The Long-run production function is given by; Y = 180 L0.8 K1.8

Where, Y = Output (mt/day), L = Labour (hours/mt) K = Capita (Rs/mt)

a) Calculate Marginal Product of Labour (MPL) and Marginal Product of Capital (MPK), if

L=12 and K=20 (05 Marks)

b) Derive the equation for Isoquent and graphically show it by assuming L= 10, 15, 20 25 and

30. (05 Marks)

c) Determine factor intensity and returns to scale of this production function. (05 Marks)

d) Prove that the elasticity of labour is 0.8 and elasticity of capital is 1.8 (05 Marks)

a)

According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuring

plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring plan

Mitsubishi conducts an analysis of how labour and capital are used in its production process. Prior

to restructuring Mitsubishi's marginal rate of technical substitution is 0.15 ( in absolute value). To

hire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 15. In the

study of production process and markets where capital is procured, suppose that Mitsubishi

determine that its marginal productivity of capital is 0.5 small cars per hour at its new targeted

level of output and that capital is procured in a highly competitive market. The same study

indicates that the average selling price of Mitsubishi's smallest car is US$ 9500. Determine the

rate at which Mitsubishi can rent capital and marginal productivity of labour at its new targeted

level of output. To minimize costs Mitsubishi should hire capital and labour until the marginal rate

of technical substitution reaches what proportion?