Question

A monopolist practices third degree price discrimination by separating its customers into two groups: consumers under 65 and senior citizens. Themonopolist’s marginal cost is MC = 0.05q, where q is the total output in both markets. The marginal cost does not depend on the market in which the goods are sold.The demand curves are

!    Adults: PA = 25 – 1/6 × QA = 25 – 0.1667 × QA

!    Seniors:        PS = 15 – c × QS = 15 – 0.125 × QS

1. What is the total industry demand curve?  (Rewrite each demand curve as Q in terms of P.  The total industry demand curve is the total Q in terms of P, soadd QA and QS.)
2. What is the price elasticity of demand for adults? (Use the equation of Q in terms of P to get MQ/MP and
   
   multiply by P/Q. Write the elasticity as a function of P.)
3. What is the price elasticity of demand for seniors?
4. Which market is more elastic? (Elasticity depends on the price; for a given price, which market is more elastic?)
5. What is the total revenue (TR) curve for adults? (TR = P × Q)
6. What is the marginal revenue (MR) curve for adults? (MR = MTR/MQ)
7. What is the total revenue curve for seniors?
8. What is the marginal revenue curve for seniors?
9. What are the equilibrium quantities QA and QS? (Marginal cost is 0.05q, where q is the combined quantity for adults and seniors. Solve the simultaneous linearequations: (i) marginal revenue for adults = marginal cost, (ii) marginal revenue for seniors = marginal cost, and (iii) adult quantity plus senior quantity = totalquantity.)
10. What are the equilibrium prices PA and PS? (Use the demand curve for each group of consumers; the prices are different.)
11. What are the price elasticities of demand for the markets at their equilibrium prices?
12. If price discrimination is prohibited, what the combined demand curve?  (This is the industry demand curve worked out above; nothing new is requiredhere.)
13. If price discrimination is prohibited, what is the equilibrium quantity QC?
14. If price discrimination is prohibited, what is the equilibrium price PC?
15. What is the price elasticity of demand at the equilibrium price PC? (These last three parts are monopoly pricing from the previous module.)

Answer 1

PA = 25 - (QA/6)

6PA = 150 - QA

QA = 150 - 6PA

Also,

PS = 15 - 0.125QS

0.125QS = 15 - PS

QS = 120 - 8PS

(a)

For industry demand function, PA = PS = P.

Industry demand (Q) = QA + QS = 150 - 6P + 120 - 8P

Q = 270 - 14P

(b)

For Adults,

Elasticity = (dQA/dP) x (P/Q) = -6 x [P / (150 - 6P)] = 6P / (6P - 150)

(c)

For Seniors,

Elasticity = (dQS/dP) x (P/QS) = -8 x [P / (120 - 8P)] = 8P / (8P - 120)

(d)

For a given P,

[6P / (6P - 150)] < [8P / (8P - 120)], therefore

Market for Seniors is more elastic and market for adults is less elastic.

(e)

Q = 270 - 14P

14P = 270 - Q

P = (270 - Q)/14

TR = PQ = (270Q - Q²)/14

(f)

MR = dTR/dQ = (270 - 2Q)/14 = (135 - Q)/7

NOTE: As per Answering Policy, 1st 6 parts are answered.