New answers tagged

0

It is safe to assume that if the consumer passes away, his creditors get his endowment. This actually happens in real life. $B$ should obviously be zero. As far as the second period is concerned you can represent it as a von Neuman-Morgenstern utility from the lottery: $\beta u(c_2)$ with probability $p$ and $0$ with probability $1-p$. I.e. $U(c_1, c_2) = ...


1

The article Quality of Information and Oligopolistic Price Discrimination by Liu and Serfes covers this topic in great detail. It also has a rather nice literature review.


2

Yes marginal refers to the last or one more unit or person. I don’t see there any contradiction if you have 2 people in room and third person joins it’s both the last person and one more person. If you are looking for a precise definition then in economics the concept of margin is connected to the first derivative (instantaneous rate of change) of function ...


1

Captive insurance is an insurance for purpose of insuring the owners of the said insurance. It’s a kind of self-insurance where multiple agents pool their capital together to insure themselves. So the term in that sentence refers to the pool of resources for insurance. It’s called captive because the modern concept of this kind of insurance was first ...


2

By definition, a direct mechanism is a mechanism that asks all agents for their types and then produces some outcome. Formally, it is a mechanism $\langle M,g\rangle$ in which $M_i$ is wlog equal to $i$'s type space, usually denoted by $\Theta_i$. In your example, there is no such restriction. However, for any indirect mechanism there exists an equivalent ...


3

At time $(t-1)$, the investor buys some risk free bond, $B_{t-1}$ and some risky asset $X_{t-1}$ at price $P_{t-1}$, such that the budget constraint holds, i.e. $$ W_{t-1} = B_{t-1} + P_{t-1}X_{t-1} $$ At period $t$, one unit of risk free bond pays off one unit, so $B_{t-1}$ units of risk free bonds pays off $B_{t-1}$ units of wealth at $t$. For a risky ...


5

One interpretation I can offer. The demand function can be expressed as: $$Q_1 = Q_1(p_1,p_2)$$ Let us take the total differential: $$dQ_1 = \frac{\partial Q_1(p_1,p_2)}{\partial p_1}dp_1+\frac{\partial Q_1(p_1,p_2)}{\partial p_2}dp_2$$ Assume that $Q_1$ remains unchanged with respect to a change in prices. This implies that $dQ_1=0$. Solving the ...


0

The gamble: $$g = \left(\pi \circ 98, (1-\pi)\circ100\right)$$ The expected value of the gamble: $$\mathbb{E}[g]= \pi\cdot 98 + (1-\pi)\cdot 100$$ Expected utility: $$u(g) = \pi \cdot \ln (98) + (1-\pi)\cdot \ln (100)$$ Risk premium is such that: $$\ln \left(\mathbb{E}[g]-P\right) = \pi \cdot \ln (98) + (1-\pi)\cdot \ln (100)$$ Where $P$ is the risk ...


4

Suppose that the vector $W=\left(w_1,w_2,\dots,w_n\right)$ represents wealth in $n$ possible states. In addition, assume the probability of each state occurring is represented by the vector $\pi=\left(\pi_1,\pi_2,\dots,\pi_n\right)$. We can express this as the simple gamble: $$g = \left(\pi_1\circ w_1,\pi_2\circ w_2, \dots, \pi_n\circ w_n\right)$$ The ...


-1

If you can do A or B and make gain of a or b, then the opportunity cost of doing B would be b-a. If a were larger then doing B would result in an opportunity loss. Alternatively if you do nothing then the opportunity cost would be the larger of a or b which you could have made by doing A or B instead of nothing.


0

$$\max \sqrt{x}+y$$ subject to $p_1x+p_2y\le m$ Lagrangian function is $$L=\ sqrt{x}+y+\lambda (m-p_1x-p_2y)$$ FOCs $$\partial L/\partial x= 1/2x^{-1/2}-\lambda p_1\le 0$$, $x[1/2x^{-1/2}-\lambda p_1]=0$ For $x>0$ $$\partial L/\partial y=1-\lambda p_2\le 0$$ $y[1-\lambda p_2]=0$ for $y>0$ $$\partial L/\partial \lambda= m-p_1x-p_2y\le 0$$ $\...


