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Question
Macroeconomics
Posted 10 months ago

Hufflepuff Industries produces badger sweaters and currently uses 20 units of labor and 30 units of capital. The marginal product of the 20th20 t h unit of labor is 100 sweaters, and the marginal product of the 30th30 t h unit of capital is 200 sweaters.

If the cost of each unit of labor (w)(w) is $20\$ 20 and this firm minimizes costs, what is the rental rate of capital (r)(r) ?

Choose 1 answer:
(A) $40\$ 40
(B) $50\$ 50
(C) $20\$ 20
(D) $10\$ 10
(E) $30\$ 30
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Answer from Sia
Posted 10 months ago
Solution
a
Cost Minimization Condition: To minimize costs, a firm will hire labor and capital until the marginal product per dollar spent on each is equal. This is expressed as MPLw=MPKr\frac{MP_L}{w} = \frac{MP_K}{r}, where MPLMP_L is the marginal product of labor, ww is the wage rate, MPKMP_K is the marginal product of capital, and rr is the rental rate of capital
b
Calculation of Rental Rate of Capital: Given MPL=100MP_L = 100 sweaters, w=$20w = \$20, MPK=200MP_K = 200 sweaters, we can solve for rr using the cost minimization condition. Plugging in the values, we get 10020=200r\frac{100}{20} = \frac{200}{r}
c
Solving for rr: Simplifying the equation from step b, we get 5=200r5 = \frac{200}{r}, which gives us r=2005=$40r = \frac{200}{5} = \$40
Answer
\$40
Key Concept
Cost Minimization in Factor Employment
Explanation
The rental rate of capital is determined by ensuring that the marginal product per dollar spent is the same for both labor and capital, which leads to cost minimization in production.$

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