Mean-variance efficient portfolio analysis is applied to situations where not all assets are perfectly price elastic in demand nor are asset moments known with certainty. Estimation and solution of such a model are based on an agricultural banking example. The distinction and advantages of a Bayesian formulation over a classical statistical approach are considered. For maximizing expected utility subject to a linear demand curve, a negative exponential utility function gives a mathematical programming problem with a quartic term. Thus, standard quadratic programming solutions are not optimal. Empirical results show important differences between classical and Bayesian approaches for portfolio composition, expected return and measures of risk.