A firm is using 500 units of capital and 200 units of labor to produce 10,000 un

Question

A firm is using 500 units of capital and 200 units of labor to produce 10,000 units of output. Capital costs $100 per unit and labor $20 per unit. The last unit of capital added 50 units of output, while the last unit of labor added 20 units of output. The firm
a) is using the cost-minimizing combination of capital and labor
b) should use more of both inputs in equal proportions
c) should use less of both inputs in equal proportions
d) could produce the same level of output at a lower cost by using more capital and less labor.
e) could produce the same level of output at a lower cost by using less capital and more labor.

Explanation / Answer

This problem gives us a hint of the slope or the change in output by telling us what happens when we added the last unit of capital and labor. The last unit of capital is 1/500 and gives 50/10,000 10,000/50 = 20 so we got more output in the last unit than the average. The last unit of labor is 1/200 and gives 20/10,000 10,000/20 = 500 so we got less output in the last unit than the average. If we take away units of capital, we can save $100 per unit. We expect to lose about 50 units of output for each unit of capital. If we use this money to by units of labor we can get five units of labor for each unit of capital we give up (5*$20 = $100). Five units of labor will give us about 5*20 or 100 units of output. So each unit of capital that we give up will allow us to buy 3 units of labor and still save $40. If we wanted the same level of output, we could buy 2.5 units of labor for each unit of capital that we do away with and lower our costs by $50. Choice e) is correct

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