Let X = R be the consumption set of a consumer and u: X → R be her utility function. Let max u(x) TEX subject to p x≤ I. . be the consumer's problem where (p, I) E A × R7 and A and A = {p € R | Σ;Pi = 1}. 1. [5pt] Let x(p, I) be a solution to the consumer's problem. Show that x(\p, λI) = x(p, I) for all >> 0. 2. [5pt] Let for all x € X and e > 0 there exists y € N₂(x) such that u(y) > u(x). Show that for all (p, I) and x = x(p, I), px = I. 3. [5pt] Show that if u is strictly concave, then x(p, I), the set of solutions to the con- sumer's problem, is a singleton for all (p, I).