The rental rate of capital for Hufflepuff Industries to minimize costs is $40.
How do we calculate the rental rate of capital?
We shall use the principle of cost minimization in production to find the rental rate of capital (r), where the marginal product of labor (MPL) to the marginal product of capital (MPK) is equal to the ratio of the cost of labor (w) to the cost of capital (r).
Marginal Product of Labor/ Price of Labor = Marginal Product of Capital / Price of Capital: MPL/MPK = w/r
Given:
MPL = 100 sweaters (marginal product of 20th unit of labor)
MPK = 200 sweaters (marginal product of 30th unit of capital)
w = $20 (cost of each unit of labor)
r = rental rate of capital
Putting the known values into the formula, we have:
100/200 = 20/r
r = (20 * 200) / 100
r = $40
Hence, the rental rate of capital for Hufflepuff Industries to minimize costs is $40.
Question completion:
Hufflepuff Industries produces badger sweaters and currently uses \[20\] units of labor and \[30\] units of capital. The marginal product of the \[20th\] unit of labor is \[100\] sweaters, and the marginal product of the \[30th\] 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 \[(r)\]?