We study dominant strategy incentive compatibility in a mechanism design setting with contingent contracts where the utility of each agent is observed by the principal and can be contracted upon. Our main focus is on the class of linear contracts (one of the most commonly observed contingent contracts) which consist of a transfer and a flat rate of profit sharing. We first demonstrate the applications of linear contracts. We show that they can achieve efficient outcomes with budget balance overcoming a known shortcoming of the VCG mechanism. Additionally, they can be used to implement social outcomes (like the Rawlsian) that are not incentive compatible using transfers alone. We then give implicit (using a condition called acyclity) and explicit characterizations of social choice functions that are implementable using linear contracts. Further, we provide a foundation for them by showing that, in finite type spaces, every social choice function that can be implemented using a more general nonlinear contingent contract can also be implemented using a linear contract.