Consider a market with differentiated products. There are 5 firms in this market. Aside for these firms, there are no other substitutes, so that to a good approximation consumers spend a constant fraction of their income in this group of products. Firm 1 has 25% market share. The following table gives the market shares of the remaining firms, together with the cross price elasticities of product j 0 s demand with respect to the price of firm one.

(a) Based on the information in this table, show that the elasticity of demand for firm 1 is equal to 2 (-2 including the sign). (Hint. You need to use something connecting elasticities of demand with cross price elasticities.) (b) The FTC is evaluating an agreement that firm 1 has made to acquire firm 3. It is expected that the marginal cost of firm 1 will fall by 20%. Assuming the 20% share of firm 3 is split equally across the remaining firms (including firm 1) and the elasticities of substitution do not change, do you expect the price of good 1 will increase or not? (Hint. You need to recompute the demand elasticity for firm one given these new market shares)

3. Consider a market with differentiated products. There are 5 firms in this market. Aside for these firms, there are no other substitutes, so that to a good approximation consumers spend a constant fraction of their income in this group of products. Firm 1 has 25% market share. The following table gives the market shares of the remaining firms, together with the cross price elasticities of product j's demand with respect to the price of firm one. Firm Ej1 market share 2 0.5 10% 3 3 0.4 20% 4 0.3 30% 5 0.2 15% 1 25% (a) Based on the information in this table, show that the elasticity of demand for firm 1 is equal to 2 (-2 including the sign). (Hint. You need to use something connecting elasticities of demand with cross price elasticities.) (b) The FTC is evaluating an agreement that firm 1 has made to acquire firm 3. It is expected that the marginal cost of firm 1 will fall by 20%. Assuming the 20% share of firm 3 is split equally across the remaining firms (including firm 1) and the elasticities of substitution do not change, do you expect the price of good 1 will increase or not? (Hint. You need to recompute the demand elasticity for firm one given these new market shares) 3. Consider a market with differentiated products. There are 5 firms in this market. Aside for these firms, there are no other substitutes, so that to a good approximation consumers spend a constant fraction of their income in this group of products. Firm 1 has 25% market share. The following table gives the market shares of the remaining firms, together with the cross price elasticities of product j's demand with respect to the price of firm one. Firm Ej1 market share 2 0.5 10% 3 3 0.4 20% 4 0.3 30% 5 0.2 15% 1 25% (a) Based on the information in this table, show that the elasticity of demand for firm 1 is equal to 2 (-2 including the sign). (Hint. You need to use something connecting elasticities of demand with cross price elasticities.) (b) The FTC is evaluating an agreement that firm 1 has made to acquire firm 3. It is expected that the marginal cost of firm 1 will fall by 20%. Assuming the 20% share of firm 3 is split equally across the remaining firms (including firm 1) and the elasticities of substitution do not change, do you expect the price of good 1 will increase or not? (Hint. You need to recompute the demand elasticity for firm one given these new market shares)