ABSTRACT
A consumer maximizes their preferences over their budget by finding their demand for each good, that is, by finding a bundle in their budget set which is strictly better any other affordable bundle. People find this preference-maximizing bundle in two ways: graphically and, more rigorously, using constrained optimization. The graphical approach provides the intuition for the necessary conditions that are used to calculate the demand functions. The solutions to preference maximization for quasilinear preferences may be interior or corner ones, depending on the prices and income. It is easy to check that when a consumer’s preferences are strictly monotonic, they will always maximize their preferences on the budget line and never inside the budget set. This is because at any bundle that is strictly inside the budget, it is possible to move slightly northeast, remain inside the budget, and yet make the consumer better off.
