Consider perfectly competitive industry composed of J identical firms. Firms produce output according to the Cobb-Douglas technology y = x K1-a where x is variable input such as labour and k is the plant size, which is fixed in the short run. Furthermore, Wx and wk are the input prices. (a) Derive the firm's short run profit-maximising input demand, output supply and the profit functions with this technology assuming an interior solution (i.e. ignoring the firm's shutdown condition). [20 marks] = (b) If now a=1/2, wx=4, and wx=1, then supposing each firm operates a plant of size k=1 and the market demand is given by Qa= 294/p, find the market supply with J=48 firms. Solve for the short-run equilibrium price, market quantity, output per firm, and firm profits. Sketch a graph for the market equilibrium. [15 marks] Consider perfectly competitive industry composed of J identical firms. Firms produce output according to the Cobb-Douglas technology y = x K1-a where x is variable input such as labour and k is the plant size, which is fixed in the short run. Furthermore, Wx and wk are the input prices. (a) Derive the firm's short run profit-maximising input demand, output supply and the profit functions with this technology assuming an interior solution (i.e. ignoring the firm's shutdown condition). [20 marks] = (b) If now a=1/2, wx=4, and wx=1, then supposing each firm operates a plant of size k=1 and the market demand is given by Qa= 294/p, find the market supply with J=48 firms. Solve for the short-run equilibrium price, market quantity, output per firm, and firm profits. Sketch a graph for the market equilibrium. [15 marks]