Explain why convex preferences means that averages are preferred to extremes?

Answer 1

Convex preferences imply that consumers derive greater satisfaction from a mix of goods rather than from consuming extreme amounts of one good over another. This is because, in the context of utility, combining two different bundles of goods typically leads to higher overall utility than consuming one of those bundles exclusively. As such, individuals prefer averages or balanced combinations, reflecting a diminishing marginal rate of substitution, where the willingness to trade one good for another decreases as one consumes more of one good. Thus, convex preferences encourage diversification and moderation in consumption.