Towards a unified theory of procurement contract design : production flexibility, spot market trading, and contract structure

Abstract

We present in this work a unified approach and provide the optimal solution to the pricing problem of option contracts for a supplier of an industrial good in the presence of spot trading. Specifically, our approach fully and jointly endogenizes the determination of three major characteristics in contract design, namely (i) Sales contracts versus options contracts; (ii) Flat fee versus volume- dependent contracts; and (iii) Volume discounts versus volume premia; combining them together with spot market trading decisions and also the option of delaying production for the seller. We build a model where a supplier of an industrial good transacts with a manufacturer who uses the supplier's product to produce an end good with an uncertain demand. We derive the general non-linear pricing solution for the contracts under information asymmetry of the buyer's production flexibility. We show that confirming industry observations, volume-dependent optimal sales contracts always demonstrate volume discounts (i.e., involve concave pricing). On the other hand the options contracts are more complex agreements, and optimal contracts for them can involve both volume discounts and volume premia. Further, we find that in the optimal contracts, there are three major pricing regimes. First, if the seller has a higher discount rate than the buyer and the production costs are lower than a critical threshold value, the optimal contract is a flat fee sales contract. Second, when the seller is less patient than the buyer but production costs are higher than the critical threshold, the optimal contract is a sales contract with volume discounts. Third, if the buyer has a higher discount rate than the seller, then the optimal contract is a volume-dependent options contract and can involve both volume discounts and volume premia. We further provide links between industry and spot market characteristics, contract characteristics and efficiency. Last, we look into an extension of our basic model, where we give an analysis for the case when the seller is given a last minute production option.