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Self-dual production functions that do not satisfy weak homothetic separability

I am looking for parametric production functions that do not satisfy weak homothetic separability (as first defined in Shephard, 1953), but that do allow for an analytical expression of the dual cost ...
hrrrrrr5602's user avatar
1 vote
2 answers

Is my solution to finding the Hicksian demand correct? Maximize $x_1^{1/2} + x_2^{1/2}$ subejct to the budget constraint

Maximize $x_1^{\frac{1}{2}} + x_2^{\frac{1}{2}}$ subejct to the budget constraint $p_1x_1+p_2x_2=m$ Setting up the Lagrange and finding the first-order conditions: $L(x_1, x_2, \lambda)=x_1^{\frac{1}{...
CorporateNationalism's user avatar
2 votes
2 answers

Finding Cobb-Douglas Hicksian Demand using Duality

I'm trying to follow the in-text examples from Mas-Colell. I can confirm I have the correct first order-conditions and hence the Marshallian demand functions for Example 3.D.1: $u(x_1,x_2) = x_1^\...
CorporateNationalism's user avatar
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Does the duality of utility maximization and cost minimization hold in practice?

I recently learned about the relationship between utilization maximization and cost minimization. Are there studies on whether this duality holds in real life? Any information on this topic for a ...
StatsScared's user avatar
18 votes
2 answers

How accurate is duality?

In economic theory we know that with the use of some calculus, Hotellings Lemma and Sheppards lemma we can derive a given firms supply function and in term its Profit function. With data of a given ...
EconJohn's user avatar
  • 8,407
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Duality Proof - Consumer Theory

For solving this question, which assumptions/axioms should be used and should Lagrange multipliers be equal or different? Think of an agent with utility function u() and wealth w. Assume that u() is ...
Ktp's user avatar
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1 vote
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Curvature of Cost and Production Function

I have been trying to understand the duality theory between cost and production function. Please let me know if my following statement is correct; If the cost function $C(w,q)$ is convex in $q$, the ...
Sher Afghan's user avatar