A car is assembled through labour (L) and capital (K)

A) Suppose a firm has access to a productive technology that allows them to produce a car strictly with one unit of labour and four units of capital. Write down the production function of the firm that produces cars out of labour and capital. Sketch the isoquant that shows all combinations of labour and capital that result in producing 50 cars. (5 marks)

B) Suppose that initially the price of capital is $1,000 and price of labour is $200. On the graph you drew for part (a), show the choices of labour and capital that minimize the cost of producing 50 cars, and draw the isocost line through the optimal basket. (5 marks)

C) Suppose now the production function for a car is Q=40L²K². The marginal products are: MP_L=80LK², MP_K=80L²K. Determine the firm's input demand functions for L and K. (10 marks)

D) If both labour and capital increase by $100 (with respect to the prices given in part B), will the firm demand more capital or labour to produce a set amount of cars using the production function in C)? How do you know? (5 marks)