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Consider an individual whose preferences are dened over bundles of non negative amounts of each of two commodities. Suppose that this individ ual's preferences can
Consider an individual whose preferences are dened over bundles of non negative amounts of each of two commodities. Suppose that this individ ual's preferences can be represented by a utility function U : R1 > R of the form U (1:1. 1:2) : 111 (1:1 + 1) + 2%. where 1:1 denotes the individual's consumption of commodity one. and 1:2 denotes the individual's consump tion of commodity two. This individual is a price taker in both commodity markets. The price of commodity one is p1 > 0. and the price of commodity two is p2 > 0. This individual is endowed with an income of y > 0. 1. Does this individual have quasilinear preferences? Justify your an swer. 2. Are this individual's preferences locally nonsatiated? Justify your answer. 3. What is this individual's budgetconstrained utility maximisation problem? 4. Suppose that the individual will optimally consume strictly positive amounts of both commodities. What is the individual's optimal c011 sumption bundle in this case? Under what circumstances. if any. will this case occur? . Can it ever be optimal for this individual to choose to consume zero units of commodity one? If so. what would be his or her optimal consumption of commodity two? Under what circumstances. if any. will this case occur? 0
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