11. A firm has a production function of Y $100 Log(K), where K is the amount of capital used in production. The slope of the production function is given by $100/K. Suppose the interest rate is 100%. What is the optimal level of capital? a. $1 b. $20 C. $50 d. $100 e. $200

11. A firm has a production function of Y $100 Log(K), where K is the amount of capital used in production. The slope of the production function is given by $100/K. Suppose the interest rate is 100%. What is the optimal level of capital? a. $1 b. $20 C. $50 d. $100 e. $200

Microeconomics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506893

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter8: Costs And The Supply Of Goods

Section: Chapter Questions

Problem 9CQ

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8. If a firm has a production function of the form: Q = L0.5K2, what can we conclude? (a) The firm has a quasi-concave production function and will experience constant marginal returns to labour and increasing marginal returns to capital. (b) The firm has a quasi-concave production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital. (c) The firm has a convex production function and will experience increasing marginal returns to labour and increasing marginal returns to capital. (d) The firm has a convex production function and will experience constant marginal returns to labour and increasing marginal returns to capital. (e) The firm has a linear production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital.
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1. Assume that a firm has the following production function: q = L0.5K0.6. a. Calculate output when L = 64 K = 32. b. What returns to scale does this production function exhibit? c. Calculate output if technology utilized by the firm increases by 25%.
Lesson 7- Production Question 8
When labor is doubled and capital is tripled, a firm's output increases 2.5 times. Which of the following is true? We need more information to determine the degree of returns to scale of this firm's production function. This firm's production function must exhibit increasing returns to scale. This firm's production function must exhibit decreasing returns to scale. This firm's production function must exhibit constant returns to scale.
1. A firm's production function is Q = 50L – 0.01Ľ , where L denotes the size of the workforce. Find the value of MPL in the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function?
8. Consider a representative firm that faces a constant returns to scale production function Y = zF(K, Nd), where Y is output of consumption goods, z is TFP, K is physical capital, and Nª is labour input. The amount of capital is assumed to be given and fixed. The production function exhibits a positive marginal product of labour, as well as diminishing returns to labour. The firm seeks to maximize profits. (a) Explain what the profit maximizing condition for the firm is and show the profit maximizing labor demand on the graph with total revenue and total variable cost curves. On another graph show the firm's demand for labour curve and the profit maximizing labor input. (b) Suppose that the government now imposes an output tax Ty < 1 per unit of con- sumption good produced. What is the effect of this tax on the firm's demand for labor? Explain.
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