Question

Suppose you are hired as an analyst for a new life center to be opened. Managers of the center will ask you for help in determining the optimal pricing strategy. As a result of your analysis, the demand for the center of life is based on age.
you saw it differentiate. For adults (Y) between the ages of 12-64 and the second over 65
You have noticed the different demand structures for spring (IB) customers as follows: PY = 9.6-0.08QY and PIB = 4-0.05QIB. As this living center area is large enough, the crowd is not a problem for you and you are acting on the assumption that marginal costs are zero. In this case:
a) What kind of price discrimination do you apply? Why?
b) When the mentioned price differentiation is applied, what are the balance prices and quantities?
is it up?
c) Demand for two groups with profit maximization under price discrimination
What relationship do you observe between their flexibility? Why?

Answer 1

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 would be applied as the consumers have been divided into two groups, that is adults between the ages of 12-64 and the second over 65. In this case, the first-degree is not possible as in that case, each consumer will be charged differently based on their willingness to pay. While second-degree discrimination is not possible as it is based on quantity and price is changed based on the number of quantities bought. Finally, the two-part tariff is not possible because, in that case the fixed price can be computed but the varying price can not be computed as it must be equal to marginal cost, which in this case is zero, making it equal to just fixed price.

(b). Under third-degree price discrimination, both types of consumers are charged with different prices based on their marginal revenues. The marginal revenue for the first type of consumers, that is, adults, the marginal revenue would be computed by multiplying the inverse demand function by the quantity and then differentiating the inverse demand function with respect to the quantity, 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 price discrimination is applied.

(c). It can be seen that the price is low for more elastic demand, which is for the second case while the price is higher for less elastic demand, which is for adults. This is so because, for more elastic demand, a small increase in price will decrease the quantity demand by a higher number than the case for less elastic demand. This is why the price is low for more elastic demand.