Q4. Consider a two-firm industry producing two differentiated products indexed by i=1,2. Production cost is zero. Inverse demand functions for these two products are P = a - Bq, - 192: Pa = a 79; Bq2; > 0, B > y? B? > y?is the assumption stating that the own-price effect dominates the cross-price effect. 1. Please invert the inverse demand functions back to the demand functions (quantities as the function of prices). 2. Show that in a Cournot game with differentiated products, the profits of firms increase when the products become more differentiated. 3. Show that in a Bertrand game with differentiated products, the profits of firms increase when the products become more differentiated. 4. Show that in a differentiated products industry the market price under Cournot is higher than it is under Bertrand. The more differentiated the products are, the smaller the difference between Cournot and Bertrand prices. This price difference is zero when the products become independent.