i) Derive the output elasticity of labour for the following further alternative productionfunction:InY = c + aK +BLii) Suppose ß = 0.5 and other factors are fixed, explain the percentage change inoutput due to a unit change in labour.

Answered: Image /qna-images/answer/6b513f81-bd39-4487-8452-61726ff16c6b.jpg

Answered: InY = c + aK + BL se ß = 0.5 and other…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 5E

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Suppose that instead the production function now is F (L, K) = 0.2L + 0.7K. The wage rate (price per unit of labour) is w = 3 and the capital rental rate (price per unit of capital) is r = 7. Obtain the cost function C∗(y), the marginal cost and the average cost. Derive the equation of the isoquant for y = 2 (with K in the vertical axis and L in the horizontal axis). Provide a graphical representation of this isoquant indicating the intersections with the vertical and horizontal axis.
For the production function q = f(K, L) the ratio of the percentage change on K/L with percentage change on PK/PL is called elasticity of substitution. Write down a constant returns to scale Cobb-Douglas production function and find its elasticity of substitution for the K = 10, L = 7, PK = 4 and PL = 3 levels.
A company uses two inputs, unskilled labour (L) and capital (K), to produce its product. The wage rate for a unit of labour is €5, while a unit of capital cost €20. a) Determine the equation and plot the isocost line for the company's expenditures on itsinputs of €1,000. Label the intercepts of the isocost with both axes. Draw a typical isoquant for an output level Q0 and indicate the optimal input levels of L and K. (Do not forget to label the axes). b) Suppose the government introduces a minimum wage for unskilled labour of €6 per unit.Show graphically and explain shortly how much it would cost the firm in the short run, with capital input fixed at K, to keep its output constant at Q0. c) Show graphically and comment shortly on the optimal factor mix that the firm would use to produce Q0 in the long run at the specified minimum wage of €6 per unit.

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InY = c + aK + BL se ß = 0.5 and other factors are fixed, explain the percenta ue to a unit change in lahour