Question 1 (7 points) Ronald is an Economics students who likes to spend his leisure time of sixty hours a month doing one of two activities: watching movies at Dendy Cinemas Newtown (I), and indoor-climbing (y). A trip to the movies takes 3 hours, and each visit to the climbing gym lasts 5 hours. Further, suppose that Ronald has a xed monthiy monetary budget to spend on leisure activi ties. He currently exhausts this entire budget by watching two movies and visiting the climbing gym fteen times. With this monthly budget, he would also have been able to afford exactly seven movies and six visits to the climbing gym. Assume that both goods are perfectly divisible. (a) Write down Ronald's money and time constraints as algebraic inequalities. (b) Show, using algebra, that Ronald's two budget lines intersect at the bundle (Ly) = (55,37). (c) Plot Ronaldis money constraint using a red dotted line. Plot. Ronaldis time constraint using a blue dotted line. Clearly label each constraint, any axis intercepts, and any points of intersection between the two constraints. Shade in Ronald's budget set, using solid black lines to indicate where the boundaries of the budget set are. Question 2 {13 points) Continue to consider Ronald from Question 2. 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 Ronaldis preferences is Mir, 3;) = :r. + y. (a) On the same picture as before, plot indifference curves for the utility levels it = 5.3, 10, 14.2, 18.4. {b} Compute Ronald's marginal utilities for each good. Using the marginal utility formulas you hc ve just computed, prove that Ronald's preferences are strongly monotone. (c) i. Label three distinct bundles (I, 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. Briey explain what you did. iii. Find Ronald's optimal consumption bundle using a mathematical argument