Question

Assume that buyers are located along a line at points 1, 2 and 3. Each has a reservation price equal to 10. Marginal cost and average cost are equal to 4. There are 4 buyers located at points 1 and 3, and 2 buyers located at point 2. Seller A is located at point 1 and seller B is located at point 3. Transport cost is t = 1. When the price for both sellers is the same for a group of buyers, then half the buyers purchase from each seller. Only integer prices are allowed.

1. When both sellers charge price 10, then each will earn profit = _____.

a) 12

b) 24

c) 36

d) 8

e) 40

2. If seller A charges a price of 8 and seller B charges a price of 9, then the profit earned by seller A is _______.

a) 20

b) 32

c) 16

d) 24

e) 18

3. When seller A charges a price of 8, seller B's best response is to charge P = _____.

a) 9 or 10

b) 8 or 9

c) 6 or 7

d) 7 or 9

e) 5 or 6.

Answer 1

1. When both sellers charge a price of 10, seller A will cater to 4 people on point 1 and seller B will cater to 4 people on point 3. The people on point 2 will not buy anything as their reservation price is 10, and to go to any of the points 1 or 3, they will face transport costs of 1. The total price paid by them would be 11 which is higher than their reservation price.

Therefore, the profits of A are

Answer:b

2. If seller A charges price 8 while B is charging 9, A will cater to the 4 people on point 1 and 2 people from point 2. People on point 2 will prefer to come to point 1 as then the total expense by them would 9 (as opposed to 10 if they went to seller B).

The higher expense by them is due to the transport costs.

People on point 3 will not come to seller A as then would have to spend 8+2 (2 to jump to points),

A's profit now is

Answer: d

3.

As discussed in the previous question, if seller A charges a price of 8 and B charges 9, B will serve only 4 people.

Here B's profits are

If he charges a price of 10, B will still serve to 4 people (they will be indifferent between traveling toA and buying from there and buying from B. So lets assume they prefer to avoiding traveling and will just buy from B). Here, B's profits are

If B charges a price of 8, then the market is split between A and B. Therefore, B serves to 5 people. The profits here are

If B charges 7, it will cater to 6 people (4 on point 3, and 2 from point 2 will travel 2 and their expense would be 8 as opposed to 9 if they went to seller A). The profits here are

If B charges 6, it will cater to 6 people again (people from point 1 can either buy from B or A and their expense would be the same but they would prefer not to travel). So B's profits are

If B charges 5, it will cater to all the 10 people (people from point 1 will prefer going to B as their total expense would be 7 as opposed to 8 if they bought from seller A). B's total profits here are

The maximum profits B gets is when it charges 9 to 10. Therefore, that is its best response.

Answer: a