Answer to Question #244899 in Economics for Wofa

Question

Consider a monopolist with the following demand functions for different

market segments

q1= 16 - 0.2P1

q2= 9 - 0.05P2

Where q1 and q2 are the quantities demanded in segments 1 and 2 respectively,

and p1, and p2 are the prices charged in the two segments.

The cost function is C = 50 + 20(q1 + q2)

b) Assume that these conditions are met. Calculate for each market segment

the equilibrium price, quantity and profit.

c) Show that the higher price is charged in the relatively more inelastic

segment of the market.

d) If the monopolist cannot discriminate and it has to charge one price what

price will it charge and what quantity would it produce? What will be the

profit under this scenario?

e) Describe the optimal two-part pricing strategy for the firm. How much

profit does the firm earn from this strategy?

Answer 1

b) The equilibrium price, quantity and profit for each market segment are:

P1 = 80 - 5Q1,

MR1 = TR1'(Q1) = 80 - 10Q1,

MC1 = C'(Q1) = 20.

MR1 = MC1,

80 - 10Q1 = 20,

Q1 = 6 units.

P1 = 80 - 5×6 = 50.

TP1 = 50×6 - (25 + 20×6) = 155.

P2 = 180 - 20Q2,

MR2 = TR2'(Q2) = 180 - 40Q2,

MC2 = C'(Q2) = 20.

MR2 = MC2,

180 - 40Q2 = 20,

Q2 = 4 units.

P2 = 180 - 20×4 = 100.

TP2 = 100×4 - (25 + 20×4) = 295.

c) The higher price is charged in the relatively more inelastic segment of the market, because in such market the increase in price will cause the increase in total revenue.

d) If the monopolist cannot discriminate and it has to charge one price, then the price it will charge and quantity it would produce are:

Q = 25 - 0.25P,

P = 100 - 4Q,

MR = 100 - 8Q,

MC = 20,

100 - 8Q = 20,

Q = 10 units,

P = 100 - 4×10 = 60,

The profit under this scenario will be:

TP = 60×10 - (50 + 20×10) = 350.

e) The two-part pricing strategy for the firm is better, as the firm can earn higher profits from this strategy.