand for money as well.

Changes in the level of inflation: higher inflation may require a higher demand for money.

Changes in the interest rates: results in movements along the liquidity preference curve. The effect is typically stronger on the speculative motive for demanding money.

Changes in overall outlook in the economy: a negative outlook may depress speculative spending which may increase the demand for money.

I believe these are the main reasons, and would like a verification as to whether what I've written is accurate.


texts: Pricing a European call option while absence of arbitrage is violated

texts:
Assume that we have a general one-period market model consisting of d+1 assets and N states.

Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with payoff $X$,  on the asset $S_1^2$ with strike price $K = 1$ given that

$$S_0 =\begin{bmatrix}
2 \\
3\\
1
\end{bmatrix}, S_1 = \begin{bmatrix}
S_1^0\\
S_1^1\\
S_1^2
\end{bmatrix}, D = \begin{bmatrix}
1 & 2 & 3\\
2 & 2 & 4\\
0.8 & 1.2 & 1.6
\end{bmatrix}$$

where the columns of D represent the states for each asset and the rows of D represent the assets for each state

What I tried:

We compute that:

$$X = \begin{bmatrix}
0\\
0.2\\
0.6
\end{bmatrix}$$

If we solve $D'\phi = X$, we get:

$$\phi = \begin{bmatrix}
0.6\\
0.1\\
-1
\end{bmatrix}$$

It would seem that the price of the European call option $\Pi(0;X)$ is given by the value of the replicating portfolio

$$S_0'\phi = 0.5$$

On one hand, if we were to try to see if there is arbitrage in this market by seeing if a state price vector $\psi$ exists by solving $S_0 = D \psi$, we get

$$\psi = \begin{bmatrix}
0\\
-0.5\\
1
\end{bmatrix}$$

Hence there is no strictly positive state price vector $\psi$ s.t. $S_0 = D \psi$. By 'the fundamental theorem of asset pricing' (or 'the fundamental theorem of finance' or '1.3.1' here), there exists arbitrage in this market.

On the other hand the price of 0.5 seems to be confirmed by:

$$\Pi(0;X) = \beta E^{\mathbb Q}[X]$$

where $\beta = \sum_{i=1}^{3} \psi_i = 0.5$ (sum of elements of $\psi$) and $\mathbb Q$ is supposed to be the equivalent martingale measure given by $q_i = \frac{\psi_i}{\beta}$.

Thus we have

$$E^{\mathbb Q}[X] = q_1X(\omega_1) + q_2X(\omega_2) + q_3X(\omega_3)$$

$$ = 0 + \color{red}{-1} \times 0.2 + 2 \times 0.6 = 1$$

$$\to \Pi(0;X) = 0.5$$

I guess $\therefore$ that we cannot determine the price of the European call using $\Pi(0;X) = \beta E^{Q}[X]$ because there is no equivalent martingale measure $\mathbb Q$

So what's the verdict? Can we say the price is 0.5? How can we price even if there is arbitrage?

Edit: I noticed that one of the probabilities, in what was attempted to be the equivalent martingale measure, is negative. I remember reading about negative probabilities, but these links 1 2 mentioned by Wiki seem to assume absence of arbitrage so I think they are not applicable. Or are they?

Is it perhaps that this market can be considered to be arbitrage-free under some quasiprobability measure that allows negative probabilities?

Edit (to address a deleted answer):

Thanks BKay.

1 So you mean there is no unique price for $X$ but we can find upper bounds? Like in your example the least upper bound so far is 0.3 then we can continue to find lower upper bounds $u_1, u_2, ...$ (or even higher lower bounds $l_1, l_2, ...$) to say the price of $X$ is in $[0,\inf_n u_n]$ (or $[\sup_n l_n,\inf_n u_n]$)?

2 Re stochastic domination, I haven't heard that term in classes, but I think I read about that before. Might that depend on the (quasi)probability measure? Under this probability measure $0.5 S_1^2$ dominates $X$ but what about under some quasiprobability measure?

