Comparative statics with linear objectives (with John K.H. Quah)

We formulate a new set order on constraint sets, called the parallelogram property, which guarantees that the minimisers of any linear objective function increase with respect to this order. With this result, we characterize the utility/production functions that lead to normal demand; we also show that this very same class of production functions have marginal costs that increase with factor prices. We can also characterize production functions with factors that are gross complements or gross substitutes. In the context of decision-making under uncertainty, our new set order leads naturally to a notion of first order stochastic dominance in multi-prior models.