Question

Michael, Dwight, and Jim run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is Q = 4K0.75 0.25 , where is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. For this production function, the marginal product of labor is MPL = 40, and the marginal product of capital is MPK = 302. The weekly cost function for the paper plant is C = 10K + 2L, where C is the total weekly cost. a. What ratio of capital to labor minimizes Michael, Dwight, and Jim's total costs? b. How much capital and labor will Michael, Dwight, and Jim need to rent and hire in order to produce 1,000 reams of paper each week? Round to the nearest whole number. Quantity of capital: units Quantity of labor: workers c. How much will hiring these inputs cost? Cost of hiring inputs: $

Answer 1

At optimum, MP = 2 ㅎ 한 7 .25 12025 345 0 0 5 1000 = L 366.7Z k 3 (366.V) 220.0로 | 5 Kad capital: 22o Labox: 367 Cost = 1C220) +2C36) = 2934 c