3 the $q_i$'s, not the $\psi_i$'s are the probabilities


texts: Does the WTO monitor the trade of players in association football? Could they?

texts: So I understand the WTO is able to settle trade disputes. If the German Bundesliga said English players had a 1% luxury fee that went towards operation costs (A \$100,000 transfer would cost \$101,000, with \$1,000 going to the Bundesliga), would the WTO be able to step in if England went to them? What if the German government were to impose a 1% tax instead? If these aren't under the purview of the WTO, could they be in a decade?


texts: How did Portugal draw down their interest rates on pubic debt?

texts:
I notice that Portugal had a very high interest rate on its national bond issues back in 2012 but since then it has drawn down significantly:

How were they able to decrease the interest rate?


texts: What is an example application of a quasilinear utility function?

texts:
I am told a quasilinear utility function is a function like $$U(x,y) = \sqrt{x}+y$$

My Question:

Can someone provide a real world example of a quasilinear utility function?


texts: Recommendations for ways to address gaps in GDP data?

texts: I am a biologist that is using GDP data as part of my next research project and I am finding large gaps in the data, both in terms of years and countries. I am wondering what the best practice is for compiling and comparing GDP? In particular how wrong would it be to take a span of 5 years and average across countries with multiple years of data, while for other countries only using single year of data? I am interested in being able to compare multiple countries and less interested in change over time. Any ideas or literature recommendations would be greatly appreciated.


texts: What percentage of economists recommend basic welfare like food stamps and temporary assistance for needy families?

texts:
Is it similar to minimum wage in that opinion is approximately split down party lines, seen in this 2006 survey: https://people.uwec.edu/jamelsem/fte/fte/efl/teacher_stuff/articles/economists_agree.pdf?

Why or why not?


texts: Gold and loss of faith in central banking

texts:
In this article here, http://www.telegraph.co.uk/investing/gold/gold-resurgence-whos-buying-gold-and-why/ , it states that "gold tends to do....best when markets lose faith in central banking".

I understand that gold does well when other assets do badly as it acts as a store of wealth, but I cannot understand why it does well when markets lose faith in central banking. I can see that if central banking isnt working markets are probably doing badly, but the quote seems to imply a deeper and more direct connection.

Also can someone think of a historical example when this happened.


texts: Meaning of Additively Separable, Linear in X

texts:
Often I see both in micro and macro two common terminology :

Additively separable.
Linear in price or linear in probability.

I understand exactly as they sound  by looking at the functional form of the object.

But can someone provide why these structures or assumptions are sensible or unreasonable and why they are "convenient" or "useful"? The context can be anything consumer, producer, choice under uncertainty, game theory or GE. But trying to see why it is repeatedly coming up and why it is important or mathematically useful in many parts both in micro and macro.


texts: How does a Pareto efficient equilibrium scale for n individuals?

texts: Say I have a starting situation with Pareto efficient allocations between 2 individuals, now a third one comes in and changes the allocations. Now a fourth one, etc. Up untill a nth individual comes in. Do we now have to resolve (n-1) equations or n^(n-1) equilibria? How does the "difficulty" scale for n individuals? I don't know if that makes sense? Thanks.


texts: (Microeconomics) Why must fims always lower prices when there is excess supply?

texts:
This may seem like a basic question but it has been really bothering me for a while. I understand what excess supply is, and my question is regarding the firms' response to it.

All economics texbooks state that when there is excess supply

"there will be a downward pressure for firms to lower prices to the new equilibrium point".

I think this statement is not always true. I don't understand why firms always receive pressure to lower prices when there is excess supply.

For instance, if price elasticity of demand (demand elasticity) for the market is inelastic, lowering prices to get to the new equilibrium may actually lower the total revenue for the firm compared to the original price(where there was excess supply). In this scenario, I believe frims can definitely choose to simply maintain their prices at the excess supply level and ignore the stock that results from it, because the Total Revenue is higher compared to when firms lower the price to get to the new equilibrium.

So the question I wish to ask is, when there is excess supply, why are prices always lowered to the new equilibrium point where the quantity of demand increases and the quantity of supply decreases?

