The bulk of economic theory and financial economics rests on leveraging the implications of the law of one price. We argue that though this may be a reasonable law for trading goods and services it may not be appropriate for trading state contingent claims exposed to unforeseen states. Simultaneously abandoning market clearing and the law of one price one arrives at economies in which the law of two prices prevails. Explicit constructions of the two prices as nonlinear martingales follow as a consequence. One thereby obtains nonlinear concave valuation functionals that serve as a guide to designing trades, managing risks, monitoring leverage and separating a theory of liability valuation from asset pricing. Applications illustrate the implications embodied in this paradigm shift, adding a formalism for concepts like risk weighted assets, capital adequacy, and leverage policy.