Q26 A firm produces output according to a production function: Q = F(K,L) = min
ID: 1200283 • Letter: Q
Question
Q26
A firm produces output according to a production function: Q = F(K,L) = min {4K.4L}. How much output is produced when K = 2 and L = 3? If the wage rate is $50 per hour and the rental rate on capital is $30 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital:___. Labor:___. How does your answer to part b change if the wage rate decreases to $30 per hour but the rental rate on capital remains at $30 per hour? Capital and labor increase. It does not change. Capital decreases and labor increases. Capital increases and labor decreases.Explanation / Answer
Q = min{4K, 4L}
(a) K = 2, L = 3
Q = min{8, 12}
Q = 8
(b) Cost is minimized when 4K = 4L, or K = L
8 = min{4K, 4L}
8 = 4K (= 4L)
K = 2
L = 2
(c) Answer does not change.
This is because it is a fixed-proportion production function where K and L are perfect completemts. Change in wage of rental rate does not affect the proportion in which K and L are used.
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