Consider the Cobb-Douglas Production function: P(L, K) = 28L0.5 -0.5 Find the marginal productivity of labor and marginal productivity of capital when 12 units of labor and 16 units of capital are invested. Give your answers to at least 4 decimal places if necessary. Marginal Productivity of Labor when L is 12 and K is 16 = P₁(12, 16) = Marginal Productivity of Capital when L is 12 and K is 16 = PK(12, 16) - =

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Chapter1: Functions And Models
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**Cobb-Douglas Production Function**

Consider the Cobb-Douglas Production function:

\[ P(L, K) = 28L^{0.5}K^{0.5} \]

**Objective:**

Find the marginal productivity of labor and marginal productivity of capital when 12 units of labor and 16 units of capital are invested. Provide your answers to at least 4 decimal places if necessary.

**Formulas:**

- Marginal Productivity of Labor when \( L \) is 12 and \( K \) is 16 is \( P_L(12, 16) = \) _______

- Marginal Productivity of Capital when \( L \) is 12 and \( K \) is 16 is \( P_K(12, 16) = \) _______
Transcribed Image Text:**Cobb-Douglas Production Function** Consider the Cobb-Douglas Production function: \[ P(L, K) = 28L^{0.5}K^{0.5} \] **Objective:** Find the marginal productivity of labor and marginal productivity of capital when 12 units of labor and 16 units of capital are invested. Provide your answers to at least 4 decimal places if necessary. **Formulas:** - Marginal Productivity of Labor when \( L \) is 12 and \( K \) is 16 is \( P_L(12, 16) = \) _______ - Marginal Productivity of Capital when \( L \) is 12 and \( K \) is 16 is \( P_K(12, 16) = \) _______
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