Question

Q2(A) Price Discrimination A small school has 100 students. You have been commissioned school photographer. From experience, you know that parents' demand for copies of each child's photograph is as given in the table below. Your fixed costs (studio rent, depreciation and various overheads) amount to $500 per week. Your variable costs (chemicals, films etc.) work out to a constant average variable cost of $1.50 per copy. Price ($/copy) Quantity Demanded 2 3 2 () Suppose that you want to charge a uniform price per copy (i.e. be a single price monopoly). (a) How much will you charge to maximise your profit? How many copies will you sell? (b) What is your total revenue? (c) What is your profit during the week? (d) How much is the parents' consumer surplus?

Answer 1

Single price monopolist can maximize profits by producing at a point where MC=MR.

You can find optimal level of price ans quantity either by looking at the quantity which maximizes profit or by equating MC=MR.

Price	Quantity	TR=P*Q	TVC=AVC*Q	Profit=TR-TVC
10	1	10	1.5	8.5
8	2	16	3	13
6	3	18	4.5	14.5
4	4	16	6	10
2	5	10	7.5	2.5
1	6	6	9	-3

a. Profit will be maximized when MR=MC,

At Q=3. MR= 18-16=2, MC=4.5-3=1.5

So,

Optimal Price $6, at this price 3 copies will be sold.

b. Total revenue at Q=3 is price times quantity. TR= 3*$6= $18

c. Total profit during the week = $14.5

d. Parent's consumer surplus is their willingness to pay - price actually paid=

At Q=1, 10-6=$4

+

At Q=2, 8-6= $2

+

At Q=3,6-6=$0

=

Consumer surplus= $4+$2=$6