CHAPTER 6 PRODUCTION
9. In Example 6.3, wheat is produced according to the production function Q = 100(K0.8L0.2 ). a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. For fixed labor and variable capital: K = 4 ⇒ Q = (100)(40.8 )(490.2 ) = 660.21
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www.uh.eduproduction in Factory 1, take the first derivative of the cost function with respect to Q: dC 1 Q (1) dQ =20 Q 1. Similarly, the marginal cost in Factory 2 is dC 2 Q (2) dQ = 40Q 2. Rearranging the marginal cost equations in inverse form and horizontally summing them, we obtain total marginal cost, MC T: Q Q Q MC MC MC = + = + = T 1 2 1 2 20 40 ...