Question

In the market for poultry there are two groups of people, those who are poor and those who are wealthy. The wealthy have a more inelastic demand than those who are poor. The firm offers a price of $90 if consumers purchase 5 units and offers a price of $80 if consumers purchase 40 units. These values are indicated on the graph below. With this price scheme, the firm wants to incentivize the wealthy to pay the higher price and purchase the smaller quantity. Price 100 Wealthy Demand 90 80 5 10 40 Quantity a. What consumer surplus do the wealthy gain by purchasing 5 units of the good for $90? b. What net consumer surplus do wealthy gain by purchasing 40 units of the good for $80: c. Is this quantity discount scheme incentive compatible (IC) for the wealthy? Type yes if it is 1C, or type no if it is not IC.

Answer 1

Consumer surplus = maximum price willing to pay – actual price

1) Here we see quantity offered is 5 and price is 90 dollars. The consumer is however willing to pay higher for 5 quantity. This area of the consumer surplus triangle ABC(refer image below) = 1/2*5*(100-90) = 25 dollars

2) Here we see that quantity offered is 40 for 80 dollars. The consumer surplus triangle will now change and take the area of the triangle ADE(refer image below) = 1/2 * 10 * (100-80)

= 100 dollars

3) No.

We see that in the second case quantity is increased by 8 times from 5 to 40 but consumer surplus is only increased by 4 times from 25 to 100. Hence the weralthy group will not find the price of 80 dollar to be incentive compatible.

Solution graph

.

GRAPH A NOT Douce (roo) (90) B TO SCALE C E (80) 1 - 5 10 40 Quantity

.

Kindly thumbs up if answer was helpful!