In consumer theory, we often express a budget set as 19 ~ 3; E ELI pix,-

In consumer theory, we often express a budget set as p ptXi < m, where p is the vector of prices for each of the k goods, is the vector of product purchased, and m is the budget. Consider, from consumer theory, as standard utility function u@), and think back to your introductory or intermediate microeconomics courses. (a) (5 points) You probably remember that "higher indifference curves are preferred to lower ones". How could you express this principle using the notion of choice functions? (b) (5 points) You probably also remember that "indifference curves cannot cross". How could you express this principle, using the notion of choice functions? (c) (5 points) Suppose a choice rule is rational. Which of these two properties are implied by rationality? Explain.