Suppose you are hired as an an
Suppose you are hired as an analyst for a new lifecenter to be opened. Managers of the center will ask you for helpin determining the optimal pricing strategy. As a result of youranalysis, the demand for the center of life is based on age.you saw it differentiate. For adults (Y) between the ages of 12-64and the second over 65You have noticed the different demand structures for spring (IB)customers as follows: PY = 9.6-0.08QY and PIB = 4-0.05QIB. As thisliving center area is large enough, the crowd is not a problem foryou and you are acting on the assumption that marginal costs arezero. In this case:a) What kind of price discrimination do you apply? Why?b) When the mentioned price differentiation is applied, what arethe balance prices and quantities?is it up?c) Demand for two groups with profit maximization under pricediscriminationWhat relationship do you observe between their flexibility?Why?
Answer:
Inverse Demand for adults is given as,
P(Y)=9.6-0.08Q(Y)
Inverse Demand for the age group above 65 is given as,
P(IB)=4-0.05Q(IB)
Assuming that the marginal cost is equal to zero.
(a). Based on these, the third-degree price discrimination wouldbe applied as the consumers have been divided into two groups, thatis adults between the ages of 12-64 and the second over 65. In thiscase, the first-degree is not possible as in that case, eachconsumer will be charged differently based on their willingness topay. While second-degree discrimination is not possible as it isbased on quantity and price is changed based on the number ofquantities bought. Finally, the two-part tariff is not possiblebecause, in that case the fixed price can be computed but thevarying price can not be computed as it must be equal to marginalcost, which in this case is zero, making it equal to just fixedprice.
(b). Under third-degree price discrimination, both types ofconsumers are charged with different prices based on their marginalrevenues. The marginal revenue for the first type of consumers,that is, adults, the marginal revenue would be computed bymultiplying the inverse demand function by the quantity and thendifferentiating the inverse demand function with respect to thequantity, such that,
dPQ/dQ=MR=9.6-1.6Q
Equating this to marginal cost,
9.6-1.6Q=0
Q=6 units
P=9.6-0.8(6)=$4.8
Now for the second group,
dPQ/dQ=MR=4-0.1Q
Equating this equal to MC,
4-0.1Q=0
Q=40 units
P=4-0.05(40)=$2
These are the balance prices and quantities when the pricediscrimination is applied.
(c). It can be seen that the price is low for more elasticdemand, which is for the second case while the price is higher forless elastic demand, which is for adults. This is so because, formore elastic demand, a small increase in price will decrease thequantity demand by a higher number than the case for less elasticdemand. This is why the price is low for more elastic demand.
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