2

This thread has some game trees. In case you want put them on your documents, you can do like this (using LaTeX with istgame package): \documentclass{standalone} \usepackage{istgame} \begin{document} \begin{istgame}[font=\scriptsize] \setistgrowdirection{east} \cntmdistance{20mm}{20mm} \cntmAistb{q_1=0}[at end,below]{q_1=1,000}[at end,above] \...


-1

Define $p_r = \frac{p_1}{p_2}$, and $m_r=\frac{m}{p_2}$. Consumer has the following maximization problem: $$\max_{x_1}a\ln x_1+ m_r-p_rx_1$$ Take the first order condition and get Marshallian Demand for $x_1(p_r)$. Use the budget constraint to get $x_2(p_r,m_r)$. You should also take the second order condition and confirm under what values of $a$ you will ...


0

Let me rewrite your Option B as follows: £10 with probability $p$ and £1 with probability $1-p$ where $p\in[0,1]$ varies across the items in the list of options. Let $\bar p$ be the point where the subject's choice switches. For example, subject chooses Option A for all $p<\bar p$ and Option B for all $p>\bar p$. Then we can use the indifference ...


0

The population standard deviation: $$\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(x_i-\mu\right)^2}$$ The sample standard deviation: $$s=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}\left(x_i-\bar{x}\right)^2}$$ Where $\mu$ is the population mean, $\bar{x}$ is the sample mean, $N$ is the size of the population, and $n$ is the size of the sample. We need to first ...


3

Rationality requires the following: Completeness For all $x, y \in X$, either $x \succsim y$ or $y \succsim x$ or both. Transitivity For all $x, y, z \in X$, if $x \succsim y$ and $y \succsim z$, then $x \succsim z$. Also note that if $x=y$ then completeness implies that $x\succsim x$. So reflexive preferences follow from completeness. So I would say ...


7

This looks like constant relative risk aversion (CRRA) utility . Usually CRRA is written like $U = \frac{C^{1-\rho}-1}{1-\rho} $ (I omitted second part for brevity) in your case $a=1-\rho$. $\rho$ is the relative risk aversion. By extension $a$ is the function of $\rho$ so as $a$ increases (due to smaller $\rho$) the person should become less risk averse.


4

Yes it can be used. The theory applies regardless of what’s the source of comparative advantage. For example, if country A is able to produce 200 widgets and 50 apples and country B is able to produce 5 widgets and 45 apples you get comparative advantages - A in widgets and B in apples - and it does not really matter if these are due to technology, ...


4

With my very limited knowledge of development economics: $\left(\frac{x_m}{x}\right)^\alpha$ represents the proportion of the population that has an income larger or equal to $x$ where $x\geq x_m>0$ and $x_m$ is the minimum income amount. Example 1: Suppose $\alpha\rightarrow 1$ and the minimum income in the economy is $50,000$. We may ask the ...


3

Hint: find $\ln(U(x))$ and then use L'Hopital's rule to find the limit as $\rho\rightarrow0$.


1

It seems the instructor is referring to the opp. cost of giving up the profit from selling x amount of apples. Which would be an opportunity cost. Opportunity cost isn't strictly alternative based, for example: If I'm selling 10 apples today, the opportunity cost of be only selling 9 apples tomorrow is whatever profit I stand to lose from not selling the ...


2

hint: you are supposed to show the utility function represents the same preferences not that the utility functions are exactly same. Recall that any monotonic transformations of function preserves the original order of preferences. So you only need to show that in the limit one function is monotonic transformation of the other.


4

Opportunity cost is the price of doing something in terms of something else. For example, cost of taking trip to Prague may be giving up new bike. In this broad sense marginal cost of producing one unit of q would be also it’s opportunity cost because you could use the same resources to produce something else. Opportunity cost of producing 1 widget at 5€ ...


0

I don’t think that there are any classes of functions where you can ex ante say that it is elastic or inelastic, since this will depend on the function parameters. However, there is a class of functions for which you can say the elasticity is always constant, these are isoelastic functions. For example, consider function: $$Q(p)=ap^b$$ By definition ...


