Consider a consumer with utility function u(x1, x2) = min{4 min{x1, x2}, x1 + x2} (a) Draw indifference curves passing through points (2, 2), (1, 2) and (4,2). Make sure you correctly determine kink points. What properties of the preferences can you deduce from the shape of indifference curves? (b) When X = R 2 +, does UMP have a solution when p1=p2 = 0? What property of the preference relation did you use to get your answer? (c) Assume that prices are such that p1, p2 ≥ 0 and that p` > 0 for some` € {1, 2} (i.e. the price of at least one good is positive). Derive Walrasian demand. What are the prices for which Walrasian demand is single-valued?

Consider a consumer with utility function u(x1, x2) = min{4 min{x1, x2}, x1 + x2} (a) Draw indifference curves passing through points (2, 2), (1, 2) and (4,2). Make sure you correctly determine kink points. What properties of the preferences can you deduce from the shape of indifference curves? (b) When X = R 2 +, does UMP have a solution when p1=p2 = 0? What property of the preference relation did you use to get your answer? (c) Assume that prices are such that p1, p2 ≥ 0 and that p` > 0 for some` € {1, 2} (i.e. the price of at least one good is positive). Derive Walrasian demand. What are the prices for which Walrasian demand is single-valued?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider a consumer with utility function u(x1, x2) = min{4 min{x1, x2}, x1 + x2} (a) Draw indifference
curves passing through points (2, 2), (1, 2) and (4, 2). Make sure you correctly determine kink points.
What properties of the preferences can you deduce from the shape of indifference curves? (b) When X =
R2 +, does UMP have a solution when p1 = p2 = 0? What property of the preference relation did you use
to get your answer? (c) Assume that prices are such that p1, p2 2 0 and that p` > 0 for some `e {1, 2}
(i.e. the price of at least one good is positive). Derive Walrasian demand. What are the prices for which
Walrasian demand is single-valued?

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Step 2: Indifference curves:

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Step 3: Indifference curves are convex

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Step 4: (b) UMP (Utility Maximization Problem):

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Step 5: (c) Deriving Walrasian Demand

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