(b) Following the increase in the wage rate, Alpha Inc. reduces the number of workers employed by significantly more than Beta Ltd. Construct the demand curve for labour for Alpha Inc. and explain how and why its shape will change if you graphed the same curve for Beta Ltd. There is a third firm in this market called Gamma plc. which also uses labour and capital to produce output, where w is the price of labour, r is the price of capital and Q is the output. Suppose that Gamma plc. is a price-taking firm and faces a cost function: 1 11 c(w,r,Q) = w²r²Q² (c) By deriving an expression for the marginal cost function, explain whether the production process that gives rise to the total cost function has increasing, decreasing or constant returns to scale. (d) Continue to use Gamma plc.'s cost function from part (c) of c(w, r, Q) = wrzQ² and continue to assume that the firm is a price taker in the competitive market. Find an expression for Gamma plc.'s supply function Q(p, w, r) and its profit function (p, w, r).

(b) Following the increase in the wage rate, Alpha Inc. reduces the number of workers employed by significantly more than Beta Ltd. Construct the demand curve for labour for Alpha Inc. and explain how and why its shape will change if you graphed the same curve for Beta Ltd. There is a third firm in this market called Gamma plc. which also uses labour and capital to produce output, where w is the price of labour, r is the price of capital and Q is the output. Suppose that Gamma plc. is a price-taking firm and faces a cost function: 1 11 c(w,r,Q) = w²r²Q² (c) By deriving an expression for the marginal cost function, explain whether the production process that gives rise to the total cost function has increasing, decreasing or constant returns to scale. (d) Continue to use Gamma plc.'s cost function from part (c) of c(w, r, Q) = wrzQ² and continue to assume that the firm is a price taker in the competitive market. Find an expression for Gamma plc.'s supply function Q(p, w, r) and its profit function (p, w, r).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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