Strategic Capacity Investment under Holdup Threats: The Role of Contract Length and Width

This article analyzes the impact of incomplete contracts’ length on investment in a bilateral relationship. The seller has the power to set the contract terms whereas the buyer decides on the investment level, which acts as a cap on future demand. Two-part tariffs succeed at implementing the optimal investment and consumption even if commitment is limited, and the contract’s duration is irrelevant. Interestingly, this efficient solution is rendered possible by subsidies on consumption during the contract. In other terms, duration matters hugely for the contract details (the timing of transfers), not for its performance. Under certain circumstances that we discuss, linear pricing may have to be used, which leads to suboptimal investment. We show that longer contracts are less efficient, meaning that a degree of completeness (pricing width) may be strictly complementary to another one (contract length). The buyer’s surplus increases with respect to the contract duration, whereas the seller loses more in profit than the social surplus decreases. A longer contract actually protects expropriable investors rather than investment itself.