Question

It sells to two types of consumers: medical (type 1) and academic type 2). The lab equipment manufacturer identifies the following demands for its two differentiated consumers:

P1= 500 - Q1

P2= 300-Q2

The marginal cost to produce and sell the equipment is $50 regardless of the consumer. Assume that the equipment company can identify each type of consumer before the point of scale.

a. What would be the optimal two-part pricing strategy for each type of consumer?

b. Which yields a higher profit - the two-part strategy or a third-degree from last week's homework? What explains the difference?

c.

Answer 1

(a) With two part pricing strategy, Price equals MC in each market.

In market 1,

500 - Q1 = 50

Q1 = 450

P1 = $50

In market 2,

300 - Q2 = 50

Q2 = 250

P2 = $50

(b) With third degree price discrimination, in each market, MR = MC.

In market 1,

Total revenue (TR1) = P1 x Q1 = 500Q1 - Q1²

MR1 = dTR1/dQ1 = 500 - 2Q1

500 - 2Q1 = 50

2Q1 = 450

Q1 = 225

P1 = 500 - 225 = $275

Profit (Z1) = Q1 x (P1 - MC) = 225 x $(275 - 50) = 225 x $225 = $50,625

In market 2,

Total revenue (TR2) = P2 x Q2 = 300Q2 - Q2²

MR2 = dTR2/dQ2 = 300 - 2Q2

300 - 2Q2 = 50

2Q2 = 250

Q2 = 125

P2 = 300 - 125 = $175

Profit (Z2) = Q2 x (P2 - MC) = 125 x $(175 - 50) = 125 x $125 = $15,625

Aggregate profit (Z) = Z1 + Z2 = $50,625 + $15,625 = $66,250

With two part pricing, in each market, profit equals entire consumer surplus (CS = Area between demand curve and price)

In market 1, when Q1 = 0, P1 = 500 (vertical intercept of demand curve)

Profit (CS1) = (1/2) x $(500 - 275) x 225 = (1/2) x $450 x 225 = $25,312.5

In market 2, when Q2 = 0, P2 = 300 (vertical intercept of demand curve)

Profit (CS2) = (1/2) x $(300 - 175) x 125 = (1/2) x $125 x 125 = $7,812.5

Aggregate profit (CS) = CS1 + CS2 = $25,312.5 + $7,812.5 = $33,125

Therefore, third degree price discrimination leads to higher aggregate profit compared to in two part pricing. The reason is that in third degree price discrimination, higher price is charged in the less elastic market and lower price is charged in more elastic market, so revenue is maximized. Cost structure being the same, higher revenue yields higher profit.