6. Each of the 10 firms has the production function q = √KL. The wage is 5 and the rent oncapital is 10. Assume we are in the long run, so firms can vary both factors.Write an expression for one firm's cost minimization problem.Use whichever method you prefer to minimize cost and derive an expression for onefirm's total cost: TC (9₁)c.Compute one firm's marginal cost and derive the inverse supply curve for one firm andthe inverse supply curve for the market. What is the elasticity of supply?a.b.

Answered: Each of the 10 firms has the production…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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6. Each of the 10 firms has the production function q = √KL. The wage is 5 and the rent on
capital is 10. Assume we are in the long run, so firms can vary both factors.
Write an expression for one firm's cost minimization problem.
Use whichever method you prefer to minimize cost and derive an expression for one
firm's total cost: TC (9₁)
c.
Compute one firm's marginal cost and derive the inverse supply curve for one firm and
the inverse supply curve for the market. What is the elasticity of supply?
a.
b.

Expert Solution

Step 1

Given

The production function of each 10 firms is of the form $q = \sqrt{K L}$ ...... (1)

Wage rate w =5

rent for capital r =10

In the cost minimization problem, a firm tries to minimize its total cost to produce a given level of output q at current input prices and technology.

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