Question

There are two groups of customers in the market. Demand of group number 1 is Q1(p) = 3−0.5p, and demand of group number 2 is Q2(p) = 5−2p. The market is served by a monopolist with MC = 1. (a) Write down the market demand function (remember that demand function should be welldefined for all possible prices). Plot it. (b) Derive the MR(Q) for the market demand and plot it on the graph from above. (c) What price will the monopolist charge if she cannot price discriminate? Find the corresponding consumer surpluses for both groups. (d) Now suppose that the monopolist can set different prices for different groups. What prices will she choose? Find the corresponding consumer surpluses for both groups. (e) Who wins and who loses when discrimination is allowed? How does total welfare change?

Answer 1

Question

Answer : Qm = Market Demand

For a straight line demand curve, its Marginal Revenue curve is a straight line bisector of demand curve.

A monopolist always operate with elastic demand markets.

Part A :

Market demand is the sum pf all individual demand curve horizontally.

Part B :

MR = Marginal Revenue, it is the first order derivative of total revenue

Qus Q2 5-2P Pari Qi-3-0:6p Cf-Market Demand Qt Q2 3-0.5t5-2P =8-2.5P Qu Qm 8-2.5P 17 QM8-2.5P 2.5p 8- QM P 3.2-n SPG 2 3 2-2QM Pa= 3.2Q- Qu 2-5 SQN MR- 3.2- 2Qn 25

yo 3.2 3 2 AR DAmand 1 MR 'Quadtry

Part C :

Consumer surplus = 1/2 * Quantity * difference in price

Pansc Q5-2P 2.5-0.5Q 5-Q 1 -050 TR- PR-50 MR STR SQ 17 2-5-Q う MR= MCうd·ら-Q=\ Q P= ら--5ら Q.50-0.75 &5-0.5x1.5 GA Hou, Meagpotist wit . Consumur Suoplus ト5× 25-135) .5 Buice 15 x O7S Demand 452.6 075 x 07ぐ Queadity 0.5625

Part D :

Parst d 3-0.5p P-6-201 う TR- PQI 2 うMR = STR 6-421 MR- MC 6-4Q -5う Q= 1.25 P 6-2X2S 3 5 6-2.50 Consumr Suplis xト-25×(6-3-5) 125 「25 × 2ら 15620 ML MR PSら

5-2P P2.6-05@2 TR= PR2= 25-0-6Q, MR= STR SQ 2.5 Q2 MR- ME 2.5-Q2 P2.5 - 0.5X1S 250.75 Consumur Supls 15 x (2.5 1 1-5 0.75 X07 MC 0.5625 MR 1-5 .

Part E :

when discrimination is allowed, monopolist start operating in both markets, charging a higher price in inelastic market and a slightly lower price in elastic market. Hence, profits of monopolist rises