Question

Suppose that you need to define the costs of delivering apples from a farm to a farmer’s market located in a small town. Supply of apples at the farm is given by ?? = 5 + 40P

where Qs is the quantity of applies produced in kilograms (kg) and P is the price of apples in $/kg. It is also known that demand for applies in the town is given by ?? = 10 − 5? where Qd is the quantity of apples demanded in kilograms (kg). You know that 6 kg of apples were shipped to the town. What are the transport costs in this case?

Answer 1

Qs = 5+40P

Qd = 10-5P

In equilibrium without any transportation costs,

Qs = Qd

5+40P = 10-5P

45P = 5

P* = 0.11

Q* = 10 - 5*0.11 = 9.44

It is given that 6 kg of apples were shipped to the town instead of 9.44 kg that were supposed to be shipped when there was no transportation costs. When Qd = 6, then price that consumer faces can be found out by putting Qd = 6

Qd = 10-5P

6 = 10-5P

5P = 4

P = 4/5 = 0.8

Therefore, buyers have to pay $0.8 per kg of apples.

The price that is received by seller when 6 kg apples are sold can be found out by putting Qs = 6

Qs = 5+40P

6 = 5+40P

40P = 1

P = 1/40 = 0.025

Therefore, sellers get $0.025 per kg of apples.

The difference between what buyers pay and what sellers receive gives the transportation costs.

Transportation costs = $0.8 - $0.025 = $0.775 per kg of apples

Since there are 6 kg of apples transported, then transportation costs = 6*0.775 = $4.65.