3

Your conjecture seems to be contradicted, at least for small values of $\sigma$. You can draw the function with the following R-code: qq_f = function(x,k,h,sig){ -pnorm(-k, sd=sig)*( (dnorm(h*(1-x), sd=sig))^2 ) - 0.5*dnorm(-k^2, sd=sig)*( 2*pnorm(h*(1-x), sd=sig) -1 )^2 } curve(qq_f(x,k=0,h=1,sig=0.5),col='blue',xlim=c(-1,3),type='l',main="A ...


0

An IEEE journal a few decades back proved that within epsilon smaller than the vig brokers would charge you that you cannot predict the stock market well enough to make money.


1

If the other two methods did not work out for you, another possibility, albeit a more difficult one: Set up the bordered Hessian: $$\bar{H}=\begin{bmatrix}0 & \frac{\partial v}{\partial p_1} & \frac{\partial v}{\partial p_2} & \frac{\partial v}{\partial p_3} & \frac{\partial v}{\partial m}\\ \frac{\partial v}{\partial p_1} & \frac{\...


5

Complete market is a market where every possible asset or good can be assigned a price and where you have perfect information, can make perfect contracts and zero transaction costs. Any market can be complete regardless of its market structure. So you can have complete market dominated by monopoly, or oligopoly or monopolistic competition etc. Perfectly ...


0

A pretty trivial assumption would do it: If the consumers preferences are strongly increasing, i.e. $$ x \succ_i y, \mbox{ if $x \geq y$ but $x \neq y$ }, $$ and unbounded for all $i$, then no $x$ can be an optimal bundle if $p \notin \mathbb{R}^C_{++}$ (assuming there are $C$ commodities). So zero price cannot arise in an Arrow-Debreu equilibrium.


1

If you want some simple model of stock prices consistent with efficient market hypothesis it would be random walk: $$p_{t+1}= a+ p_t +\epsilon_t$$ You don’t even need to model cycles there explicitly just due to random chance it will exhibit some ‘cyclical-like’ behavior. Although, I know it’s not actual cyclical behavior because it can diverge it’s ...


2

The EMH applies to assets, not just stocks, and its implications are more relevant for investors who own part of the market - not the entire thing. This is important, because it's the difference between looking at a closed system versus an open one, and between populations versus samples. People make money all the time by cycling between stocks, bonds, ...


1

Utility is not the same as consumer surplus. Consumer surplus is the difference between price an individuals pay and their individual reservation price. Utility is a measure of gratification that can be completely different from consumer surplus and depending on what kind of utility we are talking about it might not even be possible to assign integer value ...


2

Marshallian Theory is notoriously about computing consumer surplus (and then welfare changes). But it would be nonsensical to perform such calculations if at the level of one individual, the unit of valuation of surplus, i.e. the marginal utility of money (or the utility of one extra euro), were changing before and after changes in, say, prices. Also, what ...


1

Such an example does not exist. Suppose non-dictatorship is violated. WLOG, let individual $1$ be the dictator among $n$ individuals. That is, the social choice function always selects an alternative that ranks highest in $1$'s preference, i.e. $$f(\succ_1,\dots,\succ_n)\in\arg\max\{\succ_1 | x\in X\}.$$ For weak Pareto efficiency to also be violated, we ...


2

Remember that consistency describes how the estimator behaves in the limit as N asymptotically approaches infinity. Assuming no errors in your math up to this point, you need to consider how your error terms $U_i$ behave asymptotically as well.


0

I think it might have something to do with how much a phone model is valued in certain markets. For example, the amount of utility you get from a certain phone model is higher than another phone - they are not perfect substitutes for each other. Hence, the discounted utility of the phone will still be higher, because the user still values it higher. There ...


0

You need to be clear on which one is the effect and which one is the cause in the elasticity formula. Also this formula relates two percent changes of x and y and not proportions (which is a different concept). In this case, it seems that the income changes (and price remains constant), so we want to see the effect on the demand (quantity). Therefore Var%...


1

This problem is quite specific to economics. The correct statement is: Proposition If $u(\cdot)$ is quasiconcave, strictly increasing, and continuous, then $\forall x$, there exists $p \gg 0$ and $w \geq 0$ such that $x \in x^*(p, w)$, where $x^*(p, w)$ is the Marshallian demand correspondence. Proof Quasiconcavity of $u$ means the upper-contour set $\...


