Question

Question 3 You are the monopoly supplier of Soma to a pair of downstream retailers. The retailers are located in two different parts of town which we will refer to as market 1 and 2 respectively. The number of people in each market is M. The demand in each market for Soma as a function of the retail price is M(1-P). Buyers in market 1 never go to the retailer in market 2 to purchase and buyers in market 2 never patronize the retailer in market 1. There is a third market consisting of comparison shoppers. These individuals will buy only from the retailer with the lowest price. In the case when the retailers charge the same price, these comparison shoppers will divide equally between the two retailers. Let C be the number of Its got what plants crave. Page 2 comparison shoppers. The demand for Soma as a function of the price amongst comparison shoppers is C(1-P). Hence, each retailer is a monopolist in its own market but faces competition in selling to the comparison shoppers. Retailers can price discriminate between buyers in their home market and comparison shoppers without fear of arbitrage. So, they are free to charge different prices to each market. The price charged in the market for comparison shoppers must form an equilibrium. Does the ability of the retailers to price discriminate help or hurt the manufacturer's profitability? As the manufacturer you have zero production costs. Your sales contract to each retailer consists of two parts. The first is a franchise fee, F independent of the quantity purchased. The second is a wholesale price w, that must be paid on each unit acquired (by a retailer). For example, if a retailer buyers 25 units of Soma from you, they pay you F + 25 X w. You will offer the same contract to both retailers. Because of your monopoly position you can make a take it or leave it offer and the retailers will accept provided the contract generates non-negative profits for them. Under a contract with franchise fee F and wholesale price w, the price that a retailer would charge in its home market will be 1+w. This is its profit maximizing monopoly price in the home market. 1. Suppose the manufacturer sold directly to the three markets. What unit price would maxi- mize its revenue? 2. Suppose C = 0, i.e., there are no comparison shoppers. What values of F and w should the manufacturer set to maximize its revenue? 3. Suppose M = 0, i.e., everyone is a comparison shopper. What values of F and w should the manufacturer set to maximize its revenue? 4. Suppose half the population are comparison shoppers, i.e., C = 2M. What values of F and w should the manufacturer set to maximize its revenue? 5. In the case when C = 2M, is there a contract, different in kind from the one considered, the manufacturer could offer to improve its profit? Keep it simple!

Answer 1

Page 1 1. The manufacture supplies Dierelly to each market she magi mize the Poobet bonction max 17 = PM Cl-Pa)+22MQ -P2) +PeC{1=le) Pa pace changed market 1 Pa = price charged market a Per price charged in comprison market gifbestiaut Equ P., P2, Pc Equating to o > P, M-P,²4 =0 => P2M = P²M =0 > PCC -18300 solve these @wolon I P = Po = Pc="/2] post maximizing Pice 9. there are no comparison sloppers boa Retailers 182 Iwa MCI- ()) . MCA-1460 =(1560M i the quantily supplied by the manbachwe ax Cl-WR! 2-WM

Pagera Tolal porofit of the manbacture π = ft wll WM Increasing F , Maximizing it with respect to o we get w: la poobil fonction boor retailer 1 & 2 the Ti = P,9,-F Prilo = (1+0 ) M (1-0)-F-M (1-0) W w=112, Tip = Pige-F-6, 1/2 = = {1* 12% )M (1-Wale) -F-M 61-423 42 E = M16] 3. Everyone is a compassion shoppen, the profit fonction food retailer 182 T, = Pc re- f - Wrc = Wc (1-0)-F- we (1-0) E-F to con non-negative Poobits, F =0 Compassion market is cal-w) the manotectores poobit fonction

Pager3 -0+ C - CO2 C1-0 TI C Co = 1/2 Fro,o=/ aetailerg Quile supplying to beth home and comparison the markets T = Rq, & Porc-f - w C9, +9c) Pialto Pe=w q = M (1-2) q c=c(1-0) Gider that c = 2M Q-99, +290 +3H (1 - the manufactters Pootit function T = Ft Q =F+013 (1-w) function is increasing in F 3M-6M coco W = 1/2 non- negalile substituing the values ob 10. P. Per 9, Elle into Tl, we get # 1 = M/16-F

pogethe Tiz=0 faM% Co = 1/2 5. manubachower Supplies the market si greetly T = PIM (1-P.) + P2M (1-P2) + Pc (1-Pc) . P1 = P2 = Pc = 1/2 &c=24 TEM M = F two =F+ 0 X 3M (1-2) Given that F = M/16 = 1/2 TE 1/16 +34/u = = 134 LM Hence, the retailer's ability to oscarminates hurts the monopolist