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) $\$ 50$

Question

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) $\$ 50$

Accepted Answer

∻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: $\frac{100}{200} = \frac{20}{r} \Rightarrow r = \frac{20 imes 200}{100} = \$40$. ‖ ∻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. ⚹◊What is the equation for the marginal rate of technical substitution in production?⍭ Generate me a similar question◊$

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