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- What is the difference between a fixed input and a variable input?Suppose that the production function for a phone is ? = 20K^0.5L ^0.5 . The marginal product of labor is 10(k/l)^0.5 , and the marginal product of capital is 10(L/K) ^0.5 . Suppose that labor can be hired for $6 and capital can be hired for $9. a. When the firm is producing 49 units at lowest cost, what will the firm’s marginal rate of technical substitution be? b. Solve for the lowest-cost combination of labor and capital that will allow the firm to produce 49 phones. Fractional units of labor and capital are allowed. c. What is the minimum cost of producing 49 phones?What is the total cost when the marginal product of labor is 15? What is the total variable cost when the marginal product of labor is equal to 12?
- Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?You are the owner of a puppet manufacturing company. Suppose that labour is the only variable input to the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labour?Suppose that labour is the only variable input to the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labour? Assume the marginal cost of production is increasing. Determine whether the average variable cost is increasing or decreasing.
- Can you think of a cost function, so that the marginal cost at any x is exactly equal to the cost of producing the (x + 1)st item? If yes, describe as many such functions as possible. If not, show why such a function cannot exist.1/3 7 Consider the production function y = (0.5/ +0.52 of producing 8 units of output per day. It pays a wage rate wi of $40 per hour and capital cost w2 of $10 per hour. How many units of labor and capital should the firm use? Suppose the firm wants to minimize the cost