A manufacturing firm uses only capital (K)and labour (L)to produce its product, using a production function of Q = 10KL. It pays its workers w = $15 per hour and has a rental cost of capital of r = $5 per hour. If the firm wants to produce 480 units of output, the optimal bundle of inputs is:
A)(3, 16).
B)(4, 12).
C)(12, 4)
D)(6, 8).

Question

Quizplus · Accepted Answer

To find the optimal bundle of inputs, we use the condition that the marginal rate of technical substitution (MRTS) equals the ratio of the input prices (w/r). MRTS is derived from the production function Q = 10KL, which gives us MRTS = L/K. Setting MRTS equal to w/r = 15/5 = 3, we get L/K = 3, meaning L = 3K. To produce 480 units, we substitute L = 3K into the production function: 480 = 10K(3K) = 30K^2. Solving for K, we find K = 4. Substituting K = 4 into L = 3K gives L = 12. Therefore, the optimal bundle of inputs is (4, 12).

A Manufacturing Firm Uses Only Capital (K)and Labour (L)to Produce