Why is there always a 'downward pressure' when, depending on the elasticity of demand, maintaining the price at the excess supply level can result in higher Total Revenue for the firm compared to when the price is lowered to the new equilibrium?

Every economics textbook I searched states that firms will always lower prices when there is excess supply, but I really don't get it, especially learning later on about Total Revenue, elasticity of D, etc in the later chapters of Microeconomics. As stated at the beginning, no matter how much I put my thought into it I could not come up with an answer. I would sincerely appreciate it if someome could give me a clear answer on this. :D


texts: Question on profit maximization with government taxation

texts:
(I) A monopolist has a cost function $c(q)=q$. It faces the following demand function $ q(p)=100/p$ for $p\le 20$ and $q(p)=0$ for $p\ge 20$. What are the profit maximizing price and output.

(ii) a monopolist has a cost function $c(q)=\alpha q$ where alpha is fixed marginal cost. It’s demand function has a constant price elasticity of demand whose value is $-3$. The government imposes a tax of 6 dollar per unit of output. By how much will the monopolist price rise?

My solutions are as follows:

I am not sure whether it is correct or not. Please tell me and show me my mistakes.


texts: unit iso-quant curve and unit iso-value line

texts:
This question is about international trade theory.
For the labor L and capital K, I know the theory of iso-quant and iso-cost. The price will be determined where iso-cost line touches iso-quant curve. When price changes, the iso-quant curve itself doesn't change.
However, I am confused unit iso-quant and unit iso-value theory. Iso-value line is different from iso-cost line? Unit iso-quant curve is different from iso-quant curve? When price change, the unit iso-quant curve changes?


texts:
I have no background in Economics and I am just starting with it. I was reading about the basic terminologies like domestic output, income, and etc. Then, I encountered a term "depreciation" -- It was described with a "machinery" example of a car, like this:

"You purchase a car worth \$5000 with a shelf life of 10 years. It means the consumption rate of the car is $500 per year. This consumption rate is actually the "depreciation" rate. Thus if an output of an economy ignores consumption of its machine stocks, it is referred to as 'gross' concept"

Please answer with respect to this example, and explain what the example is saying.

Thank you.


texts: Short-run price competition with capacity contraints

texts:
I am doing an undergrad course in Industrial Organization and at the end of the chapter on Short-run price competition (Bertrand and Cournot models mainly), there is a question with which I'm struggling. Here it is:

  Consider a market with two price-setting firms producing a
  homogeneous product. The demand function is q = D(p) = 1 – p,
  which implies the inverse demand p = 1 – q1 – q2. The two firms
  have capacity constraints q1hat and q2hat , where q1hat + q2hat = 3/5. The
  marginal cost of production is zero for qi ≤ qihat and infinite for qi >
  qihat for any i = 1,2. Finally, assume that consumers are rationed according to the efficient rationing rule.

  i. Show that if q1hat = q2hat , there is a unique Bertrand-Nash equilibrium
  where p1 = p2 = p* = 1 – q1hat – q2hat

  ii. Show that when q1hat ≠ q2hat, the equilibrium under part (i) breaks
  down when the firms’ capacities are too dissimilar.

So for part i. I basically adapted part of the material from the chapter and said:

  To show that this is a Nash equilibrium, we need to show that none of the
  firms has an incentive to unilaterally deviate from this equilibrium.

  Is it profitable for firm 1 to set a price lower than p*, given that firm 2 sets price p*? The answer is no. By charging p* firm 1 sells exactly q1hat. Firm 1 cannot produce more than q1hat anyway, so by reducing its price below p* it would simply sell the same quantity at a lower price and would therefore make
  less profit.

