Question 1: Monopolistic Competition (15 mark)

Consider the representative consumer model where the goods are homogeneous. The inverse market demand curve isp=10-q, wherep is the market price andq is the aggregate output. There aren firms in the market. Output of firm-i is denoted byqi. Soq=q1+q2+...+qi+...+qn.

1. Suppose the cost function of a firm-i isciqi=1+4qi and the firms are symmetric. Find the monopolistic competitive outcomes consisting of the equilibrium number of firms, equilibrium output produced by each firm, the equilibrium market price and the social welfare.(5 mark)
2. Suppose there is a technological innovation that reduces the per unit cost of production but the fixed cost of accessing the new technology rises. Consequently, the cost function of a firm-i becomesciqi=4+2qi. Find the monopolistic competitive outcomes consisting of the equilibrium number of firms, equilibrium output produced by each firm, the equilibrium market price and the social welfare.(5 mark)
3. Compare the equilibrium outcomes of innovation to the pre-innovation case. What are the welfare implications of this innovation?(5 mark)