# Let the production function for the firm be Cobb-Douglass, with fixed capital (K):...

## Question:

Let the production function for the firm be Cobb-Douglass, with fixed capital

(K): Y=zF(K,N{eq}^d {/eq})=z(K){eq}^\alpha {/eq}(N{eq}^d {/eq}){eq}^{(1-\alpha)} {/eq} where 0 is less than {eq}\alpha {/eq} is less than 1.

a. Solve for labor demand as a function K, z, w, and {eq}\alpha {/eq}.

b. How does labor demand change if total factor productivity doubles?

c. How does labor demand change if capital doubles?

## Demand for Labor:

Demand for labor is a type of derived demand because firms' demand for labor is driven by consumer's demand for goods, which are produced using labor. When firms decide how many workers to hire, they compare the marginal product of labor to the wage rate.

## Answer and Explanation: 1

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View this answera. Firms hire labor until the marginal product of labor is equal to the wage rate, i.e.,

- {eq}zK^{\alpha}(1 - \alpha)(N^d)^{-\alpha} = w {/eq}

which...

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Chapter 3 / Lesson 41Learn the labor market definition and what happens in the labor market. See what the split labor market theory is and learn the different types of labor market.

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