Question

5. Consider a market with a monopolist that can price discriminate between two groups. The inverse demand equation for group 1 is R(Q.) = 156 - 50 where P is the price group 1 is charged and Q1 is the total quantity demanded by group 1. The inverse demand equation for group 2 is B(O2) = 48-22 where B, is the price group 2 is charged and Q2 is the total quantity demanded by group 2. The total amount the firm produces Q is the sum of what it produces for each group Q = Q1 + 02. The cost function for the monopolist is CO) = Q2 +20 (a) Setup the profit maximization problem for the price discriminating monopolist. (3 points) (b) Solve the profit maximization problem for the partial equilibrium quantities Q1, Q3,Q". You may need to use a calculator for this part. (5 points) Qi = 8 Q3 = Q* =

Answer 1

Detailed workout of the questions mentioning each part is attached below:

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5. The problem is based on a discoéminaling monopolist whose prices or inverse demands for different Groups are as follows: Inverse demand forgroup1, P, CQ,) Inverse demand for group.2, P2 CQ2 = 48-Q2 Cost function of the monopolist is. 156-5Q CQ) = Q2 +20 where Q = Q +Q2. a) A discriminating monopolist will maximise its profit at the equilibrium between industry & market. The condition for profit maximisation or equilibriumis on. MRI MR2 = MR. = MC

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NOTES Thus, to be clear, marginal revenue of each be equal to marjénal cost postaral should Revenue of group: PiCQ.) *Q1 = 156 Q, -59,2 MRI = 156 - 10 Q1 Revenue of Group 2: PAQ 2) * Q2 = 48Q2 –Q2. MR2 = 48-2Q2. Marginal Cost; CCQ) - Q2 +20 2 Q MC= = 2 (Q. + Q2) maximisation Hence the problem is, 156 -10 Q = 48 - 2Q2 = 22CQ, +92.),

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NOTES b) By MR = MR2 We get, 156-10 Q1 = $48-2Q2 *108 - 20.0=10 Q.1. QI 10.8 0.2 Q.2 in MC Now substituting Mc = 2 (10.8 -0. 2Q2 +Q2). = 2 (10.8 +0-802) Now by Mc = MR.2 48-2 Q 2 2 (10.8 +0.8 Q.2.) =748- 2 Q2 = 21.6 + 1.62.2 => 48-21.6 2 Q2 +1-6 Q2 => 3.6Q2 = 26.4 Q.2 = 7:3

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April 12 01116 May 2016 S M T W T F S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 Friday Thus Q = 10.8-0.2 7.3. 9.3 Q = Q + Q2 = 16.6. Hence, Q,* = 9.3 mits = 7.3 mits. 16. 6 units 2 © PicQu) = 156–5Q, = 156 - 5x9.3 Saturday = 156 - 46.5 = 109.5 units. Pa Q2). = 48-Q2 48- 7.3 = 40.7 wuts Hence, P* 109.5 mrits. P * = 40.7 units

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2016 S M T W T F S 1 2 3 4 5 6 7 8 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 9 10 11 12 در Sunday P, (Q.) = 156-5Q1 OPI elasticity of Group ! Prx OPI 5. 4 Monday T56-5Q1 X Q 1.5 6 -- 5 Qi 156 5x9.3 - 156 46.5 + 1 - 3.35 +/ 19 2.25. To Group.lis dem. and inelastica