# Firm Alpha uses capital K and labor L to produce output q. The firm's production function is...

## Question:

Firm Alpha uses capital K and labor L to produce output q.

The firm's production function is {eq}F(K,L)= 5K^{0.4}\times L^{0.6} {/eq}. The prices of capital and labor are r = 4 and w=4, respectively. Moreover, the firm also has to pay a tax T=2 for each worker L it hires. When the firm produces q=900 units of output, the firm hires L= _____ workers.

A: L = 0

B: L = 180

C: L = 141

D: L = 211

E: L = 110

Explain why the answer is B.

## Technical Rate of Substitution:

In economics, the technical rate of substitution describes the rate at which one input could replace another input while maintaining the same level of output, and is equal to the ratio of the marginal products of the two inputs. For a firm to minimize cost of production, the technical rate of substitution should be equal to the ratio of input prices.

The answer is B. L = 180

To minimize the cost of production, the firm should use capital and labor such that the technical rate of substitution is...

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