A monopolist produces a good at zero marginal cost. It knows that two equal size
ID: 2495524 • Letter: A
Question
A monopolist produces a good at zero marginal cost. It knows that two equal sized subgroups exist in the market for its produce, but cannot differentiate between them by sight. Group I value quality of service highly. The price they are willing to pay for any quality level, Q, is given by PI = 5 – Q Group II are less willing to pay for quality of service, with PII = 3 – 2Q.
The monopolist wishes to practice price discrimination, by offering two price and quality bundles, in the hope that each group will choose the bundle set for it. One economist suggests that the two choices should be: Bundle 1. Quality level Q=5 at a cost to the consumer of 12.5 and Bundle 2. Quality level Q = 1.5 at a cost to the consumer of 2.25
(i) Why may these have been suggested and why would they not be optimal?
(ii) Devise the optimal strategy for the monopolist and determine his profit level under your suggested strategy.
(iii) How much consumer surplus does each type of customer gain?
Explanation / Answer
(i)
Group 1:
P1 = 5 - Q
Q = 5 - P1
dQ / dP1 = - 1 [Slope of demand function]
Group 2:
P2 = 3 - 2Q
Q = (3 - P2) / 2 = 1.5 - 0.5P2
dQ / dP2 = - 0.5 [Slope of demand function]
Since both groups have different slopes, demand has different elasticity in each group. That is the reason why the bundle was suggested - to charge higher price from the more inelastic group & to charge lower price from the more elastic group.
Since slope of group 2 is lower in group 2, demand in group 2 is more inelastic.
(ii) Optimal strategy should be to equate marginal revenue (MR) in each group to the MC (= 0).
For group 1:
Total revenue, TR1 = P1 x Q = 5Q - Q2
Marginal revenue, MR1 = dTR1 / dQ = 5 - 2Q
Equating MR1 with MC:
5 - 2Q = 0
2Q = 5
Q = 2.5
P1 = 5 - Q = 5 - 2.5 = 2.5
For group 2:
TR2 = P2 x Q = 3Q - 2Q2
MR2 = dTR2 / dQ = 3 - 4Q
Equating MR2 with MC:
3 - 4Q = 0
4Q = 3
Q = 0.75
P2 = 3 - 2Q = 3 - (2 x 0.75) = 3 - 1.5 = 1.5
Since MC = 0, Profit = Revenue in each group.
Profit, group 1 = TR1 = P1 x Q = 2.5 x 2.5 = 6.25
Profit, group 2 = TR2 = P2 x Q = 1.5 x 0.75 = 1.3125
(iii)
From group-1 demand function: When Q = 0, P = 5 [Reservation price]
Consumer surplus (CS) = Area between demand curve & Equilibrium price
= (1/2) x (5 - 2.5) x 2.5 = (1/2) x 2.5 x 2.5 = 3.125
From group-2 demand function: When Q = 0, P = 3 [Reservation price]
CS = (1/2) x (3 - 1.5) x 0.75 = (1/2) x 1.5 x 0.75 = 0.5625