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

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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 = p m ) 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 ---- p 1,Q 1 ------ p 2, Q 2 Solve backwards! Look at period 2, Q 1 given Residual demand: Q 2 (p 2 ) = 20 - Q 1 – p 2

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!

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

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

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!!!!!

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 !

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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