  Is it profitable for firm 1 to set a price higher than p*, given that firm 2 sets price p*? The answer is again no, but the argument now is more subtle.
  Suppose that firm 1 sets a price p ≥ p*. Then it has residual demand 1 –
  p – q2hat, because at price p total market demand is given by 1 – p and firm
  2 sells q2hat. Firm 1 makes profit Π = p(1 – p – q2hat). Using the inverse demand function, the expression for profit can be written as (1 – q1 – q2hat)q1, where q1 is the quantity sold by firm 1 at price p. Note that the profit function Π = (1 – q1 – q2hat)q1 is exactly the same as the profit function of a firm that chooses output q given that the rival firm chooses output q2hat. This profit function is concave in q, that is Π''(q1) < 0. Also, ∂Π/∂q1 = 1 – 2q1 – q2hat. Evaluated at q1 = q1hat, this derivative is equal to 1 – 2q1hat – q2hat, which is positive because q1hat + q2hat = 3/5 and q1hat = q2hat so 2q1hat + q2hat = 9/10. In other words, if firm 1 starts from q1hat and marginally reduces its quantity, its profit will fall. This result and the concavity of the profit function ensure that any reduction of q1 below q1hat will reduce profit. Another way of saying this is that if firm 1 starts from p* and increases its price, its profit will fall.

So far so good, the concavity of the profit function implies that when we close in to the maximum marginal profit, the slope (or the derivative of profit with respect to q) will be closer and closer to 0.

Now part ii. gets me and I don't know how to attack it. I thought about making 2 cases, one where q1hat is close to 3/5 and one when it is close to 0. The profit function and its derivative are the same as for i. and the constraint q1hat + q2hat = 3/5 is still applicable from what I can understand, so demand can't be met. For me the part about setting a lower p is still the same as in part i. But the part about setting a p higher than p* is not as clear.

Can anybody help?


texts: Linearization of the dynamic system (I did it, but I have a mistake that I cannot catch. Help me please)

texts:
I have the following dynamic system in discrete time

For p is price, d is demand and s is supply.

$$p_{t+1}-p_t= a(d_t-s_t)$$
$$s_{t+1}-s_t=bp_ts_t-ws_t$$
$$d_t= k-gp_t$$

I have to linearize this system around the nontrivial optimal equilibrium point.

—-

What I did attempt is

In the equilibrium, $p_{t+1}=p_t=p^*$ and $s_{t+1}=s_t=s^*$ and $d_t=d^*$

So the first equation implies that $d_t=s_t$. Thus, $d^*=s^*=Q^*$

So, by the second equation, $p^*=w/b$

And the third equation implies that $s^*=d^*=Q^*=k-(gw/b)$

Now let’s linearize the second question because first and third equations are already linear.

$$s_{t+1}=[(bp^*-w+1)s^*]+[(bp^*-q+1)(s_t-s^*)]+[bs^*(p_t-p^*)]$$

$$s_{t+1}=s_t+(bk-gw)p_t -kw+(gw^2/b)$$

However, the supply curve is defined in general as $s_t=\alpha+\beta p_{t-1}$

But in my solution,  $s_{t+1}$ depends on $ s_t$. I think this is wrong. Where is my mistake?

According to the suggestion from @1muflon1

$$s_{t+1}=s_t+(bk-gw)p_t -kw+(gw^2/b)$$

$$s_{t+2}=s_{t+1}+(bk-gw)p_{t+1} -kw+(gw^2/b)$$

$$s_{t+3}=s_{t+2}+(bk-gw)p_{t+2} -kw+(gw^2/b)$$

...

$$s_{t+n}=s_{t+(n-1)}+(bk-gw)p_{t+(n-1)} -kw+(gw^2/b)$$

When we add them, we get that

$$s_{t+n}=s_t+\sum_{i=t}^{t+n-1}(bk-gw)p_{i} -\sum_t^{t+n} (kw-(gw^2/b))$$

And how to proceed that?


texts: Does Fannie Mae directly or indirectly get money that is printed from the federal reserve to buy mortgages, or have they ever? If so, when has this happened? How much money? What is the process by which it gets to them?


texts: What are the best ideas for ecological accountability / justice within capitalism?

texts:
What are some best practices for including the hidden costs of ecological disruption into economic decision making?

