17. Suppose the short-run production function is q 40 L. If the wage rate is $10

Question

17. Suppose the short-run production function is q 40 L. If the wage rate is $10 per unit of labor, then MC equals 18. Suppose that at a firm's current level of production the marginal product of capital is equal to 10 units, while the marginal rate of technical substitution between capital and labor is 3. Given this, we knovw the marginal product of labor must be 19, suppose output for a simple production process is given by Q = 2K + L, where K denotes capital, and L denotes labor. The price of labor is $3 per unit and the price of capital is $4 per unit. What would be the minimum costs of producing 10 units of output? 20. Joe's demand for spring water can be represented as Q = 15-p (where p is measured in $/gallon and Q is measured in gallons). He recently discovered a spring where water can be obtained free of charge. His consumer surplus from this water is

Explanation / Answer

17) Production function is q = 40L. Hence L = q/40. Cost function is C = (q/40)*10 = 0.25q. Hence the marginal cost is 0.25

18) We know that MRTS (KL)= MPK/MPL. Hence 3 = 10/MPL. or MPL = 10/3.

19) We are given that MPL = 1 and MPK = 2. w = 3 and r = 4. This implies MPL/w = 1/3 and MPK/r = 2/4. Since MPL/w < MPK/r , firm uses only capital. Cost function is C = rK = 4K and Q = 2K. To produce 10 units, K* = 10/2 = 5 and minimum cost C = 4*5 = $20

20) For p = 0, q = 15 and so the consumer surplus = 0.5*(15 - 0)*15 = 225/2 = 112.50

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