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Thomas has utility U = min{3C, T) over cookies and tea. Suppose the price of cookies declines by 1 dollar. How much of the change in demand for tea is a substitution effect? In other words, what is (change hr/change gr)? %3D O a. 0 O b. 1/4 О с. 13 O d. 2/3 O e. 3/4 O f. 1 Clear my choice

Thomas has utility U = min{3C, T) over cookies and tea. Suppose the price of cookies declines by 1 dollar. How much of the change in demand for tea is a substitution effect? In other words, what is (change hr/change gr)? %3D O a. 0 O b. 1/4 О с. 13 O d. 2/3 O e. 3/4 O f. 1 Clear my choice

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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### Understanding Utility, Preferences, and Substitution Effects #### Problem 1 **Thomas has utility \( U = \min\{3C, T\} \) over cookies and tea. Suppose the price of cookies declines by 1 dollar. How much of the change in demand for tea is a substitution effect? In other words, what is \( \frac{\text{change in } h_T}{\text{change in } g_T} \)?** - a. 0 - b. 1/4 - c. 1/3 - d. 2/3 - e. 3/4 - f. 1 *Selection:* a. 0 #### Problem 2 **Which of the following utility functions does NOT represent the same preferences as \( U(x, y) = x^{1/2} y^{1/2} \)?** - a. \( U(x, y) = xy \) - b. \( U(x, y) = \ln(x) + \ln(y) \) - c. \( U(x, y) = \ln(x \cdot y) \) - d. \( U(x, y) = x^{1/2} + y^{1/2} \) *Selection:* d. \( U(x, y) = x^{1/2} + y^{1/2} \) ### Detailed Explanation: In Problem 1, Thomas's utility function \( U = \min\{3C, T\} \) implies that Thomas's satisfaction depends on the lesser or limiting factor of \( 3C \) (three times the quantity of cookies) or \( T \) (the quantity of tea). When the price of cookies decreases, typically a substitution effect may be observed if the relative consumption of goods changes due to a price change. In this case, the substitution effect in question results in no change in the demand for tea, thus the ratio is \( \frac{\text{change in } h_T}{\text{change in } g_T} \) = 0. In Problem 2, four different utility functions are given, and the task is to identify which one does not represent the same preferences as \( U(x,y) = x^{1/2} y^{1/2} \). The function representing the product of \( x \) and \( y \) with
Transcribed Image Text:### Understanding Utility, Preferences, and Substitution Effects #### Problem 1 **Thomas has utility \( U = \min\{3C, T\} \) over cookies and tea. Suppose the price of cookies declines by 1 dollar. How much of the change in demand for tea is a substitution effect? In other words, what is \( \frac{\text{change in } h_T}{\text{change in } g_T} \)?** - a. 0 - b. 1/4 - c. 1/3 - d. 2/3 - e. 3/4 - f. 1 *Selection:* a. 0 #### Problem 2 **Which of the following utility functions does NOT represent the same preferences as \( U(x, y) = x^{1/2} y^{1/2} \)?** - a. \( U(x, y) = xy \) - b. \( U(x, y) = \ln(x) + \ln(y) \) - c. \( U(x, y) = \ln(x \cdot y) \) - d. \( U(x, y) = x^{1/2} + y^{1/2} \) *Selection:* d. \( U(x, y) = x^{1/2} + y^{1/2} \) ### Detailed Explanation: In Problem 1, Thomas's utility function \( U = \min\{3C, T\} \) implies that Thomas's satisfaction depends on the lesser or limiting factor of \( 3C \) (three times the quantity of cookies) or \( T \) (the quantity of tea). When the price of cookies decreases, typically a substitution effect may be observed if the relative consumption of goods changes due to a price change. In this case, the substitution effect in question results in no change in the demand for tea, thus the ratio is \( \frac{\text{change in } h_T}{\text{change in } g_T} \) = 0. In Problem 2, four different utility functions are given, and the task is to identify which one does not represent the same preferences as \( U(x,y) = x^{1/2} y^{1/2} \). The function representing the product of \( x \) and \( y \) with
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