A manufacturing firm's production function is Q = 10K0L0.5 where Q is the quantity of output...

 

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A manufacturing firm's production function is Q = 10K0L0.5 where Q is the quantity of output (units), K is the amount of capital used (machine-hours); end 2 is the amount of labor hired (worker-hours). For this production function, the marginal product of labor is MPL 5K05 and the marginal product of capital is MP L0.5 5105 The firm rents capital at a rate of R = $4 per hour and hires labor at W = $16 per hour. The firm plans to produce 720 units of output. K0.5 a. How much labor and how much capital should the firm use to minimize its cost of production? b. Suppose that a technological improvement increases the firm's total factor productivity, so the pro- duction function is now Q = 12K05L0.5 for which the marginal product of labor is MP, 6K05 and the marginal product of capital 6L0.5 K0.5 How much labor and how much capital should the firm use now to minimize is MP = the cost of producing 720 units of output? C. How does the technological improvement change the firm's costs of producing 720 units of output? d. Use calculus to show that the marginal products of labor and of capital of the new technology are as given. A manufacturing firm's production function is Q = 10K0L0.5 where Q is the quantity of output (units), K is the amount of capital used (machine-hours); end 2 is the amount of labor hired (worker-hours). For this production function, the marginal product of labor is MPL 5K05 and the marginal product of capital is MP L0.5 5105 The firm rents capital at a rate of R = $4 per hour and hires labor at W = $16 per hour. The firm plans to produce 720 units of output. K0.5 a. How much labor and how much capital should the firm use to minimize its cost of production? b. Suppose that a technological improvement increases the firm's total factor productivity, so the pro- duction function is now Q = 12K05L0.5 for which the marginal product of labor is MP, 6K05 and the marginal product of capital 6L0.5 K0.5 How much labor and how much capital should the firm use now to minimize is MP = the cost of producing 720 units of output? C. How does the technological improvement change the firm's costs of producing 720 units of output? d. Use calculus to show that the marginal products of labor and of capital of the new technology are as given.

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Q 10K 05 L 05 1 MP L 5K 05 L 05 MP k 5L 05 K 05 R 4 per unit W 16 per hour Firm plans to produce 720 ... View the full answer