PAM200_Section7_Solutions - PAM200 Section 7 Problem 7.7....

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Unformatted text preview: PAM200 Section 7 Problem 7.7. The tangency condition implies 10 10 K L L K = = Substituting into the production function yields 2 2 121,000 121,000 (10 ) 121,000 10 12,100 110 LK L L L L L = = = = = Since 10 K L = , 1,100 K = . The cost-minimizing quantities of labor and capital to produce 121,000 airframes are 1,100 K = and 110 L = . Problem 7.13. If K = 0, then the firm must hire L = 5 units of labor. For this to be optimal, it must be that MP L / w > MP K / r , or 1/ w > 6. In other words, w < 1/6. If L = 0, then the firm must hire K = 5 units of capital. For this to be optimal, it must be that MP L / w < MP K / r , or 6/ w > 1. In other words, w > 6. For the firm to use both capital and labor, it must be that 1/6 < w < 6. To see why, notice that the indifference curves will have diminishing MRTS L,K . In particular, MRTS L,K = 6 where the Q = 5 indifference curve intersects the K- axis (where L = 0). Diminishing MRTS L,K implies that the Q = 5 indifference curve will gradually flatten out until it intersects the...
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PAM200_Section7_Solutions - PAM200 Section 7 Problem 7.7....

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