For instance, how can the cost-benefit of pollution be shifted toward conservation or remediation?  How can costs to the environment in terms of air emissions, coastal erosion, or forest destruction be quantified (absolutely or relatively) and be factored in to the costs of goods and services?

Regulations/enforcement/fines?  Taxes?  Lawsuits?


texts:
Question

What are the great "constants" of economics?

Background

In his Structural Slumps (Chapter 3, p.20), Phelps refers to the great "constants" of economics. He explains that the natural unemployment rate has been treated as one of these great constants. So, what else is a great constant in economics? The natural interest rate? The natural level of output? And, so on? References would be greatly appreciated!


texts: Compound interest problem using PMT in Excel

texts:
So I found this example in the net

  Compound interest formula (including principal):

  A = P(1+r/n)(nt)

  If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, the value of the investment after 10 years can be calculated as follows...

  P = 5000. r = 5/100 = 0.05 (decimal). n = 12. t = 10.

  If we plug those figures into the formula, we get:

  A = 5000 (1 + 0.05 / 12) ^ (12(10)) = 8235.05.

  So, the investment balance after 10 years is $8,235.05.

Okay, I'm using the PMT calculator in excel and I plug in these values

I get 53.03\$ per month, okay if I multiply it by 12*10 years I should get the same amount as the site, but now I get 6 363,93$

Why not the same? I use the pmt function in excel


texts: How to explain the flattening of the SRAC curve?

texts:
I discovered that there is a way that Short-run average cost curve could become 'flatter' instead of shifting. Yet I cannot find an explanation of why and how it can become flatter.

For example, in the picture above, the SRAC4 curve is more 'flat' than the other ones. Why is this?
I already looked at Economics by John Sloman, but could not find anything.


texts: Estimating $TFP$ using Cobb-Douglas production function

texts:
Suppose we want to estimate total factor productivity (TFP) under time series framework. Let assume that the production function is given in the Cobb-Douglas form, i.e.
$$Y_t=A_tK_t^\alpha L_t^\beta,$$
where $A_t$ is the total factor productivity (TFP), $K_t$ is capital stock and $L_t$ is labor. After log-linearization the empirical model is given (time series are $I(1)$, therefore we take in the first-difference)
$$\Delta ln Y_t=\mu+\alpha \Delta lnK_t+\beta \Delta  ln L_t+\epsilon_t,$$
where $TFP_t=\widehat \mu+\widehat \epsilon_t$;$\widehat \mu$ is average factor productivity and $\widehat \epsilon$ is the deviation from average over time.
Questions

In the above specification, by construction, $\mathbb{E}\widehat \epsilon_t=0$ (moment condition). It means that by estimating the above specification yields to $TFP_t=\widehat \mu+\widehat \epsilon_t$, which hasn't any trend (upward- or dawnward-sloping). However, it is natural to assume that $TFP_t$ time series can have a time trend. If no, what is the economic interpretation of no-trend in the $TFP_t$? Is it possible to derive time-trend in the $TFP_t$?
What is the interpretation of the estimated $TFP_t$?
Suppose the estimated $TFP_{2020}=2$ or $TFP_{2019}=3$, how these numbers can be interpreted?

Thanks in advance!


texts:
What is the difference between the cash rate and interest rate? I (in Australia) googled cash rate and according to wikipedia it is the "central bank charges on overnight loans between commercial banks."
If anyone can explain what  "overnight loans" are and provide a simplification of this process would be really appreciated. Based on some superficial readings, the cash rate influence markets' interest rate? It would also be nice if someone can provide a definition for the respective terms. Many thanks.


texts: What prerequisite courses do I need in order to specialize in Mechanism/Market design theory?

texts: After seeing some lectures on Youtube, I came to learn about a few, namely, Game Theory and Microeconomics, but I am not sure whether this is all that is needed. Please do add as many courses as possible or refer to the courses that should be taken from the following list: http://www.lse.ac.uk/resources/calendar/programmeRegulations/undergraduate/BScEconomics.htm


texts:
I first wanted to ask this on philosophy@SE but, on a second thought, decided this might be a better place.

