This paper presents a dual representation of firm-level and market-level equilibrium behavior for a sole proprietorship economy with competitive and frictionless financial markets and stochastic production opportunities in a two-period setting. The dual equilibrium model is used to state conditions for the firms' production choices to be independent of their risk preferences in equilibrium. These conditions entail Pareto optimality, but do not require either that the firm's consumption choices lie within the span of financial markets or the assumption of an extreme version of linear risk tolerance.