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Consider a consumer with utility U(x) = log x₁ + √x2 for 2-good bundles. 1. Are the consumer's preferences homothetic? If so, prove it. If not, provide a coun- terexample. 2. Calculate the Marshallian demand for each good, as a function of prices and wealth. 3. Plot the Engel curve for each good when p = (1, 1). (Each plot should represent wealth on the horizontal axis and quantity on the vertical axis.) 4. Suppose that p = (1, 1). At what (positive) wealth level does the consumer purchase equal quantities of the two goods?

Consider a consumer with utility U(x) = log x₁ + √x2 for 2-good bundles. 1. Are the consumer's preferences homothetic? If so, prove it. If not, provide a coun- terexample. 2. Calculate the Marshallian demand for each good, as a function of prices and wealth. 3. Plot the Engel curve for each good when p = (1, 1). (Each plot should represent wealth on the horizontal axis and quantity on the vertical axis.) 4. Suppose that p = (1, 1). At what (positive) wealth level does the consumer purchase equal quantities of the two goods?

Economics:
Economics:
10th Edition
ISBN:9781285859460
Author:BOYES, William
Publisher:BOYES, William
Chapter21: Demand: Consumer Choic
Section: Chapter Questions
Problem 16E
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Consider a consumer with utility U(x) = log x₁ + √x2 for 2-good bundles. 1. Are the consumer's preferences homothetic? If so, prove it. If not, provide a coun- terexample. 2. Calculate the Marshallian demand for each good, as a function of prices and wealth. 3. Plot the Engel curve for each good when p = (1, 1). (Each plot should represent wealth on the horizontal axis and quantity on the vertical axis.) 4. Suppose that p = (1, 1). At what (positive) wealth level does the consumer purchase equal quantities of the two goods?
Transcribed Image Text:Consider a consumer with utility U(x) = log x₁ + √x2 for 2-good bundles. 1. Are the consumer's preferences homothetic? If so, prove it. If not, provide a coun- terexample. 2. Calculate the Marshallian demand for each good, as a function of prices and wealth. 3. Plot the Engel curve for each good when p = (1, 1). (Each plot should represent wealth on the horizontal axis and quantity on the vertical axis.) 4. Suppose that p = (1, 1). At what (positive) wealth level does the consumer purchase equal quantities of the two goods?
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