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1 Coase-rent/sell Industriøkonomi, uge 6 Christian Schultz 3 år, 2004

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2 No commitment 2 periods, good lasts these 2 periods Zero interest rate, no cost Competitive resale market. (p = p m ) In each period, demand for service of good (for instance light, cooling, transport) is Q(R) = 20 – R

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3 If monopolist rents In each period: max R RQ(R) = max R R(20-R) Foc : 20 – 2R = 0 so R = 10, Q = = 10 Profit per period 10*(20-10) = 100 For two periods 2* 100 = 200

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4 If mon. sells at start of period 1 If he can commit not to lower price in period 2. Set price = 20 sell 10 units earn 200. In period 2, everybody with reservation price above 10 has bought, so demand in period 2 is 10 – p

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5 If mon cannot commit and sells Ass: Consumers have rational expectations Time line ---- p 1,Q p 2, Q 2 Solve backwards! Look at period 2, Q 1 given Residual demand: Q 2 (p 2 ) = 20 - Q 1 – p 2

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6 Selling no commitment, II Max p2 p 2 (20 - Q 1 – p 2 ) p 2 = (20 - Q 1 )/2, Q 2 = (20 - Q 1 )/2, 2 = (20 - Q 1 ) 2 /4 Notice, second period profit depends on how much was sold in first period!

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7 Period 1 Rat exp: consumers know they can buy (or sell if they wish) in next period for p 2. If consumer pays p 1 in the first period, she is really paying R 1 = (p 1 - p 2 ) for 1st period use and R 2 = p 2 for 2nd period use. So equivalent to renting for R 1 = (p 1 - p 2 ) in first period and for R 2 = p 2 in second period. So we can analyze period 1 as if the monopolist sets rent R 1

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8 Period 1,II 1 st period demand is therefore Q 1 = 20 - R 1 Q 1 = 20 - (p 1 - p 2 ) Remember p 2 = (20 - Q 1 )/2 So Q 1 = 20 - p 1 + (20 - Q 1 )/2 Q 1 = 20 - (2/3) p 1 Total profit Q 1 p 1 + 2 = Q 1 p 1 + (20 - Q 1 ) 2 /4 = (20- (2/3) p 1 ) p 1 + (20 -(20- (2/3) p 1 )) 2 /4

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9 Period 1, III (20- (2/3) p 1 ) p 1 + (20 -(20- (2/3)p 1 )) 2 /4 Maximize wrt p 1. Foc yields p 1 = 18, Q 1 = 20- (2/3) p 1 = 20-(2/3)18 =8 p 2 = (20 - Q 1 )/2 = (20-8)/2 = 6 Q 2 = (20 - 8)/2 = 6 Total profit 18*8 + 6*6 = 180 < 200!!!!!

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10 Example end Profit lower when monopolist sells than when he rents. Problem: he is his own competitor. Notice he seeks to mitigate the problem by setting p 1 high. But not perfect solution. Coase’s conjecture When number of periods go to infinity and there is no discounting (like in ex), then price MC This has been verified in subsequent research Examples: Store Danske Encyklopædi !

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11 How to solve problem for mon Commit not to lower price. DSDE Make good non-durable Fads, fashion Make capacity constraints so expanding output costly Most favored costumer clause (NB) Buy back guarantee Reputation (de Beers)

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