Suppose that a firm's Cobb-Douglas production function involves two inputs, labour (L) and capital (K) and is represented by strictly convex isoquants. The firm is currently producing 400 units of output by hiring 25 units of labour and 10 units of capital.

Labour is half as expensive as capital to hire, and at the current input combination, the marginal productivity of labour is

twice that of the marginal productivity of capital, i.e., L = 2 K

b) Suppose that labour is kept on the horizontal axis while capital is kept on the vertical axis. What is the absolute MRTS at the current input combination? Show your working.

c) Is the firm currently minimizing cost of producing 400 units of output? If not, determine the best course of action for the firm to produce 400 units of output if it wants to minimize its costs.