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
Chapter1: Making Economics Decisions
Section: Chapter Questions
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ec70b84-8e2a-4846-85d9-f50115a864e8%2Fbd667dcf-e8c6-4972-92d6-04b7b2327bcf%2Fsygfo1p_processed.jpeg&w=3840&q=75)
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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