The optimal choice for a decision maker faced with uncertainty is the maximization of his expected
utility where the expected profit and variance are the arguments of utility. As the expected utility derived
from variable profits is equal to the utility derived from the certainty equivalent, CE, the maximization
problem can be mathematically written as CE = E(∏)- ρσ∏∕2, where the coefficient ( ρ ≥0) measures
the risk aversion and σ2π is the variance of profit (Robison & Barry, 1987).
2 A reason for this assumption is that the cost of bearing risk is generally relatively less for the processor
than for the grower (Milgrom and Roberts, 1992).
3 Linear demand systems have been used extensively in models of oligopolies, see (Coughlan, 1985;
McGuire & Staelin, 1983; Jaumandreu & Lorences, 2002).
4 From now on, the superscripts M and IC will indicate the mechanism associated, that is, spot market
and incentive contract respectively.
5 The assumption of absence of transaction costs is restrictive in the sense that the transaction costs of
offering contracts are never zero in practice, and offering individualized contracts will generate higher
transaction costs, However, the reason for this restrictiveness is to concentrate on competitive motivations
instead.
6 Let the Nash equilibrium values be denoted as *.
7 The Mathematica commands are available from the authors on request.
8 With ρσs2 =0.0001 the value of the certainty equivalent per processor is very small.