Optimal bidding and contracting strategies for capital-intensive goods

Abstract

This paper models contracting arrangements between one Seller and one or more Buyers when the “deliverable” or output under the contract is produced in a non-scalable capital-intensive production facility. The basic model proposed allows the Seller and Buyers to negotiate bilateral contracts for the good in advance. On the day, the Seller and Buyers can also sell excess capacity or buy additional non-contract output in an associated backup market, which is being referred to as the spot market for the good. The type of bilateral contract studied has a two-part contract fee structure, and it is at the foundation of practical contracts used by many capital-intensive industries, where capacity can only be expanded well in advance of output requirements. The first part is a reservation cost per unit of capacity, and the second, an execution cost per unit of output when this capacity is actually used. This paper derives the Seller's optimal bidding and Buyers' optimal contracting strategies in a von Stackelberg game with the Seller as the leader. We show that Buyers' optimal reservation level follows an index that combines the Seller's reservation and execution cost. The Seller's optimal strategy is to reveal its variable cost of producing output while extracting its margin from the Buyers using the capacity reservation charge. This structure allows for the Seller to assure in advance its ability to pay the capital costs of capacity while providing Buyers appropriate incentives to take advantage of better terms on the day if alternative, cheaper sources should arise after contracts have been set.