If we defined a general policy's objective being "to maximize well being and minimize suffering", we can say that "suffering" in that sentence is the opposite of well-being. But how do you define "well-being" by using lower level indicators, none of which are regressivly axiomatic and in a way that's so abstract that it's difficult to blame for cultural or any other kind of bias?

I would imagine that, at this point, defining well-being should be a province of economics and not philosophy. Do economists concern themselves with the question of defining well-being at an individual or collective level, by using natural/rationalist terms so that no amount of regression of the origins of any preceding term's definition runs into a proposition that will be considered "axiomatic"?


texts: Who can recommend any good blogs or other news sources on economics with a European view. I'm looking for something in the vein of FT, which is already an extremely good source, but I'd like to broaden my intake.


texts: Selecting the best utility function for households

texts:
I have little to no background in micro, but I'm learning about utility functions.

It seems that there are many forms of utility functions for households. In general terms, how does one go on to select a given functional form. Are there a class of utility functions for households that are better than others? How does one even judge better, in this context? Does the selection of a utility function depend on the context and analysis at hand?


texts: What is the optimal forecast for the following moving average model?

texts:
Suppose that we have an MA(1) model where $y_t=\epsilon_t-\frac 1 2 \epsilon_{t-1}$ and $\epsilon_t$ are i.i.d.
I want to find an optimal forecast of $y_{T+1}$ in the form of $Cy_T$ where C is a constant. What is the best choice of C?
I have computed that

$\begin{aligned}
&y_{T+1}=E(y_{T+1}|I_T)=E(\epsilon_{T+1}-\frac 1 2 \epsilon_T|I_T)\\
&=E(\epsilon_{T+1}|I_T)-\frac 1 2E(\epsilon_T|I_T)\\
&=0-\frac 1 2\epsilon_T=-\frac 1 2 \epsilon_T\\
&\epsilon_T=y_T+\frac 1 2y_{T-1}+\frac 1 4 y_{T-2}+......+{1\over 2^{t-1}}y_1+0\\
&y_{T+1}=-\frac 12 \epsilon_T=-\frac 12y_T-\frac 1 4y_{T-1}-\frac 1 8 y_{T-2}-......-{1\over 2^{t}}y_1
\end{aligned}$


texts:
In wikipedia, the main difference between GMM and MSM(Method of simulated Moments) is in the former the moment/orthogonality conditions can be evaluated analytically, while in the latter they cannot and we have to use sample analogues.

However, in wikipedia and other texts, with GMM we also use sample analogues.

So, what is the difference between both methods?

Any help would be appreciated.


texts: What stops a government in partnership with its central bank from lowering interest rates and then borrowing at this lower rate to fund investments?

texts:
For example, in the UK, after the Brexit vote, the Bank of England decided to lower reserve interest rates to 0.25%. This, as I understand it, has the knock on effect of lowering the interest rates of loans. If a government wants to borrow to fund particular investments, such as renewable energy, a new bridge, trains, etc, it would cost them less under the new, lower interest rate. So my question is, why aren't low interest rates the standard strategy for a government? Surely they would always want to borrow at cheaper prices?

I can think of a few reasons but I'm not really sure if they're correct.

Savers would get annoyed and move their money to another currency.
Ideological positions (neoliberalism/austerity instead of Keynesian economics)

Seems like I'm missing something obvious here..

Cheers!


texts: Are financial markets "unique" for each "currency pair", or are they simply "translated"?

texts:
This is something I've been long wondering about.
Let's say that I have statistics showing the daily closing Bitcoin price in USD since early 2009. Great. Now, if I wanted to get the daily closing Bitcoin price in SEK or EUR or whatever currency instead of USD, I could use historical exchange rate data to translate all the data points to SEK prices, or EUR prices...
Or could I?
This is based on the assumption that all the non-USD markets are simply "translated" from the USD price; that they are all interconnected. For example, if I buy X Bitcoin at some date using SEK or EUR, that is reflected in the USD Bitcoin price for that day, only translated into USD?
Or is each market (currency pair) "unique"? Maybe there are very, very few people trading Bitcoin in SEK, so the price could be completely different in SEK for one Bitcoin at any given date, differing completely from the USD Bitcoin price for that date?
I hope I've asked my question clearly. I'm trying to figure out if the data is simply "translated", or if there are unique markets for each currency which are their own "closed ecosystems".


