Perhaps you wondered what Ben Kinmore, who lives off in the woods quietly collecting his monopoly profits,

Question:

Perhaps you wondered what Ben Kinmore, who lives off in the woods quietly collecting his monopoly profits, is doing in this chapter on oligopoly. Well, unfortunately for Ben, before he got around to selling any stoves, the railroad built a track to the town of Deep Furrow, just 40 miles down the road, west of Bouncing Springs. The storekeeper in Deep Furrow, Huey Sunshine, was also able to get cookstoves delivered by train to his store for $20 each. Huey and Ben were the only stove dealers on the road. Let us concentrate our attention on how they would compete for the customers who lived between them. We can do this, because Ben can charge different base prices for the cookstoves he ships east and the cookstoves he ships west. So can Huey.
Suppose that Ben sets a base price, pB, for stoves he sends west and adds a charge of $1 per mile for delivery. Suppose that Huey sets a base price, pH, for stoves he sends east and adds a charge of $1 per mile for delivery. Farmers who live between Ben and Huey would buy from the seller who is willing to deliver most cheaply to them (so long as the delivered price does not exceed $120). If Ben€™s base price is pB and Huey€™s base price is pH, somebody who lives x miles west of Ben would have to pay a total of pB + x to have a stove delivered from Ben and pH + (40 ˆ’ x) to have a stove delivered by Huey.
(a) If Ben€™s base price is pB and Huey€™s is pH, write down an equation that could be solved for the distance xˆ— to the west of Bouncing Springs that
Ben€™s market extends. __________. If Ben€™s base price is pB and Huey€™s is pH, then Ben will sell __________ cookstoves and Huey will sell __________ cookstoves.
(b) Recalling that Ben makes a profit of pB ˆ’20 on every cookstove that he sells, Ben€™s profits can be expressed as the following function of pB and pH. __________.
(c) If Ben thinks that Huey€™s price will stay at pH, no matter what price Ben chooses, what choice of pB will maximize Ben€™s profits? __________Suppose that Huey thinks that Ben€™s price will stay at pB, no matter what price Huey chooses, what choice of pH will maximize Huey€™s profits? __________.
(d) Can you find a base price for Ben and a base price for Huey such that each is a profit-maximizing choice given what the other guy is doing? __________. How many cookstoves does Ben sell to farmers living west of him? 20. How much profit does he make on these sales? __________.
(e) Suppose that Ben and Huey decided to compete for the customers who live between them by price discriminating. Suppose that Ben offers to deliver a stove to a farmer who lives x miles west of him for a price equal to the maximum of Ben€™s total cost of delivering a stove to that farmer and Huey€™s total cost of delivering to the same farmer less 1 penny. Suppose that Huey offers to deliver a stove to a farmer who lives x miles west of Ben for a price equal to the maximum of Huey€™s own total cost of delivering to this farmer and Ben€™s total cost of delivering to him less a penny. For example, if a farmer lives 10 miles west of Ben, Ben€™s total cost of delivering to him is $30, $20 to get the stove and $10 for hauling it 10 miles west. Huey€™s total cost of delivering it to him is $50, $20 to get the stove and $30 to haul it 30 miles east. Ben will charge the maximum of his own cost, which is $30, and Huey€™s cost less a penny, which is $49.99. The maximum of these two numbers is __________. Huey will charge the maximum of his own total cost of delivering to this farmer, which is $50, and Ben€™s cost less a penny, which is $29.99. Therefore Huey will charge __________ to deliver to this farmer. This farmer will buy from __________ whose price to him is cheaper by one penny. When the two merchants have this pricing policy, all farmers who live within __________ miles of Ben will buy from Ben and all farmers who live within __________ miles of Huey will buy from Huey. A farmer who lives x miles west of Ben and buys from Ben must pay __________ dollars to have a cookstove delivered to him. A farmer who lives x miles east of Huey and buys from Huey must pay __________ for delivery of a stove. On the graph below, use blue ink to graph the cost to Ben of delivering to a farmer who lives x miles west of him. Use red ink to graph the total cost to Huey of delivering a cookstove to a farmer who lives x miles west of Ben. Use pencil to mark the lowest price available to a farmer as a function of how far west he lives from Ben.
Perhaps you wondered what Ben Kinmore, who lives off in

(f) With the pricing policies you just graphed, which farmers get stoves delivered most cheaply, those who live closest to the merchants or those who live midway between them? __________. On the graph you made, shade in the area representing each merchant€™s profits. How much profits does each merchant make? __________. If Ben and Huey are pricing in this way, is there any way for either of them to increase his profits by changing the price he charges to some farmers? __________.