1. In Tuftville everyone lives along Main Street that is 10 miles long. There are 1000 people uniformly spread up and down Main street, and each day each buy a fruit smoothie from one of the two stores located at either end of Main street. The motor scooter use $0.50 worth of gas per mile. Costumers ride their motor scooters to and from the store offering the lowest cost which is the store's price plus the customer's travel expenses. Ben owns the store at the west end of Main street and Will owns the store at the east end of Main street. a. If both Ben and Will charge $1 per smoothie how many will each of them sell in a day? If Ben charges $1 per smoothie and Will charges $1.40 how many smoothies will each sell in a day? b. If Ben charges $3 per smoothie what price would enable will to sell 250 smoothies per day? 500 smoothies per day? 750 smoothies per day? 1000 smoothies per day? c. If Ben charges p1 and Will charges p2 what is the location of the costumer who is indifferent between going to Ben's and going to Will's? how many customers go to Will's store and how many go to Ben's store? What are the demand functions that Ben and Will face? d. Rewrite Ben's demand function with p1 on the left-hand side. What is Ben's marginal revenue function? e. Assume that the marginal cost of a smoothie is constant and equal $1 for both Ben and Will. In addition, each of them pays Tuftville $250 per day for the right to sell smoothies. Find the equilibrium prices, quantities sold and profits.
2. Suppose that there are two firms, firm B and Firm N, producing complementary goods, say bolts and nuts. The demand curve for each firm is described as follows: Qb=Z-Pb-Pn and Qn=Z-Pn-Pb For simplicity assume further that each firm faces a constant cost of production, c=0. a. Derive the best response functions for each of these firms. b. Graph these functions. Find the Nash equilibrium.
3. Assume that two firms sell differentiated products and face the following demand curves: q1 = 15-p1+0.5p2 and q2 = 15-p2+0.5p1
a. Derive the best response function each firm. Do these indicate that prices are strategic substitutes or strategic complements?
b. What is the equilibrium set of prices in this market? What profits are earned at those prices?
4. Assume that in a small remote city there are two legal service providing firms each with maximum capacity to serve 500 individuals per day. Demand for legal services per day is described as Q=2000- 50P. Cost of providing legal service is $8 per day per service. What are the profit maximizing prices set by the two firms? How would you know there is no incentive to increase or decrease the price?