Marcelo Gelati
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  • Rio de Janeiro, State of Rio de Janeiro, Brazil
MRS of good X for good Y
Accepted answer
4 votes

It is your second answer. From MWG: $$\frac{\partial u(x^*)/\partial x_\ell}{\partial u(x^*)/\partial_k}=\frac{p_\ell}{p_k}\tag{3.D.5}$$ The expression on the left of $\text{(3.D.5)}$ is the ...

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Uncovered set versus top cycle set (voting theory)
Accepted answer
3 votes

This example comes from Miller (1980) (the paper that introduced the uncovered set definition). Suppose that the majority's preference is defined by: \begin{aligned} x \succ y \\ x \succ z \\ y \...

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Prove that in presence of many goods, the law of DMRS implies that at least one good must be a net substitute for any other good
2 votes

I don't know what is the definition of the "law of DMRS", but I think what the author meant is summarized in these lines of MWG: Proposition 3.G.2: suppose that $u(\cdot)$ is a continuous ...

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An example of preferences over a countable set that cannot be represented by a utility function
2 votes

There is a proposition that says: If there is a function $u: X \rightarrow \mathbb{R}$ that represents the preference relation $\succsim$, then $\succsim$ is rational. So, the contrapositive form ...

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How can two different utility functions represent the same preferences?
2 votes

First of all, an utility function $u: X \rightarrow \mathbb{R}$ represents the preference relation $\succsim$ if: $$\forall a, b \in X, \; u(a) \geq u(b) \iff a \succsim b.$$ Well, if another ...

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Elasticity when the demand function is given
Accepted answer
2 votes

The definition of elasticity of demand with respect to price is: $\varepsilon_{q,p} = \frac{dq}{dp} \cdot \frac{p}{q}$. So in your demand function we have: $$q = kp^{-\epsilon}$$ $$\frac{dq}{dp} = -\...

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The use of preference relations in choice theory and the $\succsim$ symbol
1 votes

About your second question, Gérard Debreu, in his book Theory of Value, says in the notes of chapter 1 that the $\succsim$ notation is due to Herstein and Milnor. So, probably, this is the origin of ...

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SPNE and Pareto Optimality
1 votes

Proof of "the SPNE of a sequential game might not necessarily be Pareto Optimal"? I don't get it, your example is a proof of this statement. So what else do you need? If you need another example, ...

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Find a subgame perfect equilibrium and a Nash equilibrium
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0 votes

As afreelunch only answered in the comment section, I'll answer it here. The SPNE (Subgame Perfect Nash Equilibrium) is a refinement of the NE (Nash Equilibrium). So, let's call $S$ the set of all ...

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Indifference curves and equivalence classes
0 votes

Michael Greinecker's comment basically answers the second question, but not to leave the question unanswered, let me try to answer your first question. In most economics courses, we don't get ...

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Price and cross price Elasticity of demand
-2 votes

Sketch your answer for the demand function $x = -p_x/p_y$.

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