(ii) A multi - product firm produces two non - related products X and Y where production functions are given by Qx = L0.25K0.75, Qy = L0.5K08, Qx and QY are quantities of outputs of X and Y per period of time and L and K are inputs of labour and capital services per period of time. Capital and labour services can be bought at constant prices per unit of Rs.300 and Rs.200 respectively. (a) Derive the returns to scale characteristics of the two production functions. (b) Calculate the Marginal Product of labour (MPL) and Marginal product of Capital (MPK) for each production function. (c) Write down the equilibrium condition for cost minimization in terms of MPL, MPK and factor prices. (d) What is the capital to labour ratios for the two plants that minimizes the firms cost at any chosen output levels of two goods?

(ii) A multi - product firm produces two non - related products X and Y where production functions are given by Qx = L0.25K0.75, Qy = L0.5K08, Qx and QY are quantities of outputs of X and Y per period of time and L and K are inputs of labour and capital services per period of time. Capital and labour services can be bought at constant prices per unit of Rs.300 and Rs.200 respectively. (a) Derive the returns to scale characteristics of the two production functions. (b) Calculate the Marginal Product of labour (MPL) and Marginal product of Capital (MPK) for each production function. (c) Write down the equilibrium condition for cost minimization in terms of MPL, MPK and factor prices. (d) What is the capital to labour ratios for the two plants that minimizes the firms cost at any chosen output levels of two goods?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

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