1 Lecture 1: Review of Monopoly Pricing by a Firm with Market Power Total Revenue (TR) = PQ Average Revenue (AR) = TR/Q=P Marginal Revenue = Revenue from an additional unit =  TR/  Q = d(TR)/dQ Marginal Revenue is lower than Average Revenue (price). Why? MR = d(TR)/dQ = P + Q dP/dQ < P

2 $ Q $ Q Optimum: MR = MC Increase Q if MR > MC Decrease Q if MR < MC MR=MC Q* ** MC D MR P*

3 Example: Automobile Industry Pricing Toyotas. Suppose that the demand for Toyotas is given by P =12000-Q, and MC =$3000. Assume than unit costs are $3000 per vehicle and fixed costs=$7,500,000 TR=PQ= (12000-Q)Q = 12000Q-Q 2 MR= Q TC= 7,500, Q MC=3000 MR=MC implies that Q*=4500

4 Price (from demand curve) = =7500 Profits = PQ - VC - FC Profits = 7500* *4500-$7,500,000 Profits = 20,250,000 –7,500,000=$12,750,000 Another way to solve problem  = TR - TC = 12000Q- Q 2 - (3000Q + 7,500,000)  = 9000Q - Q 2 -7,500,000. d  /dQ = 9000 – 2Q=0 which implies Q*=4500 as before.  Note that the fixed costs only affect the decision whether to produce or not and not how much to produce.

5 Optimal Pricing, margins and the elasticity of demand It can be shown that MR = p + Q dp/dQ = p (1  1  ) From the above equation MR=MC can be rewritten in two ways: margin  (p  MC)/p = 1 /  p = MC  (1  1  ) + low  high m + high  low m QQ P P D D MC MR

6 Example: Automobile Industry Pricing Toyotas in Two Different Markets Market 1 (US) P 1 =12000-Q 1, MC 1 =3000 Market 2 (Japan) P 2 = Q 2, MC 2 =2000 Optimal Prices: P(US)=$7500, P(JAPAN)= $8000 Is this dumping? How can the price in the U.S. exceed the price in Japan?  1 = 1.66, -(dQ 1 /dP 1 ) P 1 /Q 1  2 = 1.33, -(dQ 2 /dP 2 ) P 2 /Q 2

7 Monopolist with multiple plants Example Demand: P=100-Q Plant 1: TC 1 =2Q 1 2 Plant 2: TC 2 =Q 2 2. Optimal MR=MC 1 =MC 2 MC 1 = 4Q 1, MC 2 =2Q 2. MC 1 =MC 2 implies that Q 2 =2Q 1. Q= Q 1 +Q 2 = 3Q 1. TR=100Q-Q 2. Thus, MR=100-2Q=100-6Q 1.

8 MR=MC implies that 100-6Q 1 =4Q 1 or Q 1 =10. Since Q 2 =2Q 1, Q 2 =20 and Q=30. Check: When Q=30, MR=40, MC 1 = 4Q 1 =40, MC 2 = 2Q 2 =40.

Bundling Suppose there are two goods (A,B): There are three possible pricing strategies (options:) separate pricing – p A and p B only Pure bundling –p AB only Mixed bundling – p A, p B, and p AB Examples: ‘Hot Triple’ and restaurant pricing

Individual Pricing Value of A Value of B pApA pBpB Buys A only Buys B only Buys nothing Buys both

Pure Bundling p AB = x Value of A Value of B p AB = x Buys bundle Buys nothing

Mixed Bundling I,II,III, IV – buys both; V,VI buys B; VII,VIII buys A p A =8 p B =8 p AB =12 4 I II III IV V VI VII VIII 4

Profitability of Mixed Bundling For a monopoly, mixed bundling always (weakly) better than pure bundling Trade off between mixed bundling and separate pricing In mixed bundling, price of bundle less than the price of individual goods Optimal strategy depends on distribution of consumers and costs

Example Cost of entrée (A) = $6, cost of desert (B) =$2 Three types of consumers with following reservation values: (10,1) (8,4) (5,4) Individual pricing: p A =8, p B =4, π=2(8-6)+2(4-2)=8 (could also charge p A =10, p B =4, π=(10-6)+2(4-2)=8) Pure bundling pricing: p AB =11, π=2(11-8)=6 Mixed bundling pricing: p A =10, p B =4, p AB =11.99, π=(10-6)+(4-2)+( )=9.99 What about pricing bundle at 10.99? π=2( )+(4-2) =7.98