Specific performance, separability condition and the hold-up problem

Edlin and Reichelstein (1996) claim that an efficient solution to the hold-up problem can be implemented with a specific performance contract if a separability condition is satisfied, i.e. if the effect of investments and the effect of the state of the world enter the parties valuation functions in an additively separable manner. This note shows that this separability condition generates the same solution than if the valuation functions are independent of the sate of nature(proposition 1). This implies that a simple menu of prices that does not specify the level of trade can solve the hold-up problem (proposition 2). That is, specifying the terms of trade by writing a specific performance contract is useless with the separability condition.