Consider a competitive industry composed of J=48 identical firms. Firms produce output according to the Cobb-Douglas technology, =1, where x is some variable input such as labour, k is some input such as plant size, which is fixed in the short run, and 0 < < 1. The price of the output is p and the short-run profit function is (,)=[(2/16)1].

a) Supposing each firm operates a plant size of k=1, find the short-run supply function for firm j.

b) Find the short-run market supply function.

c) The market demand is =294/p. Solve for the short-run equilibrium price, quantity and profit.

d) Supposing again that each firm operates an unknown plant size of k, solve for the long-run equilibrium price and number of firms. Hint: you need the zero-profit and market-clearing conditions!