Question

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 xr the number of hours of horse riding, and by xc the quantity of material goods consumed. We can translate these preferences as follows. When comparing two bundles x andx′, with x = (xr,xc) and x′ = (x′r,x′c), Robin’s preferences are such that x ? x′ if and only if xr ≥ x′r. (19 points)

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