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this outcome is not RNP. Indeed, since µ2(0) = 0, following x1 = 0 the principal will
offer p2′ = L, and the agent will accept. Thus, the RNP constraint reduces the principal’s
payoff.

The next observation is that the principal is better off with L renegotiable contracts
than with ST contracts. Indeed, in the former case one possibility for the principal is
to offer an ex ante contract specifying the default outcome of the second period. In our
example, this corresponds to p2(0) = p2(1) = ∞. This will implement the ST contracting
outcome. Thus we have

Proposition 16.2.2 If an outcome is implementable with ST contracting then it is also
implementable with a LT Renegotiable contract (and therefore, by the RNP Principle, with
a LT RNP contract).

In our example, the intuition is that with LT renegotiable contracts the principal
cannot commit against reducing the 2nd-period price, while with ST contracting she
cannot commit against any modification of the 2nd-period price.

When do long-term renegotiable contracts offer an advantage relative to short-term
contracts? When the ability to commit to a low price is useful. For example, consider the
possibility of full revelation in the first period when δ > 1. With short-term contracts,
full revelation was impossible: because of the ratchet effect, the high type would only buy
in the first period at a price p1 < L, but at this price the low type would also buy - ”take
the money and run”.

It turns out, however, that the principal can achieve full revelation with a LT RNP
contract < p1, p2(0), p2(1) >. In particular, consider the following contract:

p1 = H + δL,
p2(1) = 0,
p2(0) = L.

This contract will have a full-revelation equilibrium. Indeed, (ICHL) is satisfied: H’
s surplus is δ(H − L) regardless of whether he buys or not. (ICLH) is also satisfied: L’s
surplus would be negative if he bought. Intuitively, unlike in the ST contracting case,
both incentive constraints can now be satisfied by committing against ratcheting - setting

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p2(1) = 0. This allows to make the ”take the money and run strategy” costly for the low
type - he now has to pay for the 2nd-period consumption as well. He will not be willing
to pay price H + δL for both periods’ consumptions, while the high type will pay it. The
contract is also RNP, since p2(x1) ≤ L for all x1.

Hart and Tirole (1988) reinterpret the model as describing contracting about the use
of durable good. A short-term contract in this setting is a rental contract. The long-
term contract with p2(1) = 0 can be interpreted as a sales contract. Thus, by using
sales contracts in- stead of rental contracts, the seller eliminates the ratchet effect, make
full revelation of information possible (but not always optimal). The renegotiation effect
remains.

More generally, Hart and Tirole consider a multi-period model. They show that long-
term renegotiable rental contracts give rise to the same outcome as sales contracts. The
resulting price follows a Coasian Dynamics: it decreases over time and eventually drops to
L. When the number of periods is large and δ is close to 1, the drop is almost immediate
in real-time (cf. Gul-Sonneshein-Wilson 1988, Coase 1972).

Reference

Bolton, P. and M. Dewatripont (2005), Contract Theory, MIT Press.
Mas-Colell, A., M. D. Whinston, and J. Green, Microeconomic, Oxford University Press,

1995, Chapter 14.
Segal, I. (2007), Lecture Notes in Contract Theory, Stanford University.
Wolfstetter, E., Topics in Microeconomics - Industrial Organization, Auctions, and In-

centives, Cambridge Press, 1999, Chapters 8-10.

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