Deriving a supply function. Wolfgang is a typical producer in a perfectly competitive piano

market. His fixed costs are $1,000 per month in rent. The two variable inputs are raw

materials (wire, wood, ivory) which cost $1,000 per piano and Wolfgang's time which he

values at $40 per hour. In both short-run and long-run Wolfgang can make 1 piano in 100

hours, 2 pianos in 150 hours, 3 pianos in 250 hours and 4 pianos in 400 hours.

a) (5 marks). What is the marginal cost and of each piano?

b) (5 marks). If the price is $6,000 per piano then use MR and MC analysis to determine

how many pianos Wolfgang should produce to maximize profits?

c) (5 marks). Derive Wolfgang's short-run supply function by indicating for what set of

prices (if any) Wolfgang will (i) shutdown (ii) produce 1 piano (iii) produce 2 pianos (iii)

produce 3 pianos (iv) produce 4 pianos.

d) (5 marks).What will be the long-run competitive equilibrium price? How many pianos

will Wolfgang produce in the long-run?