The company A produces cars using three inputs, labour (L), capital (K)and talent (X). AČME's production function is Y(X, L, K) = x0.5L0.25k0.25 This problem only deals within the short run, where ACME's amount of capital is fixed at K = 9. Denote by w the labour wage, by r the price of capital and by q the price of talent. a) Find A's conditional input demand for talent and labour. b) Find A's cost function. What is its shutdown price (as a function of w, r and q)? c) Find A's short run supply function. Draw it together with any other curves.
The company A produces cars using three inputs, labour (L), capital (K)and talent (X). AČME's production function is Y(X, L, K) = x0.5L0.25k0.25 This problem only deals within the short run, where ACME's amount of capital is fixed at K = 9. Denote by w the labour wage, by r the price of capital and by q the price of talent. a) Find A's conditional input demand for talent and labour. b) Find A's cost function. What is its shutdown price (as a function of w, r and q)? c) Find A's short run supply function. Draw it together with any other curves.
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
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Transcribed Image Text:Economics
The company A produces cars using three
inputs, labour (L), capital (K)and talent (X).
ACME's production function is
Y(X, L, K) - х0.5LO.25к0.25
This problem only deals within the short run,
where ACME's amount of capital is fixed at K
= 9. Denote by w the labour wage, by r the
price of capital and by q the price of talent.
a) Find A's conditional input demand for talent
and labour.
b) Find A's cost function. What is its shutdown
price (as a function of w, rand q)?
c) Find A's short run supply function. Draw it
together with any other curves.
-х0.5L0.25 к0.25
%3D
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