Coase-rent/sell
Industriøkonomi, uge 6
Christian Schultz
3 år, 2004
1
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
2
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
•
3
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
4
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
5
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!
6
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
7
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
8
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!!!!!
9
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 !
10
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)
11