A firm faces a production function with inputs capital (K) and labor (L):F(K, L) = K¹/² [1/4The 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. What is the short-run cost function for a given quantity q, given that the owner purchased Kamount of capital at the beginning of the year?C's (q, w, v, K) = vŘ¹/2 +w.qªŘ²Cs (q, w, v, K) = vK¹/2 + wKqªCs (q, w, v, K) = vK + w-K4Cs (q, w, v, K) = vK +w-qªK²

Cost minimization problem of producer: For the given output level the firm and per unit cost of…

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.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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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.

What is the short-run cost function for a given quantity q, given that the owner purchased K
amount of capital at the beginning of the year?
C's (q, w, v, K) = vŘ¹/2 +w.
qª
Ř²
Cs (q, w, v, K) = vK¹/2 + w
K
qª
Cs (q, w, v, K) = vK + w-
K
4
Cs (q, w, v, K) = vK +w-
qª
K²

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