4. Suppose that Leah's company is characterised by the following Cobb- Douglas production function z = f(x, y) = 50x¹/2²y¹/2 where is the number of units of labour, y is the number of units of capital and z is the units of production. Each unit of labour costs $25 in wages and each unit of capital is $5. Leah's company is also subject to a limit of $75,000 for the total cost of labour and capital. Find the number of units of labour and the number of units of capital that will allow Leah's company to maximise production and use this information to calculate the z for which production is maximised.

4. Suppose that Leah's company is characterised by the following Cobb- Douglas production function z = f(x, y) = 50x¹/2²y¹/2 where is the number of units of labour, y is the number of units of capital and z is the units of production. Each unit of labour costs $25 in wages and each unit of capital is $5. Leah's company is also subject to a limit of $75,000 for the total cost of labour and capital. Find the number of units of labour and the number of units of capital that will allow Leah's company to maximise production and use this information to calculate the z for which production is maximised.

ECON MICRO

5th Edition

ISBN:9781337000536

Author:William A. McEachern

Publisher:William A. McEachern

Chapter7: Production And Cost In The Firm

Section: Chapter Questions

Problem 3.8P

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Q87 Consider a firm that uses only labour and capital as inputs. At the present use of labour and capital, the MP of labour is four times the MP of capital and the price of labour is twice the price of capital. To minimise its costs for a given level of output, the firm should... a. Decrease both capital and labour. b. Increase both labour and capital. c. Decrease capital and increase labour. d. Stay at its present factor mix. e. Decrease labour and increase capital.
1) Explain in details whether the underlined part of statement is true or false. In short-run production with two inputs where land is a fixed input labor is a variable input, the relationship between marginal product of labor and marginal cost of production is positive.
(A) Consider a firm in the long-run for which production depends on two inputs, labour and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 9 and r = 8, but then the price of capital decreases to r = 6. Describe the effects on labour and capital of this change in input price, represent them graphically, and explain whether this firm will optimally use more or less labour and capital. [Graph required] (B) In the long-run, if E and K were perfect complements, a wage increase would decrease the use of K. Explain why this statement is true or false.
Q5. A bicycle manufacturer in China currently employs 40 production workers and five supervisors and produces . The marginal product of the last production worker employed is 60 units of output per hour, and production workers are paid 50 CNY per hour. The marginal product of the last supervisor employed is 120 units of output per hour, and supervisors are paid 80 CNY per hour. i. If the firm produced 2,100 bicycles per month before the last production worker was hired, how many bicycles does it produce now? ii. Assume that the firm's isoquants are smooth curves and that labor hours can be varied continuously. Is the firm producing the maximum level of bicycles given its current level of cost? Explain why or why not. If it isn't, explain what it should do to increase output.
3. We often work with production technologies that give rise to initially increasing marginal product of labor that eventually decreases. Are the following statements then True or False? Explain.The marginal product of labor becomes negative when the slope of the production frontier begins to get shallower as we move toward more labor input.
A firm's production function is: q = 20L1/2K1/2 where q is the firm's total product, L is the quantity of labor employed, and K is the quantity of capital employed. The price of labor is $25 per unit and the price of capital is $100 per unit. a. What is the equation for the marginal product of labor? b. What is the equation for the marginal product of capital? c. Given the price of labor is $25 per unit and the price of capital is $100 per unit, what is the cost-minimizing combination of capital and labor that can produce 800 units of output?
93) Explain the difference between the short run and the long run as it relates to the firm's production function. Why is this distinction important to a firm's manager? 94) Use the following information on a hypothetical short-run production function to answer questions a-c. Units of Labor/Day56789 Units of Output/Day120140155165168 The price of labor is $20 per day. Ten units of capital are used each day, regardless of output level. The price of capital is $50 per unit. a. Calculate the marginal and average variable product of each unit of labor input. b. Calculate total, average total, average variable, and marginal costs. c. Can you tell where diminishing marginal returns sets in? 95) When demand for a firm's product decreases, the firm can take a number of steps to adjust costs and quantities supplied to the market. Some are listed below. Which actions are short run and which are long run? Explain your reasoning. a. Layoff 25…
Suppose that the price of capital decreases. Explain how the firm adjusts its use of capital and labour in the long run in response to this price decrease.
6. Which of the following are true (check all that apply) Note: IRTS=increasing returns to scale, CRTS=constant returns to scale, DRTS=decreasing returns to scale a. if the production function exhibits IRTS, then the cost function will exhibit economies of scale b. if the production function exhibits IRTS, then the cost function will exhibit diseconomies economies of scale c. if the cost function exhibits diseconomies of scale, then the producing function exhibits DRTS d. if the production function exhibits CRTS, then the cost function will exhibit constant economies of scale e. if the production function exhibits DRTS then the cost function will exhibit diseconomies of scale
2. Suppose that a firm’s production function is f(L, K) = L + K. Does this production function exhibit increasing, decreasing or constant returns to scale? Demonstrate your answer.
A firm is currently employing a cost-minimizing combination of labor and capital for a given level of output. The firm is employing 20 workers, and the marginal product of the last worker is 40 units of output. The firm is employing 100 units of capital, and the marginal product of the last unit of capital is 10 units of output. If the wage rate is $20 per hour, what is the price of capital? (A) $2.5 per hour (B) $5 per hour (C) $10 per hour (D) $100 per hour (E) $200 per hour
3. Consider the following production functions along with their corresponding marginal product of labor function. I. Q = 15KL II. Q = 2K0.4L0.6 III. Q = 8K + L. a. In each case, what happens to the marginal product of labor as the firm uses more labor? b. In each case, what happens to the marginal product of labor as the firm uses more capital?