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Coase's Conjecture in Oligopoly: Rent vs. Sell Strategy Analysis

Explore the strategic decision of a monopolist to rent or sell goods in an oligopoly market scenario, considering rational consumer expectations and profit optimization over two periods. Understand Coase's conjecture and possible solutions for the monopolist amid competition.

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Coase's Conjecture in Oligopoly: Rent vs. Sell Strategy Analysis

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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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