Coase-rent/sell

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 p2 p2 (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 188 66 180
• lt 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.
• Coases 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)