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Coase-rent/sell

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

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Coase-rent/sell

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

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

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

  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

  5. If mon cannot commit and sells • Ass: Consumers have rational expectations • Time line • ---- p1 ,Q1 ------ p2 , Q2 • Solve backwards! • Look at period 2, Q1 given • Residual demand: Q2 (p2) = 20 - Q1 – p2

  6. Selling no commitment, II • Max p2p2 (20 - Q1 – p2)  • p2 = (20 - Q1)/2 , Q2 = (20 - Q1)/2 , • 2 = (20 - Q1)2/4 • Notice, second period profit depends on how much was sold in first period!

  7. Period 1 • Rat exp: consumers know they can buy (or sell if they wish) in next period for p2. • If consumer pays p1 in the first period, she is really paying R1 = (p1 - p2 ) for 1st period use and R2 = p2 for 2nd period use. • So equivalent to renting for R1 = (p1 - p2 ) in first period and for R2 = p2 in second period. • So we can analyze period 1 as if the monopolist sets rent R1

  8. Period 1 ,II • 1st period demand is therefore • Q1 = 20 - R1  Q1 = 20 - (p1 - p2 ) • Remember p2 = (20 - Q1)/2 • So Q1 = 20 - p1 + (20 - Q1)/2 • Q1 = 20 - (2/3) p1 • Total profit Q1p1 + 2 = Q1p1 + (20 - Q1)2/4 • = (20- (2/3) p1) p1 + (20 -(20- (2/3) p1))2/4

  9. Period 1, III • (20- (2/3) p1) p1 + (20 -(20- (2/3)p1))2/4 • Maximize wrt p1 . Foc yields • p1 = 18, Q1 = 20- (2/3) p1 = 20-(2/3)18 =8 • p2 = (20 - Q1)/2 = (20-8)/2 = 6 • Q2 = (20 - 8)/2 = 6 • Total profit 18*8 + 6*6 = 180 • < 200!!!!!

  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 p1 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 !

  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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