Reference no: EM13706706

Problem 1. There are two rms A and B located in dierent regions that produce an identical 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. Buyers 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 rms 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 eect on protability, and why, if each rm can also issue a coupon (production 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 customers 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 LEFT if and only if d + 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 rm charge in equilibrium?
2. For this part only, suppose that LEFTs marginal costs increase from zero. What eect
does that have on the equilibrium price?
3. For this part only, suppose that both LEFT and RIGHT have a marginal cost of production of $2. If the marginal costs of production for both rms drops, what eect will this
have on the equilibrium price? Will it decrease, increase or stay unchanged?
4. The variable manufacturing costs are zero. Suppose LEFT could choose to set its price
rst (before RIGHT announces a price and that LEFTs choice is irrevocable) or simultaneously with RIGHT. Which is more protable for LEFT?
5. The variable manufacturing costs are zero. Suppose LEFT could choose to set its price
rst (irrevocably and before RIGHT), second (after RIGHT sets a price that is irrevocable)
or simultaneously. Which is the best option for LEFT?