Question

Macroeconomics

Posted 6 months ago

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Hufflepuff Industries produces badger sweaters and currently uses 20 units of labor and 30 units of capital. The marginal product of the $20 t h$ unit of labor is 100 sweaters, and the marginal product of the $30 t h$ unit of capital is 200 sweaters.
If the cost of each unit of labor $(w)$ is $\$ 20$ and this firm minimizes costs, what is the rental rate of capital $(r)$ ?
Choose 1 answer:
(A) $\$ 40$
(B) $\$ 30$
(C) $\$ 20$
(D) $\$ 10$
(E) $\$ 50$
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Answer from Sia

Posted 6 months ago

Solution

a

Cost Minimization Condition: Firms minimize costs by equating the ratio of the marginal products to the ratio of input costs

b

Mathematical Expression: $\frac{MP_L}{MP_K} = \frac{w}{r}$ where $MP_L$ is the marginal product of labor, $MP_K$ is the marginal product of capital, $w$ is the wage rate, and $r$ is the rental rate of capital

c

Given Values: $MP_L = 100$ sweaters, $MP_K = 200$ sweaters, $w = \$20$

d

Calculation of Rental Rate: $\frac{100}{200} = \frac{20}{r} \Rightarrow r = \frac{20 \times 200}{100} = \$40$

Answer

\$40

Key Concept

Cost Minimization in Production

Explanation

The rental rate of capital is determined by the cost minimization condition where the ratio of the marginal products of labor to capital is equal to the ratio of their respective costs.

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