We present a methodology allowing to introduce manufacturers and retailers vertical contracting in their pricing strategies on a differentiated product market. We consider in particular two types of non linear pricing relationships, one where resale price maintenance is used with two part tariffs contracts and one where no resale price maintenance is allowed in two part tariffs contracts. Our contribution allows to recover price-cost margins from estimates of demand parameters both under linear pricing models and two part tariffs. The methodology allows then to test between different hypothesis on the contracting and pricing relationships between manufacturers and retailers in the supermarket industry using exogenous variables supposed to shift the marginal costs of production and distribution. We apply empirically this method to study the market for retailing bottled water in France. Our empirical evidence shows that manufacturers and retailers use non linear pricing contracts and in particular two part tariffs contracts with resale price maintenance. At last, thanks to the estimation of the our structural model, we present some simulations of counterfactual policy experiments like the change of pricing policies from two part tariffs to linear pricing between manufacturers and retailers, or the change of ownership of some products between manufacturers.