Question

Use the following information to answer questions 7 - 12. Suppose there is one buyer located at points 1 through 11, one unit of distance apart. These buyers purchase at most one unit of the product when its price is less than or equal to $10. Assume the MC and AC of producing the product is $5. Transport costs are constant per unit of distance. 7. If a seller must sell at only one point, 1-11, the profit maximizing location is a) 1 b) 5 c) 11 d) 8 e) 6 8. The total transport cost to sell to all buyers in this market when transport cost per unit distance t= 1 is a) 11 b) 15 c) 30 d) 36 e) 22

Answer 1

7) e) 6

By setting up at location 6, he can earn a profit of $110-$55-$30t = $55-$30t. This is the maximum profit he can earn. (Transport cost= t per unit of distance)

By setting up the plant at 6, he has to travel the least distance to deliver the 11 units and since the marginal cost is constant at $5 per unit of good, total cost is the sum of making cost and transport cost.

Selling price is $10 per unit of good. 11 goods are sold. Total revenue is $110.

At location 1, transport cost is (1+2+3+4+5+6+7+8+9+10)t =55t

At location 5, transport cost is (1+2+3+4+1+2+3+4+5+6)t = 31t

At location 11, transport cost is (10+9+8+7+6+5+4+3+2+1)t =55t

At location 8, transport cost is (1+2+3+4+5+6+7+1+2+3)t = 34t

At location 6, transport cost is (1+2+3+4+5+5+4+3+2+1)t = 30t

Transport cost is minimum at location 6. Given constant price and marginal cost, the maximum profit is earned at location 6.

8. c) 30

We know the profit maximizing location is 6. At location 6, total transport cost is 30t.

At t=1, transport cost in the market is 30.