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6 votes
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Does the Rybczynski theorem also hold in modern trade theory models?

The Rybczynski theorem is not directly applicable to the Melitz (2003) model, because the model the Rybczynski theorem is originating from, the Heckscher-Ohlin model, is built on different assumptions ...
Hans-Peter Schrei's user avatar
4 votes
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Approximate Pareto efficiency with ordinal preferences

Consider a game: Set of Players $= \{1,2\}$ Action Sets of the players: $\triangle_1\subseteq\mathbb{R}^n$ and $\triangle_2\subseteq\mathbb{R}^m$. For Eg: In case of Prisoner's Dilemma, $\triangle_1=\...
Amit's user avatar
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3 votes

Inductive proofs in economics

Mathematical induction is rarely relevant to economics due to the combination of three considerations: Mathematical economics is very often concerned with variables taking continuous (or so large as ...
Adam Bailey's user avatar
  • 8,346
3 votes
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Pareto optimal allocations with uncountably many agents

If (and that is a big if) you have a nonempty compact space of allocations and all utility functions are continuous, then one can prove in a highly nonconstructive way that a Pareto optimum exists. ...
Michael Greinecker's user avatar
3 votes
Accepted

Is my understanding of Arrow's dictatorship correct? The dictator is free to update her preference and the social choice will always follow her taste

Yes, this is correct. If $i=1$ is a dictator for the social choice rule $f$, then this means that for any profile $\langle R_i \rangle_{i=1}^I$, we have $f(\langle R_i \rangle_{i=1}^I)=R_1$. Hence, ...
Marcus Pivato's user avatar
3 votes

Debreu's ordinal representation theorem is unique up to a positive monotonic transformation, what is the source?

The other answer explained why the result is trivial; here is why it is not true without the modifier "on the range" and under the most literal reading. Consider $[0,1]\cup(2,3]$ with the ...
Michael Greinecker's user avatar
2 votes

Debreu's ordinal representation theorem is unique up to a positive monotonic transformation, what is the source?

It is not a 'result' because it is trivial to show that a positive strictly monotonic transformation function applied to the function that represents the preferences leaves the ordering unchanged. Say ...
Surge's user avatar
  • 135
2 votes
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$H$ is a constant? Maximizing: $\int _0^Te^{-t}f(x,u)dt$ st $x_t=g(t,x,u)$ and $g$ is independent of $t$

Consider the problem: $$ \begin{align*} \max_{u} \int_0^T f(x(t), u(t)) dt& \\ \text{ s.t. } &\dot x = g(x(t), u(t)),\\ &\text{ + boundary conditions} \end{align*} $$ Assume that $g(x,u)$ ...
tdm's user avatar
  • 11.2k
2 votes

Can FOSD-transitivity replace the transitivity in utility representation theorem?

Take as example the set of lotteries over the outcomes $(1, 5, 10)$ consider the lotteries $L_1, L_2, L_3$ where, $$ \Pr(L_1 = 1) = 0.5\\ \Pr(L_1 = 5) = 0\\ \Pr(L_1 = 10) = 0.5 $$ $$ \Pr(L_2 = 1) = 0....
tdm's user avatar
  • 11.2k
2 votes

Two step Generalized Method of Moments (Newey 1994). $\hat{W}$ matrix depending on the nuisance parameter

As long as $\hat{W}\rightarrow W$ where $W$ is the inverse of the variance-covariance matrix of moments, then all of the asymptotic properties hold. You seem to be asking if this applies in your case. ...
Michael Gmeiner's user avatar
2 votes

Reference for monotonicity: $x\geq y\implies x\succsim y$ and $x>y\implies x\succ y$

MWG defines two types of montone preferences (definition 3.B.2). For a first they define preferences to be montone if $y \gg x$ implies that $y \succ x$. Here $y \gg x$ means that every component of ...
tdm's user avatar
  • 11.2k
2 votes

Spiraling decline in labour supply due to small initial wage decreases

How do economists address or account for these feedback loops when advising policymakers based on labor supply elasticity measurements? Estimates refer to an equilibrium context. Policy analysts are ...
Iñaki Viggers's user avatar
2 votes

Mixed gambles and risk aversion

I presume that by "fair gamble" $G$ we mean a gamble whose expected value is zero, $E(G) = 0$. Risk-aversion can be expressed mathematically by showing that the utility function is strictly ...
Alecos Papadopoulos's user avatar
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
  • 29.2k
1 vote

Goods for resale are considered as producer goods?

Yes, as the definition says, the goods purchased for resale, like carrots purchased by grocer, are intermediate/producer goods.
WilliamT's user avatar
  • 1,785
1 vote

Give bundles $x,y\in \mathbb R^n$, there must exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?

Let $U$ be a $C^1$, monotone and quasi-concave utility function. Let $\nabla U(z)$ be the gradient of $U$ at the bundle $z$ (If we assume preferences are monotone then $\nabla U(z) \gg 0)$ for all $z \...
tdm's user avatar
  • 11.2k
1 vote
Accepted

Factor changes in Melitz (2003) model

Let us assume that the labor supply increases. Below I list some of the consequences that occur in the model: Wage adjustment: An increase in labor supply typically leads to a decrease in wages due ...
Hans-Peter Schrei's user avatar
1 vote

Is there a theory in economics about how companies have to withhold surplus goods or services for strategic reasons, creating artificial scarcity?

Yes there are theories like that. For example, even in standard textbook monopoly model a monopolist would purposefully limit the quantity on the market to maximize profit. A classic historical ...
1muflon1's user avatar
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