Intermediate Microeconomics Problem Set 2

Exercise 11) Consider a two-period economy with a single commodity (say leisure): x1 is the consumption of leisure in period 1, and x2 is the consumption of leisure in period2. WhenPeter evaluates consumption streams, he cares only about the best time in his life. On the other hand, Christine only cares about the worst time in her life. Provide utilityrepresentation for their preferences.Exercise 2Martina’s preferences are represented by u(x1, x2) = x121 + x132, where x1 > 0, x2 > 0.(1) What is the marginal utility of good 1 at (x1, x2)? (2, 3)?(2) What is the marginal utility of good 2 at (x1, x2)? (3, 2)?(3) What is the marginal rate of substitution of good 2 for good 1 at (x1, x2)? (2, 2)?(4) Redo (1), (2), (3) for another representation v(x1, x2) = ln(x121 + x132).Exercise 3:Assume that your preference relation % can be represented by a utility function.Show that your preference relation must then be rational, i.e. complete, transitive, andreflexive