Question

Consider the following demand curves: 1) P = 130 – 0.005Q, and 2) P = 110 – 0.008Q. Consider also that the marginal cost of an additional fan is constant at 10. The ticket seller looks to price discriminate between these two groups. At equilibrium, is the marginal revenue from an additional ticket sold to group 1 greater than, less than, or equal to the marginal revenue from an additional ticket sold to group 2? Provide the appropriate intuition for your result. c. Provide the two prices for the ticker seller in part b)

Answer 1

MR=MC

Revenue=Price *Q=(130-0.005Q)*Q=130Q-0.005Q^2

Marginal Revenue=130-0.01Q

130-0.01Q=10

120=0.01Q

Q=12000 and P=130-.005(12000)=70 (group 1)

For group 2

Revenue=Price*Q=(110-0.008Q)*Q=110Q-0.008Q^2

MR=110-0.016Q

MR=MC

110-0.016Q=10

100=0.016Q

Q=100/0.016=6250

Price=110-0.008(7500)=50...(group 2)

Hence in group 1 seller will sell at Price =$70 and in group 2 seller will sell at price =$50

Marginal Revenue from selling product to group 1 = Marginal Revenue from selling product to group 2