Questions tagged [duality]
The duality tag has no usage guidance.
7 questions
2
votes
0
answers
63
views
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 ...
- 497
1
vote
2
answers
202
views
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}{...
2
votes
2
answers
3k
views
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^\...
0
votes
1
answer
207
views
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 ...
- 583
18
votes
2
answers
626
views
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 ...
- 8,847
0
votes
1
answer
717
views
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 ...
- 23
1
vote
0
answers
371
views
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 ...
- 616