Continue to consider Ronald from Q1. Suppose that Ronald’s preferences over movies and climbing are such that he likes them exactly equally: he is always willing to trade one movie for one climbing session and remain exactly as well of as he was before. One valid utility representation of Ronald’s preferences is u(x, y) = x + y. (a) On the same picture as before, plot indifference curves for the utility levels u = 5.8, 10, 14.2, 18.4. (b) Compute Ronald’s marginal utilities for each good. Using the marginal utility formulas you have just computed, prove that Ronald’s preferences are strongly monotone. (c) i. Label three distinct bundles (x, y) on the indifference curve corresponding to a utility of 5.8. ii. Hence, or otherwise, argue that his preferences are not strictly convex.
Continue to consider Ronald from Q1. Suppose that Ronald’s preferences over movies and climbing are such that he likes them exactly equally: he is always willing to trade one movie for one climbing session and remain exactly as well of as he was before. One valid utility representation of Ronald’s preferences is u(x, y) = x + y.
(a) On the same picture as before, plot indifference curves for the utility levels u = 5.8, 10, 14.2, 18.4.
(b) Compute Ronald’s marginal utilities for each good. Using the
(c) i. Label three distinct bundles (x, y) on the indifference curve corresponding to a utility of 5.8.
ii. Hence, or otherwise, argue that his preferences are not strictly convex.
(d) i. Explain why Ronald’s optimal consumption bundle must lie on the outer boundary of his budget set.
ii. Identify Ronald’s optimal bundle by visual inspection. Briefly explain what you did.
iii. Find Ronald’s optimal consumption bundle using a mathematical argument.
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