You are the monopoly supplier of Soma to a pair of downstream retailers. The retailers are located in two dierent parts of town which we will refer…

You are the monopoly supplier of Soma to a pair of downstream retailers. The retailers are located

in two dierent 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

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 dierent 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 protability?

As the manufacturer you have zero production costs. Your sales contract to each retailer consists

of two parts. The rst 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 *w. You will offer the same

contract to both retailers. Because of your monopoly position you can make a take it or leave it

oer and the retailers will accept provided the contract generates non-negative prots 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)/ 2 . This is its profit maximizing monopoly price in the home market.

1. Suppose the manufacturer sold directly to the three markets. What price would maximize

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, dierent in kind from the one considered, the

manufacturer could offer to improve its profit? Keep it simple!

 
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