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4 votes

Minimisation problem turned into Maximisation

The Lagrangian is not really symmetric; something that is easier to see if you formulate it without the calculus implementation. First-order conditions for maxima and minima might look similar, but ...
Michael Greinecker's user avatar
2 votes
Accepted

Lump sum transfers to implement any Pareto efficient equilibrium as the market outcome

Here is the Edgeworth box of your exercise: The green dot with the curves running through it is your equilibrium allocation. The red and blue lines are indifference curves of $A$ and $B$, while the ...
Giskard's user avatar
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1 vote
Accepted

Derive indirect utility function - Problem with CES

Fix some good $r$. For notational convenience, let me drop the supscript $h$. From the first order conditions, we get: $$ x_{j} = \zeta_j + \left(\frac{p_{r}}{p_{j}}\right)^{\sigma}(x_{r} - \zeta_{r}) ...
tdm's user avatar
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4 votes
Accepted

Convex to origin - precise definition

The term "convex to the origin" seems to have been used in the prosaic meaning of "bending towards the origin" without a formal mathematical definition. The note Kozlik, Adolf. &...
Michael Greinecker's user avatar
2 votes

Finding Utility Function for Optimal Allocation in Consumer Choice Model

I think your formula is still too general, so what you want will not be possible. Given $-1 < \alpha < 0$ and $$ m^* = A \left(\frac{p}{\omega}\right)^\alpha, $$ we have $$ \frac{m^*p}{w} = A \...
Giskard's user avatar
  • 29.6k

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