ABC company is a cost-minimizer and its aim is to produce a given output level at the smallest possible total cost. The firm uses two inputs labour (L) and capital (K) to make its output.

a) Given that the input prices are w (wage rate) and r (rental rate of capital)

i. write down an equation that represents the firm total cost function (iso-cost line equation).

(1 mark)

ii. What is the slope of the iso-cost line?

(1 mark)

b) Given that the firm produces according to the following production Q = L^2/3K^1/3 determine if the

i. marginal product of labour (MP_L) and the marginal product of capital (MP_K)

(2 marks)

ii. marginal product of capital exhibits diminishing returns

(2 marks)

iii. marginal product of labour exhibits diminishing returns

(2 marks)

iv. production function returns to scale.

(2 marks)

c) Solve the firm's cost minimization problem by, deriving the conditional input demand functions for labour and capital by Minimizing cost subject to output

(5 marks)