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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

Coase-rent/sell

Industriøkonomi, uge 6

Christian Schultz

3 år, 2004


No commitment
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


If monopolist rents
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


If mon sells at start of period 1
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


If mon cannot commit and sells
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


Selling no commitment ii
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!


Period 1
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


Period 1 ii
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


Period 1 iii
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!!!!!


Example end
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 !


How to solve problem for mon
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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