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# Firm Costs and Response to Input Price Changes

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Question 2: Firm Costs and Response to Input Price Changes

Suppose a firm faces a constant returns to scale Cobb-Douglas production of the form:

2.1 Derive the total cost function for the firm, and calculate the total cost of producing 10,000 units of the output.

2.2 Calculate the elasticity of total cost with respect to output for the firm, and determine the percentage change in total costs if the firm sought to increase production by 5 percent.

2.3 Now, suppose the cost of labor rises from w = \$100 to wnew = \$400. Using isoquant-isocost analysis with labor on the horizontal axis and capital on the vertical analysis, illustrate the effect of the increase in the wage on labor utilization, carefully denoting both the input substitution and output effects of the wage increase. Discuss what factors determine the magnitude of the output effect. (NOTE: The firm faces a highly elastic (price-sensitive) demand curve in the product market.)

NOTE: Throughout the problem, assume a long-run analysis in which the firm can vary both the amount of labor and capital employed.

##### Solution Summary

This post addresses the basic concepts of production function in economics. For a special production function constant returns to scale Cobb-Douglas, it derives the total cost function and then calculates the elasticity of the total cost w.r.t. output. The post also discusses the substitution effect and income effect. The solution is presented in mathematical form (equation) and is supported with a graph for easy understanding

##### Solution Preview

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2.1 Derive the total cost function for the firm, and calculate the total cost of producing 10,000 units of the output.
The cost minimization condition is
MPL/MPK = w/r
0.5*L^-0.5*K^0.5 / (0.5*L^0.5*K^-0.5)=100/100
Solving we get K=L
So ...

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