2

Assumptions $1$ to $3$ are sufficient to obtain a linear representation when $X$ is open and convex. We proceed in two steps. Step $1$: We will repeatedely use the following consequence of continuity and $A1$: If $x \sim x^{\prime}$, then $x \sim x + \lambda (x^{\prime} - x)$ for every $\lambda \in \mathbb{R}$ such that $x + \lambda (x^{\prime} - x) \in X$....


0

...I'm confused if we can count the root of the contract curve (point M) as one of the efficient points since it's part of the contract curve? The contract curve is, by definition, the set of all Pareto efficient allocations. Therefore, any point that you choose on this curve--even the end points--is also Pareto effecient. In this case the indifference ...


0

The end points of the contract curve (assuming that preferences are strictly monotonically increasing) is efficient. Consider point $Q$ where person A consumes everything (let's call this $(x_A, y_A)$.) Since preferences are strictly monotonically increasing, any deviation from that point would make person A worse off. The usual "tangent indifference ...


2

It is almost true. There are examples of demand that have a negative definite Slutsky matrix but fails the Weak Axiom. However, if we ask that $$v \cdot S(p,w) v <0 $$ whenever $v \not = \alpha p$ for any scalar $\alpha$ (i.e. $S$ is negative definite for all vectors except those proportional to price), then the Weak Axiom holds.


0

Edit: My previous answer contained a mistake for the case where $x$ is restricted to $\mathbb{R}_{+}^{n}$. I removed this case from my answer. Take $\bar{U} > 0$. Let's denote $\delta = (\delta_{1}, \ldots, \delta_{n})$ and $p = (p_{1}, \ldots, p_{n})$. Assume $p \neq 0$. We want to solve \begin{align*} \min_{x\in\mathbb{R}^{n}} p \cdot x \qquad \text{...


3

For some intuition, rewrite the problem as the consumption problem $\max_{(c, l)\in\mathbb{R}_{+}^{2}} (cl)^{0.5}$ subject to the constraint $c/w + l \leq 1$. The optimal level of $l$ is then given by $l = 1/2$ as per the usual solution for Cobb-Douglas preferences. The intuition for why $l$ does not depend on $w$ in this example is the same intuition for ...


0

The assumptions are that the agents understand the situation, model or game they are in, that they are rational - in economic sense of the word and try to maximize their utility. I think that one reason why you might have trouble finding a list of assumptions behind rational expectations is that rational expectations don’t really rely on their own ...


1

Suppose you are one of the bidders and fix the strategy of the other one to be the one supposed. Your payoff will be $\mbox{Pr(winning the auction, i.e., b>b')}(v-b)$, with b being your bid and b' being the other's bid and v being your valuation (or type). Now, imagine you are the type-5 player. If you bid an integer less than 4, you lose for sure ...


0

Suppose we're both price-takers in the market, so prices are fixed with respect to our actions. This implies that there is enough of each good for us to trade until we are indifferent to further trading (which, as utility-maximizers, we will do by definition). Each of us will sell one good and buy another until our private MRS is equal to the slope of our ...


0

for this problem you must conciser two possible utility functions: $$u(\text{x})=x_1+x_3\ \ \text{if} \ \ x_1<x_2$$ $$u(\text{x})=x_2+x_3\ \ \text{if} \ \ x_1>x_2$$ The demands of these then proceed how you would for any case of perfect substitutes. However you must list them for each case. Hope this helps


1

The idea that the long run average cost curve (LRAC) must pass through the minimum points of the short run average cost curves (SRAC) is a fallacy, but it seems to be a remarkably plausible one. It was the source of a famous error by the economist Jacob Viner, referred to in this paper by Silberberg. Underlying the fallacy is perhaps an assumption that the ...


0

Nothing will be better than going through the textbook. Lecture's slides can be beneficial, you can google newer versions or access older here: http://www.mtholyoke.edu/~mirobins/econ212.html. I also used notes done by Łukasz Woźny, from SGH: http://web.sgh.waw.pl/lwozny/LectureNotes.pdf - they are not entirely based on Varian's textbook but might be helpful ...


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