texts: How is seigniorage redistributed in the Eurozone?

texts:
An ECB page notes that:

  As euro banknotes travel freely across borders, at any one time the number of banknotes in circulation registered at each national central bank can vary enormously. The figure for one bank could even be zero or negative. For example, when German tourists seeking a Latin adventure take euro banknotes issued by the Deutsche Bundesbank with them to Spain, these notes are finally lodged at the Banco de España. As banknote issuance is an entirely demand-driven process, this means that the Banco de España would now need to put fewer notes into circulation because it is benefiting from the notes crossing the Pyrenees. For this reason, the central banks in the euro area balance out the amount earned on banknote issuance among themselves.

How do the Eurozone central banks (yes the plural is correct in this case) do that balancing?


texts: Inflation, Future, And Value of Money - deciding to buy a house

texts:
I live in Asia where the inflation rate is approximately around 4.5-6% (average) in last 10 years. If in the next 10 years I plan to buy a house in other country (any country which I have the currency). Should I choose to buy the currency which have the lowest inflation rate?

For example, if I hold US Dollar 100,000 right now, and I can buy a house. But with the inflation rate of 1.3% in 10 years the price will be approximately 13% (USD13,000). Means my money will not enough and I must add 13,000.

However, If I hold JPY 11,000,000 right now and I can buy house too right now, with the inflation rate of 0.1%. it will be only 1% increase in next 10 years (about 110,000 JPY). It's not so much.

So, Is my idea correct?


texts: Why are US equity prices and inflation inversely correlated?

texts:
Many comments on this r/stockmarket Reddit thread hypothesize an inverse correlation between USD value and US equity prices. Why would this be true in theory?

It's not true in reality, right? Has the correlation of inflation and stock prices changed in the United States over the last two centuries? - ScienceDirect

Abstract
The relationship between stock prices and the inflation can be either negative or positive, depending on the strengths of various theoretical channels at work. In this study, we examine the dynamic conditional correlations of stock prices and inflation in the United States over the period of 1791–2015 under a time-varying framework. The results of our empirical analysis reveal that correlations between the inflation and stock prices in the United States evolve heterogeneously overtime. In particular, the correlations are significantly positive in the 1840s, 1860s, 1930s and 2011, and significantly negative otherwise. The policy implications of these findings are then discussed.


texts:
Hello in a simple treatment model

$$y=\beta_0+\beta_1w+e$$

where $w$ is unity for treatment by group.  Should you add dummies for the groups to control for differences. I read somewhere that you should never but I cannot remember where or why.


texts: How can a country develop the skills of its population and have them stay?

texts:
Suppose, I am a leader of a country, and a lot of my citizens go to the Gulf states (see 3.1, Page-09) to work as unskilled laborers. I see my population working abroad as laborers as a prestige concern of my country, and strategic baggage.
What can I do so that these laborers happily come back home, happily stay in their own country, and contribute to their own country's economy?


texts: How is it that Apple is paying no taxes in New Zealand?

texts: Apparently Apple pays no taxes in New Zealand, even though it has employees and profit-making operations there amounting to over a billion dollars per year. The cross linked article does not really explain how it is that they are paying no taxes. What are the relevant rules?


texts: Clearly explaining the concept of "normalizing" price and relative prices to undergraduate

texts:
I am trying to clearly explain to the concept of "normalization" or relative prices. Because students are so used to just think of prices in absolute terms, it is initially tough to make the leap to the "relative" or "normalization" concept.

What is your angle if you were to explain this to an econ 101 student?

For example, the toughest part is to explain the "need" for looking at the ratio of prices. Who cares? Why is it useful?

Thanks bunch.