Question

3. Robin's Preferences Robin is an ambitious young knight living in the middle ages. He is in his early career and wants to prove himself. He is detached from material things (he doesn't attend the lavish banquets or the evening entertainments in the castle) and prefers to improve his skills in horsemanship instead. As he states in his preferences "I like horses, I would always, rather always ride my horse, do more practice of it, and am completely indifferent as to the consumption of material goods." Denote by r the number of hours of horse riding, and by the quantity of material goods consumed. We can translate these preferences as follows. When comparing two bundles r and r, with only if , (19 points) (Tr, Te) and (x, 14), Robin's preferences are such that r x' if and a. Based on the information given about Robin's preferences, sketch a two representative indifference curves on a clearly labelled graph and indicate the direction of higher utility. Explain your intuition b. Are these preferences are monotonic? First define the term used, then explain your answer c. Are these preferences are convex? First define the term used, then explain your answer

Answer 1

Horse ride Material Goods

a) Given above is the utility function for such preference, the utility is increasing in the direction of the arrow, Robin is neutral for material goods and more horse ride makes him better off.

b) Monotonic preferences mean more of a good is preferred to less, here Robin is indifferent to the quantity of material good but prefers more of the horse ride, any increase in the quantity of material good, will not increase the utility of Robin, hence the preferences are not monotonic.

c) Convex preference means that averages are preferred to extremes, which implies that the consumer prefers to consume both the goods rather than any one, but here Robin is only concerned about the horse ride, therefore, his preference is not convex.