PS8(2)

# PS8(2) - Problem Set 8 Solutions 6.1 If each extra worker...

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Problem Set 8 - Solutions 6.1 If each extra worker produces an extra unit of output, how do the total product of labor, the average product of labor, and the marginal product of labor vary with labor? If every worker adds exactly one unit of output then L workers will add L units of output. Total product of labor is thus q = L . Average product of labor is q L = 1. Marginal product of labor is 1. 6.4 Why must isoquants be thin? An isoquant is the set of all input combinations ( K, L ) that will produce a particular quantity ¯ q of output. If an isoquant were thick, it would imply that adding a little of both capital and labor does not increase production. We assume that inputs are always productive so isoquants cannot be thick. 6.5 Suppose that a firm has a fixed-proportions production function in which one unit of output is produced using one worker and two units of capital. If the firm has an extra worker and no more capital, it still can produce only one unit of output. Similarly, one more unit of capital does the firm no good. (a) Draw the isoquants for this production function. See the figure that follows. The production function is q = min { L, 1 2 K } . To verify that this is the case, note that when two units of capital are combined with one unit of labor, one unit of the output good is produced. Isoquants are L-shaped with the kink line L = 1 2 K . (b) Draw the total product, average product, and marginal product of labor curves (you will probably

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