Comparing Optima: Do Simplifying Assumptions Affect Conclusions?

Consider a family of maximization models in which the optimum trades off beneficial and costly effects. Then comparative statics derived under many kinds of simplifying assumptions about the benefits technology are also true for general (convex and nonconvex) technologies. For example, any comparative statics conclusion about investment by a risk-averse decision maker under uncertainty that holds when expected returns are described by a general linear function also holds for an arbitrary nonlinear expected return function.