Non-convexity (economics)

In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences (that do not prefer extremes to in-between values) and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior is well understood.^[1][2] When convexity assumptions are violated, then many of the good properties of competitive markets need not hold: Thus, non-convexity is associated with market failures,^[3][4] where supply and demand differ or where market equilibria can be inefficient.^{[1][4][5][6][7][8]} Non-convex economies are studied with nonsmooth analysis, which is a generalization of convex analysis.^{[8][9][10][11]}