# Question 5 (20 marks) (a) i) A firm has production function y - f(x,z) -ax+Bz, for...

###### Question:

Question 5 (20 marks) (a) i) A firm has production function y - f(x,z) -ax+Bz, for y 2 0, where y is output, and x, z the factors of production. Are the returns to scale constant, increasing or decreasing? Explain your answer. (3 marks) ii) Consider the production function: f(x1,2)2 where a is a positive parame- ter. Indicate for which values of a the returns to scale in production are increasing Explain your answer. (3 marks) iii) A firm has production function y = f(x,z) = (xz)/(2+z), for y 0, where y is output and x, z the factors of production. Are the returns to scale constant, increasing or decreasing? Explain your answer. (4 marks) (b) i) The total cost function of a competitive firm is c(y) = 2 + (y2/3). At what market price is the firm producing 30 units of y? (5 marks) ii) In a competitive industry, there is a firm with cost function: c(00,y) 16+2y2 for y > 0. In the long run, what is the minimum price at which the firm is prepared to produce a positive output? (5 marks)

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