A firm faces a production function with inputs capital (K) and labor (L):K¹/2 L¹/4F(K, L)The amount of capital used for production is determined at the beginning of the year.The prices of K and L are v and w respectively.= Flash forward to next January. The owner is deciding how much capital and how many labor inputsto purchase for the current year (long run). The contingent demands for K and L areK(q, w, v) = q¹/3 ( 2w)VK(q, w, v) = q¹/3 (₁K(q, w, v)=qª2w1/31, L(q, w, v) = q¹/³ (1) 2/32wv1/32w 2/32/32w, L(q, w, v) - 2²² (20²) ²=94/31/3L(q, w, v) = q¹ (2) ¹/³22/3K(q, uw, e) = gta (20) 2², L(g, a, u) = q¹³ (1) ¹/²w,1/3v) q¹/322w

Contingent input demands are function of input prices (v and W) and level of output (q).

A firm faces a production function with inputs capital (K) and labor (L): F(K, L) = K¹/2 1/4 The amount of capital used for production is determined at the beginning of the year. The prices of K and L are v and w respectively.

A firm faces a production function with inputs capital (K) and labor (L): F(K, L) = K¹/2 1/4 The amount of capital used for production is determined at the beginning of the year. The prices of K and L are v and w respectively.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 1.5CE

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Question

100%

A firm faces a production function with inputs capital (K) and labor (L):
K¹/2 L¹/4
F(K, L)
The amount of capital used for production is determined at the beginning of the year.
The prices of K and L are v and w respectively.
=

Flash forward to next January. The owner is deciding how much capital and how many labor inputs
to purchase for the current year (long run). The contingent demands for K and L are
K(q, w, v) = q¹/3 ( 2w)
V
K(q, w, v) = q¹/3 (₁
K(q, w, v)
=
qª
2w
1/3
1, L(q, w, v) = q¹/³ (1) 2/3
2w
v
1/3
2w 2/3
2/3
2w
, L(q, w, v) - 2²² (20²) ²
=
94/3
1/3
L(q, w, v) = q¹ (2) ¹/³
2
2/3
K(q, uw, e) = gta (20) 2², L(g, a, u) = q¹³ (1) ¹/²
w,
1/3
v) q¹/3
2
2w

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