Suppose an electricity storage battery producer faces the following production function:

Q= 0.4KL

where Q is the number of batteries, K is units of capital and L is units of labour. The marginal product of labour is the marginal product of capital The wage rate (W) is $100 per hour, and the rental rate on capital (R) is $200 per hour.

a) Focusing on the short run where capital is fixed at 50. How many units of labour (L) will the business need to employ to produce 5000 batteries? How much will this production cost?

b) Explain whether this is the best combination of labour and capital for this business to produce 5000 batteries. If it is not, explain why they might choose to produce 5000 batteries in this way anyway.

c) Explain what the business should do to produce 5000 batteries at the lowest cost and calculate that cost.