Question

Macroeconomics

Posted 3 months ago

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Kraken Katchers, Inc. sells cryptid catching services in an oligopoly market. Its marginal product of capital per dollar spent on capital is 80 .
What is the marginal product of labor if the wage rate is $\$ 20$ and the firm minimizes costs?
Choose 1 answer:
(A) 0.25
(B) 4
(C) 1200
(D) $\mathbf{1 6 0 0}$
(E) 1400
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Answer from Sia

Posted 3 months ago

Solution

a

Cost Minimization Condition: In order to minimize costs, a firm will hire labor and capital until the marginal product per dollar spent is equal for both inputs. This is represented by the equation $\frac{MP_L}{W} = \frac{MP_K}{r}$, where $MP_L$ is the marginal product of labor, $W$ is the wage rate, $MP_K$ is the marginal product of capital, and $r$ is the rental rate of capital

b

Given Data: We are given that $MP_K = 80$ per dollar spent on capital and $W = \$20$. We assume that the rental rate of capital is $1 per dollar spent on capital since it's per dollar spent

c

Solving for $MP_L$: Using the cost minimization condition, we can solve for $MP_L$ by rearranging the equation to $MP_L = MP_K \times W$. Plugging in the given values, we get $MP_L = 80 \times 20$

d

Calculation: Calculating the value of $MP_L$ gives us $MP_L = 1600$

Answer

1600

Key Concept

Cost Minimization in Input Choices

Explanation

The marginal product of labor is determined by ensuring that the marginal product per dollar spent is the same for all inputs when a firm minimizes costs.

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