A consumer has preferences over two goods represented by the utility function (1.12) x1 +2√x₂. (a) Sketch this consumer's indifference curves. Solution: The indifference curves are conver, and are horizontal translations of each other. (b) Find the Marshallian demand function x(p, w). Solution: The first-order conditions have a solution with x₁, x2 ≥ 0 if w≥ w< we get a corner solution. Putting these together gives P2 [(*- -· (-)²) 4¹ (²)²³) if w≥ 4 1 (0, #1) otherwise. r(p, w) = When Since preferences are conver, the solution to the first-order conditions is indeed a maxi- mum. (c) Sketch the wealth expansion path; that is, fixing prices p, sketch the demands r(p, w) in (11, 12)-space as wealth w varies. Solution: Starting from the origin, the path moves up along the vertical axis to the point (0,2 (0, (2)²), then continues along the horizontal line x₂ = PL P2

A consumer has preferences over two goods represented by the utility function (1.12) x1 +2√x₂. (a) Sketch this consumer's indifference curves. Solution: The indifference curves are conver, and are horizontal translations of each other. (b) Find the Marshallian demand function x(p, w). Solution: The first-order conditions have a solution with x₁, x2 ≥ 0 if w≥ w< we get a corner solution. Putting these together gives P2 [(*- -· (-)²) 4¹ (²)²³) if w≥ 4 1 (0, #1) otherwise. r(p, w) = When Since preferences are conver, the solution to the first-order conditions is indeed a maxi- mum. (c) Sketch the wealth expansion path; that is, fixing prices p, sketch the demands r(p, w) in (11, 12)-space as wealth w varies. Solution: Starting from the origin, the path moves up along the vertical axis to the point (0,2 (0, (2)²), then continues along the horizontal line x₂ = PL P2

Economics For Today

10th Edition

ISBN:9781337613040

Author:Tucker

Publisher:Tucker

Chapter6: Consumer Choice Theory

Section6.A: Indifference Curve Analysis

Problem 11SQ

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