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(a) What type of preferences does Alfred have and are they homothetic and/or quasilinear? (b) What will be Alfred's optimal bundle? Illustrate this in a diagram, with good X measured on the horizontal axis, and explain your answer.

(a) What type of preferences does Alfred have and are they homothetic and/or quasilinear? (b) What will be Alfred's optimal bundle? Illustrate this in a diagram, with good X measured on the horizontal axis, and explain your answer.

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.3P
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21. Alfred's preferences are described by the following utility function U(X, Y) = 5X + 6Y, where the prices and income are Px = 3; Py = 5; M = 90. (a) What type of preferences does Alfred have and are they homothetic and/or quasilinear? (b) What will be Alfred's optimal bundle? Illustrate this in a diagram, with good X measured on the horizontal axis, and explain your answer.
Transcribed Image Text:21. Alfred's preferences are described by the following utility function U(X, Y) = 5X + 6Y, where the prices and income are Px = 3; Py = 5; M = 90. (a) What type of preferences does Alfred have and are they homothetic and/or quasilinear? (b) What will be Alfred's optimal bundle? Illustrate this in a diagram, with good X measured on the horizontal axis, and explain your answer.
(c) If Alfred's income increases to M = 120 and the price of good X is now Px = 5 (with the price of good Y unchanged), what will Alfred do? Illustrate this in a diagram and explain your answer. Now consider a different utility maximising consumer, Cherrin, who does not have a linear utility function, but instead has strictly convex preferences. At the optimum bundle of (A*, B*), good A has a negative income elasticity of demand and good B has a positive income elasticity of demand. (d) If Cherrin's utility function was the same as Alfred's U (A, B) = 5A + 6B, and she faced the same prices, such that PA = 3; PB = 5; what would her Engel curve now look like? Explain your answer. (e) Return to the original scenario for Cherrin, where she has strictly convex preferences and where good A has a negative income elasticity of demand and good B has a positive income elasticity of demand. If the price of good A increased, illustrate using a diagram and explain what would happen to Cherrin's consumption of A and B due to the income and substitution effects. Make sure you are clear about any assumption(s) you make.
Transcribed Image Text:(c) If Alfred's income increases to M = 120 and the price of good X is now Px = 5 (with the price of good Y unchanged), what will Alfred do? Illustrate this in a diagram and explain your answer. Now consider a different utility maximising consumer, Cherrin, who does not have a linear utility function, but instead has strictly convex preferences. At the optimum bundle of (A*, B*), good A has a negative income elasticity of demand and good B has a positive income elasticity of demand. (d) If Cherrin's utility function was the same as Alfred's U (A, B) = 5A + 6B, and she faced the same prices, such that PA = 3; PB = 5; what would her Engel curve now look like? Explain your answer. (e) Return to the original scenario for Cherrin, where she has strictly convex preferences and where good A has a negative income elasticity of demand and good B has a positive income elasticity of demand. If the price of good A increased, illustrate using a diagram and explain what would happen to Cherrin's consumption of A and B due to the income and substitution effects. Make sure you are clear about any assumption(s) you make.
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