Problem 1. There are two firms A and B located in different regions that produce an identi- cal good at zero cost. Each region is inhabited by a single buyer interested in purchasing at most one unit of the good. The RP of each buyer for one unit of the good is $5. If a buyer purchases the good from the seller in the distant location she incurs a transportation cost of $2.60. Buyer's will purchase from the location that results in the largest surplus. In case of ties, buyers break them in favor of the closest seller.
1. If the sellers are restricted to announcing a single price per unit for their goods, is pricing at cost (i.e. 0) for both firms an equilibrium? Explain.
2. If the sellers are restricted to announcing a single price (simultaneously) per unit for their goods, what will the equilibrium price be? Explain.
3. What is the effect on profitability, and why, if each firm can also issue a coupon (produc- tion and distribution of coupon is costless) that will be directed to buyers in distant regions? So, A will issue a coupon to the buyer who resides in the same region as B. Similarly, B will issue a coupon to the buyer who resides in the same region as A.
4. What would the equilibrium price and value of a coupon be under the above arrangement?


Problem 2. Between 0 and 1 are a 1000 customers, evenly distributed. Each of these cus- tomers wants exactly one unit of SOMA. Travel costs are a $1 a mile. Hence, the cost to a customer at distance d from LEFT of going to LEFT to purchase a unit of SOMA is d. The cost of going to RIGHT is 1 - d. Given the prices charged by LEFT and RIGHT, customers base their purchase decisions on the relative delivered cost of the product. The delivered cost is the travel cost plus price of the item. For example, the delivered cost of the customer at distance d from LEFT, is d + pL, where pL is the price per unit of SOMA being charged by LEFT. If pR were the selling price of SOMA at RIGHT, this customer would buy from LEFTifandonlyifd+pL <1-d+pR.
If the inequality were reversed, the customer would buy from RIGHT. Ignore the case of a tie. 1
1. If variable manufacturing costs are zero, what price will each firm charge in equilibrium?
2. For this part only, suppose that LEFT's marginal costs increase from zero. What effect does that have on the equilibrium price?
3. For this part only suppose that both LEFT and RIGHT have a marginal cost of produc- tion of $2. If the marginal costs of production for both firms drops, what effect will this have on the equilibrium price? Will it decrease, increase or stay unchanged?
4. Suppose LEFT could choose to set its price first (before RIGHT announces a price and that LEFT's choice is irrevocable) or simultaneously with RIGHT. Which is more profitable for LEFT?
5. Suppose LEFT could choose to set its price first (irrevocably and before RIGHT), second (after RIGHT sets a price that is irrevocable) or simultaneously. Which is the best option for LEFT?
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