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# Coase-rent/sell - PowerPoint PPT Presentation

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

Industriøkonomi, uge 6

Christian Schultz

3 år, 2004

• 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

• 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

• 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

• 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

• 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!

• 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

• 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

• (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!!!!!

• 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 !

• Commit not to lower price . DSDE

• Make good non-durable