7.1. Consider preferences defined over the nonnegative orthant by (11, 12) > (31, 32) if x1+x2 <1+y2. Do these preferences exhibit local nonsatiation? If

7.1. Consider preferences defined over the nonnegative orthant by (11, 12) > (31, 32) if x1+x2 1. What will be the form of the consumer's indirect money metric utility function now? 7.5. A consumer has a direct utility function of the form U(x1, x2) = u(x1)+x2. Good 1 is a discrete good; the only possible levels of consumption of good 1 are = 0 and 1 = 1. For convenience, assume that (0) = 0 and p2 = 1. (a) What kind of preferences does this consumer have? (b) The consumer will definitely choose = 1 if p is strictly less than what? (c) What is the algebraic form of the indirect utility function associated with this direct utility function? Exercises 115 7.6. A consumer has an indirect utility function of the form v(p, m) - A(p)m. (a) What kind of preferences does this consumer have? = (b) What is the form of this consumer's expenditure function, e(p, u)? (c) What is the form of this consumer's indirect money metric utility function, (p; q, m)? (d) Suppose instead that the consumer had an indirect utility function of the form v(p, m) = A(p)mb for b> 1. What will be the form of the consumer's indirect money metric utility function now?