There are two firms that are vertically differentiated. The values of the goods that are produced by these firms are respectively v1 and v2 : v2 > v1 .The consumers' marginal valuation of these products are uniformly distributed between b1 and b2. If a consumer of type b consumes good 1, his net utility is U1 =b v1-p1 . Similarly, if he consumes good 2 his utility is U2 =b v2-p2 . The consumer can choose not to consume anything and then his utility is U0 .
1. Determine the consumer of type ˜b~
who is indifferent between consuming good 1 and good 2.
2. Determine the demand for good 1 and good 2 as a function of model parameters.
3. Write down the profit of firm 1 . Maximize firm1's profit by choosing p1. Write best response function of firm 1's price as a function of firm 2's price, v1 and v2 and other model parameters.
4. Repeat step 3 for firm 2.
5. Now you have two bests response functions. Determine the equilibrium price choices for firm 1 and firm 2 as a function of v1,v2, and other model parameters.
STEP 2
6. Now that we know the prices as a function of v1 and v2 and other model parameters. Write the demand of each firm as a function of v1 and v2 and other model parameters only.
7. Given that firm 2 locates its product at v2 and prices at p2 ( the price you found in step e above) , what is the best location choice for firm 1.
8. Repeat step g for firm 2.
9. Now that you found best response functions for firm 1 and firm 2's location choice as a function of one another. Find the equilibrium choices of v1 and v2 .
10. Write a short discussion about where the firms should locate.
