Suppose the firm's production function is Q = K¹/3L2/3, where the MPK = [2/3 and MPL 3K-2/3 13 2K-¹/3 31¹/3 If the rental rate of capital R is $35 and the wage rate Wis $70, how many units of labor and capital should the firm use to produce 12 units of output? L = 18; K = 9 L = 12; K = 12 L = 9; K= 18 L = 24; K = 24 =
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- What is the difference between a fixed input and a variable input?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 cost6. Suppose the wage is $8, the rental rate of capital is $128, and the firm's CRS Cobb-Douglas production function is q=3L¹/3K2/3 a. What is the cost-minimizing bundle of labor and capital for producing output of q = 600 units? b. What is total cost at this bundle?
- A firm produces output according to a production function: Q = F(K,L) = min {4K,8L}. a. How much output is produced when K = 2 and L = 3? 192 Numeric ResponseEdit Unavailable. 192 incorrect.unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: 80 Numeric ResponseEdit Unavailable. 80 incorrect. Labor: 480 Numeric ResponseEdit Unavailable. 480 incorrect. c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour? multiple choice Capital and labor increase. It does not change. Capital increases and labor decreases. Incorrect Capital decreases and labor increases.2 Suppose that production for good X is characterized by the following production function, O = K0.5L0.5 where Kis the fixed input in the short run. If the per-unit rental rate of capital, r, is $25 and the per-unit wage, w, is $15, then the fixed cost of using 81 units of capital and 9 units of labor is: a. $135. b. $2,025. c. There is insufficient information to determine the fixed costs. d. $2,160.Exercise 11 Question Help Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5KO.5/L0.5 - 0.5g/L 70- and MPK = 5L0.5/K.5 - 0.5g/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- -q= 280 q= 140 98 Suppose now that the firm wants to increase output to 280 units. If capital is fixed 0- in the short run, how much labor will the firm require? 70 84 L, Units of labor 14 28 42 56 112 The firm will now require units of labor. (Enter your response rounded to two decimal places.) K, Units of capital
- dien There are two factors in a production function y = x 113 x₂¹1³. The market price of each unit ofy is p=3, and the factor prices are w₁=1 and W₂=2 for x₁ and X₂ respectively. variable (a). Calculate your cost function as a function of y if X, and x₂ are both barible factors. (b). Now derive the functions of average and marginal cost and plot them against quantity (C). Solve for your optional output of y. Calculate the ratio of two factors (X₁/X₂) (d). In the short run the fixed factor is set at X₂=1. What is the new optimal output level now?1. Assume a daily production function for a firm is Q= min(3L, 4K) a, If L = 100 and K = 100 what quantity is produced? Explain why. b. What would be the cost-minimizing labor and capital combination for this firm to produce Q = 1200? (show your work) Labor = Capital = At this level of production from part b (Q-1200), if the wage rate is: w- $30 and the rental rate of capital is: r= $100, what is the total cost of production? (show your calculations) C.• Assume that a firm is using the cost-minimizing combination of its only 2 inputs, capital and labor. If the price of a unit of capital is $200 and the price of a unit of labor is $50, what is the MPL of the last unit of labor if the marginal product of the last unit of capital is 2,000?
- 5. The production function is given by y=x₁ + 2x2. If w₁ = 10, w₂ = 8, will the firm use input factor 2 to minimize the cost? In what case will the firm use input factor 2?Use the following production function Q=1.25K0.3L0.5 where the price of Q is $10, the wage paid to labor L is $15 and rental rate for capital K is $30. Assume you can only use 6 units of capital L. What output will the firm produce? 2 2.65 3 00 O 3.65Consider the production function Y AK°Lta, where A is a constant, L is labour, K is capital and a 0. Which of the following is true? O The marginal product of labour is constant O The marginal product of labour is diminishing There are increasing returns to scale O There are decreasing returns to scale