Question

An amusement park, whose customer set is made up of two markets, adults and children, has developed demand schedules as follows: Price ($) Quantity Adults Children 5 15 20 6 14 18 7 13 16 8 12 14 9 11 12 10 10 10 11 9 8 12 8 6 13 7 4 14 6 2 The marginal operating cost of each unit of quantity is $5. Because marginal cost is a constant, so is average variable cost. Ignore fixed costs. The owners of the amusement part want to maximize profits. Calculate the price, quantity, and profit if: The amusement park charges a different price in each market. The amusement park charges the same price in the two markets combined. Explain the difference in the profit realized under the two situations.

Answer 1

a) In case of price discrimination,

A monopolist maximizes its profit by increasing output as long as MR is higher or equal to MC.

Since there are two segments, monopolist will maximize profit in each segment.

P	Adults, Qa	Children, Qc	TRa=P*Qa	TRc=P*Qc	MRa=Change in TRa/Change in Qa	MRc=Change in TRc/Change in Qc
14	6	2	84	28
13	7	4	91	52	7	12
12	8	6	96	72	5	10
11	9	8	99	88	3	8
10	10	10	100	100	1	6
9	11	12	99	108	-1	4
8	12	14	96	112	-3	2
7	13	16	91	112	-5	0
6	14	18	84	108	-7	-2
5	15	20	75	100	-9	-4

In case of adults, MR is equal to MC ($5) for Qa=8 but MR is less than MC in case of Qa=9, Optimal output, Qa=8 in this segment.

So, monopolist chooses price corresponding to this level i.e. $12 for adults.

Similarly, in case of children, MR is higher than MC ($5) for Qc=10 but MR is less than MC in case of Qc=12, Optimal output, Qc=10 in this segment.

So, monopolist chooses price corresponding to this level i.e. $10 for children

Total Cost=Qa*Pa+QcPc-(Qa+Qc)*MC=8*12+10*10-(8+10)*5.=$106

b)

P	Adults, Qa	Children, Qc	Total Demand, Q=Qa+Qc	TR=P*Q	MR=Change in TR/Change in Q
14	6	2	8	112
13	7	4	11	143	10.33
12	8	6	14	168	8.33
11	9	8	17	187	6.33
10	10	10	20	200	4.33
9	11	12	23	207	2.33
8	12	14	26	208	0.33
7	13	16	29	203	-1.67
6	14	18	32	192	-3.67
5	15	20	35	175	-5.67

In case of uniform pricing, monopolist increases its output level as long as MR>MC or MR=MC.

We can see that at MR<MC for Q=20. So, optimal Q=17. Corresponding price is $11

Total Profit=11*17-5*17=$102

We can say that profit is higher in case of price discrimination based upon age in this case.