3 votes
Accepted

Spence-Mirrlees Single Crossing Condition

Is it possible that you have a typo in the SMSC condition. I think it should be: $$ \frac{\partial}{\partial \theta} \left[-\frac{\partial u/\partial q}{\partial u/\partial p}\right] > 0. $$ If so, ...
tdm's user avatar
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3 votes

How price is determined in the following monopoly model question?

So far so good for part (a). The basic idea for part (b), is that if the parking lot goes first to set the price first, the store is going to have to allow the costumers to get at least enough ...
Whis's user avatar
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3 votes
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Prove: The law of demand holds if WA, Walras' law, homogeneity of degree 0, and homogeneity of degree 1 in wealth hold for Walrasian demand functions

We need to show that: $$ (p - p')\cdot(x(p,1) - x(p', 1)) \le 0. $$ Note that if $x(p,1) = x(p', 1)$ then this is obviously satisfied, so assume that $x(p,1) \ne x(p', 1)$. Note that the condition is ...
tdm's user avatar
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2 votes
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CES function: Lagrangian or Kuhn-Tucker

If $\rho < 1$ then the marginal utility (say with respect to $x_1$ equals): $$ \frac{\partial U}{\partial x_1}(x_1, x_2) = x_1^{\rho - 1} (x_1^\rho + x_2^\rho)^{\frac{1}{\rho}- 1},$$ This tends to $...
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2 votes

How to force two utility functions representing the same preference to generate expected utility functions representing the same order on lotteries?

That is hopeless. The preference order over certain outcomes determines the preferences over every compatible expected utility representation if and only if there are at most two indifference classes. ...
Michael Greinecker's user avatar
2 votes
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Suppose $A$ is a $2x2$ matrix and ${\bf x}=(x_1, x_2)$. What does "$f(Ax)$ is supermodular" mean?

Note that: $$ f(Ax) = f(a_{11} x_1 + a_{12} x_2, a_{21} x_1 + a_{22} x_2). $$ So the derivative with respect to $x_1$ is given by: $$ f_1 a_{11} + f_{2} a_{21}. $$ Taking the derivative of this with ...
tdm's user avatar
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1 vote

Pure exchange economy: Set of multiple equilibria endowments

The following article: TODA, A.A. and WALSH, K.J., 2017. Edgeworth box economies with multiple equilibria. Economic Theory Bulletin, 5(1), pp. 65-80. though not focusing on the properties of the ...
Jovan Jezdic's user avatar
2 votes

Proof for Marshallian Demand function

Let $x(p,w)$ be the demand at prices $p$ and income $w$. Let $x_0 = x(p_0,w)$ and $x_1 = x(p_1, w)$. Note that $p_0 x_0 = w = p_1 x_1$ Assume that WARP is violated, so $x_1 \ne x_0$, $$ p_0 x_0 \ge ...
tdm's user avatar
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1 vote

Cobb-Douglas utility function

They don't have to, look: $U(x,y) = x^2y^2$ is Cobb-Douglas type, but the exponents sum up to four. It is also true that $U()$ represents the same preferences as $\hat{U}(x,y) = \sqrt{xy}$, where the ...
Giskard's user avatar
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1 vote

Convex preference and convex utility

Q1: What are the differences between convex preferences and covex utility function They have different definitions, which imply different things. From Wikipedia Formally, a preference relation $\...
Giskard's user avatar
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1 vote
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Supply curve of what?

Is there a supply curve for each product? Yes. If so, it is strange that the supply curve is monotonically increasing. I would expect higher prices to be sold in smaller quantities and lower prices ...
Giskard's user avatar
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1 vote

Question on Isolating The Wealth Effect in Analysis of Changes in Price-Wealth Combinations - MWG Exercise 2.F.3 Parts (e) and (f)

Yes, I think for question (e), there is a bit of an "error" in the reasoning. The total demand change can always be decomposed in an income and substitution effect. If there are only two ...
tdm's user avatar
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1 vote

What is a sufficient condition on the consumption set such that monotonicity of preferences implies local nonsatiation?

As we focus on the property of monotonicity, I will consider $X \subset \mathbb{R}^L$. Consider the following condition: Assumption A: For every $x \in X$, and every $\varepsilon > 0$ there is an $...
tdm's user avatar
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1 vote

Question on The Weak Axiom of Revealed Preference and The Definition of Revealed Preference Relation

Let ${\cal B}$ be a collection of choice sets and let $C$ be a single valued choice function, picking one item $C(B)$ out of every set $B \in {\cal B}$. Let $x$ be revealed preferred to $y$ if there ...
tdm's user avatar
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1 vote
Accepted

MWG Exercise 2.E.5

Answer to 1. $$ x_l(\mathbf{p},w) = \frac{\partial x_l(\mathbf{p},w)}{\partial w}p_l \cdot \frac{w}{p_l} $$ Let $\alpha_l = \frac{\partial x_l(\mathbf{p},w)}{\partial w}p_l$. This is nice, now use ...
Giskard's user avatar
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